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bioRxiv2014

Exploiting evolutionary non-commutativity to prevent the emergence of bacterial antibiotic resistance

The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we develop a Markov Chain model of evolution in asexually reproducing populations which is an encoding of the Strong Selection Weak Mutation model of evolution on fitness landscapes. This model associates the global properties of the fitness landscape with the algebraic properties of the Markov Chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Utilizing this formalism, we analyse 15 empirical fitness landscapes of E. coli under selection by di.erent beta-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be both hindered and promoted by di.erent sequences of drug application. Further, we derive optimal drug application sequences with which we can probabilistically steer the population through genotype space to avoid the emergence of resistance. This suggests a new strategy in the war against antibiotic.therapy.resistant organisms: drug sequencing to shepherd evolution through genotype space to states from which resistance cannot emerge and by which to maximize the chance of successful therapy. BackgroundThe increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Previous studies of bacterial evolutionary dynamics have shown that populations evolving on fitness landscapes follow predictable paths. In this article, we develop a general mathematical model of evolution and hypothesise that it can be used to understand, and avoid, the emergence of antibiotic resistance. Methods and FindingsWe develop a Markov Chain model of evolution in asexually reproducing populations which is an encoding of the Strong Selection Weak Mutation model of evolution on fitness landscapes. This model associates the global properties of the fitness landscape with the algebraic properties of the Markov Chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Utilizing this formalism, we analyse 15 empirical fitness landscapes of E. coli under selection by different {beta}-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be both hindered and promoted by different sequences of drug application. We show that resistance to a given antibiotic is promoted in 61.4%, 68.6% and 70.3% of possible orderings of single, pair or triple prior drug administrations, respectively. Further, we derive optimal drug application sequences with which we can probabilistically steer the population through genotype space to avoid the emergence of resistance. ConclusionsOur model provides generalisable results of interest to theorists studying evolution as well as providing specific, testable predictions for experimentalists to validate our methods. Further, these results suggest a new strategy in the war against antibiotic-therapy-resistant organisms: drug sequencing to shepherd an evolving population through genotype space to states from which resistance cannot emerge and from which we can maximize the likelihood of successful therapy using existing drugs. While our results are derived using a specific class of antibiotics, the method is generalisable to other situations, including the emergence of resistance to targeted therapy in cancer and how species could change secondary to changing climate or geographical movement.

Evolutionary Biology↗

bioRxiv2014

The evolution of cooperation under local regulation and non-additive gene action: building on Hamilton’s ideas

We study evolution of cooperation in a population structured in a large number of groups of variable size, connected by random migration at rate m. Social interactions, including cooperation and competition occur only inside the groups. Assuming that groups are large, we define a parameter{lambda} that measures the strength of the local regulation, i.e., the rigidity of group sizes. Individuals are of two possible genotypes, one typically assumed to produce a non-cooperative phenotype and the other a phenotype that is cooperative with all members of its own group. Gene action may be additive, producing fitness functions that are linear in the number of cooperators in a group, or not. Assuming weak selection, we obtain the following two contrasting conclusions. (1) \"Hamilton regime\": If{lambda} << m, then cooperative behavior can spread under a certain condition, which in the additive, i.e., linear, case is precisely Hamiltons rule. The general version of this condition is also relatively easy to apply and is based on Wrights classical beta distribution for the frequency of alleles in infinite island models. We call it the \"beta version of Hamiltons rule\". (2) \"Taylor regime\": If m << {lambda}, then cooperation that is costly to the actor is eliminated by selection.

Evolutionary Biology↗

bioRxiv2014

Can the site-frequency spectrum distinguish exponential population growth from multiple-merger coalescents?

The ability of the site-frequency spectrum (SFS) to reflect the particularities of gene genealogies exhibiting multiple mergers of ancestral lines as opposed to those obtained in the presence of population growth is our focus. An excess of singletons is a well-known characteristic of both population growth and multiple mergers. Other aspects of the SFS, in particular the weight of the right tail, are, however, affected in specific ways by the two model classes. Using an approximate likelihood method and minimum-distance statistics, our estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiple merger coalescents, even for moderate sample size, if the number of segregating sites is high enough. A normalized version of the SFS is also used as a summary statistic in an approximate Bayesian computation (ABC) approach. The results give further positive evidence as to the general eligibility of the SFS to distinguish between the different histories.

Evolutionary Biology↗

bioRxiv2014

Postmating reproductive barriers contribute to the incipient sexual isolation of US and Caribbean Drosophila melanogaster

The nascent stages of speciation start with the emergence of sexual isolation. Understanding the influence of reproductive barriers in this evolutionary process is an ongoing effort. We present a study of Drosophila melanogaster populations from the southeast United States and Caribbean islands undergoing incipient sexual isolation. The existence of premating reproductive barriers have been previously established, but these types of barriers are not the only source shaping sexual isolation. To assess the influence of postmating barriers, we investigated putative postmating barriers of female remating and egg laying behavior, as well as hatchability of eggs laid and female longevity after mating. In the central region of our putative hybrid zone of American and Caribbean populations, we observed lower hatchability of eggs laid accompanied by increased resistance to harm after mating to less related males. These results illustrate that postmating reproductive barriers acting alongside premating barriers in a complex secondary contact zone. Furthermore, our findings suggest hybrid incompatibilities, likely due to the nature of genomic admixture of populations in the area, are influential even at the early phases of sexual isolation.

Evolutionary Biology↗

bioRxiv2014

A codon model of nucleotide substitution with selection on synonymous codon usage

The quality of phylogenetic inference made from protein-coding genes depends, in part, on the realism with which the codon substitution process is modeled. Here we propose a new mechanistic model that combines the standard M0 substitution model of Yang (1997) with a simplified model from Gilchrist (2007) that includes selection on synonymous substitutions as a function of codon-specific nonsense error rates. We tested the newly proposed model by applying it to 104 protein-coding genes in brewer's yeast, and compared the fit of the new model to the standard M0 model and to the mutation-selection model of Yang and Nielsen (2008) using the AIC. Our new model provided significantly better fit in approximately 85% of the cases considered for the basic M0 model and in approximately 25% of the cases for the M0 model with estimated codon frequencies, but only in a few cases when the mutation-selection model was considered. However, our model includes a parameter that can be interpreted as a measure of the rate of protein production, and the estimates of this parameter were highly correlated with an independent measure of protein production for the yeast genes considered here. Finally, we found that in some cases the new model led to the preference of a different phylogeny for a subset of the genes considered, indicating that substitution model choice may have an impact on the estimated phylogeny.

Evolutionary Biology↗

bioRxiv2014

How cultural transmission facilitates a long juvenile learning period

The evolution of the long, slow human life history is a major challenge to evolutionary biologists. A compelling theory states that our late age at maturity allows us to acquire the many skills needed to survive in the economically intensive human foraging niche. Cultural transmission may be a crucial part of this process, by exposing learners to a wealth of information and skills that they would otherwise not likely discover. I use mathematical models to show that whether cultural transmission allows a later age at maturity depends on the details of selection and population regulation. In particular, cultural transmission appears to readily allow a later age at maturity under density-dependent fertility, but may not under density-dependent mortality or density-independent population growth. I close with a discussion of possibilities for future theoretical and empirical research.

Evolutionary Biology↗

bioRxiv2014

Understanding Admixture Fractions

Estimation of admixture fractions has become one of the most commonly used computational tools in population genomics. However, there is remarkably little population genetic theory on their statistical properties. We develop theoretical results that can accurately predict means and variances of admixture proportions within a population using models with recombination and genetic drift. Based on established theory on measures of multilocus disequilibrium, we show that there is a set of recurrence relations that can be used to derive expectations for higher moments of the admixture fraction distribution. We obtain closed form solutions for some special cases. Using these results, we develop a method for estimating admixture parameters from estimated admixture proportion obtained from programs such as Structure or Admixture. We apply this method to HapMap data and find that the population history of African Americans, as expected, is not best explained by a single admixture event between people of European and African ancestry. A model of constant gene flow for the past 11 generations until 2 generations ago gives a better fit.

Evolutionary Biology↗

bioRxiv2014

Quantitative Genetics and Modularity in cranial and mandibular morphology of Calomys expulsus

Patterns of genetic covariance between characters (represented by the covariance matrix G) play an important role in morphological evolution, since they interact with the evolutionary forces acting over populations. They are also expected to influence the patterns expressed in their phenotypic counterparts (P), because of limits imposed by multiple developmental and functional restrictions on the genotype/phenotype map. We have investigated genetic covariances in the skull and mandible of the vesper mouse (Calomys expulsus) in order to estimate the degree of similarity between genetic and phenotypic covariances and its potential roots on developmental and functional factors shaping those integration patterns. We use a classic adhoc analysis of morphological integration based on current state of art of developmental/functional factors during mammalian ontogeny and also applied a novel methodology that makes use of simulated evolutionary responses. We have obtained P and G that are strongly similar, for both skull and mandible; their similarity is achieved through the spatial and temporal organization of developmental and functional interactions, which are consistently recognized as hypothesis of trait associations in both matrices.

Evolutionary Biology↗

bioRxiv2014

Coordinated Evolution of Influenza A Surface Proteins

Surface proteins hemagglutinin (HA) and neuraminidase (NA) of the human influenza A virus evolve under selection pressure to escape the human adaptive immune response and antiviral drug treatments. In addition to these external selection pressures, some mutations in HA are known to affect the adaptive landscape of NA, and vice versa, because these two proteins are physiologically interlinked. However, the extent to which evolution of one protein affects the evolution of the other is unknown. Here we develop a novel phylogenetic method for detecting the signatures of such genetic interactions between mutations in different genes, that is, inter-gene epistasis. Using this method, we show that influenza surface proteins evolve in a coordinated way, with substitutions in HA affecting substitutions in NA and vice versa, at many sites. Of particular interest is our finding that the oseltamivir-resistance mutations in NA in subtype H1N1 were likely facilitated by prior mutations in HA. Our results illustrate that the adaptive landscape of a viral protein is remarkably sensitive to its genomic context and, more generally, imply that the evolution of any single protein must be understood within the context of the entire evolving genome.

Evolutionary Biology↗

bioRxiv2014

Protein folding and binding can emerge as evolutionary spandrels through structural coupling

Binding interactions between proteins and other molecules mediate numerous cellular processes, including metabolism, signaling, and regulation of gene expression. These interactions evolve in response to changes in the protein's chemical or physical environment (such as the addition of an antibiotic), or when genes duplicate and diverge. Several recent studies have shown the importance of folding stability in constraining protein evolution. Here we investigate how structural coupling between protein folding and binding -- the fact that most proteins can only bind their targets when folded -- gives rise to evolutionary coupling between the traits of folding stability and binding strength. Using biophysical and evolutionary modeling, we show how these protein traits can emerge as evolutionary "spandrels" even if they do not confer an intrinsic fitness advantage. In particular, proteins can evolve strong binding interactions that have no functional role but merely serve to stabilize the protein if misfolding is deleterious. Furthermore, such proteins may have divergent fates, evolving to bind or not bind their targets depending on random mutation events. These observations may explain the abundance of apparently nonfunctional interactions among proteins observed in high-throughput assays. In contrast, for proteins with both functional binding and deleterious misfolding, evolution may be highly predictable at the level of biophysical traits: adaptive paths are tightly constrained to first gain extra folding stability and then partially lose it as the new binding function is developed. These findings have important consequences for our understanding of fundamental evolutionary principles of both natural and engineered proteins.

Evolutionary Biology↗

bioRxiv2014

Emergent speciation by multiple Dobzhansky-Muller incompatibilities

The Dobzhansky-Muller model posits that incompatibilities between alleles at different loci cause speciation. However, it is known that if the alleles involved in a Dobzhansky-Muller incompatibility (DMI) between two loci are neutral, the resulting reproductive isolation cannot be maintained in the presence of either mutation or gene flow. Here we propose that speciation can emerge through the collective effects of multiple neutral DMIs that cannot, individually, cause speciation--a mechanism we call emergent speciation. We investigate emergent speciation using a haploid neutral network model with recombination. We find that certain combinations of multiple neutral DMIs can lead to speciation. Complex DMIs and high recombination rate between the DMI loci facilitate emergent speciation. These conditions are likely to occur in nature. We conclude that the interaction between DMIs may be a root cause of the origin of species.

Evolutionary Biology↗

bioRxiv2014

Heterogeneity of dN/dS ratios at the classical HLA class I genes over divergence time and across the allelic phylogeny

The classical class I HLA loci of humans show an excess of nonsynonymous with respect to synonymous substitutions at codons of the antigen recognition site (ARS), a hallmark of adaptive evolution. Additionally, high polymporphism, linkage disequilibrium and disease associations suggest that one or more balancing selection regimes have acted upon these genes. However, several questions about these selective regimes remain open. First, it is unclear if stronger evidence for selection on deep timescales is due to changes in the intensity of selection over time or to a lack of power of most methods to detect selection on recent timescales. Another question concerns the functional entities which define the selected phenotype. While most analysis focus on selection acting on individual alleles, it is also plausible that phylogenetically defined groups of alleles (\"lineages\") are targets of selection. To address these questions we analyzed how dN/dS ({omega}) varies with respect to divergence times between alleles and phylogenetic placement (position of branches). We find that{omega} for ARS codons of class I HLA genes increases with divergence time and is higher for inter-lineage branches. Throughout our analyses, we used non-selected codons to control for possible effects of inflation of{omega} associated to intra-specific analysis, and showed that our results are not artifactual. Our findings indicate the importance of considering the timescale effect when analysing{omega} over a wide spectrum of divergences. Finally, our results support the divergent allele advantage model, whereby heterozygotes with more divergent alleles have higher fitness than those carrying similar alleles.

Evolutionary Biology↗

bioRxiv2014

Rational design and adaptive management of combination therapies for Hepatitis C virus infection

Recent discoveries of direct acting antivirals against Hepatitis C virus (HCV) have raised hopes of effective treatment via combination therapies. Yet rapid evolution and high diversity of HCV populations, combined with the reality of suboptimal treatment adherence, make drug resistance a clinical and public health concern. We develop a general model incorporating viral dynamics and pharmacokinetics/pharmacodynamics to assess how suboptimal adherence affects resistance development and clinical outcomes. We derive design principles and adaptive treatment strategies, identifying a high-risk period when missing doses is particularly risky for de novo resistance, and quantifying the number of additional doses needed to compensate when doses are missed. Using data from large-scale resistance assays, we demonstrate that the risk of resistance can be reduced substantially by applying these principles to a combination therapy of daclatasvir and asunaprevir. By providing a mechanistic framework to link patient characteristics to the risk of resistance, these findings show the potential of rational treatment design.

Evolutionary Biology↗

bioRxiv2014

C. elegans harbors pervasive cryptic genetic variation for embryogenesis

Conditionally functional mutations are an important class of natural genetic variation, yet little is known about their prevalence in natural populations or their contribution to disease risk. Here, we describe a vast reserve of cryptic genetic variation, alleles that are normally silent but which affect phenotype when the function of other genes is perturbed, in the gene networks of C. elegans embryogenesis. We find evidence that cryptic-effect loci are ubiquitous and segregate at intermediate frequencies in the wild. The cryptic alleles demonstrate low developmental pleiotropy, in that specific, rather than general, perturbations are required to reveal them. Our findings underscore the importance of genetic background in characterizing gene function and provide a model for the expression of conditionally functional effects that may be fundamental in basic mechanisms of trait evolution and the genetic basis of disease susceptibility.

Evolutionary Biology↗

bioRxiv2014

Estimating the temporal and spatial extent of gene flow among sympatric lizard populations (genus Sceloporus) in the southern Mexican highlands

Interspecific gene flow is pervasive throughout the tree of life. Although detecting gene flow between populations has been facilitated by new analytical approaches, determining the timing and geography of hybridization has remained difficult, particularly for historical gene flow. A geographically explicit phylogenetic approach is needed to determine the ancestral population overlap. In this study, we performed population genetic analyses, species delimitation, simulations, and a recently developed approach of species tree diffusion to infer the phylogeographic history, timing and geographic extent of gene flow in the Sceloporus spinosus group. The two species in this group, S. spinosus and S. horridus, are distributed in eastern and western portions of Mexico, respectively, but populations of these species are sympatric in the southern Mexican highlands. We generated data consisting of three mitochondrial genes and eight nuclear loci for 148 and 68 individuals, respectively. We delimited six lineages in this group, but found strong evidence of mito-nuclear discordance in sympatric populations of S. spinosus and S. horridus owing to mitochondrial introgression. We used coalescent simulations to differentiate ancestral gene flow from secondary contact, but found mixed support for these two models. Bayesian phylogeography indicated more than 60% range overlap between ancestral S. spinosus and S. horridus populations since the time of their divergence. Isolation-migration analyses, however, revealed near-zero levels of gene flow between these ancestral populations. Interpreting results from both simulations and empirical data indicate that despite a long history of sympatry among these two species, gene flow in this group has only recently occurred.

Evolutionary Biology↗

bioRxiv2014

Direct gamete sequencing reveals no evidence for segregation distortion in house mouse hybrids

Understanding the molecular basis of species formation is an important goal in evolutionary genetics, and Dobzhansky-Muller incompatibilities are thought to be a common source of postzygotic reproductive isolation between closely related lineages. However, the evolutionary forces that lead to the accumulation of such incompatibilities between diverging taxa are poorly understood. Segregation distorters are an important source of Dobzhansky-Muller incompatibilities between Drosophila species and crop plants, but it remains unclear if the contribution of these selfish genetic elements to reproductive isolation is prevalent in other species. Here, we genotype millions of single nucleotide polymorphisms across the genome from viable sperm of first-generation hybrid male progeny in a cross between Mus musculus castaneus and M. m. domesticus, two subspecies of rodent in the earliest stages of speciation. We then search for a skew in the allele frequencies of the gametes and show that segregation distorters are not measurable contributors to observed infertility in these hybrid males, despite sufficient statistical power to detect even weak segregation distortion with our novel method. Thus, reduced hybrid male fertility in crosses between these nascent species is attributable to other evolutionary forces.

Evolutionary Biology↗

bioRxiv2014

Rate and cost of adaptation in the Drosophila genome

Recent studies have consistently inferred high rates of adaptive molecular evolution between Drosophila species. At the same time, the Drosophila genome evolves under different rates of recombination, which results in partial genetic linkage between alleles at neighboring genomic loci. Here we analyze how linkage correlations affect adaptive evolution. We develop a new inference method for adaptation that takes into account the effect on an allele at a focal site caused by neighboring deleterious alleles (background selection) and by neighboring adaptive substitutions (hitchhiking). Using complete genome sequence data and fine-scale recombination maps, we infer a highly heterogeneous scenario of adaptation in Drosophila. In high-recombining regions, about 50% of all amino acid substitutions are adaptive, together with about 20% of all substitutions in proximal intergenic regions. In low-recombining regions, only a small fraction of the amino acid substitutions are adaptive, while hitchhiking accounts for the majority of these changes. Hitchhiking of deleterious alleles generates a substantial collateral cost of adaptation, leading to a fitness decline of about 30/2N per gene and per million years in the lowest-recombining regions. Our results show how recombination shapes rate and efficacy of the adaptive dynamics in eukaryotic genomes.

Evolutionary Biology↗

bioRxiv2014

A Consistent Estimator of the Evolutionary Rate

We consider a branching particle system where particles reproduce according to the pure birth Yule process with the birth rate {lambda}, conditioned on the observed number of particles to be equal n. Particles are assumed to move independently on the real line according to the Brownian motion with the local variance {sigma}2. In this paper we treat n particles as a sample of related species. The spatial Brownian motion of a particle describes the development of a trait value of interest (e.g. log-body-size). We propose an unbiased estimator [Formula] of the evolutionary rate{rho} 2 ={sigma}2/{lambda}. The estimator [Formula] is proportional to the sample variance [Formula] computed from n trait values. We find an approximate formula for the standard error of [Formula] based on a neat asymptotic relation for the variance of [Formula].

Evolutionary Biology↗