The coalescent and its descendants

TL;DR

This paper reviews the coalescent model's impact on population genetics, discusses the computational challenges in inference, and introduces a generalized model based on Li and Stephens for analyzing population structure with linkage disequilibrium.

Contribution

It provides a comprehensive review of the coalescent and introduces a generalized model for population structure inference considering linkage disequilibrium.

Findings

The coalescent model revolutionized population genetics analysis.

Li and Stephens model enables efficient statistical inference.

Generalization of the model improves analysis of linked genetic data.

Abstract

The coalescent revolutionised theoretical population genetics, simplifying, or making possible for the first time, many analyses, proofs, and derivations, and offering crucial insights about the way in which the structure of data in samples from populations depends on the demographic history of the population. However statistical inference under the coalescent model is extremely challenging, effectively because no explicit expressions are available for key sampling probabilities. This led initially to approximation of these probabilities by ingenious application of modern computationally-intensive statistical methods. A key breakthrough occurred when Li and Stephens introduced a different model, similar in spirit to the coalescent, for which efficient calculations are feasible. In turn, the Li and Stephens model has changed statistical inference for the wealth of data now available which documents molecular genetic variation within populations. We briefly review the coalescent and associated measure-valued diffusions, describe the Li and Stephens model, and introduce and apply a generalisation of it for inference of population structure in the presence of linkage disequilibrium.