fullsecder {demogR} | R Documentation |
Calculates the second derivatives of the dominant eigenvalue of a square matrix, A, with respect to all non-zero elements of A.
fullsecder(A)
A |
a demographic projection matrix |
Produces a matrix the columns of which are re-shaped matrices of second derivatives of the dominant eigenvalue of the projection matrix A with respect to each non-zero element in A.
See Caswell (1996, 2001) for details on second derivatives of the dominant eigenvalue.
A square matrix. If A is a Leslie matrix of rank k, then the maximum rank of the resulting matrix is 2k-1 (since there are at most k non-zero fertilities and k-1 survival probabilities in a k x k Leslie matrix).
Caswell, H. 1996. Second derivatives of population growth rate: Calculation and applications. Ecology 77 (3):870-879.
Caswell, H. 2001. Matrix population models: Construction, analysis, and interpretation. 2nd ed. Sunderland, MA: Sinauer.
secder
, elassens
,
eigen.analysis
, stoch.sens
## eigenvalue second derivatives of the US projection matrix from 1967 data(goodman) ult <- with(goodman, life.table(x=age, nKx=usa.nKx, nDx=usa.nDx)) mx <- goodman$usa.bx/goodman$usa.nKx usa <- leslie.matrix(lx=ult$nLx,mx=mx) fs <- fullsecder(usa) ## plot the survival cross-second derivatives of lambda with respect ## to infant survival plot( seq(0,40,by=5), fs["21",10:18], type="l", xlab="Age (j)", ylab=expression(paste(partialdiff^2 , lambda, "/", partialdiff, P[1] , partialdiff, P[j]))) abline(h=0,lty=3)