% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/eigen.R
\name{leslie_reproductive_values}
\alias{leslie_reproductive_values}
\title{Reproductive values for a Leslie matrix}
\usage{
leslie_reproductive_values(A)
}
\arguments{
\item{A}{A Leslie matrix (checked with \code{\link{is_leslie}}). A length-1 positive numeric
will be coerced to a 1x1 matrix.}
}
\value{
A numeric vector of length \code{nrow(A)} giving reproductive values, normalized so that
  \code{sum(v * w) = 1}.
}
\description{
Computes the reproductive value vector \code{v} for a Leslie matrix \code{A}, scaled so that
\code{sum(v * w) = 1}, where \code{w} is the stable age distribution returned by
\code{\link{leslie_stable_age}}.
}
\details{
This implementation follows Demetrius (1974) equation expressed in terms of
the stable age distribution and fertility rates.

A length-1 positive numeric is treated as a 1x1 Leslie matrix and returns \code{1}.
}
\examples{
leslie_reproductive_values(1)

L <- matrix(c(
  0, 2, 1,
  0.6, 0, 0,
  0, 0.7, 0
), nrow = 3, byrow = TRUE)
v <- leslie_reproductive_values(L)
w <- leslie_stable_age(L)
sum(v * w)  # should be 1

}
\references{
Caswell, H. (2001). \emph{Matrix population models: construction, analysis and
interpretation} (2nd ed.). Sinauer.

Demetrius, L. (1974). Demographic parameters and natural selection.
\emph{Proceedings of the National Academy of Sciences}, 71(12), 4645-4647.
\doi{10.1073/pnas.71.12.4645}
}
