Galton-Watson Process and Bayesian Inference: A Turnkey Method for the Viability Study of Small Populations

Abstract

AbstractSharp prediction of extinction times is needed in biodiversity monitoring and conservation management.The Galton-Watson process is a classical stochastic model for describing population dynamics. Its evolution is like the matrix population model where offspring numbers are random. Extinction probability, extinction time, abundance are well known and given by explicit formulas. In contrast with the deterministic model, it can be applied to small populations.Parameters of this model can be estimated through the Bayesian inference framework. This enables to consider nonarbitrary scenarios.We show how coupling Bayesian inference with the Galton-Watson model provides several features: i) a flexible modelling approach with easily understandable parameters ii) compatibility with the classical matrix population model (Leslie type model) iii) A non-computational approach which then leads to more information with less computing iv) a non-arbitrary choice for scenarios, parameters… It can be seen to go one step further than the classical matrix population model for the viability problem.To illustrate these features, we provide analysis details for two examples whose one of which is a real life example.