| betaFun {virtualspecies} | R Documentation |
Beta response function
Description
Generation of a beta response curve (see references) according to the equation:
k * (x - p1)^{\alpha} * (p2 - x)^{\gamma}
k is automatically estimated to have a maximum value of P equal to 1.
Usage
betaFun(x, p1, p2, alpha, gamma)
Arguments
x |
a numeric value or vector. The input environmental variable. |
p1 |
a numeric value or vector. Lower tolerance bound for the species |
p2 |
a a numeric value or vector. Upper tolerance bound for the species |
alpha |
a numeric value or vector. Parameter controlling the shape of the curve (see details) |
gamma |
a numeric value or vector. Parameter controlling the shape of the curve (see details) |
Details
p1 and p2 can be seen as the upper and lower critical threshold of the curve.
alpha and gamma control the shape of the curve near p1 and p2, respectively.
When alpha = gamma, the curve is symmetric. Low values of alpha and gamma
result in smooth (< 1) to plateau (< 0.01) curves. Higher values result in
peak (> 10) curves.
When alpha < gamma, the curve is skewed to the right.
When gamma < alpha, the curve is skewed to the left.
Value
a numeric value or vector resulting from the function
Author(s)
Boris Leroy leroy.boris@gmail.com
Maintainer: Boris Leroy leroy.boris@gmail.com
References
Oksanen, J. & Minchin, P.R. (2002). Continuum theory revisited: what shape are species responses along ecological gradients? Ecological Modelling 157:119-129.
See Also
linearFun, quadraticFun, custnorm
Examples
temp <- seq(-10, 40, length = 100)
# A curve similar to a thermal performance curve
P <- betaFun(x = temp, p1 = 0, p2 = 35, alpha = 0.9, gamma = 0.08)
plot(P ~ temp, type = "l")