# Stochastic Evolution of spatial populations: From configurations to genealogies and back

## TL;DR

This paper reviews recent advances in spatial population models, focusing on their large-scale behavior, genealogical structures, and universality classes, using hierarchical and continuum limits, and extends classical models to include new biological effects.

## Contribution

It introduces extended models incorporating selection, mutation, and diversity effects, and analyzes their large-scale genealogical and spatial behaviors using advanced limit methods.

## Key findings

- Identification of universality classes for large-scale behavior
- Extension of classical models to include selection and diversity
- Analysis of genealogical structures in spatial populations

## Abstract

The paper reviews the results obtained for spatial population models and the evolution of the genealogies of these populations during the last decade by the author and his coworkers. The focus is on their large scale behaviour and on the analysis of universality classes of large scale behaviour via the methods of the hierarchical mean-field limit or via the spatial continuum limit and from another angel, the finite system scheme . We use genealogical information to analyze the type and location structure and vice versa. To apply this approach and to explain effects in biological situations we extend the classical model classes in new directions. Namely we look as population models here at: Fleming-Viot genealogies in continuum geographic space, Cannings models with block resampling (reducing diversity), Fisher-Wright diffusion with coloured seedbanks (enhancing diversity) and evolving genealogies of Fleming-Viot models with selection and rare mutation.