Package 'biometrics'

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)

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, alpha, beta, upsilon = 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, upsilon must be provided
y<-asymreg.fx(x=time,alpha=20,beta=2.5,upsilon =5)
plot(time,y,type="l",ylim=c(0,20))

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)

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)

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))

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, alpha, beta, gamma, upsilon = 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,alpha=23,beta=0.08,gamma=0.89)
plot(time,y,type="l")

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)

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)

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)

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)

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, alpha, beta, upsilon = 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,alpha=20,beta=8)
plot(time,y,type="l")

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, alpha, beta, upsilon = 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,alpha=20,beta=8)
plot(time,y,type="l")

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

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

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)

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)

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)

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)

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")])

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")])

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")])

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")])

Description

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

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

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

expogral.fx(x, alpha, beta, gamma, delta, upsilon = 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 values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-expogral.fx(x=time,alpha=3,beta=8,gamma=1,delta=1)
plot(time,y,type="l",col="blue")

Description

Function of the fully generalized-exponential allometric model, based upon five parameters (i.e., coefficients) and a variable, as defined by the mathematical expression

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

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

expogralfull.fx(x, alpha, beta, gamma, delta, epsilon, upsilon = 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 values to be used
time<-seq(5,60,by=0.01)
# Using the function
y<-expogralfull.fx(x=time,alpha=20,beta=.1,gamma=10,delta=1,
epsilon=1)
plot(time,y,type="l",col="red")

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, alpha, beta, gamma, upsilon = 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,alpha=25,beta=.22,gamma=16)
plot(time,y,type="l")

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, alpha, beta, gamma, upsilon = 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,alpha=25,beta=3.6,gamma=0.17)
plot(time,y,type="l")

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)

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)

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)

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, alpha, beta, gamma, upsilon = 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,alpha=31,beta=38,gamma=1.4)
plot(time,y,type="l")

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)

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)

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, alpha, beta, upsilon = 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,alpha=25,beta=115)
# The effect of the constant term phi
inv.fx(x=40,alpha=25,beta=115, upsilon=2.5)

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)

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)

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)

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, alpha, beta, upsilon = 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, alpha=37,beta=0.05)
plot(time,y,type="l")

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")

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, alpha, beta, gamma, upsilon = 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,alpha=22,beta=1.4,gamma=.1)
plot(time,y,type="l")
#'

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, alpha, beta, gamma, upsilon = 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,alpha=22,beta=8.59,gamma=4.72)
plot(time,y,type="l")
#'

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, alpha, beta, upsilon = 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,alpha=20,beta=.07)
plot(time,y,type="l")

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, alpha, beta, upsilon = 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,alpha=30,beta=13)
plot(time,y,type="l")

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)

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)

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::