A bayesian version of Galton–Watson for population growth and its use in the management of small population

Sharp 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 various 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) An approach which leads to more information with less computing iv) inclusion of expert or previous knowledge...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 a real life example with French Pyrenean brown bears.