gen.time {demogR}

gen.time

Description

Calculates the generation time for an age or stage-classified demographic projection matrix.

Usage

gen.time(A, peryear = 5)

Arguments

A

demographic projection matrix

peryear

width of the age classes

Details

Calculates the generation time (T) for an age or stage-classified demographic projection matrix using the identity

R_0 = \exp(r*T)

where R_0 is the net reproduction number and r is the intrinsic rate of increase (=log(lambda)).

Generation time is the amount of time that it takes a typical female to produce R_0 offspring or, equivalently, the amount of time it takes a population growing with instantaneous rate r to increase by a factor of R_0.

Value

The generation time implied by the demographic projection matrix.

Note

Calls function calc.ro, which calculates R_0 from the fundamental matrix of the Markov transition matrix (Caswell 2001).

References

Keyfitz, N., and H. Caswell. 2005. Applied mathematical demography. 3rd ed. New York: Springer.

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

Preston, S.H., P. Heuveline, and F. Guillot. 2001. Demography: Measuring and modeling population processes. Oxford: Blackwell.

See Also

calc.ro, eigen.analysis

Examples

## compare generation times from two populations with very different
## R_0 values
data(goodman)
ven <- with(goodman, life.table(x=age, nKx=ven.nKx, nDx=ven.nDx))
ven.mx <- with(goodman, ven.bx/ven.nKx)
A <- leslie.matrix(lx=ven$nLx,mx=ven.mx)

usa <- with(goodman, life.table(x=age, nKx=usa.nKx, nDx=usa.nDx))
usa.mx <- with(goodman, usa.bx/usa.nKx)
B <- leslie.matrix(lx=usa$nLx,mx=usa.mx)

gen.time(A)
gen.time(B)