Offer Description
Work environment: The PhD will be conducted at the IMAG (Institut Montpellierain Alexander Grothendieck) in Montpellier, in collaboration with CEFE (Centre d'écologie fonctionnelle et évolutive) in Montpellier and LPSM (Laboratoire de probabilité et modèles aléatoires) in Paris.
Main mission: The project lies at the interface between quantitative ecology and statistical learning. It brings together the expertise of the CEFE in community ecology and species distribution models with that of IMAG in probability, statistical learning, and model validation. This project falls within the scope of statistical artificial intelligence, as it develops model learning methods based on optimization, together with predictive validation procedures designed to assess the generalization ability of models on new data.
Current approaches mainly rely on Poisson log-normal (PLN) models with Gaussian latent variables, in which the observed dependencies between species are directly interpreted as ecological interactions. Although these models are highly flexible, their inference is computationally demanding because they do not admit an analytical likelihood. Furthermore, recent studies have highlighted limitations in their predictive performance, particularly under extreme environmental conditions.
The project proposes an alternative family of regression models based on Pólya urn schemes. These models are consistent with the neutral theory of biodiversity, describing ecological communities as the stationary distribution of simple birth-death demographic processes without assuming direct interactions between species. They admit an explicit likelihood, enabling efficient parameter estimation through gradient-based optimization, whose theoretical foundations will be established, together with their stability properties.
One of the main objectives is to determine to what extent the observed correlations between species reflect genuine ecological interactions or instead arise from the underlying demographic mechanisms. The project will also develop predictive validation methods based on data thinning, exploiting the probabilistic stability properties of these models. This will make it possible to compare the predictive performance and robustness of competing models, particularly under extreme environmental conditions.
Activities:
The project will rely on an approach combining probability theory, computational statistics, statistical learning, and ecological data analysis.
Inference methods will be developed within a maximum likelihood framework, based on Newton–Raphson-type optimization algorithms. Particular attention will be paid to the structural constraints imposed by sum-stable models.
An important methodological component will focus on the development of predictive validation procedures based on data thinning, interpreted as learning/validation splitting schemes adapted to count data models. The stability properties of Pólya splitting models will make it possible to generalize these approaches to a broad family of models and to study their theoretical and practical properties. The proposed methods will first be validated on simulated data and then applied to real ecological datasets arising from community ecology.
All methodological developments will be implemented in R software to facilitate their dissemination among the statistical, ecological, and statistical learning communities.
The gross monthly salary is €2,300
Contract duration: 3 years
Contract date from 09/10/2026 to 08/10/2029