Title:	A Package for Biometrics and Modelling
Version:	1.0.3
Description:	A system of functions and datasets to carry out quantitative analyses in the biological sciences. The package facilitates data management, exploratory analyses, and model assessment. Although it currently focuses on forest ecology, silviculture and decision-making, most of the package functions are applicable across several disciplines, including economics, environmental science, and healthcare.
License:	GPL (≥ 3)
URL:	https://eljatib.com, https://biometriaforestal.uchile.cl
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 3.5)
LazyData:	true
Imports:	graphics, grDevices, gtools, nlme, stats, utils
Suggests:	datana, lattice
NeedsCompilation:	no
Packaged:	2026-03-03 08:35:59 UTC; christian
Author:	Christian Salas-Eljatib [aut, cre], Nicolas Campos [ctb] (since 2025), Marcos Marivil [ctb] (https://biometriaforestal.uchile.cl, since 2025)
Maintainer:	Christian Salas-Eljatib <cseljatib@gmail.com>
Repository:	CRAN
Date/Publication:	2026-03-03 09:00:09 UTC

Assign species botanical information to a data frame

Description

Assigns species botanical attributes to a dataset, based upon a reference column (refcol). The attributes can be any of the fields available in the spplist dataframe, such as: spp.ci.name (genus and epitetus name of the species), spp.name (common name), and spp.ci.abb (abbreviated scientific name).

Usage

assignspp(
  data,
  attri = c("spp.name", "spp.ci.name"),
  refcol = "sppcode",
  all.x = TRUE,
  attri.all = FALSE,
  ...
)

Arguments

Value

A dataframe object including the attributes defined in the parameter attri.

See Also

spplist and base::merge().

Examples

## example data frame
myData <- data.frame(narb = c(1, 2, 3),
                     sppcode = c("nob", "np", "nd"),
                     dbh = c(20, 14, 23))
myData


## assign common, scientific and abbreviated name, based on `esp` value (default)
assignspp(myData)

## Assign more than one attribute based on common name
## just to remember, adding a single attribute (different from the default)
assignspp(myData, attri = "spp.ci.name")
## now, a more real example
newData <- assignspp(myData, attri = c("spp.name","genus","spp.ci.abb"))
newData 
## by default this function preserve names not found in biometrics::spplist
missingData <- rbind(myData, c(4, "notFoundData", 30))
missingData
assignspp(missingData, attri = "spp.name")
##the latter can be modified with option `all.x` of the `merge()` function
assignspp(missingData, attri = "spp.name", all.x = FALSE)
## In the case of wanting all the attributes to be merged, set option
## `attri.all` to `TRUE`, which willl overwrite the vector `attri`.
assignspp(missingData, attri = "spp.name", attri.all=TRUE, all.x =
FALSE)

Function to compute the result of the asymptotic regression model, as an allometric functional form.

Description

Function of the asymptotic regression model, based upon its parameters and a variable, as follows

y_i= \alpha + \left(\beta-\alpha\right) \left\{\mathrm{e}^{ \left[-\left(\mathrm{e}^{-\gamma}\right) x_i \right] }\right\},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

asymreg.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Pinheiro JC, DM Bates. 2000. Mixed-effects Models in S and Splus. New York, USA. Springer-Verlag. 528 p.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

#---------------------
# 2-parameters variant
# Predictor variable values to be used
time<-seq(0,50,by=0.1)
# Using the function, phi must be provided
y<-asymreg.fx(x=time,a=20,b=2.5,phi =5)
plot(time,y,type="l",ylim=c(0,20))
 

Function that fits a list of models on a given dataframe.

Description

Function that fits a list of models on a given dataframe.

Usage

bankfit(modlist, data, file = NULL, file.full = FALSE, trace = FALSE, ...)

Arguments

Examples

model.list <- list(
    mod1 = list(expr = vtot ~ I(dap^2) + I(dap^2 * atot^2) +I(d6),
                pred.f = function(x, ...) x,
                type = "lm"),
    mod2 = list(expr = I(log(vtot)) ~ I(log(dap)) + I(log(atot)),
                pred.f = function(x, ...) exp(x),
                type = "lm"))

## example dataframe
df <- treevolruca2
head(df)

## fitting models to dataframe
bankfit(modlist = model.list, data = df)

Predicts the variable of interest for each model of the list

Description

The function predicts the variable of biometrics-interest for each model belonging to the list previously fitted, as well as, generates a dataframe with the results.

Usage

bankpred(
  file = stop("You must provide a bankfit output object"),
  data = stop("You must provide a dataframe")
)

Arguments

Examples

## Not run: 
## list of example models
model.list <- list(
    mod1 = list(expr = vtot ~ I(dap^2) + I(dap^2 * atot^2) +I(d6),
                pred.f = function(x, ...) x,
                summodel = function(x, ...) datana::modresults(x)),
    mod2 = list(expr = I(log(vtot)) ~ I(log(dap)) + I(log(atot)),
                pred.f = function(x, ...) exp(x),
                summodel = function(x, ...) datana::modresults(x)))

## example dataframe
df <- treevolruca2
head(df)

## fitting models to dataframe and saving them
bankfit(models = model.list, data = df, file = "out.rdata")


## using fitted models file from biometrics::bankfit()
bankpred(file = "out.rdata", data = df) 

## End(Not run)

Function for building a barplot for one or two factors

Description

The function creates a barplot of numeric vector by one or two factor.

Usage

barplotgr(
  yvar,
  factors,
  data = data,
  percentage = FALSE,
  errbar = !percentage,
  half.errbar = TRUE,
  conf.level = 0.95,
  xlab = NULL,
  ylab = NULL,
  main = NULL,
  names.arg = NULL,
  bar.col = "black",
  whisker = 0.015,
  args.errbar = NULL,
  legend = TRUE,
  legend.text = NULL,
  args.legend = NULL,
  legend.border = FALSE,
  box = TRUE,
  args.yaxis = NULL,
  mar = c(5, 4, 3, 2),
  ...
)

Arguments

Value

The function returns the above described graph.

Author(s)

Christian Salas-Eljatib

References

The present function was modified from a similar one available at https://github.com/mrxiaohe/R_Functions/blob/master/functions/bar

Examples

data(standtabRauli2)
df <- standtabRauli2
head(df)
barplotgr(yvar = nha.cd, factors = c(bosque.id,cd), data = df,
errbar = FALSE, ylim=c(0, 640))

A function having the mathematical expression of the Bertalanffy-Richards model.

Description

Function of the Bertalanffy-Richards model, based upon three parameters and a single predictor variable as follows

y_i= \alpha \left(1-\mathrm{e}^{-\beta {x_i}}\right)^{1/\gamma},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

bertarich.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Richards FJ. 1959. A flexible growth function for empirical use. J. of Experimental Botany 10(29):290-300.

• von Bertalanffy L. 1957. Quantitative laws in metabolism and growth. The Quarterly Review of Biology 32(3):217-231.

• Salas-Eljatib C. 2020. Height growth-rate at a given height: a mathematical perspective for forest productivity. Ecological Modelling 431:109198. doi:10.1016/j.ecolmodel.2020.109198 https://eljatib.com/myPubs/2020hgrate_ecoModelling.pdf

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. doi:10.1007/s40725-021-00145-8

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-bertarich.fx(x=time,a=23,b=0.08,c=0.89)
plot(time,y,type="l")
 

Taper equation by Biging

Description

Tree taper equation proposed by Biging (1984), that depends on model parameters and tree size variables: diameter, total height, and stem height. The mathematical model is:

d_{l_i} = d_i ( \beta_0 + \beta_1 ln(1 - \lambda (h_{l_i} / h_i )^\frac{1}{3}))

where: d_{l_i} is the stem diameter at stem-height h_{l_i} for the i-th tree; d_i and h_i are the tree-level variables diameter at breast height and total height, respectively, and

\lambda = 1 - e^{(\frac{-\beta_0}{\beta_1})}

Usage

biging.fx(d, hl, h, paramod)

Arguments

Value

Returns the diameter of the stem at the stem-height h_l, thus d_l, for the Biging (1984) functional form, based upon tree diameter d and total height h.

References

• Biging GS. 1984. Taper equations for second-growth mixed conifers of northern California. Forest Science 30(4): 1103–1117. doi:10.1093/forestscience/30.4.1103

Examples

## Parameters
b0 <- 1.016215
b1 <- 0.332529
coefs <- c(b0, b1)

## Tree attributes
dbh <- 40
toth <- 25

## Using the function
hl.int <- c(0.3, 1.3, 5)
dl.hat <- biging.fx(d = dbh, h = toth, hl = hl.int, paramod=coefs)
cbind(hl.int, dl.hat)

Contains tree-level biomass data for four species in Canada.

Description

These are tree-level variables for four species in Canada.

Usage

biomass

Format

Data contain the following columns:

tree

Tree number code.

spp

Species common name, as follows: ⁠Balsam fir⁠ is Abies balsamea, ⁠Black spruce⁠ is Picea mariana, ⁠White birch⁠ is Betula papyrifera, and ⁠White spruce⁠ is Picea glauca.

dbh

Diameter at breast height, in cm.

toth

Total height, in m.

totbiom

Total biomass, in kg.

bolebiom

Stem biomass, in kg.

branchbiom

Branches biomass, in kg.

foliagebiom

Foliage biomass, in kg.

Source

Data were provided by Prof. Timothy Gregoire, School of Forestry and Environmental Studies, Yale University (New Haven, CT, USA).

Examples

data(biomass)
head(biomass)
tapply(biomass$totbiom,biomass$spp,summary)

Biomasa a nivel de árbol para cuatro especies arbóreas de Canadá

Description

Biomasa a nivel de árbol y otras variables, para cuatro especies que crecen en bosques de Canadá.

Usage

biomass2

Format

Los datos contienen las siguientes columnas:

arbol

Número del árbol.

spp

Nombre común de la especie, como sigue: ⁠Balsam fir⁠ es Abies balsamea, ⁠Black spruce⁠ es Picea mariana, ⁠White birch⁠ es Betula papyrifera, y ⁠White spruce⁠ es Picea glauca.

dap

Diámetro a la altura del pecho (1.3 m), en cm.

atot

Altura total, en m.

wtot

Biomasa total, en kg.

wfus

Biomasa del fuste, en kg.

wramas

Biomasa de las ramas, en kg.

whojas

Biomasa del follaje, en kg.

Source

Los datos fueron cedidos cortesía del profesor Timothy Gregoire, School of Forestry and Environmental Studies, Yale University (New Haven, CT, USA).

Examples

data(biomass2)
head(biomass2)
tapply(biomass2$wtot,biomass2$spp,summary)

Compute taper volume

Description

Performs the cubication of taper data. If the data corresponds to a full tree, and pred == FALSE the calculation is performed as a cilinder for the stump, smalian for each section in the stem and a cone for the crown. Otherwise, just smalian is used and a sum is performed up to the corresponding heights.

Usage

cubica(
  dl,
  hl,
  hstump = NA,
  htop = NA,
  dlu = NA,
  hlu = NA,
  full.tree = TRUE,
  pred = FALSE,
  rel.vol = c(25, 30, 40, 50, 90),
  ...
)

Arguments

Value

A list with data.frames with the different volumes calculated.

Author(s)

Christian Salas-Eljatib and Nicolás Campos

Examples

## Not run: 
## generating suitable data
df <- data.frame(dl = c(31.1, 25.8, 21.2, 19.6, 17.9, 15.9, 13.5,  9.8,  7.3, 0),
                 hl = c(0.30, 0.80, 1.30, 4.88, 9.76, 12.20, 14.64, 19.52, 24.40, 31.1),
                 hstump = c(0.30, 0.30, 0.30, 0.30, 0.30, 0.30, 0.30, 0.30, 0.30, 0.30),
                 htop = c(24.40, 24.40, 24.40, 24.40, 24.40, 24.40, 24.40, 24.40, 24.40, 24.40))
df

cubica(dl = df$dl,
       hl = df$hl,
       hstump = unique(df$hstump),
       htop = unique(df$htop))

## adding commercial volumes
cubica(dl = df$dl,
       hl = df$hl,
       dlu = c(20, 15, 21.2),
       hstump = unique(df$hstump),
       htop = unique(df$htop))

## End(Not run)

Function to computes the result of the Curtis's allometric model.

Description

Function of the traditional Curtis' allometric model, based upon two parameters, and a single predictor variable as follows

y_i= \alpha \left(\frac{x_i}{1+x_i} \right)^{\beta},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

curtis.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Curtis RO. 1967. Height-diameter and height-diameter-age equations for second-growth Douglas-fir. Forest Sci. 13(4):365-375.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-curtis.fx(x=time,a=20,b=8)
plot(time,y,type="l")
 

Function to computes the result of the original Curtis's allometric model.

Description

Function of the originally proposed allometric model by Curtis, based upon two parameters, and a single predictor variable as follows

y_i= \frac{x_i}{\alpha +\beta x_i},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients). Please read the details on this model in Salas-Eljatib (2025).

Usage

curtisori.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Curtis RO. 1967. Height-diameter and height-diameter-age equations for second-growth Douglas-fir. Forest Sci. 13(4):365-375.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Parameters
# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-curtisori.fx(x=time,a=20,b=8)
plot(time,y,type="l")
 

Contains coarse woody debris measurement in a unit of line intersect sampling.

Description

These are log-level variables measured in the field in a single line intersect sampling (LIS) unit. The length of the line or transect is 30 m. Details on this type of sampling strategy can be reviewed in Gregoire and Valentine (2008).

Usage

cwd

Format

Data contains the following columns:

element

Element (i.e., log) number with the LIS sample.

diam

Diameter of the element, in cm.

len

Length, in m.

ang

Angle of the element with respect to the line sampling, in degrees.

Source

Data from Marshall et al 2000.

References

• Marshall PL, G Davis, VM LeMay. 2000. Using line intersect sampling for coarse woody debris. Technical Report 3, British Columbia Forest Service, Nanaimo, BC, Canada. 34 p.

• Gregoire TG, HT Valentine. 2008. Sampling Strategies for Natural Resources and the Environment. New York, USA. Chapman & Hall/CRC. 474 p.

Examples

data(cwd)
cwd

Contiene mediciones de material leñoso muerto en una unidad de muestreo de linea.

Description

Son variables medidas a nivel de trozo en la unidad de muestreo (LIS). El largo de la línea de muestreo o transecto es de 30 m. Detalles sobre este tipo de estrategia de muestreo se pueden revisar en Gregoire and Valentine (2008).

Usage

cwd2

Format

Data contiene las siguientes columnas:

elemento

Número del elemento (i.e., trozo) medido dentro de la muesta de LIS.

diam

Diámetro en la mitad del elemento, en cm.

lar

Largo, en m.

ang

Ángulo de intersección del elemento con la línea de muestreo LIS, en grados.

Source

Datos digitados desde Marshall et al (2000).

References

• Marshall PL, G Davis, VM LeMay. 2000. Using line intersect sampling for coarse woody debris. Technical Report 3, British Columbia Forest Service, Nanaimo, BC, Canada. 34 p.

• Gregoire TG, HT Valentine. 2008. Sampling Strategies for Natural Resources and the Environment. New York, USA. Chapman & Hall/CRC. 474 p.

Examples

data(cwd2)
cwd2

Mortality of lianas (vines) in tropical forests

Description

This study is part of the project "Diversity and dynamics of vascular epiphytes in Colombian Andes" supported by COLCIENCIAS (contract 2115-2013). The data corresponds to the first large-scale assessment of vascular epiphyte mortality in the neotropics. Based on two consecutive annual surveys, we followed the fate of 4247 epiphytes to estimate the epiphyte mortality rate on 116 host trees at nine sites. Additional variables were taken from the area of study in order to find relationships with epiphyte mortality.

Usage

data(deadlianas)

Format

The data frame contains four variables as follows:

PlotSite

Municipality name of the 9 study sites

Y.Plot

Latitude of the plot in decimal degrees

X.Plot

Longitude of the plot in decimal degrees

PhoroNo

ID number of the sampled host trees in each site

EpiFam

Epiphyte taxonomic family

EpiGen

Epiphyte taxonomic genus

cf.aff

Abbreviations of Latin terms in the context of taxonomy. cf. "confer" meaning "compare with". aff.: "affinis" meaning "similar to".

Species

Epiphyte (morpho) species name

Author

Author of the scientific name

EpiAzi

Azimuth of the epiphyte individual on each host tree

BraAzi

Azimuth of the branch in which the epiphyte individual was found

EpiDisTru

Distance in meters from the trunk to the epiphyte attachment site on a branch

EpiSize

Estimated size of the epiphyte individual, in cm.

EpiAttHei

Epiphyte attachment height in meters

Date0

Date of the first census

Date1

Date of the final census

Location

Section (roots, trunks, branches) of the host tree in which theepiphyte individual was found

Mortality

Dichotomous variable. 0 if the epiphyte individual was dead in the final census and 1 if otherwise

MorCat

Mechanical or non-mechanical cause of mortality

Elevation

Elevation (m a.s.l.) of the plot

AP_bio12

Annual precipitation in the plot (mm yr-1)

PDM_bio14

Precipitation of driest month in the plot (mm)

PS_bio15

Precipitation seasonality in the plot (coefficient of variation)

MDT_bio2

Mean Diurnal Range (Mean of monthly (max temp - min temp)) in the plot (oC * 10)

TS_bio4

Temperature seasonality in the plot (standard deviation * 100)

ATR_bio7

Annual temperature range in the plot (10 celsius degrees)

AET

Actual evapotranspiration in the plot (mm yr-1)

BasAre

Basal area of trees with DBH major or equal to 5 cm (AB) in the plot (m^{2}/ha)

BasAre5_10

Basal area of trees with greater or equal than 5 DBH and less than 10 cm in the plot (m^{2}/ha)

BasAre10

Basal area of trees with greater or equal than 10 cm DBH in the plot (m^{2}/ha)

Ind10

Number of canopy trees (with greater or equal than 10 cm DBH ) in the plot

Ind5

Number of understory trees (with greater or equal than 5 DBH and less than 10 cm) in the plot

Ind5_10

Number of trees with greater or equal than 5 DBH and less than 10 cm in the plot

Ind10_15

Number of trees with greater or equal than 10 DBH and less than 15 cm in the plot

Ind15_20

Number of trees with greater or equal than 15 DBH and less than 20 cm in the plot

Ind20_25

Number of trees with greater or equal than 20 DBH and less than 25 cm in the plot

Ind25_30

Number of trees with greater or equal than 25 DBH and less than 30 cm in the plot

Ind30

Number of trees with DBH major or equal to 30 cm in the plot

TreeHei

Total tree height in meters

MedHei

Median height of trees in each plot

MaxHei

Maximum height of trees in each plot

BranchNumb

Number of branches of the host tree

Obs

Observations and notes in Spanish

Source

Data were retrieved from the DRYAD repository at doi:10.5061/dryad.g5510.

References

Zuleta D, Benavides AM, Lopez-Rios V, Duque A. 2016. Local and regional determinants of vascular epiphyte mortality in the Andean mountains of Colombia. Journal of Ecology 104(3): 841-843. doi:10.1111/1365-2745.12563

Examples

data(deadlianas)
head(deadlianas)

Datos de mortalidad de lianas en árboles tropicales

Description

Los datos provienen de un estudio que fue parte del proyecto "Diversidad y dinámica de epífitas vasculares en los Andes colombianos". apoyado por COLCIENCIAS (contrato 2115-2013). Este conjunto de datos tiene 43 columnas y 4247 filas. Cada fila corresponde a un individuo epifito ubicado en secciones confiables de los árboles hospedantes Los datos corresponden a la primera gran escala evaluación de la mortalidad de epífitas vasculares en los neotrópicos. Basado en dos encuestas anuales consecutivas, Seguimos el destino de 4247 epífitas para estimar la tasa de mortalidad de epífitas en 116 árboles hospedantes. en nueve sitios. Se tomaron variables adicionales del area de estudio para encontrar relaciones con mortalidad de epifitas.

Usage

data(deadlianas2)

Format

Variables se describen a continuación::

PlotSite

Nombre del municipio de los 9 sitios de estudio.

Y.Plot

Latitud del grafico en grados decimales.

X.Plot

Longitud de la grafica en grados decimales.

PhoroNo

número de identificacion de los árboles hospedantes muestreados en cada sitio

EpiFam

Familia taxonomica de epifitas.

EpiGen

Genero taxonomico de epifitas.

cf.aff

Abreviaturas de terminos latinos en el contexto de la taxonomia. cf. "conferir" que significa "comparar con". aff .: "affinis" que significa "similar a".

Species

Nombre de la especie epifita (morfo)

Author

Autor del nombre científico.

EpiAzi

Azimut del individuo epifito en cada árbol huesped.

BraAzi

Azimut de la rama en la que se encontro el individuo epifito.

EpiDisTru

Distancia en metros desde el tronco hasta el sitio de union de la epifita en una rama.

EpiSize

Tamaño estimado del individuo epifito en centimetros.

EpiAttHei

Altura del accesorio de la epifita en metros.

Date0

Fecha del primer censo.

Date1

Fecha del censo final.

Location

Seccion (raices, troncos, ramas) del árbol anfitrion en el que se encontro el individuo epifito.

Mortality

Variable dicotomica. 0 si el individuo epifito estaba muerto en el censo final y 1 si no.

MorCat

Causa de mortalidad mecanica o no mecánica.

Elevation

Elevacion (msnm) de la parcela.

AP_bio12

Precipitación anual en la parcela, en mm.

PDM_bio14

Precipitación del mes más seco en la parcela, en mm.

PS_bio15

Estacionalidad de la precipitacion en la parcela (coeficiente de variacion)

MDT_bio2

Rango diurno medio (Media mensual (temperatura maxima - temperatura minima)) en la grafica (10°C)

TS_bio4

Estacionalidad de la temperatura en la grafica (desviacion estandar * 100)

ATR_bio7

Rango de temperatura anual en la parcela (10 grados centigrados)

AET

Evapotranspiración anual en la parcela, en mm.

BasAre

Area basal de árboles con DAP mayor o igual a 5 cm en la parcela, en m^{2}/ha.

BasAre5_10

Area basal de árboles con DAP mayor o igual a 5 y menor a 10 cm en la parcela (m^{2}/ha)

BasAre10

Area basal de árboles con DAP mayor o igual a 10 cm en la parcela (m^{2}/ha)

Ind10

Número de árboles del dosel (con un DAP superior o igual a 10 cm) en la parcela

Ind5

Número de árboles de sotobosque (con DAP mayor o igual a 5 y menor a 10 cm) en la parcela

Ind5_10

Número de árboles con un DAP mayor o igual a 5 y menos de 10 cm en la parcela

Ind10_15

Número de árboles con un DAP mayor o igual a 10 y menos de 15 cm en la parcela

Ind15_20

Número de árboles con un DAP mayor o igual a 15 y menos de 20 cm en la parcela

Ind20_25

Número de árboles con un DAP mayor o igual a 20 y menos de 25 cm en la parcela

Ind25_30

Número de árboles con un DAP mayor o igual a 25 y menos de 30 cm en la parcela

Ind30

Número de árboles con DAP mayor o igual a 30 cm en la parcela

TreeHei

Altura total del árbol en metros

MedHei

Altura media de los árboles en cada parcela

MaxHei

Altura maxima de los árboles en cada parcela

BranchNumb

Número de ramas del árbol anfitrion

Obs

Observaciones y notas en español

Source

Los datos fueron obtenidos desde el repositorio DRYAD doi:10.5061/dryad.g5510.

References

Zuleta D, Benavides AM, Lopez-Rios V, Duque A. 2016. Local and regional determinants of vascular epiphyte mortality in the Andean mountains of Colombia. Journal of Ecology 104(3): 841-843. doi:10.1111/1365-2745.12563

Examples

data(deadlianas2)
head(deadlianas2)

Densidad media en distintos tratamientos de raleo en Drymis winteri de Chile.

Description

Densidad media por tratamiento de raleo en renovales de Drymis winteri en el sector de Hueicolla, Cordillera de la Costa de Valdivia (Chile). Los datos corresponden al período 1986-1990 e incluyen diferentes intensidades de raleo (2 m, 3 m, 4 m, raleo de liberación y testigo sin intervención). Se presentan valores medios de densidad (N°/ha) con su desviación estándar, además de la mortalidad promedio anual y su tasa porcentual.

Usage

data(densidadcanelo2)

Format

Los datos contienen las siguientes columnas:

tratamiento

Distancia o tipo de raleo aplicado (2m, 3m, 4m, raleo, testigo)

anho.eval

Año de evaluación (1986 o 1990)

nha

Densidad promedio en número de individuos por hectárea (N°/ha)

nha.sd

Desviación estándar asociada a la densidad

Source

Datos tomados de: Navarro et al. (1997), Efectos del raleo en renovales de Drymis winteri, Hueicolla, Cordillera de la Costa de Valdivia, Chile.

References

Navarro, C., Donoso, P., y Rosas, M. (1997). Crecimiento de renovales de Drymis winteri sometidos a distintos tratamientos de raleo. En: Donoso, C. (Ed.), Bosques templados de Chile y Argentina. Editorial Universitaria, Santiago de Chile.

Examples

data(densidadcanelo2)
head(densidadcanelo2)
plot(densidadcanelo2$anho.eval, densidadcanelo2$nha, col="forestgreen", pch=19,
     main="Densidad por año de evaluación",
     xlab="Año", ylab="N° árboles/ha")

Function to computes the diameter of the tree of average basal area.

Description

Function to compute the diameter of the tree of average basal area (D_{\overline{g}}), which depends on stand density (N) and stand basal area (G). The aforementioned stand diameter is computed as

D_{\overline{g}} = \sqrt{ \frac{G}{N} \frac{k}{pi}}

where the constant k depends on whether the variables are in the units of measurement of the metric or imperial system.

Usage

dg.fx(n = n, g = g, metrics = TRUE)

Arguments

Value

Returns the diameter of the tree of average basal area.

Author(s)

Christian Salas-Eljatib.

Examples

##Using the function
dg.fx(n=1000, g=55)
dg.fx(n=210, g=160, metrics=FALSE)

Function to compute a dominant stand-level variable based on a sample plot data.

Description

Computes the so-called dominant stand-level variable, corresponding to the average of a tree-level variable for the nref.ha largest sorting-tree-level diameter trees in 1-ha.

Usage

domvar(data, varint, varsort, plot.area, ndom.ha = 100)

Arguments

Details

The original function was written by Dr Oscar García for computing top height, and the corresponding reference is provided. Nevertheless, several changes were applied, to make the current function provide a broader application. Regardless, the function aims to calculate a "dominant" stand-level variable by taking into account the plot area. Thus, requires having a dataframe having both the variable of interest (e.g., height) and the sorting variable used for the computation (e.g., diameter) for all trees in a sample plot, as well as, the plot area.

Value

The main output is the calculated dominant stand-variable for the given sample plot. The unit of the computed variable is the same as the one used as variable of interest.

Author(s)

Christian Salas-Eljatib.

References

• García O, Batho A. 2005. Top height estimation in lodgepole pine sample plots. Western Journal of Applied forestry 20(1):64-68.

Examples

# Dataframe to be used
df<-biometrics::eucaplot2
#' ?eucaplot2
#' head(df)
datana::descstat(df[,c("dap","atot")])
#' # Using the domvar function
domvar(data=df,varint = "atot",varsort = "atot",plot.area = 500)
domvar(data=df,varint = "atot",varsort = "dap",plot.area = 500)
domvar(data=df,varint = "atot",varsort = "dap",plot.area = 500,ndom.ha = 50)

Tree-level data from a sample plot established in a Eucalyptus globulus plantation

Description

Tree-level variables collected for all trees (even the variable height) within a sample plot in a forestry plantation of Eucalyptus globulus near Gorbea, southern Chile. The plot size is 500 m^{2}. The plantation is 15 yr-old and had been subject to three thinnings.

Usage

data(eucaplot)

Format

The dataframe contains four variables as follows:

dbh

Diameter at breast height, in cm.

health

health status (1: good, 2: medium, 3: bad).

shape

stem shape for timber purposes (1: good, 2: medium, 3: bad).

crown.class

Crown class (1: superior, 2: intermedium, 3: lower).

toth

Total height, in m.

Source

The data were provided courtesy of Dr Christian Salas-Eljatib (Universidad de Chile, Santiago, Chile).

References

• Forest biometrics lecture notes, Prof. Christian Salas-Eljatib, Universidad de Chile. Santiago, Chile

Examples

data(eucaplot)    
table(eucaplot$health)
library(datana) 
descstat(eucaplot[,c("dbh","toth")])

Lista de árboles con todas las variables medidas en una parcela de muestreo, establecida en una plantación de Eucalyptus globulus.

Description

Variables a nivel individual medidas en todos los árboles (incluso la variable altura) encontrados en una parcela de muestreo en una plantación forestal de Eucalyptus globulus cerca de Gorbea, en el sur de Chile. La superficie de la parcela es de 500 m^{2}. La plantación tiene 15 años de edad y ha estado sujeta a tres raleos.

Usage

data(eucaplot2)

Format

Los datos contienen las siguientes cuatro columnas:

dap

Diámetro a la altura del pecho, en cm.

sanidad

Evaluación cualitativa de la sanidad del árbol (1: buena, 2: media, 3: mala).

forma

Evaluación cualtitativa de la forma del fuste (1: buena, 2: media, 3: mala).

clase.copa

Clase de copa (1: superior, 2: intermedio, 3: inferior).

atot

Altura total, en m.

Source

Los datos fueron cedidos por el Prof. Christian Salas (Universidad de Chile, Santiago, Chile), y colectados por él mientras fue Profesor del Departamento de Ciencias Forestales en la Universidad de La Frontera (Temuco, Chile). La plantación se encontraba dentro de un predio del colega (QEPD) Hugo Castro.

References

• Apuntes de Biometría y Modelación Forestal, Prof. Christian Salas-Eljatib, Universidad de Chile. Santiago, Chile

Examples

data(eucaplot2)    
table(eucaplot$forma)
library(datana) 
descstat(eucaplot2[,c("dap","atot")])

Tree-list (realistic-) data in a sample plot established in a Eucalyptus globulus plantation in southern Chile.

Description

Tree-level variables collected in a sample plot (area=500 m^{2}) in a forestry plantation of Eucalyptus globulus near Gorbea, in southern Chile. The variable height, was only measured in a sub-sample of trees within the plot. The plantation is 15 yr-old and had been subject to three thinnings.

Usage

data(eucaplotr)

Format

The dataframe contains four variables as follows:

dbh

Diameter at breast height, in cm.

health

health status (1: good, 2: medium, 3: bad).

shape

stem shape for timber purposes (1: good, 2: medium, 3: bad).

crown.class

Crown class (1: superior, 2: intermedium, 3: lower).

toth

Total height (in m), only available for some trees. Otherwise missing values are denoted by NA.

Source

The data were provided courtesy of Dr Christian Salas-Eljatib (Universidad de Chile, Santiago, Chile).

References

• Forest biometrics lecture notes, Prof. Christian Salas-Eljatib, Universidad de Chile. Santiago, Chile

Examples

data(eucaplotr)    
table(eucaplotr$shape)
library(datana) 
descstat(eucaplotr[,c("dbh","toth")])

Lista de árboles con variables medidas (más realista) en una parcela de muestreo, establecida en una plantación de Eucalyptus globulus.

Description

Variables a nivel individual medidas en los árboles encontrados en una parcela de muestreo (de 500 m^{2}) en una plantación forestal de Eucalyptus globulus, cerca de Gorbea (Sur de Chile). La variable altura fue medida solo en una sub-muestra de árboles. La plantación tiene 15 años de edad y ha estado sujeta a tres raleos. Este set de datos es similar al de la dataframe eucaplot2, pero siendo más realista en el sentido que no es comun que la altura se mida en todos los árboles como es el caso de los dataframe eucaplot2.

Usage

data(eucaplotr2)

Format

Los datos contienen las siguientes cuatro columnas:

dap

Diámetro a la altura del pecho, en cm.

sanidad

Evaluación cualitativa de la sanidad del árbol (1: buena, 2: media, 3: mala).

forma

Evaluación cualtitativa de la forma del fuste (1: buena, 2: media, 3: mala).

clase.copa

Clase de copa (1: superior, 2: intermedio, 3: inferior).

atot

Altura total, en m. Esta variable fue medida solo en una submuestra de árboles, y los registros vacíos estan denotados por NA.

Source

Los datos fueron cedidos por el Prof. Christian Salas-Eljatib (Universidad de Chile, Santiago, Chile), y colectados por él mientras fue Profesor del Departamento de Ciencias Forestales en la Universidad de La Frontera (Temuco, Chile). La plantación se encontraba dentro de un predio del colega (QEPD) Hugo Castro.

References

• Forest biometrics lecture notes, Prof. Christian Salas-Eljatib, Universidad de Chile. Santiago, Chile

Examples

data(eucaplotr2)    
table(eucaplotr2$sanidad)
library(datana) 
descstat(eucaplotr2[,c("dap","atot")])

Function to compute the result of the Gompertz allometric model.

Description

Function of the Gompertz model, depending on its three parameters and a variable, defined by the following mathematical expression

y_i= \alpha \mathrm{e}^{\left(-\beta \mathrm{e}^{-\gamma x_i} \right)},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

gompertz.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Gompertz B. 1825. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115:513–583.

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. doi:10.1007/s40725-021-00145-8

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-gompertz.fx(x=time,a=25,b=.22,c=16)
plot(time,y,type="l")
 

Function that computes the result of the modified Gompertz's model.

Description

Function of the Gompertz modified model, based upon parameters (i.e., coefficients) and a variable, as follows

y_i= \alpha \mathrm{e}^{\left(-\beta \mathrm{e}^{-\gamma x_i} \right)},

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients). The Gompertz equation is a widely used allometric mathematical function.

Usage

gompertzm.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Gompertz B. 1825. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115:513–583.

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. doi:10.1007/s40725-021-00145-8

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-gompertzm.fx(x=time,a=25,b=3.6,c=0.17)
plot(time,y,type="l")
 

Function to compute basal area of a tree

Description

The function computes the basal area of a tree (g), which only depends on its diameter at breast-height (d). The basal area of a tree is computed as

g = \left(\frac{\pi}{k}\right) d^{2}

where the constant k depends on whether the diameter and the resulting basal area are in the units of the metric or imperial system.

Usage

gtree(x, metric = TRUE)

Arguments

Value

The value of basal area in m^{2} or in ft^{2}, depending on the units of measurement being defined.

Author(s)

Christian Salas-Eljatib

Examples

#Using the function
 gtree(40)
 gtree(x=30)
gtree(x=11.81,metric=FALSE)

Diameter growth increments of a tropical tree species in Hawaii

Description

Tree size, competition, and diameter growth increment of Metrosideros polymorpha trees collected in the Kilauea Volcano, Hawaii. Data containing 64 observations at the current annual growth rate (defined as dbh increment within one calendar year) of each tree. Measurements were made from 1986 to 1988.

Usage

data(hawaii)

Format

The dataframe has the following columns:

tree.code

Tree number identification. The first letter of the ID represents a cohort. Six cohorts representing a chronosequence were sampled.

dbh

Diameter at breast height, in cm.

toth

Total height, in m.

crown.area

Crown outline area, in square meters.

comp.ind

Competition index (Basal area of nearest neighbor divided by square of distance to nearest neighbor plus basal area of second nearest neighbor divided by square of distance to second nearest neighbor).

cai.1986

Current annual stem diameter increment during 1986, in mm.

cai.1987

Current annual stem diameter increment during 1987, in mm.

cai.1988

Current annual stem diameter increment during 1988, in mm.

Source

The data were obtained from Gerrish and Mueller-Dombois (1999).

References

• Gerrish G, Mueller-Dombois D. 1999. Measuring stem growth rates for determining age and cohort analysis of a tropical evergreen tree. Pacific Science. 53(4): 418-429.

Examples

data(hawaii)
head(hawaii)

Incremento corriente anual en diámetro de una especie tropical en Hawaii

Description

Tamaño del árbol, competencia, e incremento corriente anual de árboles de Metrosideros polymorpha colectado en el volcán Kilauea, Hawaii. Los datos contienen 64 observaciones de incremento corriente anual (definido como el incremento en dap en un año calendario) de cada árbol. Estos incrementos fueron medidos desde el año 1986 a 1988.

Usage

data(hawaii)

Format

Estos datos contienen las siguientes columnas:

arb.id

Código identificador del árbol. La primera letra del ID representa una cohorte. Hay seis cohortes que representan una cronosecuencia.

dap

Diámetro a la altura del pecho, en cm.

atot

Altura total, en m.

area.copa

Área de copa, en metros cuadrados.

ind.comp

Índice de competencia (Área basal del vecino más cercano dividido por la distancia al vecino más cercano al cuadrado más el área basal del segundo vecino más cercano dividio por la distancia al segundo vecino más cercano al cuadrado)

ica.1986

Incremento corriente anual durante el año 1986, en mm.

ica.1987

Incremento corriente anual durante el año 1987, en mm.

ica.1988

Incremento corriente anual durante el año 1988, en mm.

Source

Los datos fueron obtenidos desde Gerrish and Mueller-Dombois (1999).

References

• Gerrish G, Mueller-Dombois D. 1999. Measuring stem growth rates for determining age and cohort analysis of a tropical evergreen tree. Pacific Science. 53(4): 418-429.

Examples

data(hawaii2)
head(hawaii2)

Function that computes the result of the Hossfeld allometric model.

Description

Function of the Hossfeld (actually it is "Hoßfeld") allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

y_i= \alpha \left(\frac{1}{1+\frac{\beta}{x_i^{\gamma}}}\right),

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this function can be found in Salas-Eljatib (2025).

Usage

hossfeld.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Hoßfeld JW. 1822. Mathematik für Forstmänner, Oekonomen und Cameralisten. Dresden, Germany. Gotha:Hennings. 472 p.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-hossfeld.fx(x=time,a=31,b=38,c=1.4)
plot(time,y,type="l")
 

A simple linear interpolation function applicable to two vectors (X and Y), when the first element of Y is missing.

Description

A simple linear interpolation function applicable to two vectors (e.g., X and Y) of length three, suitable when the first element of Y is missing.

Usage

interpy1(xs = xs, ys = ys)

Arguments

Value

The interpolated value for the first element of vector Y.

Author(s)

Christian Salas-Eljatib.

Examples

x<-c(0.2,0.8,1.3)
y<-c(NA,41,38)
interpy1(xs=x,ys=y)

A simple linear interpolation function applicable to two vectors (X and Y), when the second element of Y is missing.

Description

A simple linear interpolation function applicable to two vectors (e.g., X and Y) of length three, suitable when the second element of Y is missing.

Usage

interpy2(xs = xs, ys = ys)

Arguments

Value

The interpolated value for the second element of vector Y.

Author(s)

Christian Salas-Eljatib.

Examples

x<-c(0.2,0.8,1.3)
y<-c(48,NA,41)
interpy2(xs=x,ys=y)

Function to compute the result of the simple linear inverse model.

Description

Function of the inverse model, based upon its two parameters and a variable, as follows

y_i = \alpha - \left(\frac{\beta}{x_i}\right),

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

inv.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable to be used is 40 
# Using the function
inv.fx(x=40,a=25,b=115)
# The effect of the constant term phi
inv.fx(x=40,a=25,b=115, phi=2.5)
 

Function to computes the stem diameter of a tree according to the Kozak (1988) taper equation.

Description

Function of the Kozak (1988) taper equation model, based upon the model parameters, and the tree variables: diameter, total height, and stem height. The mathematical expression is as follows

d_{l_{i}} = \alpha_0 d_i^{\alpha_1}\alpha_2^{d_i}X_{l_{i}}^{ \left[\beta_1 z_{l_{i}}^{2} +\beta_2 \ln{(z_{l_{i}} + 0.001)} + \beta_3\sqrt{z_{l_{i}}}+ \beta_4 \mathrm{e}^{z_{l_{i}}} +\beta_5 (d_i/h_i)\right] },

where: d_{l_{i}} is the stem diameter at stem-height h_{l_{i}} for the i-th tree; and d_i and h_i are the tree-level variables diameter at breast height and total height, respectively, for tje i-th tree. The other terms are

z_{l_{i}}=\frac{h_{l_{i}}}{h_i},

X_{l_{i}}=\frac{ 1-\sqrt{ z_{l_{i}}} }{ 1-\sqrt{p} },

with p being the inflextion point.

Usage

kozak.fx(d, h, hl, paramod, p = 0.2, c0 = 0.001)

Arguments

Value

Returns the diameter of the stem at the stem-height h_l, thus d_l, for the Kozak (1988) functional form, based upon tree diameter d and total height h.

Author(s)

Christian Salas-Eljatib.

References

Kozak A. 1988. A variable-exponent taper equation. Canadian Journal of Forest Research 18: 1363-1368. doi:10.1139/x88-213

Examples

# Parameters
a0<- 1.02453; a1<- 0.88809; a2<- 1.00035
b1<- 0.95086; b2<- -0.18090; b3<- 0.61407;
b4<- -0.35105; b5 <- 0.05686;
coefs<-c(a0,a1,a2,b1,b2,b3,b4,b5);p.coef <- 0.25
# Tree attributes
dbh <- 45; toth <- 27

# Using the function
hl.int <- c(0.3, 1.3, 5)
dl.hat <- kozak.fx(d=dbh,h=toth,hl=hl.int,paramod=coefs,p=p.coef)
cbind(hl.int,dl.hat)

Function to computes the stem diameter of a tree according to the Kozak (2004) taper equation.

Description

Function of the Kozak (2004) taper equation model, based upon the model parameters, and the tree variables: diameter, total height, and stem height. The mathematical expression is as follows (escribir la correcta)

d_{l_{i}} = \alpha_0d_i^{\alpha_1}\alpha_2^{d_i}X_{l_{i}}^{ \left[\beta_1z_{l_{i}}^{2}+\beta_2\ln{(z_{l_{i}} + 0,001)} + \beta_3\sqrt{z_{l_{i}}}+ \beta_4 e^{z_{l_{i}}}+\beta_5(d_i/h_i)\right] },

where: d_{l_{i}} is the stem diameter at stem-height h_{l_{i}} for the i-th tree; and d_i and h_i are the tree-level variables diameter at breast height and total height, respectively, for tje i-th tree. The other terms are

z_{l_{i}}=\frac{h_{l_{i}}}{h_i},

X_{l_{i}}=\frac{ 1-\sqrt{ z_{l_{i}}} }{ 1-\sqrt{p} },

with p being the inflextion point.

Usage

kozaklast.fx(d, h, hl, paramod)

Arguments

Value

Returns the diameter of the stem at the stem-height h_l, thus d_l, for the Kozak (1988) functional form, based upon tree diameter d and total height h.

Author(s)

Christian Salas-Eljatib.

References

Kozak A. 2004. My last words on taper equations. The Forestry Chronicle 80: 507–515. doi:10.1139/x88-213

Examples

# Parameters
a0<- 0.80; a1<- 0.88809; a2<- 0.2
b1<- 0.95086; b2<- -0.18090; b3<- 0.61407;
b4<- -0.35105; b5 <- 0.05686; b6 <- 0.001;
coefs<-c(a0,a1,a2,b1,b2,b3,b4,b5,b6);
# Tree attributes
dbh <- 45; toth <- 27

# Using the function
hl.int <- c(0.3, 1.3, 5)
dl.hat <- kozaklast.fx(d=dbh,h=toth,hl=hl.int,paramod=coefs)
cbind(hl.int,dl.hat)
 

Function to computes the stem diameter of a tree according to the log-transformed Kozak (1988) taper equation.

Description

Function of the natural log-transformed Kozak (1988) taper equation model, based upon the model parameters, and the tree variables: diameter, total height, and stem height. The mathematical expression is as follows

\ln{d_{l_{i}}}=\alpha_0 + \alpha_1 \ln{d_i}+\alpha_2 {d_i}+ \beta_1 \ln{(X_{l_{i}})} z_{l_{i}}^{2} + \beta_2 \ln{(X_{l_{i}})} \ln{(z_{l_{i}}+0.001)} + \beta_3 \ln{(X_{l_{i}})} \sqrt{z_{l_{i}}} +\\ \beta_4 \ln{(X_{l_{i}})} e^{z_{l_{i}}} + \beta_5 \ln{(X_{l_{i}})} \frac{d_i}{h_i},

where: d_{l_{i}} is the stem diameter at stem-height h_{l_{i}} for the i-th tree; and d_i and h_i are the tree-level variables diameter at breast height and total height, respectively, for tje i-th tree. The other terms are

z_{l_{i}}=\frac{h_{l_{i}}}{h_i},

X_{l_{i}}=\frac{ 1-\sqrt{ z_{l_{i}}} }{ 1-\sqrt{p} },

with p being the inflextion point.

Usage

kozakln.fx(d, h, hl, paramod, p = 0.2, c0 = 0.001)

Arguments

Value

Returns the diameter of the stem at the stem-height h_l, thus d_l, for the natural log-transformed Kozak (1988) functional form, based upon tree diameter d and total height h. Therefore, the result applies the back-transformation by using the anti-log function, i.e., exp().

Author(s)

Christian Salas-Eljatib.

References

Kozak A. 1988. A variable-exponent taper equation. Canadian Journal of Forest Research 18: 1363-1368. doi:10.1139/x88-213

Examples

# Parameters
a0<- 0.04338410; a1<- 0.88657485; a2<- 0.00446052;b1<- 1.978196;
b2<- -0.40676847; b3<- 3.50815520; b4<- -1.84177070;b5<- 0.19647175
coefs<-c(a0,a1,a2,b1,b2,b3,b4,b5);p.coef <- 0.25
# Tree attributes
dbh <- 40; toth <- 25

# Using the function
hl.int <- c(0.3, 1.3, 5)
dl.hat <- kozakln.fx(d=dbh,h=toth,hl=hl.int,paramod=coefs,p=p.coef)
cbind(hl.int,dl.hat)

Function to computes the result of the Curtis's allometric model.

Description

Function of the Langhmuir model, based upon two parameters, and a single predictor variable, as follows

y_i= \alpha \left(\frac{1}{1+\frac{1}{\beta x_i}}\right),

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details of this function can be found in Salas-Eljatib (2025).

Usage

lang.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Khayyun TS, Mseer AH. 2019. Comparison of the experimental results with the Langmuir and Freundlich models for copper removal on limestone adsorbent. Applied Water Science 9(8):170.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(.1,60,by=0.01)
# Using the function
y<-lang.fx(x=time, a=37,b=0.05)
plot(time,y,type="l")
 

Tree spatial coordinates in a large sample plot in Fennoscandia

Description

Data from a large (8.8 ha) fully mapped plot in a Norway spruce (Picea abies) dominated old-growth forest in the subarctic region of Fennoscandia.

Usage

data(largeplot)

Format

Contains Cartesian position of trees and other variables in a large sample plot, as follows:

tree

Tree ID.

spp.code

Species code as follows: 1=Pinus sylvestris,2=Picea abies,3=Betula pubescens, 5=Salix caprea, 8: Sorbus aucuparia.

x.coord

Cartesian position in the X-axis, in m.

y.coord

Cartesian position in the Y-axis, in m.

status

Measurement year.

dbh

Diameter at breast-height, in cm.

toth

Total height, in m.

Source

Data were retrieved from the paper cited below, where several details might be worth reading.

References

• Pouta P, Kulha N, Kuuluvainen T, Aakala T. 2022. Partitioning of space among trees in an old-growth spruce forest in subarctic Fennoscandia. Frontiers in Forests and Global Change 5: 817248. doi:10.3389/ffgc.2022.817248

Examples

data(largeplot)
head(largeplot)
df<-largeplot
pine <- df[df$spp.code==1,]
spruce <- df[df$spp.code==2,]
birch <- df[df$spp.code==3,]
plot(spruce$x.coord,spruce$y.coord,cex=(spruce$dbh)/30,col="blue")
points(birch$x.coord,birch$y.coord,cex=(birch$dbh)/30,col="green")
points(pine$x.coord,pine$y.coord,cex=(pine$dbh)/30,col="red")

A function having the mathematical expression of the Logistic model.

Description

Function of the Logistic model, based upon three parameters and a single predictor variable as follows

y_i= \frac{\alpha}{1+ \mathrm{e}^{\beta - \gamma x_i}},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

logist.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Pearl R. 1909. Some recent studies on growth. The American Naturalist 43(509):302-316.

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. doi:10.1007/s40725-021-00145-8

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-logist.fx(x=time,a=22,b=1.4,c=.1)
plot(time,y,type="l")
#'  

A function having the mathematical expression of the Logistic modified model.

Description

Function of the Logistic modified model, based upon three parameters and a single predictor variable as follows

y_i= \frac{\alpha}{1+\mathrm{e}^{-\left(x_i-\beta \right)/\gamma}},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

logistm.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Pearl R. 1909. Some recent studies on growth. The American Naturalist 43(509):302-316.

• Pinheiro JC, DM Bates. 2000. Mixed-effects Models in S and Splus. New York, USA. Springer-Verlag. 528 p.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(0.1,65,by=0.01)
# Using the function
y<-logistm.fx(x=time,a=22,b=8.59,c=4.72)
plot(time,y,type="l")
#'  

A function having the mathematical expression of the Meyer model.

Description

Function of the Meyer model, based upon two parameters and a single predictor variable as follows

y_i= \alpha \left(1-\mathrm{e}^{-\beta {x_i}}\right),

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

meyer.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Meyer HA. 1940. A mathematical expression for height curves. Journal of Forestry 38(5):415-420.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-meyer.fx(x=time,a=20,b=.07)
plot(time,y,type="l")
 

A function having the mathematical expression of the Michaelis-Menten model.

Description

Function of the Michaelis-Menten model, based upon two parameters and a single predictor variable as follows

y_i= \alpha \left(\frac{x_i}{\beta+x_i} \right),

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

mmenten.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Michaelis L, ML Menten. 1913. Die kinetik der invertinwirkung. Biochemische Zeitschrift 49:333–369.

• Salas-Eljatib C, P Corvalán, N Pino, PJ Donoso, DP Soto.

1. Modelos de efectos mixtos de altura-diámetro para Drimys winteri en el sur (41-43 S) de Chile. Bosque 40(1):71-80.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-mmenten.fx(x=time,a=30,b=13)
plot(time,y,type="l")
 

Function to estimates the parameters of the Weibull probability density function using the method of moments

Description

Estimates the parameters of the Weibull probability density function based on the method of moments. It is based on the 2-parameter reparemetrization of the function, i.e., the shape and scale parameters.

Usage

mmweibull(y)

Arguments

Details

Althought the original function was written by Dr Oscar García, and the corresponding reference is provided, the current function has some changes to make it of a broader use.

Value

The main output is a list with the two estimated parameters and the number of observations being used for estimating the parameters.

Author(s)

Dr Oscar García and Christian Salas-Eljatib.

References

• García, O. 1981. Simplified method-of-moments estimation for the Weibull distribution. New Zealand Journal of Forestry Science 11(3): 304-306.

Examples

# Random variable to be studied
library(datana)
yvar<-llancahue$dbh
summary(yvar)
hist(yvar)
# Using the  function
mmweibull(y=yvar)

Climatic, forest structure and forest mortality variables in California (USA)

Description

The data file contains one row per unique 3.5km grid cell by year combination. The data frame covers all grid cells within the state of California where at least one Aerial Detection Survey (ADS) flight was taken between 2009 and 2015, so each grid cell position has between 1 and 7 years of data (reflected as 1 to 7 rows in the data file per grid cell position). The main response variables are mort.bin (presence of any mortality) and mort.tph (number of dead trees/ha within the given grid cell by year).

Usage

data(mortaforest)

Format

The data frame contains four variables as follows:

live.bah

Live basal area from the GNN dataset

live.tph

Live trees per hectare from the GNN dataset

pos.x

rank-order x-position of the grid cell (position 1 is western-most)

pos.y

rank-order y-position of the grid cell (position 1 is northern-most)

alb.x

x-coordinate of the grid cell centroid in California Albers (EPSG 3310)

alb.y

y-coordinate of the grid cell centroid in California Albers (EPSG 3310)

mort.bin

1= dead trees observed in grid cell. 0= no dead trees observed

mort.tph

Dead trees per hectare from the aggregated ADS dataset

mort.tpa

Dead trees per acre from the aggregated ADS dataset

year

Year of the ADS flight. Most flights occurred from May-August.

Defnorm

Mean annual climatic water deficit for the grid cell, for Oct 1-Sept 31 water year, averaged from 1981-2015

Def0

Climatic water deficit for the grid cell during the Oct-Sept water year overlapping the summer ADS flight of the given year

Defz0

Z-score for climatic water deficit for the given grid cell/water year. Calculated as (Def0–Defnorm)/(standard deviation in deficit among all years 1981-2015 for the given grid cell)

Defz1

Z-score for climatic water deficit for the given grid cell in the preceeding water year.

Defz2

Z-score for climatic water deficit for the given grid cell two water years prior.

Tz0

Z-score for temperature for the given grid cell/year.

Pz0

Z-score for precipitation for the given grid cell/year.

Defquant

FDCI variable. Quantile of Defnorm of the given grid cell, relative to the Defnorm of all other grid cells with a basal area within 2.5 m^{2}/ha of the given cell is basal area.

Source

The data were obtained from the DRYAD repository doi:10.5061/dryad.7vt36

References

• Young DJN, Stevens JS, Earles JM, Moore J, Ellis A, Jirka AM, Latimer ML. 2017. Long-term climate and competition explain forest mortality patterns under extreme drought. Ecology Letters 20(1):78-86. doi:10.1111/ele.12711

• Salas-Eljatib C, Fuentes-Ramírez A, Gregoire TG, Altamirano A, Yaitul V. A study on the effects of unbalanced data when fitting logistic regression models in ecology. Ecological Indicators 85:502-508. doi:10.1016/j.ecolind.2017.10.030

Examples

data(mortaforest)
head(mortaforest)

Mortalidad en bosques, y variables climáticas y de estructura forestal en California (USA)

Description

El archivo de datos contiene una fila por combinación única de celda de cuadrícula de 3,5 km por año. El marco de datos cubre todas las celdas de la cuadrícula dentro del estado de California donde se tomo al menos un vuelo de la Encuesta de deteccion aérea (ADS) entre 2009 y 2015, por lo que cada posición de celda de la cuadrícula tiene entre 1 y 7 años de datos (reflejados como 1 a 7 filas en el archivo de datos por posición de celda de cuadrícula). Las principales variables de respuesta son mort.bin (presencia de alguna mortalidad) y mort.tph (número de árboles muertos /ha dentro de la celda de la cuadrícula por año).

Usage

data(mortaforest2)

Format

Las variables se describen a continuación::

live.bah

Área basal viva del conjunto de datos GNN

live.tph

Árboles vivos por hectárea del conjunto de datos GNN

pos.x

Posición X del orden de clasificación de la celda de la cuadrícula (la posición 1 es la más occidental)

pos.y

Posición Y del orden de clasificación de la celda de la cuadrícula (la posición 1 es la más al norte)

alb.x

Coordenada X del centroide de la celda de la cuadrícula en California Albers (EPSG 3310)

alb.y

Coordenada Y del centroide de la celda de la cuadrícula en California Albers (EPSG 3310)

mort.bin

Codificación para identificar mortalidad. 1 = árboles muertos observados en la celda de la cuadrícula. 0 = no se observaron árboles muertos

mort.tph

Árboles muertos por hectárea del conjunto de datos ADS agregado

mort.tpa

Árboles muertos por acre del conjunto de datos ADS agregado

year

año del vuelo de ADS. La mayoría de los vuelos se realizaron entre mayo y agosto

Defnorm

Déficit hídrico climático anual medio para la celda de la cuadrícula, para el año hídrico del 1 de octubre al 31 de septiembre, promediado de 1981 a 2015

Def0

Déficit de agua climática para la celda de la cuadrícula durante el año hidrológico de octubre a septiembre que se superpone al vuelo ADS de verano del año dado

Defz0

Puntaje Z para el déficit hídrico climático para la celda de cuadrícula / año hídrico dado. Calculado como (Def0–Defnorm) / (desviación estándar en el déficit entre todos los años 1981-2015 para la celda de la cuadrícula dada)

Defz1

Puntuación Z para el déficit hídrico climático para la celda de la cuadrícula dada en el año hidrológico anterior.

Defz2

Puntuación Z para el déficit hídrico climático para la celda de la cuadrícula dada dos años antes.

Tz0

Puntaje Z para la temperatura para la celda de cuadrícula / año dado.

Pz0

Puntaje Z para la precipitación para la celda / año de la cuadrícula dado.

Defquant

Variable FDCI. Cuantil de Defnorm de la celda de la cuadrícula dada, en relación con la Defnorm de todas las demás celdas de la cuadrícula con un área basal dentro de 2.5 m^{2}/ha de la celda dada

Source

Los datos fueron obtenidos desde el repositorio DRYAD en doi:10.5061/dryad.7vt36

References

• Young DJN, Stevens JS, Earles JM, Moore J, Ellis A, Jirka AM, LatimerML. 2017. Long-term climate and competition explain forest mortality patterns under extreme drought. Ecology Letters 20(1):78-86. doi:10.1111/ele.12711

• Salas-Eljatib C, Fuentes-Ramírez A, Gregoire TG, Altamirano A, and Yaitul V. 2018. A study on the effects of unbalanced data when fitting logistic regression models in ecology. Ecological Indicators 85:502-508. doi:10.1016/j.ecolind.2017.10.030

Examples

data(mortaforest2)
head(mortaforest2)

A function having the mathematical expression of the Naslund model.

Description

Function of the Naslund model, based upon two parameters and a single predictor variable as follows

y_i= \frac{x_i^2}{\left(\alpha + \beta x_i \right)^{2}},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

naslund.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Näslund M. 1947. Skogsförsöksanstaltens gallringsförsök i tallskog. Technical report. Biochemische Zeitschrift 49:333–369.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-naslund.fx(x=time,a=1.5,b=.37)
plot(time,y,type="l")
 

Extract the n-th element from a list

Description

Extract the n-th element from a list

Usage

nele.list(lst, n)

Arguments

Value

object with elements of each list

Author(s)

Christian Salas-Eljatib

Examples

x <- list(list("z","x","y"), list(3,4,99,23,45), list(1,67,5,6,89))
nele.list(x,1)
nele.list(x,2)
nele.list(x,3)

Function that computes the result of the Ogawa allometric model.

Description

Function of the Ogawa allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

\frac{1}{y_i}= \frac{1}{\alpha} + \frac{1}{\beta {x_i}^{\gamma}},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this function can be found in Salas-Eljatib (2025).

Usage

ogawa.fx(x, alpha, beta, gamma, phi = 0)

Arguments

Value

Returns the inverse of the response variable based upon the predictor variable and the coefficients shown above.

Author(s)

Christian Salas-Eljatib.

References

• Kohyama T, T Hara, T Tadaki. 1990. Patterns of trunk diameter, tree height and crown depth in crowded abies stands. Annals of Botany 65(5):567–574.

• Salas-Eljatib C. 2026. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 53 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
d<-ogawa.fx(x=time,alpha=22,beta=0.013,gamma=1.13)
plot(time,d,type="l")
 

Tree volume for Pinus pinaster in the Baixo-Mino, Galicia, Spain

Description

These are volume measurements data of sample trees in the Baixo-Mino region in Galicia, Spain.

Usage

data(pinaster)

Format

Contains tree-level variables, as follows:

stand

Stand number from the sample tree was selected.

si

Site index of the stand.

tree.no

Tree number.

dbh

Diameter at breast height, in cm.

toth

Total height, in m.

d4

Upper-stem diameter at 4 m, in cm.

volwb

Tree gross volume, in m^{3} with bark.

volwob

Tree gross volume, in m^{3} without bark.

Source

The data are provided courtesy of Dr. Christian Salas-Eljatib at the Universidad de Chile (Santiago, Chile).

References

• Salas C, Nieto L, Irisarri A. 2005. Modelos de volumen para Pinus pinaster Ait. en la comarca del Baixo Mino, Galicia, España. Quebracho 12: 11-22. https://eljatib.com/publication/2005-12-01_modelos_de_volumen_p/

Examples

data(pinaster)
head(pinaster)

Volumen individual de árboles de Pinus pinaster en Galicia, España

Description

Variables de volumen y otras a nivel de árbol para una muestra de árboles de Pinus pinaster en la comarca del Baixo-Mino en Galicia, España.

Usage

data(pinaster2)

Format

Contiene las siguientes variables a nivel de árbol:

rodal

Rodal desde donde el árbol fue muestreado

ind.sitio

Índice de sitio del rodal, en m.

arbol

Número del árbol.

dap

Diámetro a la altura del pecho, en cm.

atot

Altura total, en m.

d4

Diámetro fustal a los 4 m, en cm.

vtcc

Volumen bruto total con corteza, en m^{3}.

vtsc

Volumen bruto total sin corteza, en m^{3}.

Source

Lo datos fueron cedidos cortesía del Dr. Christian Salas-Eljatib de la Universidad de Chile (Santiago, Chile).

References

• Salas C, Nieto L, Irisarri A. 2005. Modelos de volumen para Pinus pinaster Ait. en la comarca del Baixo Miño, Galicia, España. Quebracho 12: 11-22. https://eljatib.com/publication/2005-12-01_modelos_de_volumen_p/

Examples

data(pinaster2)
head(pinaster2)

Tree-level variables of several sample plots of invasive Pinus spp in Chile

Description

These are tree-lavel measurement data from Pinus spp invasion in Araucaria-Nothofagus forests in the Malalcahuello National Reserve in La Araucanía region in southhern Chile, measured in 2012. There are 26 plots and plot size is 100 m².

Usage

data(pinusSpp)

Format

Contains eight variables, as follows:

plot.id

Plot sample ID.

plot.size

Plot size, en m^{2}.

lat.s

Decimal coordinate of S latitude.

long.w

Decimal coordinate of W longitude.

indv.id

Tree identificator number in each plot. Same indv.id for multi-stem trees.

stem.id

Stem identificator number in each plot.

spp

Species.

dbh

Diameter at breast-height, in cm.

toth

Total height, in m.

hcb

Height to crown base, in m.

crown.lenght

Crown lenght, in m.

Source

The data is provided courtesy of Drs. Aníbal Pauchard and Rafael García at the Laboratorio de Invasiones Biológicas, Universidad de Concepción (Concepción, Chile).

References

• Cobar-Carranza A, Garcia R, Pauchard A, Pena E. 2014. Effect of Pinus contorta invasion on forest fuel properties and its potential implications on the fire regime of Araucaria araucana and Nothofagus antarctica forests. Biological Invasions. 16(11): 2273-2291. doi:10.1007/s10530-014-0663-8

Examples

data(pinusSpp)
head(pinusSpp)
length(unique(pinusSpp$plot.id))
boxplot(dbh~plot.id, data=pinusSpp)

Variables a nivel de árbol en parcelas de muestreo de Pinus spp en Chile.

Description

Mediciones a nivel de árbol para estudiar la invasión de Pinus spp en bosques de Araucaria-Nothofagus en la Reserva Nacional Malalcahuello en la región de la Araucanía en el sur de Chile. Hay 26 parcelas, y la superficie de cada una es de 100 m^{2}.

Usage

data(pinusSpp2)

Format

Los datos contienen ocho columnas que se detallan a continuación:

parcela

Número de la parcela.

sup.parcela

Superficie de la parcela, en m^{2}.

lat.s

Coordenada decimal latitud S.

long.w

Coordenada decimal longitud W.

indv.id

Identificador del árbol en la parcela. Mismo indv.id para árboles multi-fustales

fuste.id

Identificador del fuste.

espe

Especie.

dap

Diámetro a la altura del pecho, en cm.

atot

Altura total, en m.

hcc

Altura comienzo de copa, en m.

largo.copa

Largo de copa, en m.

Source

Los datos fueron cedidos por los Drs. Aníbal Pauchard y Rafael García del Laboratorio de Invasiones Biológicas, Universidad de Concepción (Concepción, Chile).

References

• Cobar-Carranza A, Garcia R, Pauchard A & Pena E. 2014. Effect of Pinus contorta invasion on forest fuel properties and its potential implications on the fire regime of Araucaria araucana and Nothofagus antarctica forests. Biological Invasions. 16(11):2273-2291. doi:10.1007/s10530-014-0663-8

Examples

data(pinusSpp2)
head(pinusSpp2)
length(unique(pinusSpp2$parce))
boxplot(dap~parce, data=pinusSpp2)

Maximum plant size in the Hawaiian archipelago

Description

Maximum plant size of 58 tree species, shrub and tree fern species that occur in 530 forest plots across the Hawaiian archipelago.

Usage

data(plantshawaii)

Format

Contains six columns, as follows:

species

Genus and epithet of the species.

family

Family of each species.

native.status

Categorical variable (native, alien, uncertain) indicating alien status of each individual following Wagner et al. (2005).

n

Number of individuals used to estimate maximum plant size.

d95

Maximum plant size, estimated as D950.1 (King et al. 2006).

dmax3

Maximum plant size, estimated as Dmax3 (King et al. 2006).

Source

The data were obtained from the DRYAD repository at doi:10.5061/dryad.1kk02qr.

References

• Craven D, Knight T, Barton K, Bialic-Murphy L, Cordell S, Giardina C, Gillespie T, Ostertag R, Sack L,Chase J. 2018. OpenNahele: the open Hawaiian forest plot database. Biodiversity Data Journal 6: e28406.

Examples

data(plantshawaii)
head(plantshawaii)
tapply(plantshawaii$d95,plantshawaii$native.status,summary)

Population of stand-volume for 400 elements.

Description

The data corresponds to a list of 400 elements of a population of the variable forest volume (in m^{3}/ha) measured in field plots of 0.1 ha of area. Therefore, the data emerge from a grid of 20 rows by 20 columns, completely covering a forest of 40 ha.

Usage

data(popvol)

Format

Contains two variables, as follows:

plot.id

Plot number, or ID.

vol

Stand volume, in m^{3}/ha

Source

The values were digitized from Table No. 11 of Zohrer (1980), which is actually based upon Loetsch and Haller (1964).

References

• Zohrer F. 1980. Forstinventur. Ein Leitfaden fur Studium und Praxis. Pareys Studientexte Nr. 26. Parey. Berlin, Germany. 207

• Loetsch F, Haller KE. 1964. Forest inventory. Volume 1. Bayerischer Landwirtschaftsverlag Gmbh. Munchen, Germany. 436 p.

Examples

data(popvol)
sum(popvol$vol)
mean(popvol$vol)
hist(popvol$vol)

Población de 400 elementos de la variable volumen de bosque

Description

Los datos corresponden a una lista de 400 elementos de un población de la variable volumen de bosque (en m^{3}/ha), medida en parcelas de 0.1 ha de superficie. Por lo tanto, los datos provienen de una grilla de 20 filas por 20 columnas, que cubren por completo un bosque de 40 ha de superficie.

Usage

data(popvol2)

Format

Contiene las siguientes dos columnas:

plot.id

Número de parcela (i.e., elemento de la población).

vol

Volumen en m^{3}/ha

Source

Datos digitados desde el cuadro No. 11 de Zohrer (1980), el cual es en realidad un cuadro citado del libro de Loetsch y Haller (1964).

References

• Zohrer F. 1980. Forstinventur. Ein Leitfaden fur Studium und Praxis. Pareys Studientexte Nr. 26. Parey. Berlin, Germany. 207

• Loetsch F, Haller KE. 1964. Forest inventory. Volume 1. Bayerischer Landwirtschaftsverlag Gmbh. Munchen, Germany. 436 p.

Examples

data(popvol2)
sum(popvol2$vol)
mean(popvol2$vol)
hist(popvol2$vol)

Function to computes the result of the power model, as a classical allometric functional form.

Description

Function of the power model, based upon the model parameters, and a single predictor variable as follows

y_i = \alpha x_i^{\beta}

where: y_i and x_i are the response and predictor variable, respectively for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

power.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable to be used is 30 
# Using the function
power.fx(x=30,a=2.86,b=.49)
 

A function having the mathematical expression of the Naslund model.

Description

Function of the Naslund model, based upon three parameters and a single predictor variable as follows

y_i= \frac{x_i^2}{\left(\alpha + \beta x_i \right)^{2}},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

prodan.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Näslund M. 1947. Skogsförsöksanstaltens gallringsförsök i tallskog. Technical report. Biochemische Zeitschrift 49:333–369.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-prodan.fx(x=time,a=2.06,b=.41,c=.03)
plot(time,y,type="l")
 

Sampling plots data from a Pinus radiata plantation near Capitán Pastene, La Araucanía region, Chile.

Description

Tree-level information collected within sample plots in a forestry 13 years-old plantation of Pinus radiata near Capitán Pastene, Southern Chile. The sample plots size is 150 m², and the total area of the plantation is 45 ha.

Usage

data(radiatapl)

Format

The data frame contains four variables as follows:

plot

Plot number identification.

tree

Tree number identification.

dbh

Diameter at breast height (1.3 m), in cm.

heigth

Total height, in m. Not measured for all trees.

sanity

Tree-health clasification, assigned to any of the following levels: good, medium, and bad.

Source

The data are provided courtesy of Mr. Mauricio Lobos-Beneventi (Temuco, Chile), and were collected with the help of his colleague, Christian Salas-Eljatib.

Examples

data(radiatapl)
head(radiatapl)

Datos a nivel de árbol de parcelas de muestreo en plantaciones de Pinus radiata

Description

Es un listado de árboles con características de árboles medidos dentro de unidades de muestreo en una plantación de 13 años de edad de Pinus radiata ubicada cerca a Capitán Pastene, región de la Araucanía, Chile. Las parcelas de muestreo tienen 150 m², y la plantación cubre una superficie total de 45 ha.

Usage

data(radiatapl2)

Format

Los datos contienen las siguientes columnas

parce

Número de identificación de la parcela de muestreo.

arbol

Número de identificación del árbol dentro de la parcela.

dap

Diámetro a la altura del pecho (1.3 m), en cm.

atot

Altura total, en m. Solo registrada para algunos árboles muestra.

sanidad

Clasificación sobre el estado sanitario del árbol, en tres niveles: buena, media, y mala.

Source

Los datos son cortesía del Ing. Forestal Mauricio Lobos-Beneventi (Temuco, Chile), y fueron recolectados en conjunto con su colega Christian Salas-Eljatib.

Examples

data(radiatapl2)
head(radiatapl2)

Function that computes the result of the Ratkowsky allometric model.

Description

Function of the Ratkowsky allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

y_i= \alpha \mathrm{e}^{\left(\frac{-\beta}{x_i +\gamma}\right)},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this function can be found in Salas-Eljatib (2025).

Usage

ratkow.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Zhang L. 1997. Cross-validation of non-linear growth functions for modelling tree height-diameter relationships. Annals of Botany 79(3):251–257.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
d<-seq(5,60,by=0.01)
# Using the function
h<-ratkow.fx(x=d,a=28,b=34,c=.85)
plot(d,h,type="l")
 

Function that computes the result of the Schnute allometric model.

Description

Function of the Schnute allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

y_i=\left\{\phi^{\alpha}+(\gamma^{\alpha}-\phi^{\alpha}) \frac{1-\mathrm{e}^{-\beta(x_i)}}{1-\mathrm{e}^{-\beta(x_2)}} \right \}^{1/\alpha},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this function can be found in Salas-Eljatib et al (2021).

Usage

schnute.fx(
  x,
  a = alpha,
  b = beta,
  c = gamma,
  phi = 0,
  x1 = min(x),
  x2 = max(x)
)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Schnute I. 1981. A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 38(9):1128-1140.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
d<-seq(5,60,by=0.01)
# Using the function
h<-schnute.fx(x=d,a=1.77,b=0.01,c=28)
plot(d,h,type="l")
 

A function having the mathematical expression of the Johnson-Schumacher model.

Description

Function of the Johnson-Schumacher model, based upon two parameters and a single predictor variable as follows

y_i= \alpha \mathrm{e}^{\left(-\beta/ {x_i} \right)},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this model can be found in Salas-Eljatib et al (2021) and Salas-Eljatib (2025).

Usage

schuma.fx(x = x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Johnson NO. 1935. A trend line for growth series. J. Am. Stat. Assoc. 30(192):717-717.

• Schumacher FX. 1939. A new growth curve and its application to timber yield studies. J. of Forestry 37(10):819-820.

• Salas-Eljatib C, Mehtatalo L, Gregoire TG, Soto DP, Vargas-Gaete R. 2021. Growth equations in forest research: mathematical basis and model similarities. Current Forestry Reports 7:230-244. doi:10.1007/s40725-021-00145-8

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
d<-seq(5,60,by=0.01)
# Using the function
h<-schuma.fx(x=d,a=3.87,b=4.38)
plot(d,h,type="l")
 

A function having the mathematical expression of the Sibbesen model.

Description

Function of the Sibbesen model, based upon three parameters and a single predictor variable as follows

y_i= \alpha \left( {x_i} \right)^{{-\beta x_i}^{-\gamma}},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

sibbesen.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Sibbesen E. 1981. Some new equations to describe phosphate sorption by soils. Journal of Soil Science 32:67-74.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-sibbesen.fx(x=time,a=32,b=0.52,c=4.83)
plot(time,y,type="l")
 

Tree locations within sample plots in an experimental forest in Austria

Description

The Austrian Research Center for Forests established a spacing experiment with Norway spruce (Picea abies) in the Vienna Woods. In the “Hauersteig” experiment, several tree-level variables were measured within four sample plots over time. The current dataframe has only the measurements carried out in 1944, for all years see biometrics::spatimepsp.

Usage

data(spataustria)

Format

Contains cartesian position of trees, and covariates, in sample plots, as follows:

plot

Plot number.

tree

Tree number.

species

Species code as follows: PCAB=Picea abies, LADC=Larix decidua, PNSY=Pinus sylvestris, FASY=Fagus Sylvatica, QCPE=Quercus petraea, BTPE=Betula pendula.

x.coord

Cartesian position in the X-axis, in m.

y.coord

Cartesian position in the Y-axis, in m.

year

Measurement year.

dbh

Diameter at breast-height, in cm.

Source

Data were retrieved from the paper cited below, where several details might be worth reading. For instance, plot size slightly varies among plots: Plot No. 1=2509.7 m^{2}, Plot No. 2=2474.8 m^{2}, Plot No. 3=2415.9 m^{2}, and Plot No. 4=2482.8 m^{2}.

References

• Kindermann G. Kristofel F, Neumann M, Rossler G, Ledermann T & Schueler. 2018. 109 years of forest growth measurements from individual Norway spruce trees. Sci. Data 5:180077 doi:10.1038/sdata.2018.77

Examples

data(spataustria)
head(spataustria)
df<-spataustria
oldpar<-par(mar=c(4,4,0,0))
bord<-data.frame(
 x=c(min(df$x.coord),max(df$x.coord),min(df$x.coord),max(df$x.coord)),
 y=c(min(df$y.coord),min(df$y.coord),max(df$y.coord),min(df$y.coord))
 )
plot(bord,type="n", xlab="x (m)", ylab="y (m)", asp=1, bty='n')
points(df$x.coord,df$y.coord,col=df$plot,cex=0.5)
par(oldpar)

Temporal tree locations within a sample plot in the Vienna woods

Description

The Austrian Research Center for Forests established a spacing experiment with Norway spruce (Picea abies) in the Vienna Woods. In the “Hauersteig” experiment, several tree-level variables were measured within four sample plots over time.

Usage

data(spatimepsp)

Format

Contains cartesian position of trees, and covariates, in a sample plot, as follows:

plot

Plot number.

tree

Tree number.

species

Species code as follows: PCAB=Picea abies, LADC=Larix decidua, PNSY=Pinus sylvestris, FASY=Fagus Sylvatica, QCPE=Quercus petraea, BTPE=Betula pendula.

x.coord

Cartesian position in the X-axis, in m.

y.coord

Cartesian position in the Y-axis, in m.

year

Measurement year.

dbh

diameter at breast-height, in cm.

Source

Data were retrieved from the paper cited below, where several details might be worth reading.

References

• Kindermann G. Kristofel F, Neumann M, Rossler G, Ledermann T & Schueler. 2018. 109 years of forest growth measurements from individual Norway spruce trees. Sci. Data 5:180077 doi:10.1038/sdata.2018.77

Examples

data(spatimepsp)
head(spatimepsp)
df<-spatimepsp
lattice::xyplot(y.coord~x.coord|as.factor(year),
data=df,as.table=TRUE)

List of botanical attributes of plant species

Description

List of botanical attributes of plant species

Usage

data(spplist)

Format

The list contains the following fields:

numtaxon

Unique number of the taxon (i.e., species).

kingdom

Taxonomic rank Kingdom. In this datase, all species belong to the Kingdom Plantae.

division

Taxonomic rank division or phylum within the Kingdom.

class

Taxonomic rank Class within the Kingdom.

orden

Taxonomic rank Order within the Class.

family

Taxonomic rank Family within the Order.

spp.ci.full

Full scientific name including author.

spp.ci.gen

Solely the genus of the scientific name.

spp.ci.epi

Solely the epithet of the scientific name.

authorspp

Species botanical-author.

subspp

Subspecies: one of two or more populations of a species varying from one another by morphological characteristics.

authorsubspp

Sub-species botanical-author.

variety

authorvar

shape

Shape

authorshape

Shape's author.

comnames

Species common name(s). With blank spaces, no special characters.

synonymy

Synonyms of the scientific name by which the species has been or is known.

borcount

Border countries given the species distribution range.

habit

The general appearance, growth form, or architecture e.g., tree, shrub, grass.

lifecycle

Life cycle.

statusori

Status according to the species origin: Native or Endemic

regdist

Distribution range of the species, within Chile administrative regions

elerange

Elevation range of the species, in meters above sea level.

note

sppcode

Abreviattion of the species according to the Forest Biometrics and Modelling Lab at the Universidad de Chile (https://biometriaforestal.uchile.cl). For instance, ap stands for the species Aextoxicon punctatum, lh for Lomatia hirsuta, and alike. Meanwhile nob is Nothofagus obliqua and nal to Nothofagus alpina.

spp.name

Species common name. No blank spaces, no special characters.

spp.ci.abb

Species scientific name abbreviation.

spp.ci.name

Species scientific name.

spp.co.name.latex

Species common name in LaTeX

spp.co.name

Species single common name.

Function that computes the result of the Stage allometric model.

Description

Function of the Stage allometric model, based upon parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

y_i= \alpha \mathrm{e}^{\left(-\beta ({x_i}^{-\gamma}) \right)},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients). Further details on this function can be found in Salas-Eljatib (2025).

Usage

stage.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Stage AR. 1963. A mathematical approach to polymorphic site index curves for Grand Fir. Forest Sci. 9(2):167-180. doi:10.1093/forestscience/9.2.167

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
d<-stage.fx(x=time,a=28,b=56,c=1.19)
plot(time,d,type="l")
 

Stand table for a Nothofagus dombeyi (coihue) forest

Description

Stand table for a secondary forest of Nothofagus dombeyi (coihue) en Chile.

Usage

data(standtabCoihue)

Format

The data has the following columns

diam.cl

Diameter class, in cm.

nha

Density for the respective diameter class, in trees/ha.

gha

Basal area for the respective diameter class, in m^{2}/ha.

Source

The forest was located in the Andean foothills in the Araucanía region in southern Chile. Data from Prof. Christian Salas-Eljatib, Universidad de Chile, Santiago, Chile.

References

• Donoso C. 1995. Bosques Templados de Chile y Argentina. Editorial Universitaria. Santiago, Chile.

Examples

data(standtabCoihue)
df<-standtabCoihue
df<-df[-nrow(df),]
# Diameter distribution plot 
barplot(df$nha, legend = TRUE, beside = TRUE, las=1,
        names.arg = as.numeric(df$diam.cl),
        ylab="Density (trees/ha)",xlab="Diameter class (cm)")
abline(h=0)

Tabla de rodal para bosque de Nothofagus dombeyi (coihue)

Description

Tabla de rodal para un bosque secundario de Nothofagus dombeyi (coihue) en Chile.

Usage

data(standtabCoihue2)

Format

Los datos tienen las siguientes columnas

cd

Marca de la clase diamétrica, en cm.

nha

Densidad de la clase diamétrica, en arb/ha.

gha

Área basal de la clase diamétrica, en m^{2}/ha.

Source

Bosque ubicado en sector Andino de la Región de la Araucanía en el sur de Chile. Cuadro cedido por el Prof. Christian Salas-Eljatib, Universidad de Chile, Santiago, Chile.

References

• Donoso C. 1995. Bosques Templados de Chile y Argentina. Editorial Universitaria. Santiago, Chile.

Examples

data(standtabCoihue2)
df<-standtabCoihue2
df<-df[-nrow(df),]
# Diameter distribution plot 
barplot(df$nha, legend = TRUE, beside = TRUE, las=1,
        names.arg = as.numeric(df$cd),
        ylab="Densidad (arb/ha)",xlab="Clase diametrica (cm)")
abline(h=0)

Stand tables for Nothofagus alpina (raulí) forests

Description

Stand tables for secondary Nothofagus alpina-dominated forests in different locations in southern Chile.

Usage

data(standtabRauli)

Format

The data has the following columns

site

Study site.

sector

Location within a study site.

low.cd

Lower limit of the diameter class, in cm.

upp.cd

Upper limit of the diameter class, in cm.

dclass

Diameter class, in cm.

nha.dcl

Tree density for the respective diameter class, in trees/ha.

forest.id

Forest ID code, a combination of columns site and sector.

Source

Tree density by diameter classes (i.e., stand table). Data were digitized from table No. 4 of Wadsworth (1976).

References

• Wadsworth RK. 1976. Aspectos ecologicos y crecimiento del raulí (Nothofagus alpina) y sus asociados en bosques de segundo crecimiento de las provincias de Bío-Bío, Malleco y Cautín, Chile. Boletin Técnico No. 37, Fac. Cs. Forestales, Universidad de Chile, Santiago, Chile.

Examples

data(standtabRauli)
head(standtabRauli)
df<-standtabRauli
table(df$site,df$sector,df$dclass)

Tablas de rodal para bosques de Nothofagus alpina (raulí)

Description

Tablas de rodal para bosques secundarios dominados por Nothofagus alpina en diferentes localidades del sur de Chile.

Usage

data(standtabRauli2)

Format

Los datos tienen las siguientes columnas

sitio

Nombre del sitio de estudio.

sector

Código identificador de un sector específico dentro del sitio en estudio.

linf.cd

Límite inferior de la clase diamétrica, en cm.

lsup.cd

Límite superior de la clase diamétrica, en cm.

cd

Marca de la clase diamétrica, en cm.

nha.cd

Densidad de la clase diamétrica, en arb/ha.

bosque.id

Identificador del bosque, combinación de sitio y sector.

Source

Densidad de árboles por clase diamétrica, i.e., tabla de rodal. Datos digitados desde el cuadro No. 4 de Wadsworth (1976).

References

• Wadsworth RK. 1976. Aspectos ecologicos y crecimiento del raulí (Nothofagus alpina) y sus asociados en bosques de segundo crecimiento de las provincias de Bío-Bío, Malleco y Cautín, Chile. Boletin Técnico No. 37, Fac. Cs. Forestales, Universidad de Chile, Santiago, Chile.

Examples

data(standtabRauli2)
head(standtabRauli2)
df<-standtabRauli2
table(df$sitio,df$sector,df$cd)

Stand table for Nothofagus obliqua (roble) secondary forests

Description

Average stand table for secondary forests of Nothofagus obliqua (roble) forests, between 40 and 50 years-old, in the Malleco, Cautín, and Valdiva provinces in southern Chile.

Usage

data(standtabRoble)

Format

The data has the following columns

diam.cl

Diameter class, in cm.

nha

Density for the respective diameter class, in trees/ha.

Source

The stand table is from Puente et al. (1979), as a part of a study regarding secondary Nothofagus forests in southern Chile.

References

• Puente M, C Donoso, R Peñaloza, E Morales. 1979. Estudio de raleo y otras técnicas para el manejo de renovales de raulí (Nothofagus alpina) y roble (Nothofagus obliqua). Etapa I: Identificación y caracterización de renovales de raulí y roble. Informe de convenio No. 5, Proyecto CONAF/PNUD/FAO-CHI/76/003, Santiago, Chile. 88 p.

Examples

data(standtabRoble)
df<-standtabRoble
df<-df[-nrow(df),]
# Diameter distribution plot 
barplot(df$nha, legend = TRUE, beside = TRUE, las=1,
        names.arg = df$diam.cl,
        ylab="Density (trees/ha)",xlab="Diameter class (cm)")
abline(h=0)

Tabla de rodal media para renovales de Nothofagus obliqua (roble)

Description

Tabla de rodal media para renovales dominados por Nothofagus obliqua (roble), que tienen entre 40 y 50 años, en las provincias de Malleco, Cautín, y Valdiva, en el sur de Chile.

Usage

data(standtabRoble2)

Format

Las columnas son las siguientes

cd

Clase diamétrica, en cm.

nha

Densidad para la respectiva clase diamétrica, en arb/ha.

Source

La tabla de rodal proviene de Puente et al. (1979), y es el resultado de un estudio sobre los bosques secundarios de Nothofagus en el sur de Chile.

References

• Puente M, C Donoso, R Peñaloza, E Morales. 1979. Estudio de raleo y otras técnicas para el manejo de renovales de raulí (Nothofagus alpina) y roble (Nothofagus obliqua). Etapa I: Identificación y caracterización de renovales de raulí y roble. Informe de convenio No. 5, Proyecto CONAF/PNUD/FAO-CHI/76/003, Santiago, Chile. 88 p.

Examples

data(standtabRoble2)
df<-standtabRoble2
df<-df[-nrow(df),]
# Grafico de distribucion diametrica 
barplot(df$nha, legend = TRUE, beside = TRUE, las=1,
        names.arg = df$cd,
        ylab="Densidad (arb/ha)",xlab="Clase diametrica (cm)")
abline(h=0)

Function to compute stand-level variables for a given imputed-tree-list.

Description

Computes stand-level variables for a given sample plot. The variables are the following: density, basal area, quadratic diameter diameter, average height, top height, and stand volume.

Usage

standvar(
  data,
  plot.id,
  plot.area,
  time = NA,
  d,
  y,
  h = NA,
  factvar = NA,
  metric = TRUE,
  eng = TRUE,
  ...
)

Arguments

Details

For a given imputed tree list of a sample plot, several stand-level variales are computed. Note that the imputed-tree list must have all the tree-level variables needed to obtain the stand-level ones, such as, height, and volume. If there remeasurement for a plot, the computation is by plot and measurement year.

Value

Returns a data frame with the the stand variables per plot. If factvar is provided, the stand variables will be a also computed for each level of the factvar. Dominant diameter and dominant height are computed using the function domvar().

Author(s)

Christian Salas-Eljatib.

References

• Salas-Eljatib C. 2025. Biometría y Modelación Forestal. Borrador de libro, en revisión. 352 p.

Examples

df<-biometrics::eucaplot2
#see the metadata by typing ?eucaplot2
head(df)
datana::descstat(df[,c("dap","atot")])
## Preparing the treelist, in the required format
df$parce<-1;df$sup.plot<-500
## Estimating tree-volume using an artifical factor form
df$vol<-gtree(x=df$dap)*df$atot*0.35
## Using the function
standvar(data=df,plot.id="parce",plot.area="sup.plot",
         d="dap",h="atot",y="vol")
# Do the same as before, but adding the computation by a factor
standvar(data=df,plot.id="parce",plot.area="sup.plot",
         d="dap",h="atot",y="vol",factvar = "clase.copa")
## More than one aggregated variable. For instance, adding biomass
##  and tree carbon, aside of volume. A naive estimation
##  of tree-biomass and carbon, could be 
df$biom<-df$v*420 #(kg/m3)
df$carb<-df$biom*0.5 #50% of biomass is carbon
df
standvar(data=df,plot.id="parce",plot.area="sup.plot",
         d="dap",h="atot",y=c("vol","biom","carb"))
 #what if the sample plot has a remeasurement
df$measu.yr<-2025;df$measu.yr[1:5]<-2020
df
#' ## Using the function per measurement year
standvar(data=df,plot.id="parce",plot.area="sup.plot",
         d="dap",h="atot",y=c("vol","biom","carb"),time="measu.yr")
# Do the same as before, but adding the computation by a factor
standvar(data=df,plot.id="parce",plot.area="sup.plot",
         d="dap",h="atot",y=c("vol","biom","carb"),time="measu.yr",
         factvar = "clase.copa")
# More than one plot
df<-biometrics::radiatapl2
table(df$parce)
## naive imputation of tree-height
df[is.na(df$atot),"atot"]<-df[is.na(df$atot),"dap"]*0.8
## Estimating tree-volume using an artifical factor form
df$vtot<-gtree(x=df$dap)*df$atot*0.35
datana::descstat(df[,c("dap","atot","vtot")])
df$sup.plot<-150
standvar(data=df,plot.id="parce",plot.area="sup.plot",
         d="dap",h="atot",y="vtot")
standvar(data=df,plot.id="parce",plot.area="sup.plot",
             d="dap",h="atot",y="vtot",factvar = "sanidad")

A function having the mathematical expression of the Strand model.

Description

Function of the Strand model, based upon two parameters and a single predictor variable as follows

y_i= \left(\frac{x_i}{\alpha +\beta x_i}\right)^3,

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

strand.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Strand L. 1964. Numerical constructions of site-index curves. Forest Sci. 10(4):410-414.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-strand.fx(x=time,a=1.15,b=.37)
plot(time,y,type="l")
 

A function having the mathematical expression of the Strand model.

Description

Function of the Strand generalized model, based upon three parameters and a single predictor variable as follows

y_i= \left(\frac{x_i}{\alpha +\beta x_i}\right)^{\gamma},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

strandg.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Strand L. 1964. Numerical constructions of site-index curves. Forest Sci. 10(4):410-414.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-strandg.fx(x=time,a=0.98,b=0.52,c=4.83)
plot(time,y,type="l")
 

Datos de ahusamiento de Eucalyptus regnans

Description

Corresponde a mediciones de diámetros fustales, con y sin corteza, para árboles muestra en plantaciones de Eucalyptus regnans en la comuna de Gorbea, región de la Araucanía, Chile. Note que existen por lo tanto, varias mediciones para cada árbol.

Usage

data(tapereuca2)

Format

Contiene las siguientes variables:

narb

Número del árbol.

sec

Número de sección del árbol narb.

hl

Altura fustal de la sección sec, en m.

dlcc

Diámetro de la sección sec con corteza, en cm.

dlsc

Diámetro de la sección sec sin corteza, en cm.

ec

Espesor de corteza de la sección sec.

forma

Forma del árbol, en donde 1 = Fuste cilíndrico y 2 = Fuste acilíndrico (pequeña curvatura).

dap

Diámetro a la altura del pecho (1.3 m) en cm.

decdap

Doble espesor de corteza en el dap.

htot

Altura total del árbol narb, en m.

dtoc

Diámetro con corteza en hcc.

hcc

Altura de comienzo de copa del árbol narb, m.

Source

Los datos provienen de la Tesis de Ingeniero Forestal de Manuel Morales, UFRO.

References

• Morales, M. (2003). Modelos fustales para Eucalyptus regnans F. Muell., en la comuna de Gorbea, Novena Región. Tesis Ingeniero Forestal. Universidad de La Frontera. Temuco, Chile. 43p.

Examples

data(tapereuca2)
lattice::xyplot(dlcc~hl, data=tapereuca2, type = "l", groups = narb)

Carrasco polynomial function

Description

Polynomial function of Carrasco (1986)

Usage

taperpoly.fx(hl = hl, hcc = hcc, paramod = paramod, n = (length(paramod) - 1))

Arguments

Details

This function takes the form of

\frac{d_{l_{i}}}{d_i} = \beta_0 + \beta_1 X + \beta_2 X^2 + \beta_3 X^3 + \cdots + \beta_n X^{n},

where: d_{l_{i}} is the stem diameter at stem-height h_{l_{i}} for the i-th tree; d_i and h_i are the tree-level variables diameter at breast height and total height respectively for the i-th tree, and $n$ is the degree of the polynomial. The other term is

X = \frac{hcc_i - h_{l_i}}{hcc_i - 1.3},

Value

Returns the diameter of the stem at the stem-height h_l, thus d_l, divided by the diameter at breast height (1.3). This is

\frac{d_{l_i}}{d_i}

Author(s)

Christian Salas-Eljatib and Nicolás Campos

References

• Carrasco, J. 1986. Estudio Comparativo de dos Métodos para Evaluar la Calidad a árboles en pie y para representar la Forma del Fuste en el Bosque Siempreverde valdiviano. Tesis Ingeniero Forestal. Universidad Austral de Chile. Valdivia, Chile. 117 p.

Examples

dl <- seq(40, 0, -5)
hl <- seq(0, 16, 2)
d <- 30
hcc <- 12
h <- max(hl)
df <- data.frame(dl = dl,
                 hl = hl,
                 d = d,
                 hcc = hcc,
                 h = h)
df

myparams <- c(0.3, 0.8, 0.00003)

taperpoly.fx(hl = df$hl, hcc = df$hcc, paramod = myparams, n = 2)

df$y <- taperpoly.fx(hl = df$hl, hcc = df$hcc, paramod = myparams, n = 2)
## the n parameter is not necesary
df$y2 <- taperpoly.fx(hl = df$hl, hcc = df$hcc, paramod = myparams)
df$dl.h <- df$y * df$d
df

Diameter and height growth of Grand-fir sample trees.

Description

Diameter and height growth of 66 Grand-fir trees. Data derived from stem analysis sample trees collected by Dr. Albert Stage (US Forest Service, Moscow, ID, USA.)

Usage

data(treegrowth)

Format

Contains seven column, as follows:

tree.no

Tree number identificator. An unique number to each sample tree.

forest

Forest type.

habitat

Forest habitat type.

tree.code

A composite tree code representing the following columns: tree.id-forest-habitat

age

Age, in yr

dbh

Diameter at breast-height, in cm. Originally measured in inches, and was converted to cm using a single decimal.

toth

Total height, in m. Originally measured in feet, and was converted to m using a single decimal.

Source

Originally, the data were provided by Dr. Albert Stage (R.I.P) to Professor Andrew Robinson (University of Idaho, USA), whom used them to explain the fitting of statistical models. Dr Christian Salas-Eljatib was a former graduate student of Statistics of Prof. Robinson at the Univ. of Idaho.

References

• Stage, A. R., 1963. A mathematical approach to polymorphic site index curves for Grand fir. Forest Science 9 (2), 167–180.

Examples

data(treegrowth)
df<-treegrowth
head(df)
require(lattice)
xyplot(dbh~age, groups = tree.code,data=df, type="b")

Crecimiento en diámetro y altura de árboles muestra de Grand-fir.

Description

Crecimiento en diámetro y altura de 66 árboles de Grand-fir. Los datos fueron derivados a partir de árboles muestras de análisis fustal colectados por el Dr. Albert Stage (US Forest Service, Moscow, ID, USA.)

Usage

data(treegrowth)

Format

Contiene las siguientes siete columnas:

num.arb

Número identificador del árbol. Único para cada árbol muestra.

bosque

Tipo forestal.

habitat

Clasificacion de tipo de hábitat.

cod.arb

Un código que combina a las siguientes columnas: num.arb-bosque-habitat

edad

Edad, en años.

dap

Diámetro a la altura del pecho, en cm. Originalmente fue medido en pulgadas, y acá se transformó empleando un solo decimal.

atot

Altura total, in m. Originalmente esta variable fue medido en pies, y acá se transformó empleando un solo decimal.

Source

En un principio los datos fueron cedidos por el Dr. Albert Stage (Q.E.P.D) al Profesor Andrew Robinson (University of Idaho, USA), quien los usaba para explicar el ajuste de modelos estadísticos. El Dr. Christian Salas-Eljatib fue un estudiante de postgrado en estadistica del Prof. Robinson en la Univ. of Idaho.

References

• Stage, A. R., 1963. A mathematical approach to polymorphic site index curves for Grand fir. Forest Science 9 (2), 167–180.

Examples

data(treegrowth2)
df<-treegrowth2
head(df)
require(lattice)
xyplot(dap~edad, groups = cod.arb,data=df, type="b")

Tree-list data from a forest sampling work

Description

Tree-level variables measured within three sample plots in a forest sampling effort. This sort of work is commonly referred as a forest inventory. Notice that plots might have different areas. The sampling was carried out in a secondary forest of Nothofagus obliqua in the Rucamanque experimental station, near the city of Temuco, in southern Chile.

Usage

data(treelistinve)

Format

Contains tree-level variables, as follows:

plot

Plot number.

plot.size

Plot size, in m^{2}.

tree

Tree identificator

species

Species common name as follows: Olivillo=Aextocicon puncatatum, Tepa=Laureliopsis philippiana, Lingue=Persea lingue, Coigue=Nothofagus dombeyi, Roble=Nothofagus obliqua, Other=Other

dbh

Diameter at breast-height, in cm.

toth

Total height, in m. Only measured for some sample trees.

Source

The data is provided courtesy of Prof. Christian Salas-Eljatib, Universidad de Chile (Santiago, Chile).

References

• Salas C. 2001. Caracterización básica del relicto de Biodiversidad Rucamanque. Bosque Nativo, 29:3-9. https://eljatib.com/publication/2001-06-01_caracterizacion_basi/

• Salas C. 2002. Ajuste y validación de ecuaciones de volumen para un relicto del bosque de Roble-Laurel-Lingue. Bosque 23(2): 81-92. doi:10.4067/S0717-92002002000200009 https://eljatib.com/publication/2002-07-01_ajuste_y_validacion_/

Examples

data(treelistinve)
head(treelistinve)
tapply(treelistinve$dbh,treelistinve$species,summary)

Lista de árboles en un muestreo forestal

Description

Variables a nivel de árbol medidas en tres unidades de muestreo (i.e., parcelas) establecidas en un muestreo forestal. Este tipo de muestreo de bosques, es comunmente conocido como “inventario forestal”. Note que las parcelas podrían tener diferentes superficies. El muestreo fue realizado en un bosque secundario dominado por Nothofagus obliqua en el predio Rucamanque, en las cercanías de la ciudad de Temuco, en el sur de Chile.

Usage

data(treelistinve2)

Format

Contiene variables a nivel de árbol dentro de parcelas.

parce

Número de la parcela de muestreo.

sup.parce

Superficie de la parcela, en m^{2}.

arbol

Número identificador del árbol.

spp

Nombre común de especies como sigue: Olivillo=Aextocicon puncatatum, Tepa=Laureliopsis philippiana, Lingue=Persea lingue, Coigue=Nothofagus dombeyi, Roble=Nothofagus obliqua, Other=Other

dap

Diámetro a la altura del pecho, en cm.

atot

Altura total, en m. Solo medida en algunos árboles muestra.

Source

Los datos fueron cedidos por el Prof. Christian Salas-Eljatib, Universidad de Chile (Santiago, Chile).

References

• Salas C. 2001. Caracterización básica del relicto de Biodiversidad Rucamanque. Bosque Nativo, 29:3-9. https://eljatib.com/publication/2001-06-01_caracterizacion_basi/

• Salas C. 2002. Ajuste y validación de ecuaciones de volumen para un relicto del bosque de Roble-Laurel-Lingue. Bosque 23(2): 81-92. doi:10.4067/S0717-92002002000200009 https://eljatib.com/publication/2002-07-01_ajuste_y_validacion_/

Examples

data(treelistinve2)
unique(treelistinve2$parce)
table(treelistinve2$parce,treelistinve2$sup.parce)
tapply(treelistinve2$dap,treelistinve2$spp,summary)

Function to compute descriptive statistics at tree-level, segregated by a factor (factvar) per sample plot.

Description

Computes several descriptive statistics of variables at the tree-level per sample plot. It can also be be applied to compute them by levels of factor within each available plot.

Usage

treestat(
  data,
  plot.id,
  t = NA,
  y,
  d = NA,
  factvar = NA,
  full = FALSE,
  short.names = TRUE,
  metric = TRUE,
  eng = TRUE,
  want.add.d = FALSE,
  want.add.g = FALSE,
  ...
)

Arguments

Details

For a given tree list of a sample plot, several descriptive statistics are computed for the selected random variables, by plot and measurement year.

Value

Returns a data frame with the statistics per plot and time for the selected y variables. If factvar is given, the same statistics will be added but segregated by each level (or category) of the factvar.

Author(s)

Christian Salas-Eljatib.

References

• Salas-Eljatib C. 2025. Biometría y Modelación Forestal. Borrador de libro, en revisión. 352 p.

Examples

# Dataframe to be used
df<-biometrics::eucaplot2
#?eucaplot2
head(df)
datana::descstat(df[,c("dap","atot")])
df$parce<-1
## Using the function
treestat(data=df,plot.id="parce",y="atot")
# Now, for two random variables, instead of a single one 
treestat(data=df,plot.id="parce",y=c("dap","atot"))
# If the d is provided, Do you want to add both the diameter
# and the basal area (g), as random variables? 
treestat(data=df,plot.id="parce",y="atot",d="dap",want.add.d=TRUE,want.add.g=TRUE)
## Do the same as before, but adding the computation by a factor

treestat(data=df,plot.id="parce",y="atot",factvar="clase.copa")
df$time<-2025;df$time[1:5]<-2020
df
## Using the function per measurement year
treestat(data=df,plot.id="parce",y="atot",t="time",full=TRUE)
# Do the same as before, but adding the computation by a factor
treestat(data=df,plot.id="parce",y="atot",t="time",
         factvar="clase.copa",full = TRUE)
## same as before, but for two random variables
treestat(data=df,plot.id="parce",y=c("dap","atot"),t="time",
          factvar="clase.copa",full = TRUE)

Tree-level volume by species in the Rucamanque forest

Description

These is tree-level measurement data of sample trees in the Rucamanque experimental forest, near Temuco, in the Araucanía region in south-central Chile. Data were measured in 1999.

Usage

data(treevolruca)

Format

Contains tree-level variables, as follows:

tree

Tree number identification.

spp

Tree species common name as follows: "Laurel" is Laurelia sempervirens, "Lingue" is Persea lingue, "Olivillo" is Aextoxicon punctatum, "Tepa" is Laureliopsis philippiana, "Tineo" is Weinmannia trichosperma, y "Ulmo" is Eucryphia cordifolia.

dbh

Diameter at breast height, in cm.

toth

Total height, in m.

d6

Upper-stem diameter at 6 m, in cm.

totv

Tree gross volume, in m³ with bark.

Source

The data were provided courtesy of Dr. Christian Salas-Eljatib, Universidad de Chile (Santiago, Chile).

References

• Salas C. 2002. Ajuste y validación de ecuaciones de volumen para un relicto del bosque de Roble-Laurel-Lingue. Bosque 23(2): 81-92. doi:10.4067/S0717-92002002000200009 https://eljatib.com/publication/2002-07-01_ajuste_y_validacion_/

Examples

data(treevolruca)
head(treevolruca)
table(treevolruca$spp)

Volumen a nivel de árbol para especies nativas del bosque de Rucamanque

Description

Volumen, altura y diámetro, entre otras para árboles muestra en el bosque de Rucamanque, cerca de Temuco, en la región de la Araucanía, en el sur de Chile.

Usage

data(treevolruca2)

Format

Las siguientes columnas son parte de la dataframe:

arbol

Número del árbol.

spp

Codificación de la especie como sigue: "Laurel" es Laurelia sempervirens, "Lingue" es Persea lingue, "Olivillo" es Aextoxicon punctatum, "Tepa" es Laureliopsis philippiana, "Tineo" es Weinmannia trichosperma, y "Ulmo" es Eucryphia cordifolia.

dap

Diámetro a la altura del pecho, en cm.

atot

Altura total, en m.

d6

Diámetro fustal a los 6 m, en cm.

vtot

Volumen bruto total, en m³ con corteza.

Source

Los datos fueron cedidos por el Dr. Christian Salas-Eljatib, Universidad de Chile (Santago, Chile).

References

• Salas C. 2002. Ajuste y validación de ecuaciones de volumen para un relicto del bosque de Roble-Laurel-Lingue. Bosque 23(2): 81-92. doi:10.4067/S0717-92002002000200009 https://eljatib.com/publication/2002-07-01_ajuste_y_validacion_/

Examples

data(treevolruca2)
head(treevolruca2)
table(treevolruca2$spp)

Tree-level information of forest plots across the Hawaiian archipelago.

Description

Diameter at breast height (or occurrence) of individual trees, shrubs and tree ferns across 530 plots across the Hawaiian archipelago and includes native status and cultivated status of the 185 species.

Usage

data(trlhawaii)

Format

Contains 18 variables, as follows:

island

Island name.

plot.id

Unique numeric identifier for each plot.

study

Brief name of study.

plot.area

Plot area in m^{2}.

longitude

Longitude of plot in decimal degrees; WGS84 coordinate system.

latitude

Latitude of plot in decimal degrees; WGS84 coordinate system.

year

Year in which plot data was collected.

census

Numeric identifier for each census.

tree.id

Unique numeric identifier for each individual.

scientific.name

Genus and species of each individual following TPL v. 1.1.

family

Family of each individual following TPL v. 1.1.

angiosperm

Binary variable (1 = yes, 0 = no) indicating whether an individual is classified as an angiosperm following APG III.

monocot

Binary variable (1 = yes, 0 = no) indicating whether an individual is classified as a monocot following APG III.

native.status

Categorical variable (native, alien, uncertain) indicating alien status of each individual following Wagner et al. (2005).

cultivated.status

Binary variable (1 = yes, 0 = no, NA = not applicable) indicating if species is cultivated following PIER.

abundance

Number of individuals (all = 1).

abundance.ha

Abundance of each individual on a per hectare basis.

dbh

Diameter at 1.3 m (in cm) for each individual; NA indicates that size was not measured, but was classified by size class.

Source

The data were obtained from the DRYAD repository at doi:10.5061/dryad.1kk02qr.

References

• Craven D, Knight T, Barton K, Bialic-Murphy L, Cordell S, Giardina C, Gillespie T, Ostertag R, Sack L,Chase J. 2018. OpenNahele: the open Hawaiian forest plot database. Biodiversity Data Journal 6: e28406.

Examples

data(trlhawaii)
table(trlhawaii$island,trlhawaii$study)
unique(trlhawaii$plot.id)
table(trlhawaii$plot.id)
tapply(trlhawaii$plot.area,trlhawaii$study,summary)

Long term tree-list data from permanent sample plots

Description

Temporal tree-level data within four sample plots in an experimental forest in Austria. The dataframe contains several tree-level variables. Plot sizes are 2500 m^{2} (approx.).

Usage

data(trlpsptime)

Format

Contains tree-level variables, as follows:

plot

Plot number.

tree

Tree identificator.

species

Species code as follows: PCAB=Picea abies, LADC=Larix decidua, PNSY=Pinus sylvestris, FASY=Fagus Sylvatica, QCPE=Quercus petraea, BTPE=Betula pendula.

year

Year of measurement.

obs

Observation.

dbh

Diameter at breast-height, in mm.

dbh2

Orthogonal measured second diameter, in mm.

hmk

Selection criteria to measure tree height. 1=systematic, 2=systematic and in the group of the 100 thickest, 3=belongs to the 100 thickest, 4=lying tree, 5=Standing tree with a ladder, 6=outlier, 7=from stem analysis.

kh

Type of the height measurement. 0=tree height, 1=angle and distances.

ho

Tree height in dm when kh=0. When kh=1 then distance to the tree in dm or in 1977 length of the base bar in cm.

ka

Height to the crown base in dm when kh=0. When kh=1 then angle to the tree top in 1/10 degree.

kb

Crown width in dm when kh=0. When kh=1 then angle to 1.3 m above tree base in 1/10 degree.

wka

Angle to crown base in 1/10 degree.

crown.cl

Crown class according to Kraft. 1=predominant, 2=dominant, 3=co-dominant, 4=dominated, 5=overtopped.

crown

Crown quality. 0=normal, 1=broken in the crown region, 2=substituted tree top, 3=forked, 4=bushy, stork nest, witches' broom, 5=wizen tree top, 6=again broken tree top.

stem

Stem quality. 0=typical, 1=crooked, 2=abiotic damaged, 3=biotic damaged, 4=forked stem without damage, 5=forked stem with damage, 6=up to 1/3 of the girth is peeled, 7=more than 1/3 of the girth is peeled, 8=broken stem, 9=other stem damages.

defoliation

crown defoliation. 1=low, 2=medium, 3=much.

Source

The Austrian Research Center for Forests established a spacing experiment with Norway spruce (Picea abies) in the Vienna Woods. In the “Hauersteig” experiment, several tree-level variables were measured within four sample plots over time. Data were retrieved from the paper cited below, where several details might be worth reading.

References

• Kindermann G. Kristofel F, Neumann M, Rossler G, Ledermann T & Schueler. 2018. 109 years of forest growth measurements from individual Norway spruce trees. Sci. Data 5:180077 doi:10.1038/sdata.2018.77

Examples

data(trlpsptime)
df<-trlpsptime
head(df)
tapply(df$dbh, list(df$year,df$plot), mean)

Tree-level remeasurements for a sample plot in a Pinus radiata plantation

Description

Temporal tree-level data from a sample plot established in a Monterey pine (Pinus radiata) forestry plantation in Chile. The plot size is 1600 m^{2}, and the plantation was established in 1990.

Usage

data(trlremeasu)

Format

Tree list data for a sample plot remeasured through time, and having the following columns

plot.id

Plot code.

tree

Tree number.

x.coord

Cartesian position in the X-axis, in m.

y.coord

Cartesian position in the Y-axis, in m.

year

Measurement year.

dead

Dead identificator, 0 means alive, and 1 otherwise.

dbh

diameter at breast-height, in cm.

Source

Data were retrieved from the paper cited below, where several details might be worth reading.

References

• Pommerening A, Trincado G, Salas-Eljatib C, Burkhart H. 2023. Understanding and modelling the dynamics of data point clouds of relative growth rate and plant size. Forest Ecology and Management Volume 529:120652 doi:10.1016/j.foreco.2022.120652

Examples

data(trlremeasu)
head(trlremeasu)
df<-trlremeasu
df$fe<-10000/1600
df$garb.ha<- (pi/40000)*df$dbh^2*df$fe
gha.t<-tapply(df$garb.ha, df$year, sum)
nha.t<-tapply(df$fe, df$year, sum);
time<-as.numeric(rownames(gha.t))
plot(nha.t~time, type="b",las=1)
plot(gha.t~time, type="b",las=1)

Smoothed tree list data from permanent sample plots

Description

Temporal tree-level variables (smoothed-values) within four sample plots in an experimental forest in Austria. The dataframe contains all the variables for all trees, where observation gaps were filled from monotone increasing predictive functions. Plot sizes are 2500 m^{2} (approx.) and the current dataframe only keeps the measurement years having a more reliable amount of records.

Usage

data(trlsmoopsp)

Format

Contains tree-level variables, as follows:

plot

Plot number.

tree

Tree identificator.

year

Year of measurement.

species

Species code as follows: PCAB=Picea abies, LADC=Larix decidua, PNSY=Pinus sylvestris, FASY=Fagus Sylvatica, QCPE=Quercus petraea, BTPE=Betula pendula.

obs

Observation in this year.

dbh

Diameter at breast-height, in cm.

toth

Tree height, in m.

hcb

Height to the crown base, in m.

Source

The Austrian Research Center for Forests established a spacing experiment with Norway spruce (Picea abies) in the Vienna Woods. In the “Hauersteig” experiment, several tree-level variables were measured within four sample plots over time. Data were retrieved from the paper cited below, where several details might be worth reading.

References

• Kindermann G. Kristofel F, Neumann M, Rossler G, Ledermann T & Schueler. 2018. 109 years of forest growth measurements from individual Norway spruce trees. Sci. Data 5:180077 doi:10.1038/sdata.2018.77

Examples

data(trlsmoopsp)
df<-trlsmoopsp
head(df)
table(df$year,df$plot)
tapply(df$dbh, list(df$year,df$plot), length)

Function to compute the U-estimator for a sorted random variable, measured in a given sample plot.

Description

Computes the U-estimator for a number of trees per-are (1 ha=100ares)

Usage

uestimator(sorty, n.per.are)

Arguments

Details

Althought the original function was written by Dr Oscar García, and the corresponding reference is provided, the current function has several changes that makes it of a broader use.

Value

The main output is the U-estimator for the random variable of interest.

Author(s)

Dr Oscar García and Christian Salas-Eljatib.

References

• Garcia O, Batho A. 2005. Top height estimation in lodgepole pine sample plots. Western Journal of Applied forestry 20(1):64-68.

Examples

#Creates a fake dataframe
h <- c(29.1,28, 24.5, 26, 21,20.5,20.1);
sort.h<-sort(h,decreasing=FALSE);sort.h
plot.area.m2<-500;plot.area.ha<-plot.area.m2/10000;plot.area.ha
ndom.ha<-100;n.per.are<-plot.area.ha*ndom.ha;
# Using the  function
uestimator(sort.h,n.per.are)

Compute volume of objects

Description

Calculate the volume of objects, depending on their shapes or available measurements, to carry out the computation.

Usage

volume(
  form = "trapesoid",
  d = NA,
  h = NA,
  l = NA,
  d.u = "cm",
  h.u = "m",
  l.u = "m",
  o.u = "m3"
)

Arguments

Value

Value of volume.

Author(s)

Christian Salas-Eljatib and Nicolás Campos and Victor Pacheco

Examples

##- Data, diameters at different stem heights
df <- data.frame(hl = c(0.3, 3.9, 7), dl = c(40, 20, 10))
df

##- Cilinder, needs a single diameter and height
dst <- df$dl[1]
hst <- df$hl[1]
## output in cubic centimeters
volume(form = "cilinder", d = dst,  l = hst, o.u = "cm3")
## in meters
volume(form = "cilinder", d = dst,  l = hst, o.u = "m3")

##- Trapesoid between first and second measurement,
## thus is for a single section.
dl.a <- df$dl[c(1, 2)]
hl.a <- df$hl[c(1, 2)]

vs1<-volume(h = hl.a, d = dl.a)
vs1

##- Trapesoid, between first and third measurement
## thus is for a single section.
dl.b <- df$dl[c(1, 3)]
hl.b <- df$hl[c(1, 3)]
volume(h = hl.b, d = dl.b)


dl.b <- df$dl[c(2, 3)]
hl.b <- df$hl[c(2, 3)]
vs2<-volume(h = hl.b, d = dl.b)
vs2
vs1+vs2
##- Newton (only possible if three measurements are given)
volume(form = "newton",  h = df$hl, d = df$dl)

##- Huber, for all available measurements
volume(form = "huber", d = df$dl, h = df$hl)

##- Huber given 1 diameter and 1 distance
l.a <- diff(c(df$hl[1], df$hl[3]))
volume(form = "huber", d = df$d[2], l = l.a)

A function having the mathematical expression of the Weibull allometric model.

Description

Function of the Weibull allometric model, based upon three parameters and a single predictor variable as follows

y_i= \alpha \left( 1-\mathrm{e}^{-\beta {x_i}}\right)^{\gamma},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

weib.fx(x, a = alpha, b = beta, c = gamma, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Weibull W. 1951. A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME 18(3):293-297.

• Yang RC, A Kozak, JH Smith. 1978. The potential of Weibull-type functions as flexible growth curves. Can. J. For. Res. 8(2):424-431.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-weib.fx(x=time,a=23.06,b=.13,c=.63)
plot(time,y,type="l")
 

A function having the mathematical expression of the Wykoff model.

Description

Function of the Wykoff model, based upon two parameters and a single predictor variable as follows

y_i= \mathrm{e}^{\left(\alpha+\frac{\beta}{x_i+1} \right)},

where: y_i and x_i are the response and predictor variable, respectively, for the i-th observation; and the rest are parameters (i.e., coefficients).

Usage

wykoff.fx(x, a = alpha, b = beta, phi = 0)

Arguments

Value

Returns the response variable based upon the predictor variable and the coefficients.

Author(s)

Christian Salas-Eljatib.

References

• Wykoff WR, NL Crookston, AR Stage. 1982. User’s guide to the Stand Prognosis Model. USDA For. Serv. Gen. Tech. Rep. INT-133, USA. 112 p.

• Salas-Eljatib C. 2025. Funciones alométricas: reparametrizaciones y características matemáticas. Documento de trabajo No. 1, Serie: Cuadernos de biometría, Laboratorio de Biometría y Modelación Forestal, Universidad de Chile. Santiago, Chile. 51 p. https://biometriaforestal.uchile.cl

Examples

# Predictor variable values to be used
d<-seq(5,60,by=0.01)
# Using the function
h<-wykoff.fx(x=d,a=3.87,b=4.38,phi=1.3)
plot(d,h,type="l")