The loss of a Dobzhansky-Muller incompatibility by immigration

Andreia Teixeira, Alexandre Blanckaert, Mark Schmitz, Claudia Bank
( : contributed equally, : website implementation )

Introduction/Background [Click to (un)fold section below.]

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.

Model parameters [Click to (un)fold section below.]

Migration rate `m`:

indicates which fraction of the population is replaced by aB immigrants from the continent each generation.

Recombination rate `r`:

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.

Incompatibility coefficients, `s[1]`, `s[2]` and `s[4]`:

determine the deleterious effect of the DMI, and how strongly it affects double heterozygotes for the incompatible alleles A and B (s[1]), double homozygotes AB/AB (s[4]), and individuals homozygous for one and heterozygous for the other incompatible allele (s[2]).
In general, we assume 0<=s[1]<=s[2]<=s[4] (i.e., the more incompatible combinations, the stronger the effect); we call the DMI recessive when s[1]=0 (i.e., there is no selective disadvantage in F1 individuals) and codominant if s[1]>0.

Selection:

Each parameter can be envisioned as the factor by which the reproductive success of a given individual is reduced compared to the ancestral genotype `ab/ab`. For example:
`s[1]=0.1` indicates a reduction of 10% for the F1 hybrids `AB/ab` and `Ab/aB` while
`s[4]=.9` indicates a 90% reduction of the fitness of the `AB/AB` genotype.
All three parameters range from 0 to 1, with 0 indicating no negative effect on the reproductive success of the individual while a value of 1 is indicating its death.
Noticeable dominance schemes include:
codominance `s[4]=2s[2]=4s[1]` and
recessivity `s[4]=2*s[2]; s[1]=0`

Incompatibility coefficients for s[x] number of conflicts

s[1]

s[2]

s[4]

Recombination rate 10

Migration rate 10

Generations

Frequency of the four possible haplotypes: the ancestral type `ab` (blue), the island type `Ab` (green), the hybrid type `AB` (red) and the continental type `aB` (orange) as a function of time (in generations) [Click to (un)fold the "What happens" section below.]

The plot above displays the frequency of the four possible haplotypes: the ancestral type ab (blue), the island type Ab (green), the hybrid type AB (red) and the continental type aB (orange) as a function of time (in generations).

What happens following secondary contact can be roughly decomposed into three phases.

The first phase is characterized by the formation of the hybrid haplotype AB (in red) as well as the ancestral haplotype ab (in blue). Individuals carrying the hybrid haplotype are directly selected against and remain rare. At the same time, the ancestral type has an indirect advantage over the derived types, because it suffers no fitness disadvantages if it appears in genomes with any of these. Thus, the ancestral type increases in frequency quickly, whereas the arriving immigrants mate predominantly with island types and thus suffer from the production of unfit offspring in the F1 (for a codominant DMI) or the F2 (for a recessive DMI) generations.
Recombination tends to accelerate the first phase as it increases the production of the hybrid and ancestral haplotypes, making them more available for selection and therefore rendering the purging of both alleles A and B more efficient. Migration has a similar impact by bringing the aB haplotype onto the island and therefore increasing the odds of pairing the the Ab and aB haplotypes. Codominance of the DMI (when compared to the recessive scenario) slows down this phase because it allows for more immediate selection against immigrant B alleles.

The second phase begins when the ancestral haplotype ab becomes frequent enough such that the derived types are less likely to encounter each other. This annihilates the indirect advantage of the ancestral type, and its frequency begins to diminish as the continental type becomes increasingly frequent due to its constant immigration. As the island haplotype Ab becomes more rare, it is not able to counteract the inflow of the continental type aB any more. The maximum frequency reached by the ancestral haplotype ab roughly indicates how harsh the purging phase was for the population. As before, recombination speeds up the process. Similarly, codominance of the incompatibility accelerates purging because it exposes the allele A to epistatic selection.

The third phase begins when allele A is lost. Only migration matters at this stage; recombination and selection are now irrelevant. A larger migration rate leads to faster fixation of the continental haplotype aB.