Discrete Euler-Lotka equation
= Discrete Euler-Lotka equation
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For annual survival probabilities $1-\mu_i$, age-specific offspring numbers $b_a$, and a population multiplier $\gamma$, the discrete Euler-Lotka equation is
$$
1=\sum_{a=1}^{\infty}
\left[\prod_{i=0}^{a-1}(1-\mu_i)\right]\gamma^{-a}b_a.
$$
Its 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.