Age-structured population model

An age-structured population model tracks a density $n(a,t)$ transported toward greater age, reduced by age-dependent mortality, and replenished at age zero by births.

For birth rate $b(a)$, death rate $d(a)$ and exponential population growth rate $r$, the Euler-Lotka equation is

For annual survival probabilities $1-{\mu }_i$, age-specific offspring numbers $b_a$, and a population multiplier $\gamma$, the discrete Euler-Lotka equation isIts value at $\gamma =1$ is the expected lifetime offspring count of a newborn under the fixed vital rates. A value above one implies a growing mode $\gamma >1$, while a value below one implies decline.