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Theoretical Models of the Influence of Genomic Architecture on The Molecular Ecology (2014) 23, 4074–4088 doi: 10.1111/mec.12750 Theoretical models of the influence of genomic architecture on the dynamics of speciation SAMUEL M. FLAXMAN,* AARON C. WACHOLDER,*† JEFFREY L. FEDER‡ and PATRIK NOSIL§ *Department of Ecology and Evolutionary Biology, University of Colorado, Boulder, CO 80309, USA, †Interdisciplinary Quantitative Biology, University of Colorado, Boulder, CO 80309, USA, ‡Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA, §Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK Abstract A long-standing problem in evolutionary biology has been determining whether and how gradual, incremental changes at the gene level can account for rapid speciation and bursts of adaptive radiation. Using genome-scale computer simulations, we extend previous theory showing how gradual adaptive change can generate nonlinear popula- tion transitions, resulting in the rapid formation of new, reproductively isolated spe- cies. We show that these transitions occur via a mechanism rooted in a basic property of biological heredity: the organization of genes in genomes. Genomic organization of genes facilitates two processes: (i) the build-up of statistical associations among large numbers of genes and (ii) the action of divergent selection on persistent combinations of alleles. When a population has accumulated a critical amount of standing, diver- gently selected variation, the combination of these two processes allows many muta- tions of small effect to act synergistically and precipitously split one population into two discontinuous, reproductively isolated groups. Periods of allopatry, chromosomal linkage among loci, and large-effect alleles can facilitate this process under some con- ditions, but are not required for it. Our results complement and extend existing theory on alternative stable states during population divergence, distinct phases of speciation and the rapid emergence of multilocus barriers to gene flow. The results are thus a step towards aligning population genomic theory with modern empirical studies. Keywords: divergent selection, genomic architecture, linkage disequilibrium, population genet- ics, speciation phases Received 13 August 2013; revision received 17 March 2014; accepted 19 March 2014 be more common and evolve more quickly than previ- Introduction ously thought (e.g. Lawniczak et al. 2010; Michel et al. Evolutionary biologists have long sought the mecha- 2010; Hancock et al. 2011; Hohenlohe et al. 2012; Jones nisms by which gradual adaptive change, as epitomized et al. 2012; Nosil et al. 2012; Roesti et al. 2012). However, by Darwin (1859), can be reconciled with observations a predictive theory of the population genomics of diver- that population divergence can occur in sudden bursts, gence and speciation is far from solidified. Towards as for example, during adaptive radiations (Schluter that goal, we sought to extend multilocus speciation 2000; Gavrilets & Losos 2009). The past several decades theory (e.g. Felsenstein 1981; Barton 1983; Barton & Ben- have seen significant advances in this regard. Most gtsson 1986; Barton & de Cara 2009; Yeaman & Whit- recently, next-generation DNA sequencing and the lock 2011) in order to make predictions about the emerging field of population genomics have revealed genome-level dynamics that should be observed in a that widespread differentiation across the genome may variety of conditions involving selection, migration, recombination and drift. Specifically, our aim is to make Correspondence: Samuel M. Flaxman, Fax: 303 492 8699; steps towards enhancing theory so that statistical distri- – E-mail: samuel.fl[email protected] butions of measurable metrics such as FST, linkage © 2014 John Wiley & Sons Ltd GENOMES AND THE ORIGIN OF SPECIES 4075 disequilibrium (LD), allele frequency differences loci and thus may contribute to the build-up of linkage between demes, effective migration rates, local disequilibrium (LD). LD is crucial for speciation (Felsen- adaptation – can eventually be predicted with greater stein 1981), and our simulations thus focused on two accuracy. Hence, here we investigate: How should gen- general properties of genomic architecture that enable ome-wide patterns of differentiation for divergently nonrandom combinations of alleles to persist over gen- selected loci change across the speciation continuum? erations and hence may facilitate the build-up of LD. Much previous theory has demonstrated how genetic First, the most general hereditary consequence of the discontinuities can evolve between populations and gen- organization of genes in genomes is that offspring are erate new species, even in the face of gene flow. Multilo- not formed gene-by-gene from a population ‘beanbag’ cus theory has shown how genetic barriers to gene flow of alleles (Mayr 1959), but rather, parents pass on sets of can become coupled to sharply differentiate populations genes to offspring. We show below with comparisons to with nonlinear transitions between species in space, and null models that this well-known property of genetics implicitly, in time (Barton 1983; Barton & Bengtsson 1986; can have profound consequences for the dynamics of Gavrilets 2004; Barton & de Cara 2009; Gavrilets & Vose population divergence. Second, subsets of genes within 2009; Bierne et al. 2011; Abbott et al. 2013). However, genomes are physically linked on chromosomes, creat- explicit predictions from previous theory are generally ing variation in recombination rates among different sets limited to restricted numbers of loci (a few dozen or less) of loci. The importance of chromosomal linkage relative and/or specific relationships between the strength of to other factors for speciation is debated (Feder & Nosil selection, the migration rate and the recombination rate. 2010; Feder et al. 2011; Via 2012; Yeaman 2013), because Furthermore, these theoretical works generally predict a while LD is crucial for speciation (Felsenstein 1981), single state of divergence for a given set of parameters, chromosomal linkage is not necessarily required for LD but as noted by Barton (2010), there is a need for theory to build. Our results help to clarify in which situations that makes predictions about when alternative stable chromosomal linkage strongly affects the pace of build- population genomic states – that is, a well-mixed popula- up of LD and thus has effects on speciation dynamics. tion vs. nearly reproductively isolated species – are possi- To generate reference points for quantitatively deter- ble. Barton (2010) found alternative stable states in a mining how these genomic features contribute to speci- Levene-type model, due to the build-up of LD, although ation, we created a null ‘beanbag’ model of no genomic the parameter range where such states were possible was architecture, in which the dynamics of alleles at all loci limited. We address these issues here. were independent of each other (see Methods and Fig. Although progress has been made, a broad range of S1, Supporting information). We also created two mod- general theoretical considerations for genomic diver- els in which genes were organized in genomes: (i) a gence remains unexplored. Indeed, next-generation ‘genome-only’ model lacking chromosomal linkage of genomic data collection is to some degree currently loci, implying independent assortment of all loci (i.e. a outpacing the development of theoretical frameworks model of unlinked loci, or as if each locus was situated for interpreting the results (Hudson 2008; Stapley et al. on its own unique chromosome) and (ii) a ‘linkage’ 2010). In essence, the ability to gather extensive gen- model in which loci were arrayed at map locations ome-level data sets presents a problem of scale (sensu along linear chromosomes (i.e. the usual biological con- Levin 1992): Mendelian inheritance at individual loci figuration of genes in the genome). We refer to the lat- has long formed the basis of population genetics, but ter two models as those with genomic architecture. The how do we turn knowledge about individual genes into ‘beanbag’ and ‘genome-only’ models are not meant to predictions about genome-level patterns? When do be representations of real biological systems, per se; gene-level predictions fail to scale up to the genome rather, they are in silico experiments representing null level, and what mechanisms could explain such discon- models that are required to partition the effects of fea- tinuities across scales? Instead of restricting analyses to tures of genomic architecture on divergence (akin to an groups of loci that show exceptional characteristics empirical experiment with a treatment involving the (‘statistical outliers’), can we make predictions about presence of a factor, and a control with the factor the genome-wide distributions across all loci? absent). Hence, comparing results between these three Here, we begin to address these issues using com- models allowed us to determine the roles of the two puter simulations that examine how genomic architec- general genomic features described above – sets of ture affects speciation dynamics. By ‘genomic genes organized together in genomes but on separate architecture’, we are referring to the features of how chromosomes and subsets of genes linked on chromo- genes are organized and arranged in genomes. This somes – in driving speciation dynamics. term is meant to include any features of the genome that We report how gradual adaptive change can generate
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