virtualspecies (version 1.6)

betaFun: 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)

Value

a numeric value or vector resulting from the function

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)

Author

Boris Leroy

Maintainer: Boris Leroy

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.

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")