Comparative Species Divergence across Eight Triplets of Spiny Lizards (Sceloporus) Using Genomic Sequence Data

Abstract

Species divergence is typically thought to occur in the absence of gene flow, but many empirical studies are discovering that gene flow may be more pervasive during species formation. Although many examples of divergence with gene flow have been identified, few clades have been investigated in a comparative manner, and fewer have been studied using genome-wide sequence data. We contrast species divergence genetic histories across eight triplets of North American Sceloporus lizards using a maximum likelihood implementation of the isolation–migration (IM) model. Gene flow at the time of species divergence is modeled indirectly as variation in species divergence time across the genome or explicitly using a migration rate parameter. Likelihood ratio tests (LRTs) are used to test the null model of no gene flow at speciation against these two alternative gene flow models. We also use the Akaike information criterion to rank the models. Hundreds of loci are needed for the LRTs to have statistical power, and we use genome sequencing of reduced representation libraries to obtain DNA sequence alignments at many loci (between 340 and 3,478; mean = 1,678) for each triplet. We find that current species distributions are a poor predictor of whether a species pair diverged with gene flow. Interrogating the genome using the triplet method expedites the comparative study of species divergence history and the estimation of genetic parameters associated with speciation.

Introduction

Estimating the population genetic parameters associated with species divergence is critical for understanding speciation. The coalescent times of alleles across species contain useful information about species divergence times, current and ancestral population sizes, and gene exchange (Kingman 1982a, 1982b; Beerli and Felsenstein 1999; Nielsen and Wakeley 2001). Speciation is typically thought to occur in the absence of gene flow, because genetic exchange constrains population differentiation and prevents the formation of reproductive isolation (Mayr et al. 1963; Coyne et al. 2004). However, strong disruptive selection can overwhelm genetic exchange, particularly when combined with factors that contribute to linkage disequilibrium, including reduced heterozygote fitness, tight linkage, assortative mating, or chromosomal rearrangements (Felsenstein 1981; Servedio 2008; Pinho and Hey 2010). The growing number of empirical examples supporting divergence with gene flow suggests that this mode of speciation might be more common than expected (Pinho and Hey 2010).

Identifying common trends in speciation requires a comparison of species divergence history across many replicate species pairs. Most studies aimed at investigating divergence with gene flow use the isolation–migration (IM) model (Nielsen and Wakeley 2001; Hey and Nielsen 2004) in which an ancestral population gives rise to two descendent populations, during which time there may be gene exchange between the two populations. The IM model provides a convenient statistical framework for comparing speciation models (i.e., divergence with or without gene flow), and the population data used in this approach have the added benefits of providing fine-scale phylogeographic information for mapping genetic diversity across space and for pinpointing areas of putative or actual genetic exchange. However, a focus on dense geographic sampling of populations has the drawback of diverting resources away from contrasting speciation histories across many replicate species pairs. The approach is computationally demanding (Hey 2010), and scaling-up to genomic data sets containing hundreds or thousands of loci does not seem feasible. The ease of acquiring comparative genomic data for non-model organisms is increasing steadily (Lemmon and Lemmon 2012; Peterson et al. 2012; Smith et al. 2013), and methods capable of analyzing these large, complex data sets are needed. The triplet method of Yang (2010) only requires one sample for each of three species, including a species pair and an outgroup for rooting the tree. By removing the need for phylogeographic sampling, the triplet method can help expedite the study of comparative species divergence across replicate species pairs.

The North American lizard genus Sceloporus is a large (95+ species) and diverse clade that is suitable for a comparative study of species divergence histories. Many species pairs are strictly allopatric or peripheral isolates (Sites et al. 1992), but others seem to have diverged along environmental gradients or are only narrowly sympatric along habitat gradients (Rosenblum et al. 2007; Leaché et al. 2010), which is suggestive of divergence with gene flow. Investigating species divergence histories in Sceloporus with the goal of identifying any common trends is relevant for understanding the general mode of speciation in the group. Increases in diversification rates in Sceloporus are correlated with chromosomal changes (Leaché and Sites 2010), and several episodes of rapid radiation have produced well-supported clades (species groups) containing as many as 18 species. Sister species are often distinguished by chromosomal rearrangements, and models of chromosomal evolution in Sceloporus include some degree of gene flow during species formation (Hall 2010). Out of the large number of speciation events available to study in Sceloporus, the few studies conducted that test speciation models all support divergence with gene flow (Leaché and Mulcahy 2007; Leaché 2011; Leaché et al. 2013).

In this study, we test models of divergence with gene flow in eight triplets of Sceloporus (fig. 1). The likelihood ratio test (LRT) used in the triplet method requires many loci to achieve statistical power, because the historical signature of gene flow is recorded as variable gene tree divergence times, and differences in divergence times might be subtle if speciation was recent or if gene flow only occurred for a short time interval following speciation. We sequence reduced representation libraries to acquire hundreds and thousands of homologous loci shared across closely related species. A comparison of species divergence histories across these eight triplets suggests that current geographic distributions alone are not reliable indicators of the model of species divergence.

Fig. 1.—

Time-calibrated species tree for the species groups of Sceloporus lizards used in the study (Leaché and Sites 2010) and the geographic distributions of the eight species triplets.

Materials and Methods

Sampling

We sampled 22 species of Sceloporus for comparative population divergence analysis (fig. 1 and table 1). From these, we compiled eight triplets, each containing two closely related species that may have diverged with gene flow and a third species (the outgroup) that is assumed not to have exchanged migrants with the other species or their common ancestor. Two species, Sceloporus clarkii and S. hunsakeri, were each used in two triplets. A time-calibrated species tree estimated using BEAST (Drummond and Rambaut 2007) with four nuclear protein-coding genes and one fossil calibration (Leaché and Sites 2010) was used to estimate the relationships among the species groups containing triplets used in this study (fig. 1). Nuclear loci support a species tree for Sceloporus that is at odds with the mitochondrial DNA (mtDNA) gene tree (Leaché 2010) as well as with those that concatenate mtDNA and nuclear loci (Wiens et al. 2010, 2013). Introgression of mtDNA across species boundaries is the likely cause for some instances of discordance (Leaché 2010), and we therefore avoided gene trees from mtDNA and concatenated nuclear + mtDNA phylogenies for triplet selection whenever possible. Detailed phylogeographic studies support the species pair selections in the following groups: magister group (Leaché and Mulcahy 2007), grammicus group (Marshall et al. 2006), undulatus group (Leaché 2009, 2011), spinosus group (Grummer JA, Calderon M, Smith E, Nieto Montes de Oca A, Leaché AD, in preparation), formosus group (Smith 2001) group. However, population substructure, species paraphyly, and species that are sister to clades containing multiple species could all pose significant challenges in Sceloporus triplet selection that could impact the accuracy of the method (see Discussion section).

Table 1.

Comparative Genomic Data for 22 Sceloporus Lizards

Species	Vouchera	Total Reads (Million)b	de novo Contigs	N50c	de novo Coverage	Contigs Post-filterd	Average Coverage	Blast to WGS
adleri	UWBM 6608	58.0	368,090	474	13×	99,530	39×	54,687
bicanthalis	UWBM 7307	47.7	247,932	495	16×	67,201	48×	29,136
clarkii	MVZ 245876	47.0	59,562	376	55×	57,269	57×	33,998
cowlesi	AMNH 154059	48.8	278,468	949	10×	91,726	22×	39,858
edwardtaylori	UWBM 6588	44.6	272,080	495	12×	71,730	36×	36,772
formosus	UWBM 6623	63.6	590,161	495	9×	113,302	33×	56,277
gadoviae	UWBM 7309	54.3	288,885	383	14×	90,567	32×	45,720
grammicus	UWBM 6585	46.4	258,309	539	13×	93,738	30×	49,602
horridus	UWBM 6632	35.3	131,289	567	20×	55,706	43×	27,101
hunsakeri	SDSNH 76079	41.8	158,212	533	17×	53,719	44×	26,557
jalapae	UWBM 7318	65.1	741,561	467	8×	102,957	33×	41,309
licki	SDSNH 76080	31.6	133,173	550	17×	54,206	36×	26,497
magister	UWBM 7395	31.9	103,055	650	19×	48,023	35×	24,597
occidentalis	UWBM 6281	409.2	955,511	2,967	29×	834,098	27×	—
ochoterenae	UWBM 6641	58.2	292,345	533	15×	105,403	34×	45,955
orcutti	UWBM 7654	36.6	154,480	514	15×	51,898	39×	26,519
palaciosi	UWBM 7313	61.0	163,616	605	22×	69,449	46×	34,775
scalaris	UWBM 6589	53.6	465,770	454	10×	102,001	30×	50,642
spinosus	UWBM 6672	57.7	546,964	475	9×	92,601	37×	47,358
taeniocnemis	MVZ 264322	45.0	74,107	388	41×	69,169	45×	41,755
tristichus	AMNH 153948	53.1	311,638	937	10×	93,465	24×	37,253
zosteromus	SDSNH 76081	21.6	88,389	628	16×	43,057	28×	20,664

Note.—RRLs were sequenced for all species, with the exception of one WGS library for Sceloporus occidentalis.

^aFull specimen information is available on the arctos database: http://arctos.database.museum/SpecimenSearch.cfm, last accessed November 28, 2013.

^bTotal reads = unfiltered reads.

^cN50 = median contig size.

^dContigs post-filter = contigs >8× average coverage and >250 bp.

Divergence with gene flow might be expected in species that have parapatric geographic distributions, and most of the species included here have this type of distribution (fig. 1). Exceptions include two species pairs with allopatric distributions, including S. hunsakeri and S. orcutti and S. jalapae and S. ochoterenae. We include one species pair, S. cowlesi and S. tristichus, that have different chromosomal rearrangements and are from opposite sides of a hybrid zone that may have formed as a result of either primary divergence or secondary contact (Leaché and Cole 2007; Leaché 2011).

Reduced Representation Libraries

To obtain homologous DNA sequences between species, we reduced the complexity of the genome using a reduced representation library (RRL) approach to library preparation (Van Tassell et al. 2008; Kerstens et al. 2009). First, whole genomic DNA was digested to completion in enzymatic reactions using StuI (AGGCCT). In silico computer experiments using empirical data from the Anolis carolinensis lizard genome directed our molecular lab protocols for selecting the appropriate restriction enzyme and identifying the specific size distribution of fragments to sequence. The in silico experiments suggested that a complete genome digest using the restriction enzyme StuI should produce approximately 31,000 fragments in the 1.5–2 kb size class (representing 2.7% of the genome) and provide >20× sequencing coverage. Second, a small subset of the whole-genome digest ranging in size from 1.5 to 2 kb was captured using agarose gel electrophoresis or using a Blue Pippin Prep (Sage Science). Third, this isolate of genomic DNA was purified and then sheared with a Bioruptor to produce genomic DNA fragments with a mean size of 300 bp. Finally, libraries were prepared using standard TruSeq multiplexing protocols supplied by Illumina. The quality of completed libraries (insert size and quantity) was verified using an Agilent 2100 Bioanalyzer. We conducted 100 bp, paired-end sequencing on 3.5 Illumina HiSeq2000 lanes at the QB3 facility at UC Berkeley.

Whole-Genome Shotgun

We conducted whole-genome shotgun (WGS) sequencing on the Western fence lizard, Sceloporus occidentalis, to provide a genome-wide scaffold to aid the downstream comparisons of the RRL data sets. As an alternative to investing in a low coverage whole-genome assembly, the RRL data could be assembled into a provisional reference genome using available techniques (Hird et al. 2011). Genomic DNA for S. occidentalis was sheared with a Bioruptor to produce genomic DNA fragments with a mean size of 300 bp. The WGS library was prepared using standard TruSeq protocols. Library quality was verified using an Agilent 2100 Bioanalyzer, and we conducted 100 bp, paired-end sequencing on one Illumina HiSeq2000 lane at the QB3 facility at UC Berkeley.

De Novo Assembly

We used CLC Genomics Workbench v6 to quality filter and de novo assemble the RRL and WGS data sets. Raw data were imported into CLC using the Illumina import function, specifying paired-end reads with a minimum and maximum distance that matched the Bioanalyzer trace. Quality filtering followed the NCBI/Sanger or Illumina pipeline 1.8 and later function to trim low-quality reads and filter out failed reads. The remaining high-quality paired sequences were used for de novo assembly using scaffolding and autodetection of paired distances with default mapping options. CLC Genomics Workbench was used to visualize assembly quality and extract consensus sequences.

Bioinformatics

Following de novo assembly, the 21 RRL data sets were filtered, masked, and compared with the S. occidentalis WGS assembly. Individual 100 bp reads are phased, but the contigs that they form are not. Inability to phase large segments is a limitation of the short-read technology. Downstream population divergence analyses utilized unphased genotype data.

We retained consensus sequences with average coverage >8× and length >250 bp. As repetitive DNA is abundant in lizards (Janes et al. 2010; Alföldi et al. 2011), precautions were taken to exclude repetitive elements and potential chimeras from downstream analyses. Assembled contigs with excessive coverage discrepancies ≥3,000 were discarded. In addition, assemblies were scanned with RepeatMasker (http://www.repeatmasker.org/, last accessed November 28, 2013) against the Anolis genome to remove contigs identified as repeats or containing repetitive elements. Finally, we removed mtDNA using both RepeatMasker and Blast using the S. occidentalis mitochondrial genome as a reference library with default settings (Kumazawa and Nishida 1995).

We removed multiple copy loci by searching each RRL data set against itself using Blast+ (Camacho et al. 2009) and discarding sequences with multiple hits. Cross-species comparisons of loci utilized the S. occidentalis WGS as a reference genome. We used Blast+ to search S. occidentalis for hits to each single copy RRL locus. We generated homologous loci for triplets by merging three filtered and masked RRL data sets based on their mapping to S. occidentalis. Triplet loci containing ≥100 bp minimum overlap were subsequently aligned using MUSCLE v3.8.31 (Edgar 2004). Alignments were trimmed based on levels of missing data, allowing for internal gaps ≤20 bp. Alignments with ≤80% identical sites were also discarded. Finally, each locus was exported in PHYLIP format for downstream analyses.

Divergence with Gene Flow

We used the program 3s v2.1 (Yang 2010; Zhu and Yang 2012) to test models of divergence with gene flow for each triplet of Sceloporus. This program estimates gene-tree species-tree mismatch probabilities over time and compares three different population divergence models using LRTs (Zhu and Yang 2012). The three models include M0, speciation with no gene flow; M1, variable divergence times across the genome between sister species, which is interpreted as evidence for gene flow; and M2, the SIM3s model (Yang 2010; Zhu and Yang 2012), which includes an explicit migration parameter. All three models provide estimates of ancestral population sizes () and divergence times (). Additionally, model M1 estimates a q parameter, which allows the divergence time of the sister species to vary along a beta distribution (Yang 2010). The q parameter is inversely related to the variance in , and model M1 reduces to the null model of no migration (M0) when , which represents a constant (Yang 2010). The M1 model is an approximation of divergence with gene flow, and because it is not a biological model the parameter estimates are unreliable (Yang 2010). The M2 model estimates the migration rate between sister species (), as well as , the population size for species 1 and 2 (which is assumed to be equal for both species). The migration rate M₁₂ is measured by the expected number of migrants from population 1 to population 2, with M₂₁ defined similarly. The SIM3s model assumes M₁₂ = M₂₁ = M. The 3s program currently uses just one sequence per species at each locus, and it removes alignment gaps and ambiguous nucleotides from the alignment. Therefore, when using genotype data, this effectively reduces the information content of the data. The method also assumes that there is no recombination within a locus and free recombination between loci. Recombination can skew population genetic parameter estimates in the context of IM analysis (Strasburg and Rieseberg 2010), and ideally, we could accommodate recombination into the analytical framework (Becquet and Przeworski 2009). Under the SIM3s model, high recombination rates and large numbers of loci can lead to high false-positive rates for the LRTs (Zhu and Yang 2012). For each triplet, we ran ten replicates of 3s from random starting seeds to ensure convergence. Following recommendations in the 3s manual, we set the Gauss–Legendre quadrature to 32 points and the number of categories to discretize the beta distribution to 5. The Gauss–Legendre quadrature was increased up to 128 for some analyses to help convergence.

An LRT was used to compare the null model (M0) to alternative gene flow models M1 and M2. The test for the comparison between M0 and M1 uses the 5% critical value 2.71 (Yang 2010). The comparison between models M0 and M2 uses a χ² distribution with two degrees of freedom, and the 5% critical value is 5.99 (Zhu and Yang 2012). Models M1 and M2 cannot be compared using an LRT, because they are not nested. Instead, we use the Akaike information criterion (AIC) to rank the M0, M1, and M2 models.

Results

Genomic Data and Alignments

Multiplexed RRLs of up to 12 samples were successfully sequenced on single Illumina lanes with high average coverage (table 1). Sequenced libraries (RRLs) contained 21.6–65.1 million bp of sequence data before filtering (mean = 47.8 million bp) and resulted in assemblies of 59,562–741,561 de novo contigs (mean = 265,874) with high average coverage (9×–55×, mean = 17×; table 1). Quality filtering of assembly contigs for size and average coverage resulted in 43,057–113,302 (mean = 76,390) contigs. Raw read count is generally correlated with the number of assembled contigs. Quality filtering for coverage less than 8× was necessary to account for sequencing error associated with NGS data and resulted in an average loss of 62% of the de novo assembled contigs. The S. occidentalis WGS resulted in 409.2 million bp of data. CLC quality control filtering and de novo assembly followed by filtering for average coverage and sequence length resulted in 834,098 contigs with an N50 (median contig size) of 2,967 bp (table 1). The percentage of assembled contigs that were removed from all assemblies after repeat masking ranged from 2.1% to 3.0% (mean = 2.6%).

For each of the eight triplets, cleaned and filtered RRL library contigs were compared with the S. occidentalis WGS library to determine homology. The number of homologous fragments (after alignment and trimming) for a triplet varied between 340 and 3,478 loci (mean = 1,678) and ranged in length from 98 to 1,588 bp (mean = 506 bp; table 2). The number of postfiltered contigs that Blast to the WGS for the three species in a triplet was not a predictor for the number of overlapping loci (i.e., BSC average contigs = 37,925 for 340 loci vs. HOL average contigs = 26,524 for 3,478 loci). Expected time to common ancestry for a triplet was not a predictor of loci number. HOL has a more recent divergence than BSC, which may explain the increased number of overlapping loci, but this trend disappears when other triplets are included. It is difficult to predict the resulting data set size based on sequencing effort using the RRL approach. Sequence variation between sister species varied from 0.7% (CTO) to 4.4% (JOG) and increased to as high as 9.5% (JOG) when including the outgroup species (table 2).

Table 2.

Alignments for Eight Triplets of Sceloporus Lizards

Triplet (Name, Species)		Species Pair Distribution	Loci	Length	% Variable Sites
					Sister Pair	Triplet
AFT	adleri	Parapatric	458	338 (104–592)	2.5 (0–3.6)	4.1 (1–5.4)
	formosus
	taeniocnemisa
BSC	bicanthalis	Parapatric	340	336 (102–635)	3.5 (0–3.8)	7.3 (1.9–7.6)
	scalaris
	clarkiia
CTO	cowlesi	Parapatric	3,015	745 (236–1,588)	0.7 (0–0.9)	2.4 (0.8–2.5)
	tristichus
	occidentalisa
GPC	grammicus	Parapatric	914	349 (98–644)	1.7 (0–2.0)	4.7 (2.0–5.4)
	palaciosi
	clarkiia
HOL	hunsakeri	Allopatric	3,478	639 (172–1,391)	2.0 (0.6–2.1)	3.1 (1.2–3.2)
	orcutti
	lickia
HSE	horridus	Parapatric	3,044	602 (152–1,296)	1.9 (0–2.2)	3.8 (2.0–3.9)
	spinosus
	edwardtayloria
JOG	jalapae	Allopatric	533	454 (124–1,043)	4.4 (1.6–4.7)	9.5 (4.8–9.8)
	ochoterenae
	gadoviaea
MZH	magister	Parapatric	1,644	587 (138–1,316)	2.8 (0.7–2.9)	3.9 (1.4–4.1)
	zosteromus
	hunsakeria

^aThe outgroup for each triplet.

Divergence with Gene Flow

3s results for each triplet are summarized in table 3. Based on the LRTs, a model of no gene flow during divergence is supported in three of the triplets, including AFT, CTO, and HOL. For each of these triplets, the 2 scores for the alternative gene flow models are 0.0. The five remaining triplets each support a model of gene flow during speciation with strong support exceeding the 5% critical value. The LRTs cannot distinguish between models M1 and M2, because they are not nested. The AIC results (table 4) provide ranks for the triplets that support the M1 and M2 models. The AIC results are consistent with the LRTs in their strong support for the migration models (AIC weights ≥ 0.05; table 4). Model M1 ranks higher than M2 for the triplets GPC, HSE, and JOG, but given that model M1 is an approximation of divergence with gene flow that does not explicitly estimate a migration rate parameter, we prefer to summarize parameter estimates from the M2 model.

Table 3.

LRT Results of Species Divergence in Eight Triplets of Sceloporus

Triplet	Loci	ℓ M0	2Δℓ M1a	2Δℓ M2b
AFT	458	−25,960.3	0	0
BSC	340	−37,126.1	+34.1	+39.2
CTO	3,015	−290,344.7	0	0
GPC	914	−71,165.1	+49.9	+43.0
HOL	3,478	−335,756.5	0	0
HSE	3,044	−368,037.6	+90.9	+67.1
JOG	533	−100,221.5	+74.0	+57.5
MZH	1,644	−201,949.2	0	+7.0

Note.—Significant LRT results are in italic, and zero values indicate no difference in ℓ score.

^a5% critical value = 2.71.

^b5% critical value = 5.99.

Table 4.

AIC Comparison of Population Divergence Models

Triplet	Model	-ℓ	Parameters	AIC	Rank	ΔAIC	Weight
BSC	M0	37,126.1	4	74,260	3	35.2	0
	M1	37,109.1	5	74,228	2	3.1	0.18
	M2	37,106.5	6	74,225	1	0	0.82
GPC	M0	71,165.1	4	142,338	3	47.9	0
	M1	71,140.2	5	142,290	1	0	0.99
	M2	71,143.6	6	142,299	2	8.9	0.01
HSE	M0	368,037.6	4	736,083	3	88.9	0
	M1	367,992.2	5	735,994	1	0	1.00
	M2	368,004.1	6	736,020	2	25.8	0
JOG	M0	100,221.5	4	200,451	3	72	0
	M1	100,184.5	5	200,379	1	0	1.00
	M2	100,192.8	6	200,397	2	18.5	0

Maximum likelihood parameter estimates for the eight triplets are shown in figure 2. Speciation appears to be most recent in triplets AFT ( = 0.0003 ± 0.00089) and CTO ( = 0.0003 ± 0.00004). These divergence times occurred in the Pleistocene around 300,000 years ago (±40,000 years) assuming a mutation rate in the order of 10⁻⁹ (Zhang and Hewitt 2003). However, without an accurate substitution rate for the RRL loci, it is not possible to obtain reliable parameter estimates on a demographic scale. Population size estimates and are generally unequal (fig. 2), and is typically larger. In one instance under the M0 model, exceeds in the triplet AFT ( = 0.1313, = 0.00101). Under the M2 model, the divergence time is exceptionally close to for triplets JOG, MZH, GPC, and BSC (fig. 2). Under the M0 model, the maximum likelihood estimates for are more recent and indicate that speciation was not simultaneous in these triplets (fig. 2). This observed decrease in is accompanied by an increase in . Therefore, if gene flow exists between the species pair, then ignoring gene flow in M0 causes overestimation of and underestimation of , because the model incorrectly attributes the excessive variation in divergence times among loci to a large ancestral population size . The triplet parameters and are stable across the M0 and M2 models (results not shown), although these estimates may be influenced by rate variation among loci.

Fig. 2.—

Maximum likelihood estimates of population genetic parameters for eight triplets of Sceloporus. Divergence without gene flow (model M0) is supported in triplets HOL (B²), CTO (E), and AFT (G). The remaining triplets support divergence with gene flow and are shown with parameter estimates from model M2 (black branches and text) and M0 (gray branches and text). Estimates of θ and τ are scaled by 100.

Discussion

Testing Species Divergence

Empirical examples of divergence with gene flow span a wide array of organisms (Pinho and Hey 2010), including salamanders (Niemiller et al. 2008), lizards (Rosenblum et al. 2007), plants (Osborne et al. 2013), and butterflies (Stölting et al. 2013). Speciation with gene flow appears to be common among the great apes (Mailund et al. 2012; Prado-Martinez et al. 2013), including examples of admixture between modern humans and their recent Neandertal (Green et al. 2010) and Denisovan ancestors (Reich et al. 2011). The IM method (Nielsen and Wakeley 2001; Hey and Nielsen 2004) is the most commonly used approach for conducting statistical test of speciation models, because it offers a robust framework for model testing using the LRT (Hey and Nielsen 2007) or the AIC (Carstens et al. 2009). Explicit model testing is important for rigorous statistical phylogeography analysis (Knowles 2009; Carstens et al. 2013), and new methods that can handle large genomic data sets are becoming increasingly necessary to keep pace with the growing number of studies using next-generation sequencing data (Smith et al. 2013). The popular IM/IMa program has difficulty with large numbers of loci, and it is not quite able to scale-up to next-generation sequence data levels. By reducing the number of samples required for analysis, the triplet method (Yang 2010; Zhu and Yang 2012) provides a feasible approach for conducting comparative species divergence analysis using genomic data.

One of the limitations of the triplet method is that it cannot distinguish gene flow resulting from primary divergence versus secondary contact. The method quantifies variation in across loci, and it does not attempt to discern whether the variability in this parameter is reflective of gene flow during speciation or gene flow after divergence in allopatry (Yang 2010). This is important to consider when attempting to make inferences about the process of speciation supported by the LRT. New Bayesian phylogeography methods may be better suited for this purpose (Lemey et al. 2010), and complementing this approach with population genetic analyses can help distinguish allopatric divergence followed by secondary contact from primary intergradation (Pettengill and Moeller 2012).

IM analyses typically emphasize robust population sampling and assume that there are no unsampled populations exchanging genes with the sampled populations or their ancestors. Ancestral population subdivision can increase the frequency of incorrect gene trees (Slatkin and Pollack 2008) and lead to increased estimates of (Yang 2010). Some methods exploit this expectation of gene tree frequency differences to test for admixture between closely related populations (Durand et al. 2011). However, gene flow and ancestral population subdivision can produce similar coalescent times between two individuals from different populations, and distinguishing the two requires more than just one sample per species (Durand et al. 2011). The problems associated with population substructure could extend to triplets that include paraphyletic species or species pairs that include a focal species that is sister to a clade containing multiple species. The effect of population subdivision and species paraphyly on type I and type II error rates using the triplet method remains unstudied.

The use of two extra parameters into the M2 model, M₁₂ and , have a major impact on the estimation of in some triplets. For example, we found that is nearly equal to under the M2 model, but estimates for under the M0 model provide more recent estimates for speciation times. Estimates of and of under models of gene flow implemented in 3s (M1 and M2) are unreliable due to the use of only three sequences at every locus, with only one sequence from each species. Zhu and Yang (2012) discussed the issue of nonidentifiability for and M₁₂, and even though and are identifiable, their estimates may be inaccurate due to a lack of information in the data. Extending the method to accommodate two or three sequences from the same species may increase the information content substantially, leading to more reliable parameter estimates. Despite the potential for poor parameter estimation, the method provides accurate LRT results (Yang 2010; Zhu and Yang 2012).

Comparative Species Divergence in Sceloporus

The new comparative genomic data sets collected for Sceloporus provide a robust statistical assessment of the model of species divergence history and the associated population genetic parameter estimates for the model. Three of the eight triplets of Sceloporus studied here support a history of speciation that does not include gene flow (table 3). Interestingly, one of these triplets (CTO) was found to support high rates of gene flow using multilocus DNA sequences (Leaché 2011). The sister pair in this triplet, S. cowlesi and S. tristichus, were sampled from opposite sides of a hybrid zone, and although the specific samples selected for this study have species-specific mtDNA, introgression has distributed S. cowlesi mtDNA haplotypes throughout the contact zone and into populations of S. tristichus (Leaché and Cole 2007). The recent divergence time for the species pair ( = 0.0003; fig. 2) suggests that the S. cowlesi sample used in this study may in fact be S. tristichus with introgressed mtDNA. Presumably, selecting different specimens from the hybrid zone that show some degree of admixture based on chromosomal polymorphisms or phenotypic traits would provide support for divergence with gene flow using the triplet method, even if the hybrid zone formed via secondary contact.

The two other triplets supporting speciation without gene flow include AFT and HOL, each contain a species pair with one widespread species and one species with a small and restricted distribution. In the formosus group, S. adleri is a high-elevation species that occurs in cool habitats above 2,183 m in the Sierra Madre del Sur (Smith and Savitzky 1974). The sister species S. formosus is more widely distributed at lower elevations, and we used a sample from an adjacent area on the same mountain range. The extrinsic environmental or intrinsic lineage-specific traits that contributed to the isolation of these species is unknown but occurred recently (; fig. 2). In the magister group, S. hunsakeri is restricted to the Cape Region of Baja California, Mexico, while the sister species S. orcutti is distributed throughout the Baja California Peninsula and into southern California. Divergence in the Baja California group is likely due to allopatric divergence resulting from the La Paz Embayment that isolated the Cape Region during the late Miocene/early Pliocene (Leaché and Mulcahy 2007), and this older divergence is supported by the estimate for (0.0074; fig. 2).

The five species pairs of Sceloporus that support divergence with gene flow have not been previously studied in the context of population divergence genetics. Many of these species are widespread generalists that occupy a wide diversity of environments and show extensive population substructure (Bryson et al. 2012). If the ancestral populations exhibited similar levels of substructure, then it is possible that the evidence for divergence with gene flow is an artifact of biases in instead of gene flow. However, discovering triplets that support divergence with gene flow is not surprising given that chromosomal speciation is a dominant theme in Sceloporus diversification, and that models of chromosomal evolution involve stages of partial population subdivision that would facilitate continued gene flow (Sites et al. 1992; Hall 2010; Leaché and Sites 2010).

Compared with similar approaches for estimating population parameters, the triplet method requires not only a minimal number of samples but also a large number of loci for statistical power. Acquiring large numbers of loci for non-model organisms is no longer a challenge when utilizing emergent genomic techniques. An obvious trade-off associated with scanning triplets for evidence of divergence with gene flow is the loss of phylogeographic information within a species. However, developing the large numbers of nuclear loci necessary for the triplet test has the benefit of creating a wealth of new comparative genomics information for subsequent phylogeographic investigations.