Why do sex chromosomes progressively lose recombination?

Progressive recombination loss is a common feature of sex chromosomes. Yet, the evolutionary drivers of this phenomenon remain a mystery. For decades, differences in trait optima between sexes (sexual antagonism) have been the favoured hypothesis, but convincing evidence is lacking. Recent years have seen a surge of alternative hypotheses to explain progressive extensions and maintenance of recombination suppression: neutral accumulation of sequence divergence, selection of nonrecombining fragments with fewer deleterious mutations than average, sheltering of recessive deleterious mutations by linkage to heterozygous alleles, early evolution of dosage compensation, and constraints on recombination restoration. Here, we explain these recent hypotheses and dissect their assumptions, mechanisms, and predictions. We also review empirical studies that have brought support to the various hypotheses.

The infinitesimal model with dominance.

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the "shared" and "residual" components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M. We illustrate our results with some numerical examples.

Drosophilids with darker cuticle have higher body temperature under light.

Cuticle pigmentation was shown to be associated with body temperature for several relatively large species of insects, but it was questioned for small insects. Here we used a thermal camera to assess the association between drosophilid cuticle pigmentation and body temperature increase when individuals are exposed to light. We compared mutants of large effects within species (Drosophila melanogaster ebony and yellow mutants). Then we analyzed the impact of naturally occurring pigmentation variation within species complexes (Drosophila americana/Drosophila novamexicana and Drosophila yakuba/Drosophila santomea). Finally we analyzed lines of D. melanogaster with moderate differences in pigmentation. We found significant differences in temperatures for each of the four pairs we analyzed. The temperature differences appeared to be proportional to the differently pigmented area: between Drosophila melanogaster ebony and yellow mutants or between Drosophila americana and Drosophila novamexicana, for which the whole body is differently pigmented, the temperature difference was around 0.6 °C ± 0.2 °C. By contrast, between D. yakuba and D. santomea or between Drosophila melanogaster Dark and Pale lines, for which only the posterior abdomen is differentially pigmented, we detected a temperature difference of about 0.14 °C ± 0.10 °C. This strongly suggests that cuticle pigmentation has ecological implications in drosophilids regarding adaptation to environmental temperature.

Sheltering of deleterious mutations explains the stepwise extension of recombination suppression on sex chromosomes and other supergenes.

Many organisms have sex chromosomes with large nonrecombining regions that have expanded stepwise, generating "evolutionary strata" of differentiation. The reasons for this remain poorly understood, but the principal hypotheses proposed to date are based on antagonistic selection due to differences between sexes. However, it has proved difficult to obtain empirical evidence of a role for sexually antagonistic selection in extending recombination suppression, and antagonistic selection has been shown to be unlikely to account for the evolutionary strata observed on fungal mating-type chromosomes. We show here, by mathematical modeling and stochastic simulation, that recombination suppression on sex chromosomes and around supergenes can expand under a wide range of parameter values simply because it shelters recessive deleterious mutations, which are ubiquitous in genomes. Permanently heterozygous alleles, such as the male-determining allele in XY systems, protect linked chromosomal inversions against the expression of their recessive mutation load, leading to the successive accumulation of inversions around these alleles without antagonistic selection. Similar results were obtained with models assuming recombination-suppressing mechanisms other than chromosomal inversions and for supergenes other than sex chromosomes, including those without XY-like asymmetry, such as fungal mating-type chromosomes. However, inversions capturing a permanently heterozygous allele were found to be less likely to spread when the mutation load segregating in populations was lower (e.g., under large effective population sizes or low mutation rates). This may explain why sex chromosomes remain homomorphic in some organisms but are highly divergent in others. Here, we model a simple and testable hypothesis explaining the stepwise extensions of recombination suppression on sex chromosomes, mating-type chromosomes, and supergenes in general.

The role of mode switching in a population of actin polymers with constraints.

In this paper, we introduce a stochastic model for the dynamics of actin polymers and their interactions with other proteins in the cellular envelop. Each polymer elongates and shortens, and can switch between several modes depending on whether it is bound to accessory proteins that modulate its behaviour as, for example, elongation-promoting factors. Our main aim is to understand the dynamics of a large population of polymers, assuming that the only limiting quantity is the total amount of monomers, set to be constant to some large N. We first focus on the evolution of a very long polymer, of size [Formula: see text], with a rapid switch between modes (compared to the timescale over which the macroscopic fluctuations in the polymer size appear). Letting N tend to infinity, we obtain a fluid limit in which the effect of the switching appears only through the fraction of time spent in each mode at equilibrium. We show in particular that, in our situation where the number of monomers is limiting, a rapid binding-unbinding dynamics may lead to an increased elongation rate compared to the case where the polymer is trapped in any of the modes. Next, we consider a large population of polymers and complexes, represented by a random measure on some appropriate type space. We show that as N tends to infinity, the stochastic system converges to a deterministic limit in which the switching appears as a flow between two categories of polymers. We exhibit some numerical examples in which the limiting behaviour of a single polymer differs from that of a population of competing (shorter) polymers for equivalent model parameters. Taken together, our results demonstrate that under conditions where the total number of monomers is limiting, the study of a single polymer is not sufficient to understand the behaviour of an ensemble of competing polymers.

Bayesian Estimation of Population Size Changes by Sampling Tajima's Trees.

The large state space of gene genealogies is a major hurdle for inference methods based on Kingman's coalescent. Here, we present a new Bayesian approach for inferring past population sizes, which relies on a lower-resolution coalescent process that we refer to as "Tajima's coalescent." Tajima's coalescent has a drastically smaller state space, and hence it is a computationally more efficient model, than the standard Kingman coalescent. We provide a new algorithm for efficient and exact likelihood calculations for data without recombination, which exploits a directed acyclic graph and a correspondingly tailored Markov Chain Monte Carlo method. We compare the performance of our Bayesian Estimation of population size changes by Sampling Tajima's Trees (BESTT) with a popular implementation of coalescent-based inference in BEAST using simulated and human data. We empirically demonstrate that BESTT can accurately infer effective population sizes, and it further provides an efficient alternative to the Kingman's coalescent. The algorithms described here are implemented in the R package phylodyn, which is available for download at https://github.com/JuliaPalacios/phylodyn.

Full likelihood inference from the site frequency spectrum based on the optimal tree resolution.

We develop a novel importance sampler to compute the full likelihood function of a demographic or structural scenario given the site frequency spectrum (SFS) at a locus free of intra-locus recombination. This sampler, instead of representing the hidden genealogy of a sample of individuals by a labelled binary tree, uses the minimal level of information about such a tree that is needed for the likelihood of the SFS and thus takes advantage of the huge reduction in the size of the state space that needs to be integrated. We assume that the population may have demographically changed and may be non-panmictically structured, as reflected by the branch lengths and the topology of the genealogical tree of the sample, respectively. We also assume that mutations conform to the infinitely-many-sites model. We achieve this by a controlled Markov process that generates 'particles' in the hidden space of SFS histories which are always compatible with the observed SFS. To produce the particles, we use Aldous' Beta-splitting model for a one parameter family of prior distributions over genealogical topologies or shapes (including that of the Kingman coalescent) and allow the branch lengths or epoch times to have a parametric family of priors specified by a model of demography (including exponential growth and bottleneck models). Assuming independence across unlinked loci, we can estimate the likelihood of a population scenario based on a large collection of independent SFS by an importance sampling scheme, using the (unconditional) distribution of the genealogies under this scenario when the latter is available. When it is not available, we instead compute the joint likelihood of the tree balance parameter ß assuming that the tree topology follows Aldous' Beta-splitting model, and of the demographic scenario determining the distribution of the inter-coalescence times or epoch times in the genealogy of a sample, in order to at least distinguish different equivalence classes of population scenarios leading to different tree balances and epoch times. Simulation studies are conducted to demonstrate the capabilities of the approach with publicly available code.

A Beta-splitting model for evolutionary trees.

In this article, we construct a generalization of the Blum-François Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric shares of diversification rates (or diversification 'potential') between two sister species in an evolutionarily interpretable manner, as well as the addition of extinction to the model in a natural way. We describe the incremental evolutionary construction of a tree with n leaves by splitting or freezing extant lineages through the generating, organizing and deleting processes. We then give the probability of any (binary rooted) tree under this model with no extinction, at several resolutions: ranked planar trees giving asymmetric roles to the first and second offspring species of a given species and keeping track of the order of the speciation events occurring during the creation of the tree, unranked planar trees, ranked non-planar trees and finally (unranked non-planar) trees. We also describe a continuous-time equivalent of the generating, organizing and deleting processes where tree topology and branch lengths are jointly modelled and provide code in SageMath/Python for these algorithms.

Finding the best resolution for the Kingman-Tajima coalescent: theory and applications.

Many summary statistics currently used in population genetics and in phylogenetics depend only on a rather coarse resolution of the underlying tree (the number of extant lineages, for example). Hence, for computational purposes, working directly on these resolutions appears to be much more efficient. However, this approach seems to have been overlooked in the past. In this paper, we describe six different resolutions of the Kingman-Tajima coalescent together with the corresponding Markov chains, which are essential for inference methods. Two of the resolutions are the well-known n-coalescent and the lineage death process due to Kingman. Two other resolutions were mentioned by Kingman and Tajima, but never explicitly formalized. Another two resolutions are novel, and complete the picture of a multi-resolution coalescent. For all of them, we provide the forward and backward transition probabilities, the probability of visiting a given state as well as the probability of a given realization of the full Markov chain. We also provide a description of the state-space that highlights the computational gain obtained by working with lower-resolution objects. Finally, we give several examples of summary statistics that depend on a coarser resolution of Kingman's coalescent, on which simulations are usually based.