The structured coalescent in the context of gene copy number variation

The Structured Coalescent was introduced to describe the coalescent process in spatially subdivided populations with migration. Here, we re-interpret migration routes of individuals in the original model as "migration routes" of single genes in tandemly arranged gene arrays. A gene copy may change its position within the array via unequal recombination. Hence, in a coalescent framework, two copies sampled from two chromosomes may coalesce only if they are at exactly homologous positions. Otherwise, one or multiple recombination events have to occur before they can coalesce, thereby increasing mean coalescence time and expected genetic diversity among the copies in a gene array. We explicitly calculate the transition probabilities on these routes backward in time. We simulate the structured coalescent with migration and coalescence rates informed by the unequal recombination process of gene copies. With this novel interpretation of population structure models we determine coalescence times and expected genetic diversity in samples of orthologous and paralogous copies from a gene family. As a case study, we discuss the site frequency spectrum of a small gene family in the two scenarios of high and of no gene copy number variation among individuals. These examples underline the significance of our model, since standard test-statistics may lead to misinterpretations when analyzing sequence data of multi-copy genes due to their different expected genetic diversity.