Back to the future: a simplified and intuitive derivation of the Lotka-Euler equation

TL;DR

This paper presents a simplified, intuitive derivation of the Lotka-Euler equation by reversing the traditional birth process to a death process, enhancing understanding in population dynamics.

Contribution

It introduces a novel perspective by reversing the process to a death process, making the derivation of the Lotka-Euler equation more straightforward and accessible.

Findings

Reversing the birth process to a death process simplifies the derivation.

The approach applies to both discrete and continuous time models.

Provides a more intuitive understanding of population growth equations.

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 an individual produce their offspring. It is essentially a birth process, and here it is shown that by reversing the process to a death process, in which 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.