popdemo (version 0.1-2)

reactivity: Calculate reactivity

Description

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

Usage

reactivity(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 reactivity

return.N

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

Value

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

Details

reactivity is a standardised measure of first-timestep amplification, so discounts the effects of both initial population size and asymoptotic growth (Stott et al. 2011) If vector is not specified then the bound on reactivity (the largest reactivity that may be achieved) is returned, otherwise a case-specific reactivity for the specified PPM and demographic structure is calculated. Note that not all specified demographic structures will yield a reactivity: if the model does not amplify in the first timestep then an error is returned and firststepatt 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). reactivity works with imprimitive and irreducible matrices, but returns a warning in these cases.

References

Neubert & Caswell (1997) Ecology, 78, 653-665. 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: firststepatt, 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(1,3,2)
    initial

    # Calculate the bound on reactivity of A
    reactivity(A)

    # Calculate case-specific reactivity of A
    # when projected using specific demographic structure
    reactivity(A, vector=initial)

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