stoch.sens {demogR}

stoch.sens

Description

Calculates the sensitivity of the stochastic growth rate to perturbations in the mean demographic projection matrix.

Usage

stoch.sens(env, amat, k)

Arguments

env

environmental sequence

amat

matrices describing the population dynamics in the different environmental states, organized as columns of a matrix

k

rank of the projection matrices

Details

See Caswell (2001, section 14.4) for details.

Value

A list with two elements:

sensitivities

sensitivities of the stochastic growth rate

elasticities

elasticities of the stochastic growth rate

Note

This is essentially a translation of Caswell's (2001, section 14.4.1.1) MATLAB code.

References

Caswell, H. 2001. Matrix population models: Construction, analysis, and interpretation. 2nd ed. Sunderland, MA: Sinauer.

Haridas, C. V., and S. Tuljapurkar. 2005. Elasticities in variable environments: Properties and implications. American Naturalist 166 (4):481-495.

Tuljapurkar, S. 1990. Population dynamics in variable environments. Vol. 85, Lecture notes in biomathematics. Berlin: Springer-Veralg.

Tuljapurkar, S., and C. V. Haridas. 2006. Temporal autocorrelation and stochastic population growth. Ecology Letters 9 (3):324-334.

See Also

lams, eigen.analysis

Examples

## Simulate an i.i.d. sequence of 3 environmental states

env <- floor(runif(100,0,3))+1
px1 <- rbeta(4,9.5,0.5)
px2 <- rbeta(4,7.5,2.5)
px3 <- rbeta(4,5,5)
mx <- c(0,rgamma(4,5,10))

A1 <- odiag(px1,-1)
A2 <- odiag(px2,-1)
A3 <- odiag(px3,-1)
A1[1,] <- leslie.row1(mx,px1)
A2[1,] <- leslie.row1(mx,px2)
A3[1,] <- leslie.row1(mx,px3)
amat <- cbind(matrix(A1,nr=25), matrix(A2,nr=25), matrix(A3,nr=25))
stoch.sens(env,amat,k=5)