Biophysics and population size constrains speciation in an evolutionary model of developmental system drift.

Bhavin S Khatri,Richard A Goldstein,Ville Mustonen

doi:10.1371/journal.pcbi.1007177

Bhavin S Khatri, Richard A Goldstein + Show 1 more

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https://doi.org/10.1371/journal.pcbi.1007177

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Abstract

Developmental system drift is a likely mechanism for the origin of hybrid incompatibilities between closely related species. We examine here the detailed mechanistic basis of hybrid incompatibilities between two allopatric lineages, for a genotype-phenotype map of developmental system drift under stabilising selection, where an organismal phenotype is conserved, but the underlying molecular phenotypes and genotype can drift. This leads to number of emergent phenomenon not obtainable by modelling genotype or phenotype alone. Our results show that: 1) speciation is more rapid at smaller population sizes with a characteristic, Orr-like, power law, but at large population sizes slow, characterised by a sub-diffusive growth law; 2) the molecular phenotypes under weakest selection contribute to the earliest incompatibilities; and 3) pair-wise incompatibilities dominate over higher order, contrary to previous predictions that the latter should dominate. The population size effect we find is consistent with previous results on allopatric divergence of transcription factor-DNA binding, where smaller populations have common ancestors with a larger drift load because genetic drift favours phenotypes which have a larger number of genotypes (higher sequence entropy) over more fit phenotypes which have far fewer genotypes; this means less substitutions are required in either lineage before incompatibilities arise. Overall, our results indicate that biophysics and population size provide a much stronger constraint to speciation than suggested by previous models, and point to a general mechanistic principle of how incompatibilities arise the under stabilising selection for an organismal phenotype.

Highlights

The detailed genetic mechanisms by which non-interbreeding species diverge is still poorly understood
In the converse limit, when population sizes are sufficiently small that all molecular phenotypes are neutral, we find only small differences between the rise of each of the pair-wise incompatibility types; this is again consistent with simple models of transcription factor DNA binding, where the phenotypic distribution of binding energies is dominated by their sequence entropy and not fitness at small population sizes and there is only a weak dependence on sequence length [27]
For the first time we examine how incompatibilities arise in allopatry for a simple evolutionary model of developmental system drift, where a higher level organismal spatial patterning phenotype is Biophysics and population size constrains speciation maintained by stabilising selection, whilst the underlying molecular binding energy phenotypes and the sequences that determine them, the genotype, are allowed to drift in the evolutionary simulations

Summary

Introduction

The detailed genetic mechanisms by which non-interbreeding species diverge is still poorly understood. Consider a common ancestor with alleles ab across two loci, which after a period of allopatric divergence give rise to two lineages which have fixed genotypes Ab and aB, respectively Interbreeding between these two populations would result in the heterozygotic hybrid genotype Aa|Bb, combining the potentially incompatible A and B, a combination that could not arise in either population mating separately. The number of untested combinations involving n loci would increase as Kn, suggesting that, with evolutionary time, potential incompatibilities would become increasingly dominated by more complex epistatic interactions [5] This would occur, firstly, because there are a larger number of combinations, and secondly, because there are more ways for separate lineages to evolve around incompatible genotypes when there is a larger number of loci. This highlights the need for considering more realistic models that better capture the salient aspects of the underlying biology, whilst remaining sufficiently simple for tractable evolutionary modelling and simulation

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