Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical Models of Speciation with Gene Flow
Ilse Hoellinger, Joachim Hermisson

Last modified: 2014-04-01


Even though historically, speciation research focused on a distinction of allopatric (complete isolation) versus sympatric (common habitat of the diverging sister-populations) scenarios, this seems to be an extreme simplification of biological reality. Hence we investigate the process of speciation including variable rates of gene flow, which is called parapatric speciation.


It is still unclear, how the homogenizing effect of gene flow and recombination can be counteracted to give rise to new species in parapatry, as even low migration rates can already interfere quite strongly with beginning divergence.

The classical model for postzygotic isolation barriers in allopatry, the (Bateson-)Dobzhansky-Muller model (DMM), is constituted by newly emerging substitutions on different genetic backgrounds. When brought into secondary contact these previously untested alleles might be incompatible with each other, forming Dobzhansky-Muller incompatibilities (DMIs), and thus reducing hybrid fitness. Among others, a recent theoretical study by Bank et al., 2012, supported the hypothesis, that the DMM for autosome-autosome DMIs provides a viable mechanism for the evolution of postzygotic isolation, also in the presence of gene flow - as long as migration rates do not exceed a critical value. There is also widespread empirical evidence for the occurrence of DMIs in natural populations.

Moreover, the frequently observed phenomena like

  • Haldane's rule, i.e. the observation that in species which show sex specific reduced hybrid fitness, the concerned sex is heterogametic, and

  • large-X-effect, i.e. the overproportional amount of genes involved in postzygotic isolation that maps to the X-chromosome

point to a major role of sex-chromosomes in speciation.

Therefore, we model the initial phase of the speciation process with a deterministic continent island model, by investigating how the involvement of X-chromosomes in two-locus DMIs, i.e. a locus on the X-chromosome is incompatible with a locus on an autosome, affects DMI stability. Additionally, we implement different concepts of dominance, such as codominance or recessitivity. The latter case is of special importance in the context of Haldane's rule. We determine the maximal migration rate, where island alleles are not swamped by continental immigrants and compare our findings with the dynamics of autosome-autosome DMIs.

Ultimately, we are able to show that different genomic architectures of DMIs (incompatibilities between autosome and/or X-chromosome) and different types of dominance cause substantial differences in the maximally tolerated migration rates and thus significantly alter the dynamics of the initial build up of divergence in our early-phase-speciation model.


speciation with gene flow; Dobzhansky-Muller incompatibility; sex-chromosomes