A General Formula for the Generation Time

TL;DR

This paper introduces a universal formula for generation time, framing it as a return time in a finite Markov chain, applicable to any process modeled by a primitive weighted directed graph.

Contribution

It provides a general, mathematically rigorous way to define generation time across diverse processes using Markov chain theory.

Findings

The formula aligns with previous discrete-time population models.

It extends the concept of generation time to any process with a primitive weighted directed graph.

The approach unifies biological and mathematical perspectives on generation time.

Abstract

We show that the generation time -- a notion usually described in a biological context -- can be defined in a general way as a return time in a conveniently constructed finite Markov chain. The simple formula we obtain agrees with previous results derived for structured populations projected in discrete time, and allows to define the generation time of any process described by a weighted directed graph whose matrix is primitive.