Simple Biophysical Model Predicts Faster Accumulation of Hybrid Incompatibilities in Small Populations Under Stabilizing Selection

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Genetic drift promotes and recombination hinders speciation on holey fitness landscapes

Dobzhansky and Muller proposed a general mechanism through which microevolution, the substitution of alleles within populations, can cause the evolution of reproductive isolation between populations and, therefore, macroevolution. As allopatric populations diverge, many combinations of alleles differing between them have not been tested by natural selection and may thus be incompatible. Such genetic incompatibilities often cause low fitness in hybrids between species. Furthermore, the number of incompatibilities grows with the genetic distance between diverging populations. However, what determines the rate and pattern of accumulation of incompatibilities remains unclear. We investigate this question by simulating evolution on holey fitness landscapes on which genetic incompatibilities can be identified unambiguously. We find that genetic incompatibilities accumulate more slowly among genetically robust populations and identify two determinants of the accumulation rate: recombination rate and population size. In large populations with abundant genetic variation, recombination selects for increased genetic robustness and, consequently, incompatibilities accumulate more slowly. In small populations, genetic drift interferes with this process and promotes the accumulation of genetic incompatibilities. Our results suggest a novel mechanism by which genetic drift promotes and recombination hinders speciation.

Environment-dependent epistasis increases phenotypic diversity in gene regulatory networks

Mutations to gene regulatory networks can be maladaptive or a source of evolutionary novelty. Epistasis confounds our understanding of how mutations affect the expression patterns of gene regulatory networks, a challenge exacerbated by the dependence of epistasis on the environment. We used the toolkit of synthetic biology to systematically assay the effects of pairwise and triplet combinations of mutant genotypes on the expression pattern of a gene regulatory network expressed in Escherichia coli that interprets an inducer gradient across a spatial domain. We uncovered a preponderance of epistasis that can switch in magnitude and sign across the inducer gradient to produce a greater diversity of expression pattern phenotypes than would be possible in the absence of such environment-dependent epistasis. We discuss our findings in the context of the evolution of hybrid incompatibilities and evolutionary novelties.

A computational investigation of cis-gene regulation in evolution

In biological processes involving gene networks, genes regulate other genes that determine the phenotypic traits. Gene regulation plays an important role in evolutionary dynamics. In a genetic algorithm, a trans-gene regulatory mechanism was shown to speed up adaptation and evolution. Here, we examine the effect of cis-gene regulation on an adaptive system. The model is haploid. A chromosome is partitioned into regulatory loci and structural loci. The regulatory genes regulate the expression and functioning of structural genes via the cis-elements in a probabilistic manner. In the simulation, the change in the allele frequency, the mean population fitness and the efficiency of phenotypic selection are monitored. Cis-gene regulation increases adaption and accelerates the evolutionary process in comparison with the case involving absence of gene regulation. Some special features of the simulation results are as follows. A low ratio of regulatory loci and structural loci gives higher adaptation for fixed total number of loci. Plasticity is advantageous beyond a threshold value. Adaptation is better for large number of total loci when the ratio of regulatory loci to structural loci is one. However, it reaches a saturation beyond which the increase in the total loci is not advantageous. Efficiency of the phenotypic selection is higher for larger value of the initial plasticity.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Multi-locus interactions and the build-up of reproductive isolation

All genes interact with other genes, and their additive effects and epistatic interactions affect an organism's phenotype and fitness. Recent theoretical and empirical work has advanced our understanding of the role of multi-locus interactions in speciation. However, relating different models to one another and to empirical observations is challenging. This review focuses on multi-locus interactions that lead to reproductive isolation (RI) through reduced hybrid fitness. We first review theoretical approaches and show how recent work incorporating a mechanistic understanding of multi-locus interactions recapitulates earlier models, but also makes novel predictions concerning the build-up of RI. These include high variance in the build-up rate of RI among taxa, the emergence of strong incompatibilities producing localized barriers to introgression, and an effect of population size on the build-up of RI. We then review recent experimental approaches to detect multi-locus interactions underlying RI using genomic data. We argue that future studies would benefit from overlapping methods like ancestry disequilibrium scans, genome scans of differentiation and analyses of hybrid gene expression. Finally, we highlight a need for further overlap between theoretical and empirical work, and approaches that predict what kind of patterns multi-locus interactions resulting in incompatibilities will leave in genome-wide polymorphism data. This article is part of the theme issue 'Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers'.

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

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.

The process of speciation is of fundamental importance to the field of evolution as it is intimately connected to understanding the immense bio-diversity of life. There is still relatively little understanding of the underlying genetic mechanisms that give rise to hybrid incompatibilities with results suggesting that divergence in transcription factor DNA binding and gene expression play an important role. A key finding from the field of evo-devo is that organismal phenotypes show developmental system drift, where species maintain the same phenotype, but diverge in developmental pathways; this is an important potential source of hybrid incompatibilities. Here, we explore a theoretical framework to understand how incompatibilities arise due to developmental system drift, using a tractable biophysically inspired genotype-phenotype for spatial gene expression. Modelling the evolution of phenotypes in this way has the key advantage that it mirrors how selection works in nature, i.e. that selection acts on phenotypes, but variation (mutation) arise at the level of genotypes. This results, as we demonstrate, in a number of non-trivial and testable predictions concerning speciation due to developmental system drift, which would not be obtainable by modelling evolution of genotypes or phenotypes alone.

Population structure promotes the evolution of costly sex in artificial gene networks

We build on previous observations that Hill-Robertson interference generates an advantage of sex that, in structured populations, can be large enough to explain the evolutionary maintenance of costly sex. We employed a gene network model that explicitly incorporates interactions between genes. Mutations in the gene networks have variable effects that depend on the genetic background in which they appear. Consequently, our simulations include two costs of sex-recombination and migration loads-that were missing from previous studies of the evolution of costly sex. Our results suggest a critical role for population structure that lies in its ability to align the long- and short-term advantages of sex. We show that the addition of population structure favored the evolution of sex by disproportionately decreasing the equilibrium mean fitness of asexual populations, primarily by increasing the strength of Muller's Ratchet. Population structure also increased the ability of the short-term advantage of sex to counter the primary limit to the evolution of sex in the gene network model-recombination load. On the other hand, highly structured populations experienced migration load in the form of Dobzhansky-Muller incompatibilities, decreasing the effective rate of migration between demes and, consequently, accelerating the accumulation of drift load in the sexual populations.

Spiraling Complexity: A Test of the Snowball Effect in a Computational Model of RNA Folding

Genetic incompatibilities can emerge as a byproduct of genetic divergence. According to Dobzhansky and Muller, an allele that fixes in one population may be incompatible with an allele at a different locus in another population when the two alleles are brought together in hybrids. Orr showed that the number of Dobzhansky-Muller incompatibilities (DMIs) should accumulate faster than linearly-i.e., snowball-as two lineages diverge. Several studies have attempted to test the snowball effect using data from natural populations. One limitation of these studies is that they have focused on predictions of the Orr model, but not on its underlying assumptions. Here, we use a computational model of RNA folding to test both predictions and assumptions of the Orr model. Two populations are allowed to evolve in allopatry on a holey fitness landscape. We find that the number of inviable introgressions (an indicator for the number of DMIs) snowballs, but does so more slowly than expected. We show that this pattern is explained, in part, by the fact that DMIs can disappear after they have arisen, contrary to the assumptions of the Orr model. This occurs because DMIs become progressively more complex (i.e., involve alleles at more loci) as a result of later substitutions. We also find that most DMIs involve >2 loci, i.e., they are complex. Reproductive isolation does not snowball because DMIs do not act independently of each other. We conclude that the RNA model supports the central prediction of the Orr model that the number of DMIs snowballs, but challenges other predictions, as well as some of its underlying assumptions.

Gene Regulation and Speciation

Understanding the genetic architecture of speciation is a major goal in evolutionary biology. Hybrid dysfunction is thought to arise most commonly through negative interactions between alleles at two or more loci. Divergence between interacting regulatory elements that affect gene expression (i.e., regulatory divergence) may be a common route for these negative interactions to arise. We review here how regulatory divergence between species can result in hybrid dysfunction, including recent theoretical support for this model. We then discuss the empirical evidence for regulatory divergence between species and evaluate evidence for misregulation as a source of hybrid dysfunction. Finally, we review unresolved questions in gene regulation as it pertains to speciation and point to areas that could benefit from future research.