calc.ro: Caclulate net reproduction number from a demographic...
In hanase/demogR: Analysis of Age-Structured Demographic Models

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculate the net reproduction number (R_0) from an age or stage-classified demographic projection matrix.

1	calc.ro(A, N.out = FALSE)

`A`	A demographic projection matrix
`N.out`	Return the fundamental matrix (N) of the Markov chain?

Calculates the net reproduction number (R_0) from an age or stage-classified demographic projection matrix by first decomposing the k x k projection matrix A into two component matrices, T and F. T collects the transitions between life-cycle stages while F collects the fertility transitions. For an age-classified Leslie matrix, T will contain only the sub-diagonal of A and F will contain only the first row of A. The fundamental matrix is given by N = (I-T)^{-1}, where I is a k x k identity matrix. R_0 is the leading eigenvalue of the matrix FN.

If the (default) option N.out=FALSE is used, the net reproduction number is returned as a single value. If N.out=TRUE, the returned value is a list of two items:

`ro`	Net reproduction number
`N`	Fundamental matrix

...

James Holland Jones

Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation, Second edition. Sinauer, Sunderland, Massachusetts, USA.

see leslie.matrix

## Create a Leslie matrix
Px <- c(0.77, 0.95, 0.98, 0.97)
Fx <- c(0,0,1,1.2,1)
L <- odiag(Px,-1)
L[1,] <- Fx
## Calculate R_0
calc.ro(L)
## look at the fundamental matrix
calc.ro(L, N.out=TRUE)