popdemo (version 0.2-3)

dr: Calculate damping ratio

Description

Calculate the damping ratio of a given population projection matrix (PPM).

Usage

dr(A, return.time=FALSE, x=10)

Arguments

A

a square, irreducible, non-negative numeric matrix of any dimension

return.time

(optional) a logical argument determining whether an estimated convergence time should be returned.

x

(optional) the logarithm used in determining estimated time to convergence (see details).

Value

• If return.time=FALSE, the damping ratio of A. If return.time=TRUE, a list containing components:
• dr
  the damping ratio of A
• t
  the estimated time to convergence.

Details

The damping ratio is calculated as the ratio of the dominant eigenvalue to the modulus of the largest subdominant eigenvalue. Time to convergence can be found by calculating log(dr)/log(x), which is the time taken for the dominant eigenvalue to become x times larger than the largest subdominant eigenvalue.

References

Caswell (2001) Matrix Population Models 2nd. ed. Sinauer. Stott et al. (2010) Ecol. Lett., 14, 959-970.

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

    # Calculate damping ratio
    dr(A)

    # Calculate damping ratio and time to convergence using a 
    # multiple of 10
    dr(A, return.time=TRUE, x=10)