popdemo (version 0.2-3)

firststepatt: Calculate first-timestep attenuation

Description

Calculate first-timestep attenuation for a specified population projection matrix (PPM) model.

Usage

firststepatt(A, vector="n", return.N=FALSE)

Arguments

A

a square, non-negative numeric matrix of any dimension

vector

(optional) a specified initial age/stage distribution of class vector or class matrix with which to calculate a case-specific first-timestep attenuation

return.N

(optional) if TRUE, returns population size in the first time interval (including effects of asymptotic growth and initial population size), alongside standardised first-timestep attenuation.

Value

• If vector="n", the bound on first-timestep attenuation of A. If vector is specified, the case-specific first-timestep attenuation of the model. If return.N=TRUE, a list with components:
• firststepatt
  the bound on or case-specific first-timestep attenuation
• N
  the population size at the first timestep, including the effects of initial population size and asymptotic growth.

Details

firststepatt returns a standardised measure of first-timestep attenuation, so discounting the effects of both initial population size and asymoptotic growth (Stott et al. 2011). If vector is not specified then the bound on first-timestep attenuation (the smallest first-timestep attenuation that may be achieved) is returned, otherwise a case-specific first-timestep attenuation for the specified matrix and demographic structure is calculated. Note that not all specified demographic structures will yield a first-timestep attenuation: if the model does not attenuate in the first timestep then an error is returned and reactivity should be used. If return.N=T then the function also returns realised population size (including the effects of asymptotic growth and initial population size). firststepatt works with imprimitive and irreducible matrices, but returns a warning in these cases.

References

Stott et al. (2011) Ecol. Lett., 14, 959-970. Townley & Hodgson (2008) J. Appl. Ecol., 45, 1836-1839.

See Also

Other indices of transient density: reactivity, maxamp, maxatt, inertia

Examples

# Create a 3x3 PPM
    A <- matrix(c(0,1,2,0.5,0.1,0,0,0.6,0.6), byrow=TRUE, ncol=3)
    A

    # Create an initial stage structure
    initial <- c(3,1,1)
    initial

    # Calculate the bound on first-timestep attenuation of A
    firststepatt(A)

    # Calculate case-specific first-timestep attenuation of A 
    # and initial
    firststepatt(A, vector=initial)

    # Calculate case-specific first-timestep attenuation of A 
    # and initial and return realised population size
    firststepatt(A, vector=initial, return.N=TRUE)