Calculate stochastic elasticities from a time-series of matrix population models and corresponding population vectors

Source: R/perturb_stochastic.R

Calculate stochastic elasticities given a time-series of matrix population models and corresponding population vectors, using the method described in Haridas et al. (2009).

perturb_stochastic(X_t, u_t)

Arguments

X_t

A list of matrix population models

u_t

A list of corresponding population vectors

Value

A list of three matrices:

E

matrix of stochastic elasticities

E_mu

matrix of stochastic elasticities to mean transition rates

E_sigma

matrix of stochastic elasticities to the variance in transition rates

References

Haridas, C. V., Tuljapurkar, S., & Coulson, T. 2009. Estimating stochastic elasticities directly from longitudinal data. Ecology Letters, 12, 806-812. <doi:10.1111/j.1461-0248.2009.01330.x>

See also

Other perturbation analysis: perturb_matrix(), perturb_trans(), perturb_vr(), pop_vectors()

Author

Patrick Barks <patrick.barks@gmail.com>

Examples

# generate list of random MPMs
N <- 20 # number of years
s <- 3 # matrix dimension
X <- list() # matrix population model at time t
u <- list() # population vector at time t

for (t in 1:N) {
  X[[t]] <- matrix(runif(s^2), nrow = s, ncol = s)
}

# derive corresponding series of population vectors
u <- pop_vectors(X)

# calculate stochastic elasticities
perturb_stochastic(X, u)
#> $E
#>           [,1]      [,2]       [,3]
#> [1,] 0.1131968 0.1160238 0.12261977
#> [2,] 0.1325760 0.1101893 0.10196380
#> [3,] 0.1137971 0.1159435 0.07368995
#> 
#> $E_mu
#>           [,1]      [,2]       [,3]
#> [1,] 0.1292196 0.1331185 0.13149498
#> [2,] 0.1308115 0.1099255 0.10556746
#> [3,] 0.1157530 0.1163644 0.08433978
#> 
#> $E_sigma
#>              [,1]          [,2]         [,3]
#> [1,] -0.016022818 -0.0170947104 -0.008875206
#> [2,]  0.001764544  0.0002638290 -0.003603657
#> [3,] -0.001955948 -0.0004209305 -0.010649827
#>