# eigenl: Calculating lambda, u and v In lmf: Functions for estimation and inference of selection in age-structured populations

## Description

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

## Usage

 `1` ```eigenl(pm) ```

## Arguments

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

## 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.

## 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

Thomas Kvalnes

## 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.

`procomp`, `promat`
 ```1 2 3 4 5 6 7 8 9``` ```#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) ```