Likelihood of social-ecological genetic model

Abstract The genetic structure of populations depends on two parallel processes - genetic and social-ecological - providing mutual information. Models that describe species’ responses within social-ecological systems are increasingly important in the context of modern environmental crises. Advances in genetic data collection now provide access to vast numbers of markers, enabling a more comprehensive understanding of species dynamics. However, current statistical inference methods do not fully integrate these processes into a single cohesive model, and rely on summary statistics derived from separate inferences and simulations. In this work, I propose a probabilistic framework based on a coalescent model to compute the likelihood of a demogenetic model represented as connected graphs. The population graph, linking population nodes, is characterized by a backward gene adjacency matrix, which describes the probability of gene origins and is influenced by niche and dispersal functions. The genetic graph, linking allele nodes, captures mutation probabilities. A third graph represents the coalescence process of genes within the demographic and genetic graphs. Coalescence is simulated within the demographic model, and its probability is estimated based on the genetic model, or vice versa. Likelihood estimation is performed using a Monte Carlo algorithm. This framework allow likelihood-based sampling and Bayesian inference, offering a robust approach for environmental niche and meta-population modeling. I also discuss the practical applications of this model. By combining environmental niche functions with a coalescent framework, this approach enables probabilistic reconstructions of past species distributions based on present and historical occurrence data. It can incorporate various data sources, including historical records, absence data, and genetic information. By integrating niche and dispersal processes into a unified model, this framework provides a powerful tool for improving species distribution forecasting and deepening our understanding of species’ responses to environmental change as interconnected systems. Author summary Inferring biodiversity responses to social-ecosystem history using population genetic and environmental history data is crucial in the context of modern environmental crises. However, existing models do not fully integrate key processes such as niche modeling, coalescent modeling, and genetic modeling, often relying on approximate Bayesian computation for inference. In this work, I propose a method to estimate the likelihood of a fully integrated demo-genetic model that links population genetic data with socio-ecosystem history. The proposed method is based on a hidden coalescent process simulated within a social-ecosystem graph, along with a sampling process represented in a genetic mutation graph. In the social-ecosystem graph, nodes represent populations, and their effective sizes are estimated using niche models that account for environmental variables. The edges of the graph represent effective migration, which is estimated through connectivity models. The resulting likelihood function can be used for Bayesian or maximum likelihood inference of genetic changes within socio-ecosystems. This approach offers a flexible framework for inferring demo-genetic models across various fields, including phylogeography, agrobiodiversity evolution, ecology, and epidemiology. It can be applied for forecasting or hypothesis testing, providing a comprehensive tool for understanding genetic dynamics in relation to socio-ecosystem processes.