lmf (version 1.2)

eigenl: Calculating lambda, u and v

Description

Calculates the deterministic multiplicative growth rate (lambda), the stable age distribution (u) and the reproductive values (v) from a given projection matrix.

Usage

eigenl(pm)

Arguments

pm

a projection matrix. For instance, the output from the function procomp.

Value

eigenl returns a list containing the following components:

lambda

the deterministic multiplicative growth rate of the population from which the projection matrix was estimated

u

the stable age distribution of the population from which the projection matrix was estimated

u

the reproductive values of the population from which the projection matrix was estimated

Details

Given a projection matrix (l), this function calculates the real dominant eigenvalue (lambda), and the left (u) and right (v) eigenvectors, defined by l*u = lambda*u and v*l = lambda*v.

References

Engen, S., Saether, B.-E., Kvalnes, T. and Jensen, H. 2012. Estimating fluctuating selection in age-structured populations. Journal of Evolutionary Biology, 25, 1487-1499.

See Also

procomp, promat

Examples

#Data set from Engen et al. 2012
data(sparrowdata)
#The uniue age classes
unique.age <- unique(sparrowdata$age)
#Estimate the projection matrix
pro.comp <- procomp(a = sparrowdata, uage = unique.age)
projection.matrix <- promat(pc = pro.comp, nage = length(unique.age))
#Estimate lambda, u and v
eigenl(pm = projection.matrix)