Populations and Evolution (q-bio.PE)

Abstract: The Lotka-Euler equation is a mathematical expression used to study population dynamics and growth, particularly in the context of demography and ecology. The growth rate $\lambda$ is the speed at which $N$ individuals produce their offspring, resulting in a population size of $N R_0$, where $R_0$ is the average offspring size. It is essentially a birth process, and here it is shown that by reversing the process to a death process, in which $N R_0$ individuals die at a rate $\lambda^{-1}$, the derivation of the Lotka-Euler equation becomes more intuitive and direct, both in discrete and continuous time.