LearningLearning aboutabout modesmodes ofof speciationspeciation byby computationalcomputational approaches:approaches: goodgood andand badbad newsnews CelineCeline BecquetBecquet andand MollyMolly PrzeworskiPrzeworski Dept.Dept. ofof HumanHuman Genetics,Genetics, UniversityUniversity ofof Chicago,Chicago, ChicagoChicago ILIL USAUSA

BackgroundBackground ResultsResults Enduring debate in evolutionary biology centers around the question of whether the AllopatricAllopatric divergencedivergence fromfrom aa structuredstructured ancestralancestral populationpopulation early stages of speciation can occur in the presence of gene flow. Applications of MIMAR and IM to real data often yield an estimate of the ancestral AllopatricAllopatric speciationspeciation ParapatricParapatric && sympatricsympatric speciationspeciation effective population size larger than either of the descendant populations. Could such . Early stage of divergence occurs in the . Species start diverging while hybridizing results reflect geographical structure in the ancestral population? We investigated this absence of gene flow, when an exogenous and exchanging migrants (i.e., they occupy possibility by estimating the parameters of the I-M model from data simulated under barrier isolates the populations. contiguous areas, or the same area) models of isolation from a structured ancestral population (model c). We find that: . Divergence occurs homogeneously across . Divergence occurs in a number of stages: . IM tends to provide large estimates of NA when there is structure in the ancestral population. the genome, as the populations accumulate 1. Natural selection plays a major role . Nonetheless, the results of IM would usually be interpreted correctly as allopatric speciation (i.e. • Leads to fixation of alleles that contribute to the estimates of gene flow are not biased). differences through either genetic drift or differential adaptation. . MIMAR does not seem to provide biased estimates of N . local adaptation. • These RI loci reduce the hybrid fitness, preventing MIMAR does not seem to provide biased estimates of A. gene flow in linked regions; while other unlinked regions . Reproductive isolation (RI) is a by-product . However, the results would often be interpreted incorrectly as rejecting a model of allopatric are free to introgress. speciation (i.e., the estimates of gene flow tend to be biased upwards). of divergence rather than its cause. • Hence, these models lead to far greater heterogeneity than expected under allopatriy. MIMAR IM . Many cases documented. 2. Over time, more RI genes accumulate. Estimates of NA divided by . This model is sometimes approximated by 3. Speciation is complete when gene flow is the true value for data prevented throughout the genome. simulated with models a (see the isolation model: Methods). . These modes are sometimes approximated by the isolation-migration model (I-M):

Isolation without structure

AllopatricAllopatric divergencedivergence followedfollowed byby secondarysecondary contactcontact Recent papers have argued that applications of IM lends support to parapatric speciation (Hey, 2006; Niemiller et al., 2008). We investigated the effect of isolation T generations ago, a panmictic ancestral population of constant followed by secondary contact on estimates provided by IM and MIMAR (model d). We find N effective population size A suddenly split into two panmictic that: populations of constant effective population sizes N1 and N2, respectively, which subsequently diverged neutrally in total Two populations split T generations ago as for the isolation . The estimates are less precise then when the data follow the simple isolation model. reproductive isolation (i.e., the number of migrants exchanged model, but then diverged in the presence of constant gene between the populations each generation, M, is 0). flow M. . Because the methods consider a constant gene flow rate since the split, recent gene flow may be incorrectly interpreted as reflecting parapatry (i.e., gene flow at the early stage). Modeling as well as from empirical studies suggest that the early stages of speciation MIMAR IM may often occur in presence of some gene flow. However, the parapatric model of Estimates of T divided by speciation remains controversial, in part because of the difficulty of distinguishing Estimates of divided by Isolation without the true value for data parapatry from allopatry followed by secondary contact. secondary contact simulated with models b (see Methods). IM tends to Recently, computational approaches have been developed to test the predictions of overestimate the time of simple models of divergence (usually an I-M model). Application of these to a variety of divergence, while MIMAR tends to underestimate this species has yielded extensive evidence for migration, and the results have been parameter. interpreted as supporting the widespread occurrence of parapatric speciation. However, the methods rely on numerous simplifying assumptions, which may make them unreliable. We conducted a simulation study to assess the reliability of such inferences using a program that we recently developed (MIMAR) as well as the program IM of Hey and ParapatryParapatry withwith genegene flowflow atat anan earlyearly stagestage Nielsen (2004) and more generally, investigated how violations of model assumptions affect parameter estimates of the I-M model. We investigated the effect of a change in gene flow rates over time on the parameter estimates (model e).

. Estimates of NA are qualitatively similar than for model a; thus, large estimates of NA provided by MethodsMethods IM on real data may also reflect non constant gene flow since the split. Simulated data. We simulated data sets of 20 independently-evolving 1kb non- . Moreover, IM tends not to detect gene flow, which could be interpreted incorrectly as consistent recombining loci under I-M models but with assumptions of the model violated. The with allopatric speciation. parameter values were such that T=3.2N1. We generated 10 data sets for each of the . Both methods tend to underestimate T in this case. combination of parameters: T =0.25, 0.50 and 0.75xT (where T=2x106 generations) and 1 DetectingDetecting lociloci linkedlinked toto aa RIRI factorfactor oror aa targettarget ofof locallocal selectionselection M=1 or 10 for the following models: a) Model of isolation from a b) Model of isolation followed by c) Model of isolation with To date, only a few genes involved in RI between species have been characterized, structured ancestral population secondary contact migration at an early stage. through time-consuming molecular approaches. Could computational approaches such as Neutral cartoons of Neutral cartoons of MIMAR be used to help identify candidate loci for further investigation? To assess this, allopatric speciation parapatric speciation we simulated two series of data sets in which one locus is assumed to be linked to a RI locus, using models i and ii, and analyzed them using MIMAR. . MIMAR does not seem greatly affected by the inclusion of a locus with a different history. Structured MIMAR does not seem greatly affected by the inclusion of a locus with a different history. ancestral populations A simple locus-specific goodness-of-fit tests may help to detect the locus of interest: . We obtained the posterior predictive distribution of statistics for each single locus in the data set ≠ from the given the model estimated by MIMAR (see Table below). populations in isolation . We ranked the loci by the p-values (in increasing order for all but Sf and FST) and considered how often the locus of interest is an outlier (i.e., has high rank).

Data with a modeled RI locus. The best statistics to identify outlier loci modeled with model We assumed that a sample of 20 independently-evolving loci contains one locus closely i or ii are highlighted. linked to a RI factor. Specifically, polymorphism data at the loci were simulated under a model of I-M with one outlier that has experienced either no gene flow since the split (model i), or positive directional selection in population one recently (model ii). Estimation approaches. We analyzed the simulated data with MIMAR and IM. . Both programs use a Markov Chain Monte Carlo approach and rely on multi-locus polymorphism data from two species to estimate the parameters of the I-M model. . IM relies on the full polymorphism data, but assumes no intra-locus recombination, a ConclusionConclusion limitation that can lead to biased estimates. limitation that can lead to biased estimates. We find that when one of many assumptions of the I-M model are violated, the methods . MIMAR estimates parameters of the I-M model from recombining loci. In contrast to tend to yield upwardly biased estimates of gene flow, potentially lending spurious support IM, it relies on summaries of the polymorphism data at each of multiple independently- for parapatric speciation. To some extent, this problem can be avoided by carefully evolving loci – specifically, four summary statistics known to be sensitive to the testing the fit of estimated models to the data. When a parapatric model is appropriate, parameters of the I-M model: we propose a test that can help to pinpoint candidate loci involved in RI. • the number of derived polymorphisms unique to the samples from populations 1 and 2 (S1 and S2) • the number of shared derived alleles between the two samples (Ss) References • the number of fixed derived alleles in either sample (Sf ) assuming a known ancestral state. Becquet and Przeworsli 2007 Genome Res. 17:1505-1519. Hey and Nielsen 2004 Genetics 167:747-760. . In simulations, MIMAR performs comparably to IM for medium size data sets, Hey 2006 Curr. Opin. Genet. Dev. 16:592-596. providing unbiased estimates of the parameters and reasonable power to detect gene Niemiller et al. 2008 Molecular Ecology 17:2258-2275. flow (Becquet and Preeworski 2007).