dr {popdemo}

Calculate damping ratio

Description

Calculate the damping ratio of a given population matrix projection model.

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).

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 estmimated 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.

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.

References

• Caswell (2001) Matrix Population Models 2nd. ed. Sinauer.

• Stott et al. (2010) Ecol. Lett., 14, 959-970.

See Also

Other ConvergenceMeasures: convt(), truelambda()

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)

  # Calculate damping ratio
  dr(A)

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