R/AllometricFunctions.R
In trenchproject/TrenchR: Tools for Microclimate and Biophysical Ecology
Defines functions
proportion_silhouette_area_shapes
Documented in
proportion_silhouette_area_shapes
#' @title Organism Surface Area from Mass
#'
#' @description The function estimates surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}) from mass (g) for one of a variety of taxa.
#'
#' @param m \code{numeric} vector of mass (g).
#'
#' @param taxon \code{character} taxonomic classification of organism, current choices: \code{"lizard"}, \code{"salamander"}, \code{"frog"}, \code{"insect"}.
#'
#' @return \code{numeric} surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details All models follow (\ifelse{html}{\out{SA = a M<sup>b</sup>}}{\eqn{SA = a M^b}{ASCII}}) with mass in grams and surface area in \ifelse{html}{\out{meters<sup>2</sup>}}{\eqn{meters^2}{ASCII}}.
#' \cr
#' \itemize{
#' \item Lizards \insertCite{Norris1965,Porter1979,Roughgarden1981,OConnor1999,Fei2012}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.000314 \pi}
#' \cr \eqn{b = 2/3}
#' \item Salamanders \insertCite{Whitford1967,Riddell2017}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.000842}
#' \cr \eqn{b = 0.694}
#' \item Frogs \insertCite{McClanahan1969}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.00099}
#' \cr \eqn{b = 0.56}
#' \item Insects \insertCite{Lactin1997}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.0013}
#' \cr \eqn{b = 0.8}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' surface_area_from_mass(m = 1:50,
#' taxon = "lizard")
#' surface_area_from_mass(m = 1:50,
#' taxon = "salamander")
#' surface_area_from_mass(m = 1:50,
#' taxon = "frog")
#' surface_area_from_mass(m = seq(0.1, 5, 0.1),
#' taxon = "insect")
#'
#' @export
#'
surface_area_from_mass <- function (m,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("lizard", "salamander", "frog", "insect"),
m > 0)
if (taxon == "lizard") {
a <- 0.000314 * pi
b <- 2/3
} else if (taxon == "salamander") {
a <- 0.000842
b <- 0.694
} else if (taxon == "frog") {
a <- 0.00099
b <- 0.56
} else if (taxon == "insect" ) {
a <- 0.0013
b <- 0.8
}
a * m ^ b
}
#' @title Organism Mass from Length
#'
#' @description The function estimates mass (g) from length (m) for a variety of taxa.
#'
#' @param l \code{numeric} vector of length (m). Can be 1 or more values.
#' \cr
#' Snout-vent length is used for amphibians and reptiles, except turtles where length is carapace length.
#'
#' @param taxon \code{character} taxon of organism, current choices: \code{"insect"}, \code{"lizard"}, \code{"salamander"}, \code{"frog"}, \code{"snake"}, \code{"turtle"}.
#'
#' @return \code{numeric} mass (g).
#'
#' @family allometric functions
#'
#' @details All models follow (\ifelse{html}{\out{m = a l<sup>b</sup>}}{\eqn{m = a * l^b}{ASCII}}) with mass in grams and length in meters.
#' \itemize{
#' \item Lizards: \insertCite{Meiri2010;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 16368.17}
#' \cr \eqn{b = 3.022}
#' \item Salamanders: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 13654.4}
#' \cr \eqn{b = 2.94}
#' \item Frogs: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 181197.1}
#' \cr \eqn{b = 3.24}
#' \item Snakes: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 723.6756}
#' \cr \eqn{b = 3.02}
#' \item Turtles: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 93554.48}
#' \cr \eqn{b = 2.69}
#' \item Insects: \insertCite{Sample1993;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 806.0827}
#' \cr \eqn{b = 2.494}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' mass_from_length(l = 0.04,
#' taxon = "insect")
#' mass_from_length(l = 0.04,
#' taxon = "lizard")
#' mass_from_length(l = 0.04,
#' taxon = "salamander")
#' mass_from_length(l = 0.04,
#' taxon = "frog")
#' mass_from_length(l = 0.04,
#' taxon = "snake")
#' mass_from_length(l = 0.04,
#' taxon = "turtle")
#'
#' @export
#'
mass_from_length <- function (l,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("insect", "lizard", "salamander", "frog", "snake", "turtle"),
l > 0)
if (taxon == "insect") {
a <- 806.0827
b <- 2.494
} else if (taxon == "lizard") {
a <- 16368.17
b <- 3.022
} else if (taxon == "salamander"){
a <- 13654.4
b <- 2.94
} else if (taxon == "frog") {
a <- 181197.1
b <- 3.24
} else if (taxon == "snake") {
a <- 723.6756
b <- 3.02
} else if (taxon == "turtle") {
a <- 93554.48
b <- 2.69
}
a * l ^ b
}
#' @title Organism Surface Area from Volume
#'
#' @description The function estimates surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}) from volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}) for a variety of taxa following \insertCite{Mitchell1976;textual}{TrenchR}.
#'
#' @param V \code{numeric} vector of volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}). Can be one or more values.
#'
#' @param taxon \code{character} taxon of organism, current choices: \code{"lizard"}, \code{"frog"}, \code{"sphere"}.
#'
#' @return \code{numeric} surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details All models follow (\ifelse{html}{\out{SA = Ka V<sup>2/3</sup>}}{\eqn{SA = Ka * V^{2/3}}{ASCII}}) with surface area and volume in meters.
#' \itemize{
#' \item Lizards: \insertCite{Norris1965;textual}{TrenchR}:
#' \cr
#' \cr \eqn{Ka = 11.0}
#' \item Frogs: \insertCite{Tracy1972;textual}{TrenchR}:
#' \cr
#' \cr \eqn{Ka = 11.0}
#' \item Sphere: \insertCite{Mitchell1976;textual}{TrenchR}:
#' \cr
#' \cr \eqn{Ka = 4.83}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' surface_area_from_volume(V = 0.001,
#' taxon = "lizard")
#' surface_area_from_volume(V = 0.001,
#' taxon = "frog")
#' surface_area_from_volume(V = 0.001,
#' taxon = "sphere")
#'
#' @export
#'
surface_area_from_volume <- function (V,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("lizard", "frog", "sphere"),
V > 0)
if (taxon == "lizard") {
Ka <- 11
} else if (taxon == "frog") {
Ka <- 11
} else if (taxon == "sphere") {
Ka <- 4.83
}
Ka * V^(2/3)
}
#' @title Organism Volume from Length
#'
#' @description The function estimates volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}) from length (m) for a variety of taxa following \insertCite{Mitchell1976;textual}{TrenchR}.
#'
#' @param l \code{numeric} length (m).
#' \cr
#' Use snout-vent length for lizards and frogs.
#'
#' @param taxon \code{character} taxon of organism, current choices: \code{"lizard"}, \code{"frog"}, \code{"sphere"}.
#'
#' @return \code{numeric} volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details Relationships come from \itemize{
#' \item Lizards: \insertCite{Norris1965;textual}{TrenchR}
#' \item Frogs: \insertCite{Tracy1972;textual}{TrenchR}
#' \item Sphere: \insertCite{Mitchell1976;textual}{TrenchR}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' volume_from_length(l = 0.05,
#' taxon = "lizard")
#' volume_from_length(l = 0.05,
#' taxon = "frog")
#' volume_from_length(l = 0.05,
#' taxon = "sphere")
#'
#' @export
#'
volume_from_length <- function (l,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("lizard", "frog", "sphere"),
l > 0)
if (taxon == "lizard") {
Kl <- 3.3
} else if (taxon == "frog") {
Kl <- 2.27
} else if (taxon == "sphere") {
Kl <- 1.24
}
(l / Kl) ^ 3
}
#' @title Organism Surface Area from Length
#'
#' @description This function estimates surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}) from length (m) by approximating the animal's body as a rotational ellipsoid with half the body length as the semi-major axis.
#'
#' @param l \code{numeric} length (m).
#'
#' @return \code{numeric} surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details Following \insertCite{Samietz2005;textual}{TrenchR} and \insertCite{Lactin1998;textual}{TrenchR}.
#'
#' @export
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' surface_area_from_length(l = 0.04)
#'
surface_area_from_length <- function (l) {
stopifnot(l > 0)
# convert m to mm
l_mm = l * 1000
# inital units: mm
# c- semi-major axis (half of grasshopper length),
# a- semi-minor axis (half of grasshopper width)
c <- l_mm/2
a <- (0.365 + 0.241 * l_mm * 1000) / 1000
e <- sqrt(1 - a^2 / c^2)
sa <- 2 * pi * a^2 + 2 * pi * a * c / (e * asin(e))
# to m^2
sa / (1000^2)
}
#' @title Organism Silhouette Area
#'
#' @description The function estimates the projected (silhouette) area as a portion of the surface area of the organism as a function of zenith angle. The function is useful for estimating absorbed solar radiation.
#'
#' @param psi \code{numeric} zenith angle in degrees between \code{0} and \code{360}.
#'
#' @param taxon \code{character} organism name. Current choices are \code{"lizard"}, \code{"frog"}, and \code{"grasshopper"}.
#'
#' @param raz \code{numeric} relative solar azimuth angle (in degrees). Required if \code{taxon = "lizard"}. This is the horizontal angle of the sun relative to the head and frontal plane of the lizard and options currently include \code{0} (in front), \code{90} (to side), and \code{180} (behind) degrees.
#'
#' @param posture \code{character} value describing posture. Required if \code{taxon = "lizard"}. Options include \code{"prostrate"} (default) and \code{"elevated"}.
#'
#' @return \code{numeric} silhouette area as a proportion.
#'
#' @family allometric functions
#'
#' @details Relationships come from \itemize{
#' \item Lizards: \insertCite{Muth1977;textual}{TrenchR}
#' \item Frogs: \insertCite{Tracy1976;textual}{TrenchR}
#' \item Grasshoppers: \insertCite{Anderson1979;textual}{TrenchR}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' proportion_silhouette_area(psi = 60,
#' taxon = "frog")
#' proportion_silhouette_area(psi = 60,
#' taxon = "grasshopper")
#' proportion_silhouette_area(psi = 60,
#' taxon = "lizard",
#' posture = "prostrate",
#' raz = 90)
#' proportion_silhouette_area(psi = 60,
#' taxon = "lizard",
#' posture = "elevated",
#' raz = 180)
#'
proportion_silhouette_area <- function (psi,
taxon,
raz = 0,
posture = "prostrate") {
stopifnot(length(taxon) == 1,
taxon %in% c("frog", "lizard", "grasshopper"),
psi >= 0,
psi < 360)
if (taxon == "frog"){
(1.38171e-6 * psi^4 - 1.93335e-4 * psi^3 + 4.75761e-3 * psi^2 - 0.167912 * psi + 45.8228) / 100
} else if (taxon == "grasshopper") {
0.19 - 0.00173 * psi
} else if (taxon == "lizard") {
stopifnot(raz %in% c(0, 90, 180), posture %in% c("prostrate", "elevated"))
if (posture == "prostrate") {
if (raz == 0) {
A <- -2.3148*10^(-6)
B <- -2.1024*10^(-3)
C <- -4.6162*10^(-2)
D <- 30.7316
} else if (raz == 90) {
A <- -1.0185*10^(-5)
B <- 1.3574*10^(-3)
C <- -9.5589*10^(-3)
D <- 30.87255
} else if (raz == 180) {
A <- 0
B <- -2.7105*10^(-3)
C <- -6.3915*10^(-2)
D <- 29.8534
}
} else if (posture == "elevated") {
if (raz == 0) {
A <- 3.6979*10^(-5)
B <- -4.7752*10^(-3)
C <- -6.4026*10^(-2)
D <- 26.2831
} else if (raz == 90) {
A <- 0
B <- -1.1756*10^(-4)
C <- -9.2594*10^(-2)
D <- 26.2409
} else if (raz == 180) {
A <- 0
B <- -1.5662*10^(-3)
C <- -5.6423*10^(-2)
D <- 26.6833
}
}
(A * psi^3 + B * psi^2 + C * psi + D) / 100
}
}
#' @title Organism Silhouette Area using Shape Approximations
#'
#' @description The function estimates the projected (silhouette) area as a portion of the surface area of the organism. The function estimates the projected area as a function of the dimensions and the angle between the solar beam and the longitudinal axis of the solid, using Figure 11.6 in \insertCite{Campbell1998;textual}{TrenchR}. The function is useful for estimating absorbed solar radiation.
#'
#' @param shape \code{character} Shape to use to approximate an organism. Shapes are assumed to be prolate or have the longest axis parallel with the ground. Current choices are \code{"spheroid"}, \code{"cylinder flat ends"}, and \code{"cylinder hemisphere ends"}.
#'
#' @param theta \code{numeric} angle between the solar beam and the longitudinal axis (degrees).
#'
#' @param h \code{numeric} height (long axis in m). Cross section length for spheroid.
#'
#' @param d \code{numeric} diameter (short axis in m). Cross section length for spheroid.
#'
#' @return \code{numeric} silhouette area as a proportion.
#'
#' @references
#' \insertAllCited{}
#'
#' @family allometric functions
#'
#' @export
#'
#' @examples
#' proportion_silhouette_area_shapes(shape = "spheroid",
#' theta = 60,
#' h = 0.01,
#' d = 0.001)
#' proportion_silhouette_area_shapes(shape = "cylinder flat ends",
#' theta = 60,
#' h = 0.01,
#' d = 0.001)
#' proportion_silhouette_area_shapes(shape = "cylinder hemisphere ends",
#' theta = 60,
#' h = 0.01,
#' d = 0.001)
#'
proportion_silhouette_area_shapes <- function(shape,
theta,
h,
d){
stopifnot(length(shape) == 1,
shape %in% c("spheroid", "cylinder flat ends", "cylinder hemisphere ends"),
theta >= 0,
theta < 360,
h >= 0,
d >= 0)
theta_r <- degrees_to_radians(theta)
if (shape == "spheroid") {
x <- d / h
sqrt(1 + (x^2 - 1) * cos(theta_r)^2) / (2 * x+ (2 * asin(sqrt(1 - x^2)) / sqrt(1 - x^2)))
}
else if (shape == "cylinder flat ends") {
(cos(theta_r) + 4 * h * sin(theta_r) / (pi * d)) / (2 + 4 * h / d)
}
else if (shape == "cylinder hemisphere ends") {
(1 + 4 * h * sin(theta_r) / (pi * d)) / (4 + 4 * h / d)
}
}
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Defines functions proportion_silhouette_area_shapes
Documented in proportion_silhouette_area_shapes
#' @title Organism Surface Area from Mass
#'
#' @description The function estimates surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}) from mass (g) for one of a variety of taxa.
#'
#' @param m \code{numeric} vector of mass (g).
#'
#' @param taxon \code{character} taxonomic classification of organism, current choices: \code{"lizard"}, \code{"salamander"}, \code{"frog"}, \code{"insect"}.
#'
#' @return \code{numeric} surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details All models follow (\ifelse{html}{\out{SA = a M<sup>b</sup>}}{\eqn{SA = a M^b}{ASCII}}) with mass in grams and surface area in \ifelse{html}{\out{meters<sup>2</sup>}}{\eqn{meters^2}{ASCII}}.
#' \cr
#' \itemize{
#' \item Lizards \insertCite{Norris1965,Porter1979,Roughgarden1981,OConnor1999,Fei2012}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.000314 \pi}
#' \cr \eqn{b = 2/3}
#' \item Salamanders \insertCite{Whitford1967,Riddell2017}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.000842}
#' \cr \eqn{b = 0.694}
#' \item Frogs \insertCite{McClanahan1969}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.00099}
#' \cr \eqn{b = 0.56}
#' \item Insects \insertCite{Lactin1997}{TrenchR}:
#' \cr
#' \cr \eqn{a = 0.0013}
#' \cr \eqn{b = 0.8}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' surface_area_from_mass(m = 1:50,
#' taxon = "lizard")
#' surface_area_from_mass(m = 1:50,
#' taxon = "salamander")
#' surface_area_from_mass(m = 1:50,
#' taxon = "frog")
#' surface_area_from_mass(m = seq(0.1, 5, 0.1),
#' taxon = "insect")
#'
#' @export
#'
surface_area_from_mass <- function (m,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("lizard", "salamander", "frog", "insect"),
m > 0)
if (taxon == "lizard") {
a <- 0.000314 * pi
b <- 2/3
} else if (taxon == "salamander") {
a <- 0.000842
b <- 0.694
} else if (taxon == "frog") {
a <- 0.00099
b <- 0.56
} else if (taxon == "insect" ) {
a <- 0.0013
b <- 0.8
}
a * m ^ b
}
#' @title Organism Mass from Length
#'
#' @description The function estimates mass (g) from length (m) for a variety of taxa.
#'
#' @param l \code{numeric} vector of length (m). Can be 1 or more values.
#' \cr
#' Snout-vent length is used for amphibians and reptiles, except turtles where length is carapace length.
#'
#' @param taxon \code{character} taxon of organism, current choices: \code{"insect"}, \code{"lizard"}, \code{"salamander"}, \code{"frog"}, \code{"snake"}, \code{"turtle"}.
#'
#' @return \code{numeric} mass (g).
#'
#' @family allometric functions
#'
#' @details All models follow (\ifelse{html}{\out{m = a l<sup>b</sup>}}{\eqn{m = a * l^b}{ASCII}}) with mass in grams and length in meters.
#' \itemize{
#' \item Lizards: \insertCite{Meiri2010;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 16368.17}
#' \cr \eqn{b = 3.022}
#' \item Salamanders: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 13654.4}
#' \cr \eqn{b = 2.94}
#' \item Frogs: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 181197.1}
#' \cr \eqn{b = 3.24}
#' \item Snakes: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 723.6756}
#' \cr \eqn{b = 3.02}
#' \item Turtles: \insertCite{Pough1980;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 93554.48}
#' \cr \eqn{b = 2.69}
#' \item Insects: \insertCite{Sample1993;textual}{TrenchR}:
#' \cr
#' \cr \eqn{a = 806.0827}
#' \cr \eqn{b = 2.494}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' mass_from_length(l = 0.04,
#' taxon = "insect")
#' mass_from_length(l = 0.04,
#' taxon = "lizard")
#' mass_from_length(l = 0.04,
#' taxon = "salamander")
#' mass_from_length(l = 0.04,
#' taxon = "frog")
#' mass_from_length(l = 0.04,
#' taxon = "snake")
#' mass_from_length(l = 0.04,
#' taxon = "turtle")
#'
#' @export
#'
mass_from_length <- function (l,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("insect", "lizard", "salamander", "frog", "snake", "turtle"),
l > 0)
if (taxon == "insect") {
a <- 806.0827
b <- 2.494
} else if (taxon == "lizard") {
a <- 16368.17
b <- 3.022
} else if (taxon == "salamander"){
a <- 13654.4
b <- 2.94
} else if (taxon == "frog") {
a <- 181197.1
b <- 3.24
} else if (taxon == "snake") {
a <- 723.6756
b <- 3.02
} else if (taxon == "turtle") {
a <- 93554.48
b <- 2.69
}
a * l ^ b
}
#' @title Organism Surface Area from Volume
#'
#' @description The function estimates surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}) from volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}) for a variety of taxa following \insertCite{Mitchell1976;textual}{TrenchR}.
#'
#' @param V \code{numeric} vector of volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}). Can be one or more values.
#'
#' @param taxon \code{character} taxon of organism, current choices: \code{"lizard"}, \code{"frog"}, \code{"sphere"}.
#'
#' @return \code{numeric} surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details All models follow (\ifelse{html}{\out{SA = Ka V<sup>2/3</sup>}}{\eqn{SA = Ka * V^{2/3}}{ASCII}}) with surface area and volume in meters.
#' \itemize{
#' \item Lizards: \insertCite{Norris1965;textual}{TrenchR}:
#' \cr
#' \cr \eqn{Ka = 11.0}
#' \item Frogs: \insertCite{Tracy1972;textual}{TrenchR}:
#' \cr
#' \cr \eqn{Ka = 11.0}
#' \item Sphere: \insertCite{Mitchell1976;textual}{TrenchR}:
#' \cr
#' \cr \eqn{Ka = 4.83}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' surface_area_from_volume(V = 0.001,
#' taxon = "lizard")
#' surface_area_from_volume(V = 0.001,
#' taxon = "frog")
#' surface_area_from_volume(V = 0.001,
#' taxon = "sphere")
#'
#' @export
#'
surface_area_from_volume <- function (V,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("lizard", "frog", "sphere"),
V > 0)
if (taxon == "lizard") {
Ka <- 11
} else if (taxon == "frog") {
Ka <- 11
} else if (taxon == "sphere") {
Ka <- 4.83
}
Ka * V^(2/3)
}
#' @title Organism Volume from Length
#'
#' @description The function estimates volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}) from length (m) for a variety of taxa following \insertCite{Mitchell1976;textual}{TrenchR}.
#'
#' @param l \code{numeric} length (m).
#' \cr
#' Use snout-vent length for lizards and frogs.
#'
#' @param taxon \code{character} taxon of organism, current choices: \code{"lizard"}, \code{"frog"}, \code{"sphere"}.
#'
#' @return \code{numeric} volume (\ifelse{html}{\out{m<sup>3</sup>}}{\eqn{m^3}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details Relationships come from \itemize{
#' \item Lizards: \insertCite{Norris1965;textual}{TrenchR}
#' \item Frogs: \insertCite{Tracy1972;textual}{TrenchR}
#' \item Sphere: \insertCite{Mitchell1976;textual}{TrenchR}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' volume_from_length(l = 0.05,
#' taxon = "lizard")
#' volume_from_length(l = 0.05,
#' taxon = "frog")
#' volume_from_length(l = 0.05,
#' taxon = "sphere")
#'
#' @export
#'
volume_from_length <- function (l,
taxon) {
stopifnot(length(taxon) == 1,
taxon %in% c("lizard", "frog", "sphere"),
l > 0)
if (taxon == "lizard") {
Kl <- 3.3
} else if (taxon == "frog") {
Kl <- 2.27
} else if (taxon == "sphere") {
Kl <- 1.24
}
(l / Kl) ^ 3
}
#' @title Organism Surface Area from Length
#'
#' @description This function estimates surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}) from length (m) by approximating the animal's body as a rotational ellipsoid with half the body length as the semi-major axis.
#'
#' @param l \code{numeric} length (m).
#'
#' @return \code{numeric} surface area (\ifelse{html}{\out{m<sup>2</sup>}}{\eqn{m^2}{ASCII}}).
#'
#' @family allometric functions
#'
#' @details Following \insertCite{Samietz2005;textual}{TrenchR} and \insertCite{Lactin1998;textual}{TrenchR}.
#'
#' @export
#'
#' @references
#' \insertAllCited{}
#'
#' @examples
#' surface_area_from_length(l = 0.04)
#'
surface_area_from_length <- function (l) {
stopifnot(l > 0)
# convert m to mm
l_mm = l * 1000
# inital units: mm
# c- semi-major axis (half of grasshopper length),
# a- semi-minor axis (half of grasshopper width)
c <- l_mm/2
a <- (0.365 + 0.241 * l_mm * 1000) / 1000
e <- sqrt(1 - a^2 / c^2)
sa <- 2 * pi * a^2 + 2 * pi * a * c / (e * asin(e))
# to m^2
sa / (1000^2)
}
#' @title Organism Silhouette Area
#'
#' @description The function estimates the projected (silhouette) area as a portion of the surface area of the organism as a function of zenith angle. The function is useful for estimating absorbed solar radiation.
#'
#' @param psi \code{numeric} zenith angle in degrees between \code{0} and \code{360}.
#'
#' @param taxon \code{character} organism name. Current choices are \code{"lizard"}, \code{"frog"}, and \code{"grasshopper"}.
#'
#' @param raz \code{numeric} relative solar azimuth angle (in degrees). Required if \code{taxon = "lizard"}. This is the horizontal angle of the sun relative to the head and frontal plane of the lizard and options currently include \code{0} (in front), \code{90} (to side), and \code{180} (behind) degrees.
#'
#' @param posture \code{character} value describing posture. Required if \code{taxon = "lizard"}. Options include \code{"prostrate"} (default) and \code{"elevated"}.
#'
#' @return \code{numeric} silhouette area as a proportion.
#'
#' @family allometric functions
#'
#' @details Relationships come from \itemize{
#' \item Lizards: \insertCite{Muth1977;textual}{TrenchR}
#' \item Frogs: \insertCite{Tracy1976;textual}{TrenchR}
#' \item Grasshoppers: \insertCite{Anderson1979;textual}{TrenchR}
#' }
#'
#' @references
#' \insertAllCited{}
#'
#' @export
#'
#' @examples
#' proportion_silhouette_area(psi = 60,
#' taxon = "frog")
#' proportion_silhouette_area(psi = 60,
#' taxon = "grasshopper")
#' proportion_silhouette_area(psi = 60,
#' taxon = "lizard",
#' posture = "prostrate",
#' raz = 90)
#' proportion_silhouette_area(psi = 60,
#' taxon = "lizard",
#' posture = "elevated",
#' raz = 180)
#'
proportion_silhouette_area <- function (psi,
taxon,
raz = 0,
posture = "prostrate") {
stopifnot(length(taxon) == 1,
taxon %in% c("frog", "lizard", "grasshopper"),
psi >= 0,
psi < 360)
if (taxon == "frog"){
(1.38171e-6 * psi^4 - 1.93335e-4 * psi^3 + 4.75761e-3 * psi^2 - 0.167912 * psi + 45.8228) / 100
} else if (taxon == "grasshopper") {
0.19 - 0.00173 * psi
} else if (taxon == "lizard") {
stopifnot(raz %in% c(0, 90, 180), posture %in% c("prostrate", "elevated"))
if (posture == "prostrate") {
if (raz == 0) {
A <- -2.3148*10^(-6)
B <- -2.1024*10^(-3)
C <- -4.6162*10^(-2)
D <- 30.7316
} else if (raz == 90) {
A <- -1.0185*10^(-5)
B <- 1.3574*10^(-3)
C <- -9.5589*10^(-3)
D <- 30.87255
} else if (raz == 180) {
A <- 0
B <- -2.7105*10^(-3)
C <- -6.3915*10^(-2)
D <- 29.8534
}
} else if (posture == "elevated") {
if (raz == 0) {
A <- 3.6979*10^(-5)
B <- -4.7752*10^(-3)
C <- -6.4026*10^(-2)
D <- 26.2831
} else if (raz == 90) {
A <- 0
B <- -1.1756*10^(-4)
C <- -9.2594*10^(-2)
D <- 26.2409
} else if (raz == 180) {
A <- 0
B <- -1.5662*10^(-3)
C <- -5.6423*10^(-2)
D <- 26.6833
}
}
(A * psi^3 + B * psi^2 + C * psi + D) / 100
}
}
#' @title Organism Silhouette Area using Shape Approximations
#'
#' @description The function estimates the projected (silhouette) area as a portion of the surface area of the organism. The function estimates the projected area as a function of the dimensions and the angle between the solar beam and the longitudinal axis of the solid, using Figure 11.6 in \insertCite{Campbell1998;textual}{TrenchR}. The function is useful for estimating absorbed solar radiation.
#'
#' @param shape \code{character} Shape to use to approximate an organism. Shapes are assumed to be prolate or have the longest axis parallel with the ground. Current choices are \code{"spheroid"}, \code{"cylinder flat ends"}, and \code{"cylinder hemisphere ends"}.
#'
#' @param theta \code{numeric} angle between the solar beam and the longitudinal axis (degrees).
#'
#' @param h \code{numeric} height (long axis in m). Cross section length for spheroid.
#'
#' @param d \code{numeric} diameter (short axis in m). Cross section length for spheroid.
#'
#' @return \code{numeric} silhouette area as a proportion.
#'
#' @references
#' \insertAllCited{}
#'
#' @family allometric functions
#'
#' @export
#'
#' @examples
#' proportion_silhouette_area_shapes(shape = "spheroid",
#' theta = 60,
#' h = 0.01,
#' d = 0.001)
#' proportion_silhouette_area_shapes(shape = "cylinder flat ends",
#' theta = 60,
#' h = 0.01,
#' d = 0.001)
#' proportion_silhouette_area_shapes(shape = "cylinder hemisphere ends",
#' theta = 60,
#' h = 0.01,
#' d = 0.001)
#'
proportion_silhouette_area_shapes <- function(shape,
theta,
h,
d){
stopifnot(length(shape) == 1,
shape %in% c("spheroid", "cylinder flat ends", "cylinder hemisphere ends"),
theta >= 0,
theta < 360,
h >= 0,
d >= 0)
theta_r <- degrees_to_radians(theta)
if (shape == "spheroid") {
x <- d / h
sqrt(1 + (x^2 - 1) * cos(theta_r)^2) / (2 * x+ (2 * asin(sqrt(1 - x^2)) / sqrt(1 - x^2)))
}
else if (shape == "cylinder flat ends") {
(cos(theta_r) + 4 * h * sin(theta_r) / (pi * d)) / (2 + 4 * h / d)
}
else if (shape == "cylinder hemisphere ends") {
(1 + 4 * h * sin(theta_r) / (pi * d)) / (4 + 4 * h / d)
}
}
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