stoch.sens: stoch.sens
In demogR: Analysis of Age-Structured Demographic Models

Description Usage Arguments Details Value Note References See Also Examples

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

1	stoch.sens(env, amat, k)

`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

See Caswell (2001, section 14.4) for details.

A list with two elements:

`sensitivities`	sensitivities of the stochastic growth rate
`elasticities`	elasticities of the stochastic growth rate

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

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.

lams, eigen.analysis

## 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)