Populations are dynamical entities: they split and merge depending on various factors including habitat changes and their genetic composition. If a population remains isolated for some time, mutations will start to accumulate in its genome, either through adaptation to its specific environment (local adaptation) or by chance (genetic drift). Due to the geographic isolation, some combinations of mutations are not tested by natural selection. Bringing these mutations together through the mating of two individuals, one from each subpopulation, may result in less fit (lower life expectancy, sensitivity to diseases, reduced fertility…), sterile, or even inviable offspring. This specific form of interactions between mutations is called a genetic incompatibility.
This classical model for the evolution of reproductive isolation was first introduced and described by Bateson (1909), Dobzhansky (1936), and Muller (1942). In its simplest form, consider two isolated populations and two genetic loci, where each population accumulates a unique single mutation from the ancestral haplotype ab to respectively Ab and aB. Upon hybridization and recombination, the AB haplotype is formed; carriers of this haplotype may suffer from reduced fitness (according to the "dominance" of the incompatibility; see below). The interaction between alleles A and B is commonly referred to as a (Bateson-)Dobzhansky-Muller incompatibility or, in short, DMI. We call the DMI neutral when none of the derived alleles A and B confers a direct selective benefit or disadvantage.
Here, we present a visualization tool to track the discrete-time dynamics of a neutral DMI upon secondary contact, i.e. upon reconnection of two previously isolated populations. For simplicity, we focus on a continent-island model in which one (focal) population (the island) receives migrants from the other (the continent). The ultimate fate of the DMI is clear, when there is no direct selection for any of the incompatible alleles (Bengtsson '86, Gavrilets '97, Bank et al. 2012) : the haplotype that continually immigrates from the continent will "swamp" the island and replace the resident island haplotype. Our goal here is to visualize the genetic composition of the population during this process, and on comparing specific genetic scenarios.
Our tool allows for the comparison of diploid and haplodiploid populations; it has previously been hypothesized that speciation may be easier in haplodiploid organisms (Ross et. al 2015). Haplodiploidy is widespread in the Hymenoptera genus (bees, ants, wasps, ...) and characterized by females being diploid and males haploid. The deterministic framework allows us to understand the effect of the different evolutionary forces in the model without the interference of genetic drift.
indicates which fraction of the population is replaced by aB immigrants from the continent each generation.
corresponds to the genetic distance between the two loci. It corresponds to the probability that the two alleles in a haplotype passed to the offspring are inherited from two different (grand) parents.
determine the deleterious effect of the DMI, and how strongly it affects double heterozygotes for the incompatible alleles A and B (
s), double homozygotes AB/AB (
s), and individuals homozygous for one and heterozygous for the other incompatible allele (
In general, we assume
0<=s<=s<=s (i.e., the more incompatible combinations, the stronger the effect); we call the DMI recessive when
s=0 (i.e., there is no selective disadvantage in F1 individuals) and codominant if
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