Controlling for the Effects of History and Nonequilibrium Conditions in

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Copyright  2004 by the Genetics Society of America DOI: 10.1534/genetics.104.027987

Controlling for the Effects of History and Nonequilibrium Conditions in Gene Flow Estimates in Northern Bullfrog (Rana catesbeiana) Populations James D. Austin,1 Stephen C. Lougheed2 and Peter T. Boag Department of Biology, Queen’s University, Kingston, Ontario, Canada, K7L 3N6 Manuscript received February 24, 2004 Accepted for publication June 22, 2004 ABSTRACT Nonequilibrium conditions due to either allopatry followed by secondary contact or recent range expansion can confound measurements of gene flow among populations in previously glaciated regions. We determined the scale at which gene flow can be estimated among breeding aggregations of bullfrogs (Rana catesbeiana) at the northern limit of their range in Ontario, Canada, using seven highly polymorphic DNA microsatellite loci. We first identified breeding aggregations that likely share a common history, determined from the pattern of allelic richness, factorial correspondence analysis, and a previously published mtDNA phylogeography, and then tested for regional equilibrium by evaluating the association between pairwise F ST and geographic distance. Regional breeding aggregations in eastern Ontario separated by !100 km were determined to be at or near equilibrium. High levels of gene flow were measured using traditional F-statistics and likelihood estimates of Nm. Similarly high levels of recent migration (past one to three generations) were estimated among the breeding aggregations using nonequilibrium methods. We also show that, in many cases, breeding aggregations separated by up to tens of kilometers are not genetically distinct enough to be considered separate genetic populations. These results have important implications both for the identification of independent “populations” and in assessing the effect of scale in detecting patterns of genetic equilibrium and gene flow.


major and often untested assumption in many studies of genetic structure is that populations are at equilibrium for the reduction of variation through drift and the replacement of variation from migration (Wright 1969). Species from temperate regions are arguably the best represented in studies of the scale and extent of gene flow, despite the fact that current population genetic structure is often confounded by historical events. This means that a number of assumptions, of particular importance being that populations are at equilibrium for drift and migration, may be violated due to lingering effects of range expansion, secondary contact, and geographic scale. The impacts of potential confounds will depend on the characteristics of the organism under study (e.g., effective population size, generation time, dispersal ability), the scale at which gene flow is measured, and the portion of the range considered (e.g., previously vs. never glaciated). Although the importance of testing for nonequilibrium conditions is well established (Templeton and Georgiadis 1996; Templeton 1998; Hutchinson and Templeton 1999; Pogson et al. 2001), numerous studies either failed to test for this condition before estimating levels of gene flow

1 Present address: Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, NY 14853-2701. 2 Corresponding author: Department of Biology, Queen’s University, Kingston, Ontario, Canada, K7L 3N6. E-mail: [email protected]

Genetics 168: 1491–1506 (November 2004)

or estimated and interpreted gene flow despite evidence of nonequilibrium conditions (e.g., Driscoll 1998; Lougheed et al. 1999; Congdon et al. 2000; Walker et al. 2001; Friesen et al. 2002; Bittner and King 2003). The importance of equilibrium is reflected in the fact that drift and migration jointly affect genetic differentiation in the product Nm (the effective number of migrants per generation), where drift is proportional to 1/N, and N is the effective population size. Testing the assumption of equilibrium under Wright’s (1931) infinite island model is difficult, if not impossible (Pogson et al. 2001). However, for many species dispersal is constrained by distance, and Kimura’s (1953) steppingstone model makes possible the identification of potential equilibrium conditions through patterns of isolation by distance. Amphibians have a number of life-history attributes that make them excellent candidates for testing for the scale and extent of gene flow. Amphibians typically have low vagility related to their small size and saltatory mode of locomotion on land and, in many species, to their presumed high level of philopatry to breeding sites that are often patchily distributed (e.g., Berven and Grudzien 1990; Driscoll 1997). Thus, gene flow is likely to be limited by distance (e.g., Barber 1999; Storfer 1999). Numerous studies on amphibians have estimated dispersal or migration directly (Twitty et al. 1964; Sinsch and Seidel 1995; Driscoll 1997; Seburn et al. 1997; Dodd and Cade 1998; Sjo¨gren-Gulve 1998;


J. D. Austin, S. C. Lougheed and P. T. Boag

Peter 2001; Pilliod et al. 2002). However, few if any are of the duration and scale necessary to confidently determine levels of gene flow because of the low probability of detecting long-distance dispersers (Slatkin 1985; Koenig et al. 1996) and the inability to evaluate the establishment of dispersing alleles in new populations. The North American bullfrog (Rana catesbeiana) is a widely distributed species native to central and eastern North America, as far north as 47# (Conant and Collins 1998). R. catesbeiana is highly aquatic, requiring permanent water bodies for reproduction, foraging, and over-wintering (Graves and Anderson 1987). However, they are frequently encountered on land some distance from permanent aquatic habitat (e.g., hundreds of meters; J. D. Austin, personal observation; R. Segel, personal communication), and dispersal patterns in R. catesbeiana and other ranid frogs suggest that seasonal movement distances can span kilometers (Raney 1940; Seburn et al. 1997; Marsh and Trenham 2001; Pilliod et al. 2002; D. Ireland, unpublished results). At the northern limit of its range in Ontario, R. catesbeiana is represented by multiple mitochondrial (mtDNA) lineages that have undergone range expansion and have come into secondary contact in southern Ontario following the most recent glacial retreat (Austin et al. 2004). The impact of successive Pleistocene range fragmentations and expansions on the genetic structure of populations is well known (Hewitt 1996), and a major challenge for studies of genetic spatial structure is disentangling the influence of historical events from contemporary patterns of gene flow. Given the known pattern of colonization (i.e., separate mtDNA lineages colonizing southwestern and eastern Ontario; Austin et al. 2004), the genetic structure of microsatellite loci in R. catesbeiana populations in Ontario will potentially be shaped by (i) mixing of divergent allele pools from southwest and southeast refugial areas and (ii) nonequilibrium conditions from recent expansion, resulting in genetic similarity that may inflate estimates of contemporary gene flow. For the present study focused on Ontario populations of R. catesbeiana, our primary objectives were to determine: (1) the relative impact of historical (range expansion and secondary contact) and contemporary (drift and gene flow) influences on population genetic structure at microsatellite loci; (2) the geographic scale that gene flow can be measured accurately [i.e., the scale at which we can assume (i) equilibrium or (ii) a limited effect on genetic structure from mutation]; and (3) the extent of gene flow at the appropriate geographic scale. MATERIALS AND METHODS Sampling: R. catesbeiana are most conspicuous during the breeding season, forming breeding aggregations when males congregate in choruses, and females arrive asynchronously to choose mates (Howard 1978, 1988). Breeding aggregations were sampled across southern Ontario during May and June

of 1998–2000. Toe-clips were obtained from 753 R. catesbeiana from 28 sites across southern Ontario (mean " 26.9, SD " 8.5; Table 1). These included aggregations sampled along parallel watersheds in the Madawaska Highlands for examining fine geographic scale population structure (Figure 1, inset). We also sampled regionally peripheral (relative to the Madawaska samples) pairs of breeding aggregations in eastern Ontario, as well as representative locations from southwestern Ontario (Figure 1; Table 1). We use the term “regional” simply to refer to a set of samples within an arbitrarily defined geographic area (see Hutchinson and Templeton 1999). Genotypic data and testing for Hardy-Weinberg equilibrium and linkage disequilibrium: Genomic DNA was extracted using the Dneasy tissue kit (QIAGEN, Valencia, CA), and samples were screened for variation at seven highly polymorphic R. catesbeiana microsatellite loci as described elsewhere (Austin et al. 2003). We tested the null hypothesis of random union of gametes between pairs of loci within sample locations using a Markov Chain approximation of an exact test as implemented in GENEPOP web version 3.1 (Raymond and Rousset 1995; Hendrie et al. 1998). P-values were Bonferroni corrected for multiple tests (Rice 1989). Deviations from Hardy-Weinberg were estimated for each locus at each sample site using Weir and Cockerham’s (1984) f (analogous to FIS), using GENEPOP. Population level f was estimated across loci and 95% confidence intervals were estimated by 10,000 bootstrap replicates as implemented in GENETIX version 4.03 (Belkhir et al. 2000). We tested for the relative contribution of stepwise mutations to global and pairwise population differentiation using the randomization test of Hardy et al. (2003). Briefly, this test examines the contribution of stepwise mutation [stepwise mutation model (SMM)], relative to drift, to population differentiation by randomizing allele sizes within a locus while maintaining genotypic states of individuals. If allele size shifts are resulting predominantly from stepwise mutations, then the observed estimates of RST should be greater than those estimated from the permutated data set (pRST). We conducted global and pairwise population tests running 1000 permutations each, using SPAGeDi version 1.1 (Hardy and Vekemans 2002). The effect of historical isolation on genetic differentiation: The presence of multiple mitochondrial lineages in southwestern Ontario (Austin et al. 2004) brings into question the validity of including all breeding aggregations for determining the scale or pattern of gene flow, as refugial history would undoubtedly confound estimates. We assessed the possible influence of population isolation on microsatellite allelic variation by examining the apportionment of allelic richness across breeding aggregations, followed by a factorial correspondence analysis (FCA) to determine the relative influence of breeding aggregations on the global pattern of genetic variance. We estimated r(g ), the number of alleles found within g sampled genes using the rarefaction method of Hurlbert (1971). Petit et al. (1998) devised a method to partition the contribution of each population to the total r(g ) into components relating to the diversity of the population and to the divergence of that population from other populations. We excluded KA, HA, and MH (see Table 1 for definitions) because of small sample sizes and calculated r(g ) using CONTRIB (available online at labo/Software/Contrib). FCA (implemented using GENETIX) conducted on all 28 locations revealed that alleles at two locations were driving the global pattern of variation (see results). Removal of these samples further revealed the influential effect of southwest samples on the global pattern. On the basis of the results from the analyses of allelic richness and FCA (see below) we restricted subsequent analyses to

Equilibrium and Gene Flow in Bullfrog


TABLE 1 Rana catesbeiana sample locations and population diversity measures based on seven highly polymorphic microsatellite loci Regional group SW ON

Bancroft Pembroke Perth QUBS SLINP Madawaska Highlands







h (SE)


r (30)

Lake St. Clair Big Creek Niagara Aberfoyle Mill Pigeon River Little Joseph Watt Creek Hamilton Bay Wilbur Lake Hazley Bay Muskrat Lake Tay Marsh McEwan Bay Cow Island Telephone Bay Grenadier Island Hill Island Dalhousie Kashwakamak Mosquito Pond Big Gull Michelle Pond Harlowe Earl’s Bay Miller Lake Mud Lake Mississippi Island Mill Haven


42#23$ 42#36$ 42#56$ 43#28$ 44#16$ 45#12$ 45#10$ 45#09$ 45#33$ 45#47$ 45#44$ 44#53$ 45#02$ 44#34$ 44#31$ 44#25$ 44#21$ 44#58$ 44#52$ 44#52$ 44#50$ 44#49$ 44#49$ 44#49$ 44#56$ 44#56$ 44#54$ 44#49$

82#24$ 80#27$ 79#15$ 80#09$ 78#36$ 79#40$ 78#05$ 78#04$ 77#10$ 77#02$ 77#02$ 76#14$ 76#14$ 76#19$ 76#22$ 75#52$ 75#58$ 76#30$ 77#00$ 76#53$ 76#57$ 77#07$ 77#04$ 77#03$ 76#41$ 76#54$ 76#56$ 77#03$

20 26 20 18 29 23 30 30 45 37 42 30 27 32 26 27 30 39 12 25 36 29 9 20 25 29 24 13

0.664 0.495 0.714 0.594 0.700 0.596 0.629 0.676 0.623 0.728 0.612 0.667 0.593 0.536 0.584 0.587 0.652 0.634 0.631 0.697 0.655 0.581 0.560 0.621 0.577 0.626 0.637 0.621

0.585 (0.06) 0.427 (0.05) 0.704 (0.04) 0.575 (0.05) 0.647 (0.04) 0.616 (0.05) 0.673 (0.04) 0.663 (0.04) 0.682 (0.04) 0.657 (0.05) 0.644 (0.05) 0.699 (0.04) 0.731 (0.05) 0.674 (0.05) 0.670 (0.05) 0.668 (0.04) 0.660 (0.05) 0.605 (0.04) — 0.711 (0.04) 0.671 (0.05) 0.657 (0.05) — 0.655 (0.05) 0.629 (0.05) 0.629 (0.05) 0.616 (0.04) —

%0.163* %0.003 %0.020 %0.043 0.045 0.048 0.001 %0.004 %0.011 %0.105* %0.012 %0.012 0.029 0.094 0.068 0.073 0.047 0.033 0.022 0.012 0.047 %0.045 0.083 0.172* 0.198 0.153* 0.146* 0.052

6.79 2.84 6.19 5.49 5.27 4.68 4.67 4.16 5.77 4.37 5.55 6.00 5.52 5.71 5.47 5.93 5.32 3.80 — 5.15 4.49 4.15 — 5.31 5.14 4.47 4.84 —

Allelic richness is rarefied to a common sample of 30 genes per locus [r (30)]. Dashes denote diversity measures not taken due to small sample sizes. HO, observed heterozygosity; h, Nei’s (1973) estimate; ƒ, population inbreeding coefficient (significantly different from zero indicated by *); SW ON, southwestern Ontario; QUBS, Queen’s University Biology Station; SLINP, St. Lawrence Islands National Park.

the remaining 22 breeding aggregations that likely have a common postglacial history. Determining the scale of regional genetic equilibrium: Under a stepping-stone model of gene flow (Kimura 1953; Kimura and Weiss 1964), isolation by distance (IBD) is generally expected under conditions of population equilibrium for drift and migration (Male´cot 1955). A number of methods have been suggested for identifying IBD (Slatkin 1993; Rousset 1997; Hutchinson and Templeton 1999). These methods vary in their assumptions and objectives; the former methods are used primarily to estimate demographic parameters (e.g., genetic neighborhood size), while the Hutchinson and Templeton method tests specific predictions related to IBD. For example, assuming populations over all distance classes are at equilibrium and that there is a negligible impact of mutation relative to migration (i.e., & ' m ), we would predict a positive, monotonic relationship between population differentiation (e.g., F ST) and geographic distance (Hutchinson and Templeton 1999), because at close proximity (barring geographic or ecological barriers), populations should be less differentiated than farther apart populations. As geographic distances and population differentiation increase, so too should the variance around estimates of F ST. Although each of the previously mentioned methods works well for estimating the significance of the relationship between genetic and distance

measures using Mantel’s test, the ability of the Slatkin (1993) and Rousset (1997) methods of estimating demographic parameters is probably more appropriate over limited geographic distances, defined by the variance in gene dispersal and mutation rate (Rousset 1997). Therefore, confidence in the assumption of equilibrium (and for a low mutation rate effect, i.e., & ' m ) over the geographic scale being considered should be a priority before estimating demographic parameters or Nm. We used ( (an estimator of F ST ; Weir and Cockerham 1984) to quantify pairwise genetic relationships. Geographic distances were calculated as greater circle distances using R PACKAGE version 4.0 (Casgrain and Legendre 2001). The significance of the correlations between pairwise ( and geographic distance was determined using Mantel’s tests (Mantel 1967) as implemented in IBD version 1.5 (Bohonak 2002) running 10,000 permutations. We also used a permutation procedure (RESAMPLING STATS EXCEL ADD-IN version 2.0, available online at to construct confidence intervals to test (i) whether the regression slopes differed significantly from zero for ( vs. distance and (ii) whether the absolute values of the residuals from i increased with distance (i.e., slope ) 0). Our method randomly sampled 10,000 data sets, holding sample sizes constant, from which new slopes were estimated and compared to the original slope


J. D. Austin, S. C. Lougheed and P. T. Boag

Figure 1.—Geographic locations of sampled Rana catesbeiana breeding aggregations in southern Ontario. Inset, series of 11 aggregations sampled in the southern portion of the Madawaska Highlands region. Locations are defined in Table 1. Asterisks indicate Ontario populations where mtDNA haplotypes have been genotyped (Austin et al. 2004).

values. If )5% of the resampled slopes were less than or equal to zero, the null hypothesis of a slope of zero could not be rejected. After estimating an appropriate scale at which to confidently estimate Nm, we compared slopes (estimated using IBD) between straight-line geographic distances and major aquatic corridors within the Madawaska Highlands breeding aggregations (Figure 1, inset) to determine whether gene flow was structured differently on the basis of these geographic measures. Traditional estimates of population structure and gene flow: We used Wright’s (1969) approximation to quantify average levels of gene flow among regional samples. F ST was calculated two ways: First, global ( (Weir and Cockerham 1984) was estimated within regional groupings. Within the Madawaska and Pembroke regions (the two regions with more than two samples), we also calculated pairwise ( to compare estimates of Nm [Nm " 0.25(1/F ST % 1)] with the maximum-likelihood estimates of pairwise Nm (see below). Although global F-statistics are more conservative than their pairwise counterparts because of the assumption of an infinite number of populations (but see Neigel 2002), pairwise estimates relax the assumption of equal migration among island populations (because by definition migration is calculated between two populations only). Bayesian estimate of population structure: Traditional F-statistics rely on a predefined population organization, sometimes driven by the exigencies of field sampling rather than

reflecting biological reality; however, hidden population structure may confound traditional estimates of genetic structure (Weir 1996). For example, using breeding aggregations as the predefined “population” unit may or may not accurately reflect true population structure. To test the assumption that distinct breeding aggregations represent independent genetic populations we used a Bayesian inference procedure that assesses the plausibility of structure for all population combinations based on the genetic data. The program BAPS version 1.3 (Corander et al. 2003) treats the allele frequencies and the predefined number of populations as random variables and jointly calculates the posterior distributions of the population structure and allele frequencies. Uncertainty of the predefined population structure (i.e., the probability that allele frequencies are the same) is estimated for all pairwise population comparisons, and final posterior likelihood(s) of population structure is estimated. Finally, an estimate of F ST (Nei 1977) is calculated as a weighted average over the probabilities of different estimated population configurations. For each run the lower bound for posterior probability for structure was set at 0.01 (i.e., hidden structure with a posterior probability of )0.01 would be detected). For the Madawaska locations we omitted the smaller sample sizes (KA, MH, and HA) from this calculation, estimating population structure and F ST on the remaining eight populations. Likelihood estimate of population structure and gene flow: We applied the likelihood approach implemented in MIGRATE version 1.6.9 (Beerli 2002) to estimate the direction and magnitude of gene flow between pairs of breeding aggregations. MIGRATE assumes that populations are at drift-migration equilibrium and that each has had constant size and migration between population pairs over the coalescent period (!4Ne generations). However, unlike F-statistics, this method allows for the possibility of nonsymmetrical migration and differences in population sizes, both biologically realistic scenarios. MIGRATE jointly estimates the effective population sizes and migration rates between pairs of populations by estimating allele genealogies and then approximates the sum of probabilities across possible genealogies using Metropolis-Hastings Markov chain Monte Carlo (MCMC) sampling. MCMC concentrates the sampling in areas of the coalescent space that contribute most to the final likelihood and ignores genealogies that contribute little to the final likelihood (Beerli and Felsenstein 2001). For a given run, MIGRATE provides a likelihood-based value for 4Nm, which we simply divided by four for comparative purposes. Parameters for the Madawaska Highlands (Figure 1, inset) were estimated using MIGRATE mounted on a symmetric multiprocessor consisting of eight SunFire 6800 servers running the Solaris 9 operating environment. Regional subsets of populations in eastern Ontario (Table 1) were calculated separately on MacIntosh computers operating OSX 10.2.5. We relied on default search settings (10 short chains of 10,000 sampled, 500 recorded, followed by 3 long chains of 100,000 sampled, 5000 recorded) but implemented four-chain heating (Metropolis-coupled Markov chain Monte Carlo), which swaps between simultaneously run neighboring chains along a temperature gradient, “hotter” chains sampling more parameter space than “colder” chains. This method permits the exploration of the very large “data space” and improves confidence interval estimation (Beerli 2002). Temperatures were set at 1, 1.5, 3, and 6, with interval swapping set to one. We used the Brownian motion approximation to the ladder model (Ohta and Kimura 1973) and assumed equal mutation rates among loci. We ran MIGRATE a minimum of four times per data set to verify that final chains were estimating the same ML values for * (i.e., population size) and 4Nm (as determined by overlapping 95% confidence intervals). For each run we changed the random number seed and the starting values of

Equilibrium and Gene Flow in Bullfrog * and 4Nm. The first run estimated * and 4Nm from F ST values, and subsequent runs incorporated the ML estimates of * and 4Nm from the previous run as the starting parameters. Reported are the ML estimates from the final run. We omitted one locus (Rcat J54) from the MIGRATE runs because the frequency of single-base-pair mutations suggests that this locus does not adhere to a strict stepwise mutation model assumed by MIGRATE. Alleles from other loci that violated the stepwise mutation pattern (Rcat 3-2b *147, Rcat J11 *125, Rcat J11 *129, and Rcat J44b *90) were rare (global frequencies !0.01%) and these individual alleles were marked as unknown for MIGRATE runs. Estimates of recent migration: New methods for identifying migrants that make no assumptions of equilibrium (Rannala and Mountain 1997; Pritchard et al. 2000), combined with estimates of longer-term gene flow over many generations, provide different temporal dimensions to the investigation of gene movement among populations (Wilson and Rannala 2003). Recent immigrants display temporary disequilibrium in their genotypes, relative to their host population, allowing for their identification as immigrants or recent descendants of immigrants. Because these methods relate only to the past one to three generations, mutation and effective population size are not as important as they are for estimates of gene flow (which is an average value of Nm over a number of generations; see below). We used a recently developed Bayesian method for estimating migration rates (Wilson and Rannala 2003) to calculate the proportion of migrants (m ) between breeding aggregations. Relative to indirect estimators of long-term gene flow, this nonequilibrium approach is relatively assumption free (e.g., does not assume Hardy-Weinberg equilibrium within populations). The method allows for arbitrary genotype frequencies within and calculates separate inbreeding coefficients for each population, the joint probabilities of which are used to estimate recent migration rates (Wilson and Rannala 2003). The program BAYESASS version 1.1 (Wilson and Rannala 2003) was run for 3 + 106 iterations, sampled every 2000, and the first 1 + 106 iterations were discarded as “burn in.” The first run used default settings, with subsequent runs incorporating different random seed and delta values, the latter chosen to ensure that proposed changes between chains at the end of the run were between 40 and 60% (Wilson and Rannala 2003). This step is recommended to ensure that neither chain mixing gets stuck on a local maximum nor the chain slips out of the global maximum too easily (G. Wilson, personal communication). Each data set was run a minimum of four times to check for consistency of results, and the values for the final three runs were averaged. Accuracy of nonequilibrium methods of estimating population assignment or migration rates depends on large population sample sizes and/or large numbers of loci. We chose to omit small samples from the Madawaska region (MH, HA, and KA) for this reason.


Following Bonferroni correction, only 2 of the 589 pairwise tests for linkage disequilibrium were significant; those 2 tests involved different loci comparisons and occurred in different breeding aggregations, suggesting that assayed loci likely evolve independently. Seven of 196 tests of heterozygote deficiency were significant: 3 for locus J11 (MC, WA, and BG), 3 for J44b (EB, KA, and ML), and 1 for J3-2 (GI). The frequency of heterozygote deficiency for J11 and J44b may be due to nonamplifying alleles (Callen et al. 1993) or in at

1495 TABLE 2

Significance of SMM vs. IAM in global patterns of allelic variation No. alleles All loci




P (RST ) pRST)

0.1078 0.1235 0.105 (0.077–0.136)




0.1042 0.100

0.105 (0.032–0.178)




0.1068 0.933

0.105 (0.047–0.181)




0.1432 0.1418 0.133 (0.043–0.225)








0.0902 0.1441 0.091 (0.039–0.169)




0.0996 0.1611 0.096 (0.041–0.183)




0.1016 0.0698 0.094 (0.046–0.139)


0.1629 0.118 (0.056–0.249)

Stepwise mutation contributed significantly to genetic differentiation for locus J44 only (*P ! 0.05).

least one instance (KA) may reflect sampling error due to small sample size. Tests for only three locations (EB, MD, and MI) suggest significant inbreeding while two others had significant heterozygote excess (SC and HZ) across all loci. These results, together with the pairwise tests of heterozygote deficiency, suggest that inbreeding is not pervasive. Overall, the SMM estimator RST did not perform better than F ST in estimating population differentiation. For the global test, only one locus had an observed RST greater than that estimated from random (i.e., pRST, Table 2). Similarly, only 1 of 251 pairwise comparisons was significant after Bonferroni correction. Therefore, we restricted estimates of genetic divergence to F ST, given the tendency of RST estimates toward larger variance and the relatively conservative performance of F ST when sample size and number of loci are small (Gaggiotti et al. 1999; Turgeon et al. 1999; Balloux and Goudet 2002). Influence of secondary contact: The pattern of allelic richness reflected a disproportionate amount of differentiation attributed to breeding aggregations sampled from the southwestern portion of Ontario (Figure 2). These populations accounted for much of the total allelic richness assayed, and many of these populations (SC, BC, NI, and AM) had divergent mtDNA lineages relative to eastern (GI, PR, ML, and BG) populations (see Figure 1 and Austin et al. 2004). Although not conclusive, these results suggest that the pattern of allelic richness may be, in part, structured by past isolation, rather than simply being due to geographic proximity. FCA on all 28 samples revealed two prominent outliers (NI and MC) and identified allelic information con-


J. D. Austin, S. C. Lougheed and P. T. Boag

Figure 2.—Contribution to the total allelic richness per location subdivided into diversity and differentiation components. Populations are approximately ordered as they appear from southwest to northeast. Overall, southwest populations contribute the greatest to global differentiation of allelic richness.

tributing to this pattern. FCA axis 1 explained 16% of the variance associated with the relationship between alleles and breeding aggregations. Six alleles strongly contributed to the first factorial axis ( J54 *89, J54 *101, J41*135, J44b *77, J21*175, and J3-2 *158). These alleles were globally rare (all !2% occurrence), although they occurred in high frequency in NI (45, 33, 25, 29, 20, and 40%, respectively). The second axis explained !8% of the variance and was attributable primarily to the contribution of two alleles: J8 *86 was a private allele accounting for 33% of the variation at this locus in MC; J21*157 was globally rare (!1%), accounting for 22% of the variance at this locus in MC, and occurred only once in a neighboring breeding sample (HA). This latter result was intriguing given that MC is geographically close to a number of sampled locations (Figure 1; Table 3). Reanalysis omitting NI and MC resulted in the first three axes representing similar amounts of the total variation (11, 10, and 8%, respectively), with few samples providing large absolute and relative contributions to these axes. Axis 1 was influenced by populations BC and SC, axis 2 by LJ (Figure 3), and axis 3 by WA and HB. FCA identified five alleles that had the highest absolute contribution to and whose pattern of variation was best represented by (i.e., highest relative contribution to) factorial axis 1: J11*110, J3-2 *146, J44b *77, J54 *109, and J8 *90. Axis 2 had contributions predominantly from J8 *118 and J21*171; and axis 3, from J44b *103, J21*173, and J11*126. Few of these alleles had low global frequencies relative to those discussed above, and none were private alleles (allele frequencies are available at"lougheed/ publications.htm). On the basis of the pattern of population distribution depicted in the FCA, as well as the relative contributions of southwestern populations to allelic diversity (Figure

2, Table 1), together with the historical evidence for integration of refugial mtDNA lineages in the southwestern portion of Ontario (Austin et al. 2004), it is apparent that populations across such a large geographic scale do not share a common population history, an important assumption when testing for scale and pattern of gene flow. Therefore, we restricted the subsequent analyses to 22 populations in the eastern portion of the sampled range, omitting populations SC, BC, NI, PR, LJ, and AM. Scale of regional equilibrium: For the remaining populations pairwise ( and geographic distances were strongly correlated (r " 0.723, P ! 0.001; slope " 0.00066, P ! 0.001, Figure 4A). The degree of scatter also increased positively with geographic distance (r " 0.305, P ! 0.01; slope " 0.00012, P ! 0.001, Figure 4B). However, one attribute of this approach to examining the geographic scale of equilibrium is that it is possible to identify patterns that may reflect differing roles for gene flow and drift over different distances (Hutchinson and Templeton 1999) or the possible impact of high mutation rates confounding divergence estimates. Because our within-region comparisons (Table 1) were all separated by !100 km, we examined the pattern of IBD on the first 100- and second 100-km distance classes separately to determine whether our assumptions of equilibrium would be met if Nm were estimated among regions. This was also done because of an inconsistent distribution of points between the first and last 100 km (Figure 4). The correlation between populations separated by !100 km remained highly significant (r " 0.637, P ! 0.01, n " 156) and the permutation analysis of the slope was significantly greater than zero (slope " 0.00065, P ! 0.0001). This was also true for the degree of scatter (r " 0.36, P ! 0.01; slope " 0.00017, P ! 0.0001). Populations separated by )100

Equilibrium and Gene Flow in Bullfrog


TABLE 3 Pairwise ! and corresponding Nm estimates from Madawaska Highlands R. catesbeiana breeding aggregations in eastern Ontario, corresponding to Figure 1 inset, and pairwise geographic and pairwise aquatic distances in kilometers DA DA KA MP BG MC HA EB MR MD MI MH


— 0.060 0.074 0.035 0.095 0.058 0.030 0.037 0.057 0.068 0.044

— 41.2 32.3 37.9 50.9 48.1 46.7 14.8 32.0 35.1 47.0







Pairwise ( (below diagonal) and corresponding Nm (above 3.9 3.1 6.8 2.4 4.1 8.0 — 4.5 15.3 2.5 4.8 15.5 0.053 — 11.7 4.1 6.6 5.1 0.016 0.021 — 4.2 7.1 16.2 0.089 0.057 0.057 — 5.8 5.0 0.050 0.036 0.034 0.042 — 15.9 0.016 0.047 0.015 0.048 0.016 — 0.021 0.037 0.014 0.072 0.030 0.010 0.035 0.015 0.024 0.058 0.036 0.031 0.008 0.029 0.018 0.102 0.058 0.035 0.019 0.040 0.005 0.051 0.011 0.003

42.6 — 10.2 6.4 10.4 8.6 7.9 26.5 10.3 6.5 8.1



diagonal) estimates 6.6 4.2 3.4 11.8 6.9 29.9 6.5 16.4 8.3 17.7 10.0 13.3 3.2 4.0 2.2 8.0 6.7 4.1 25.8 7.7 6.9 — 15.0 8.9 0.016 — 10.0 0.027 0.024 — 0.013 0.039 0.031

Pairwise geographic distances in kilometers (below diagonal) and pairwise aquatic distances (above diagonal) 32.6 38.2 52.9 49.0 47.0 14.8 32.2 45.6 51.2 10.4 62.1 60.1 27.8 10.3 — 5.6 56.0 16.5 14.5 17.8 35.3 5.6 — 61.6 10.8 8.8 23.4 40.9 18.7 13.2 — 72.4 70.4 38.2 20.7 15.8 10.3 3.2 — 1.5 34.3 51.7 14.5 8.8 4.7 1.5 — 32.3 49.7 17.8 23.4 36.2 33.5 32.2 — 17.5 8.4 10.9 20.7 18.7 17.7 17.5 — 7.2 7.7 16.9 14.8 13.9 20.4 3.8 14.7 9.1 4.4 0.7 1.2 32.5 17.9

km were also significantly correlated with pairwise geographic distance (r " 0.172, P ! 0.05, n " 54; slope " 0.00041, P ! 0.01); however, the relationship between residual scatter and distance no longer fit predictions of equilibrium (r " 0.046, P ) 0.05; slope " %0.00009, P ) 0.05). One possibility explaining the difference between distance classes is the unequal sample sizes being used to estimate confidence in slopes. We tested this by randomly sampling 54 points from the total set of 156 observations within the first 100-km distance class, running 10,000 permutations and reestimating the slope of each. All 10,000 permutated data sets had slopes greater than zero, suggesting that the pattern cannot be explained simply by the larger number of data points in the 1- to 100-km distance class. The effect of the nonlinear pattern is also evident in the linearized ( vs. ln distance graph (Figure 4C), where the observed slope appears to be inflated (potentially inflating the inferred demographic parameters) due to the nonlinear pattern across all distance classes. Given the evidence, our data reflect a lack of equilibrium across all distance classes and/or an increased effect of mutation between populations separated by ) !100 km. Because of the regional structuring of our samples,


36.1 6.5 39.1 44.7 16.9 55.6 53.6 21.3 3.8 — 14.1

MH 5.5 13.0 6.0 52.9 4.7 22.3 92.3 19.8 6.2 7.7 —

48.0 61.1 15.5 9.8 71.4 0.7 1.2 33.3 50.7 54.6 —

an appropriate, conservative approach is to restrict estimates of gene flow to within regional groups, where the assumptions of genetic equilibrium, common population histories, and a lack of mutation effect in highly variable markers appear unlikely to be violated. Patterns of gene flow: Among the Madawaska Highlands sample locations (Figure 1, inset), both geographic (i.e., straight-line distance) and aquatic distances were significantly correlated with ( (straight-line r " 0.574, P ! 0.01; aquatic r " 0.511, P ! 0.01). The slopes of the regressions were not significantly different (straight-line slope " 0.73, 95% C.I. 0.35–1.06; aquatic slope " 0.59, 95% C.I. 0.32–0.89), suggesting that aquatic connectivity does not underlie genetic structure at this geographic scale. Pairwise estimates of ( resulted in Nm estimates ranging from 2 to 92 migrants per generation among populations within the Madawaska region (Table 3) and 2 to 16 migrants per generation between populations from the remaining regional comparisons (Figure 5). Within the Madawaska region, extremely high Nm values ()10) were often (but not exclusively) associated with small samples (MH, HA, and KA). Results from the Bayesian analysis of population structure of the eight large Madawaska Highland breeding


J. D. Austin, S. C. Lougheed and P. T. Boag

Figure 3.—Factorial correspondence analysis showing the relative position of 26 breeding aggregations (omitting MC and NI) in multivariate space as defined by the first and second axes. The inset shows relative position of aggregations indicated by X. See text for details.

aggregations (i.e., excluding KA, MH, and HA) suggested that breeding aggregations MP, BG, EB, MR, MD, and MI represent a single genetic population and that DA and MC are independent populations with a high (0.999) probability (Table 4). DA is peripherally isolated from the other breeding aggregations (Figure 1), and MC differs in allele frequency from the other populations (see above). The posterior value of global F ST among Madawaska sites was 0.059, corresponding to an Nm of 3.99. The corresponding global ( (calculated over the same eight predefined populations) was 0.047 (Nm " 5.1). Bayesian estimates of population structure varied from region to region. Breeding aggregations within both the SLINP and the Perth region appear to have independent genetic population structures with a high posterior probability of )0.999 (Table 4). In contrast, breeding aggregations from the Bancroft region and QUBS have a common population structure with high posterior probabilities (0.998 and 0.999, respectively). Finally, the Pembroke locations resulted in a single partition with a high probability (0.999) that contained two distinct clusters

Figure 4.—Scatterplots of (A) pairwise ( vs. geographic distance. Indicated are trends for pairwise patterns over the first 100 km and pairwise comparisons )100 km. Slopes of both partitions are significantly greater than zero. (B) Residuals from a regression of pairwise ( against pairwise distance plotted against pairwise distance to test whether scatter increased with geographic distance. A significant trend is found over the first distance partition but not over the last partition. See text for details. (C) Pairwise linearized ( vs. the logarithm of pairwise geographic distances. The best-fit linear trend line (dashed) is indicated, along with an exponential trend line. The vertical line indicates the 100-km point.

of populations (Table 4). The posterior value of F ST among Pembroke sites was 0.045 (Nm " 5.3), compared with the global ( of 0.067 (Nm " 3.5). All Nm estimates, based on ( or Bayesian population structure, were )2.6 migrants per generation, suggesting moderate to high levels of gene flow over scales of 2–20 km. Analyses based on coalescent theory indicated moderate levels of gene flow between most aggregation pairs from the Madawaska Highlands (Table 5). Unidirectional Nm estimates ranged from less than one to greater than six. Of the 55 pairwise comparisons, 41 had asymmetrical Nm values, meaning the 95% confidence intervals around estimates of Nm did not overlap between pairs of breeding aggregations. Most aggregations alternated between being a net “gainer” of immigrants (i.e., significantly larger incoming Nm values) and a net “pro-

Equilibrium and Gene Flow in Bullfrog


Figure 5.—Pairwise contemporary gene flow and recent migration rates between regional population pairs. Population codes are defined in Table 1. (A) Gene flow among the four population pairs in eastern Ontario. Nm estimates (95% C.I.) from Bayesian F ST estimates are located below the dotted line between populations. Nm estimates from ( are above the dotted line. Directional likelihood estimates of Nm with 95% confidence intervals are also indicated along corresponding arrows. Likelihood estimates of population size (*) are located within population circles. (B) Results from Bayesian analyses of recent migration rates (i.e., proportion of migrants) between the four population pairs in eastern Ontario. Means of the posterior distributions of m (SD) from three independent runs are given. Values within population circles are the proportion of individuals derived from the source population. (C) Historical gene flow estimates between three populations from the Pembroke region (HZ, ML, and WL) are shown. Nm estimated from pairwise ( is presented on dotted lines joining populations. Directional pairwise likelihood estimates of Nm (95% C.I.) are along outer arrows. Likelihood estimates of population size (*) are located within population circles. (D) Bayesian estimates of recent migration between three Pembroke region populations.

ducer” of emigrants, depending on the breeding aggregation to which it was compared. None displayed entirely symmetrical migration patterns across comparisons, and only MH had exclusively larger immigration values across comparisons. As expected likelihood estimates of Nm were weakly negatively correlated with distance (excluding MH, KA, and HA comparisons; r " %0.17, P ! 0.05), depicting a general pattern of IBD, but also demonstrating that asymmetries in Nm, particularly at shorter distances (not shown) can decrease the correlative pattern identified from pairwise (. Although pairwise Nm appear lower for likelihood estimates relative to ( or Bayesian estimates of F ST, the overall immigration rates into individual Madawaska breeding aggregations (summing across pairwise likelihood Nm values) reflect high levels of gene flow (all

Nm )6; Table 5). Unlike pairwise estimates based on F ST where the interdependence of populations often strongly violates the validity of pairwise comparisons (Fu et al. 2003), the coalescent method implemented in MIGRATE estimates the migration rate (M) and population size (*) directly, allowing for the summation across all immigration possible. However, the accuracy of these summations may depend on the number of populations included, as having too few sampled locations (e.g., less than four or five) may result in inflated population size estimates, thereby inflating Nm (see below; Beerli 2004). Results from other regional pairs of aggregations are illustrated in Figure 5A. Gene flow was asymmetrical in three of seven pairwise comparisons (CI-TB, TM-MB, and HZ-ML). Within the Pembroke region, likelihood


J. D. Austin, S. C. Lougheed and P. T. Boag TABLE 4 Bayesian posterior probabilities of regional groupings of breeding aggregations of R. catesbeiana Region Madawaska Bancroft QUBS Perth SLINP Pembroke

Breeding aggregation groupings (MP, MR, MD, EB, BG, MI) (MC) (DA) (WA, HB) (CI, TB) (TM) (MB) (HI) (GI) (HZ, ML) (WL)

FST (SD) 0.056 0.022 0.020 0.056 0.058 0.045

(0.004) (0.001) (0.001) (0.003) (0.009) (0.005)

Posterior probability 0.999 0.998 0.999 0.999 0.999 0.999

Location codes within parentheses represent nondistinct genetic groupings. Within each region, no other combinations of breeding aggregations had a probability )0.01. Posterior probability-derived FST was calculated after Nei (1977).

estimates of Nm were high between distant locations HZ and WL (Figure 5C), in contrast to ( or Bayesian estimates of F ST and recent migration, each of which detected high migration values between neighboring breeding aggregations HZ and ML. This discrepancy may be related to the effect of under-sampling the global population on estimates of * (Beerli 2004). Estimated demographic sizes of both HZ and WL are considerably smaller than that of ML (Ontario Ministry of Natural Resources, unpublished data), although the estimates of * are larger than that in ML (Figure 5). When the number of sampled populations is few (i.e., 2 or 3; Beerli 2004), the effect of unsampled populations on pairwise estimates may be to inflate estimates of * and thus Nm (which is the product of * and M). This pattern is reflected in the divergence in population sizes among smaller regional samples (Figure 5) and the larger Madawaska data set (Table 5). The addition of a “ghost population” to these smaller regional data sets would likely reduce any upward bias in these estimates of Nm (Beerli 2004), although the results from the larger Madawaska data set would be unlikely to change significantly given the robust behavior of the coalescent method with a small sample of the “global” population (Bittner and King 2003; Beerli 2004). Patterns of recent migration: Stability of the Bayesian estimates of recent migration was determined when repeated independent runs reached the same posterior probabilities. For most data sets this took only four runs (including the initial run from which delta values were adjusted). This was the case for all four regional pairs and the three samples from the Pembroke region (see Figure 5, B and D). However, for the Madawaska region, some migration rates still varied highly between analyses after four runs. We reran the Madawaska data set, increasing the number of iterations to 10 + 106 and discarding the first 7 + 106. After three runs, results continued to be inconsistent for the same locations (i.e., MP, EB, MR, and MI) with estimated migrants varying from 1 to 34% between runs (Table 6). This result likely

reflects the lack of genetic structure detected by the Bayesian analysis (see below). As for likelihood estimates of Nm, patterns of recent migration were often asymmetrical between pairs of breeding aggregations, and the pattern of asymmetry was frequently different from that of likelehood estimates of Nm (Tables 5 and 6, Figure 5). In all cases in which stable estimates of migration were obtained, results suggest that where recent migration was detected, it appeared to be very high (!30%) or very low (!3%).


Measuring gene flow through indirect methods [e.g., estimating Nm from F ST (Wright 1951) or one of its analogs (e.g., Nei 1973; Weir and Cockerham 1984; Slatkin 1985)] has been critical to understanding patterns of gene flow in natural populations due to the relative ease of collecting large amounts of data from an array of organisms and to the challenges of detecting long-distance dispersal (let alone gene flow) using direct (e.g., mark-recapture) methods (Slatkin 1985; Koenig et al. 1996). However, despite its wide use, F ST based estimates of Nm have been criticized for having high variance and for the biologically unrealistic infinite island model (Wright 1951) on which it is based (Bossart and Prowell 1998; Whitlock and McCauley 1999). The effect of the interdependence of populations under Wright’s model can have a strong influence on the accuracy of estimates of pairwise F ST (Fu et al. 2003). Likelihood methods (Beerli and Felsenstein 1999, 2001; Vitalis and Couvet 2001) and Bayesian approaches (Wilson and Rannala 2003) permit the use of more complex and “biologically realistic” models that do not share the same interdependence among samples. However, their application has yet to find wide use (but see Congdon et al. 2000; Friesen et al. 2002; Bittner and King 2003) due primarily to their computational demands and the limited understanding of

Equilibrium and Gene Flow in Bullfrog


TABLE 5 Contemporary gene flow estimates between 11 Madawaska region R. catesbeiana breeding aggregations in Figure 1 Nm Population i DA KA MP BG MC HA EB MR MD MI MH


DA → i

0.393 0.357–0.435 0.263 0.225–0.312 0.327 0.314–0.368 0.691 0.616–0.780 0.356 0.320–0.398 0.170 0.149–0.195 0.363 0.317–0.420 0.256 0.230–0.285 0.400 0.360–0.447 0.207 0.187–0.214 0.729 0.615–0.774

— 0.37 0.30–0.46 1.09 0.98–1.23 1.11 0.95–1.28 0.96 0.85–1.08 0.12 0.09–0.15 1.15 1.01–1.31 1.36 1.25–1.49 0.63 0.54–0.62 0.56 0.50–0.64 5.13 4.74–5.54

KA → i

MP → i

BG → i

MC → i

0.11 0.08–0.16 —

1.11 0.99–1.25 1.60 1.45–1.77 —

1.13 1.02–1.26 1.43 1.28–1.58 1.13 1.00–1.26 —

0.69 0.59–0.79 1.11 0.99–1.26 1.89 1.73–2.06 1.19 1.03–1.36 —

1.91 1.75–2.08 2.07 1.85–2.29 0.82 0.72–0.93 0.11 0.08–0.14 1.14 1.00–1.30 0.93 0.83–1.03 0.52 0.44–0.61 0.53 0.47–0.60 2.36 2.10–2.64

2.47 2.25–2.72 2.58 2.39–2.77 0.30 0.25–0.35 2.06 1.87–2.27 1.07 0.96–1.18 2.32 2.14–2.51 0.28 0.23–0.33 2.55 2.27–2.84

0.55 0.46–0.64 1.17 1.07–1.28 1.03 0.89–1.17 1.04 0.94–1.15 1.14 1.02–1.27 0.68 0.60–0.76 2.75 2.47–3.05

0.56 0.48–0.64 2.37 2.16–2.59 1.04 0.93–1.15 1.52 1.37–1.67 0.52 0.46–0.60 3.22 2.92–3.55

Nm Population i DA KA MP BG MC HA EB MR MD MI MH

HA → i

EB → i

MR → i

MD → i

MI → i

MH → i

0.89 0.78–1.01 0.44 0.36–0.53 0.68 0.59–0.79 2.06 1.84–2.29 0.56 0.48–0.66 —

1.41 1.27–1.56 0.43 0.35–0.52 1.13 1.00–1.26 1.02 0.87–1.18 1.51 1.37–1.66 0.70 0.62–0.79 —

1.24 1.11–1.38 2.08 1.90–2.27 1.15 1.02–1.28 3.70 3.41–4.00 1.54 1.40–1.70 0.63 0.56–0.72 3.81 3.54–4.09 —

0.41 0.34–0.50 1.35 1.21–1.51 2.69 2.49–2.89 2.02 1.81–2.25 1.37 1.24–1.52 0.25 0.21–0.30 1.08 0.95–1.24 0.58 0.51–0.67 —

1.11 0.99–1.24 0.58 0.49–0.69 0.39 0.32–0.47 1.80 1.61–2.02 0.96 0.25–1.08 0.46 0.40–0.53 2.96 2.73–3.21 0.62 0.55–0.71 0.95 0.84–1.08 —

2.43 2.25–2.62 0.92 0.81–1.05 1.23 1.10–1.37 2.93 2.67–3.21 1.78 1.63–1.94 1.71 1.58–1.84 0.97 0.84–1.11 1.70 1.56–1.84 1.89 1.73–2.06 2.00 1.87–2.14 —

1.17 1.03–1.33 1.56 1.43–1.69 0.82 0.72–0.94 0.20 0.16–0.24 3.76 3.44–4.11

1.95 1.81–2.10 1.54 1.40–1.69 1.28 1.17–1.39 2.06 1.82–2.32

1.30 1.17–1.44 0.60 0.53–0.68 6.16 5.75–6.61

0.44 0.38–0.51 5.12 4.73–5.52

6.36 5.93–6.81

Total Nm → i 10.53 9.42–11.77 10.31 9.14–11.64 13.62 11.98–14.69 21.06 18.29–22.60 12.99 10.79–13.98 6.18 5.34–6.74 18.10 16.02–19.62 12.11 10.77–13.01 12.63 11.37–13.89 7.09 6.37–7.89 39.47 36.17–42.99

Shown are maximum-likelihood estimates and 95% C.I.s of * and maximum-likelihood estimates of effective number of migrants (Nm) into population i. Migration occurs from populations at top into populations in left column. Total Nm → i is the total estimated migration into population i (sum of all Nm → I, see text).

their robustness to violations of the underlying likelihood and Bayesian models (Neigel 2002). Our results show that these methods appear to provide more precise estimates of genetic structure than do traditional esti-

mates and are likely more accurate, assuming potential confounds and major assumptions are addressed (see below). The pairwise estimates of Nm based on F ST within the


J. D. Austin, S. C. Lougheed and P. T. Boag TABLE 6 Expected proportion of individuals in location i that have location j as their ancestral (past one to three generations) location Population j Population i DA MP BG MC EB MR MD MI









0.989 (0.00) 0.008 (0.00) 0.024 (0.00) 0.015 (0.00) 0.019 (0.01) 0.006 (0.01) 0.015 (0.00) 0.015 (0.01)

0.001 (0.00) 0.777 (0.15) 0.031 (0.04) 0.015 (0.02) 0.008 (0.00) 0.010 (0.01) 0.095 (0.14) 0.066 (0.10)

0.001 (0.00) 0.006 (0.00) 0.680 (0.00) 0.005 (0.00) 0.007 (0.00) 0.006 (0.00) 0.006 (0.00) 0.005 (0.00)

0.001 (0.00) 0.007 (0.00) 0.008 (0.00) 0.905 (0.00) 0.007 (0.00) 0.006 (0.00) 0.007 (0.00) 0.005 (0.00)

0.002 (0.00) 0.008 (0.00) 0.068 (0.09) 0.312 (0.45) 0.781 (0.15) 0.088 (0.13) 0.007 (0.00) 0.023 (0.03)

0.001 (0.00) 0.013 (0.01) 0.053 (0.03) 0.009 (0.00) 0.075 (0.04) 0.777 (0.06) 0.009 (0.00) 0.007 (0.00)

0.002 (0.00) 0.015 (0.02) 0.058 (0.08) 0.005 (0.00) 0.084 (0.12) 0.093 (0.13) 0.693 (0.03) 0.006 (0.00)

0.001 (0.00) 0.160 (0.12) 0.077 (0.05) 0.022 (0.01) 0.016 (0.01) 0.009 (0.00) 0.167 (0.11) 0.872 (0.15)

Shown are mean (SD) migration rates between Madawaska region locations calculated from three independent runs of 10 + 106 iterations, discarding the initial 7 + 106. Underlined values (diagonal) are the average proportion of individuals derived from the source location. Locations with varying values between runs (SD ) 0.05) are italicized.

Madawaska region were almost always )4. However, the relationship between F ST and Nm is nonlinear, and small values of F ST result in Nm estimates that have very high variance (Whitlock and McCauley 1999). In other words, Nm ) 4 cannot be interpreted other than “Nm ) 4.” Because likelihood values are not based on F ST it is more likely that large values of Nm can be interpreted as more precise estimates of Nm. In the smaller regional comparisons, likelihood estimates of Nm were generally higher than those from the Madawaska region. As mentioned above, this likely reflects the influence of sampling only two or three locations. The addition of more samples would improve these estimates, although not many would be required because the coalescent method is fairly robust with only a few sampled populations (Beerli 2004). The relationship between the number of populations and the upward bias in Nm values is also related to the migration rate; in a high-migration system, as appears to be the case with R. catesbeiana, the upward bias is likely increased (Beerli 2004). However, even if estimates of total Nm summed across breeding aggregations are somewhat inflated, the results are ultimately more useful than Nm ) 4. Pairwise values estimated from F ST are not directly comparable with likelihood estimates as the latter are “one-way” estimates, allowing for asymmetry in gene flow, which is common among the breeding aggregations of R. catesbeiana studied here. The nonlinearity between Nm and F ST means that, in a system where asymmetry in gene flow is common, the global F ST -values will severely underestimate Nm (Whitlock and McCauley 1999).

Finally, global estimates based on ( were not consistently related to those based on Bayesian estimates of population structure. Although both are related to F ST, Bayesian estimates presumably reflect the “true” population structure better than breeding aggregations do. Both methods assume symmetrical patterns of gene flow and equal population size, and both likely underestimate the extent of migration. Overall it appears that the likelihood method should provide more accurate estimates of Nm than F ST -based methods. Although both assume the global population has been adequately sampled, the coalescent method appears more robust to violations of this assumption, particularly if more than a few populations are sampled. This greater accuracy is also pronounced if gene flow is asymmetrical, as is likely the case in many organisms. The method is also precise (i.e., small confidence intervals) with even a few loci, and over a greater range of Nm. Likelihood also provides much more information than traditional methods. However, inferences from both likelihood and F ST methods may be equally compromised if the effects of history and nonequilibrium conditions are not addressed. Secondary contact: Large geographic-scale analyses can lead to erroneous conclusions about the patterns of genetic structure in the absence of a historical perspective. Mitochondrial sequence data from range-wide R. catesbeiana populations illustrate the impact of postglacial colonization on contemporary mtDNA genetic structure in northern populations, with multiple refugial lineages occurring across a longitudinal gradient

Equilibrium and Gene Flow in Bullfrog

from southwestern Ontario eastward (Austin et al. 2004). In the absence of this historical information, the observed pattern of differentiation among eastern and western samples at microsatellite loci, revealed by both FCA and the relative contributions to overall allelic diversity, might have been attributed to isolation by distance. Inadequate sampling of southwestern Ontario precluded an analysis of clinal allelic variation to detect the relative influence of refugial lineages on population structure from across the range considered here (e.g., Turgeon and Bernatchez 2001). Further geographic sampling will be required to adequately determine the scale and extent of admixture in R. catesbeiana relative to other species in this important phylogeographic region (e.g., Austin et al. 2002; Zamudio and Savage 2003). Range expansion: The influence of history is apparent not only in the mixing of separate refugial lineages coming into secondary contact, but also in the imprint of recent range expansion. Rapid leading-edge dispersal of colonizing individuals should result in repeated bottlenecks and genetic homogenization over large geographic areas (Hewitt 1996). Numerous empirical studies suggest that northern temperate populations are likely not at equilibrium (e.g., King and Lawson 1995; Comes and Abbott 1998; Hutchinson and Templeton 1999; Latta and Mitton 1999; Bittner and King 2003) due to insufficient time since colonization. The time to reach drift-migration equilibrium depends primarily on the migration rate (proportional to 1/m) or the effective population size, whichever is greatest (Slatkin 1994). Given the effective population sizes and high migration rates detected in R. catesbeiana populations (Table 5 and 6; Figure 5), the scale of equilibrium inferred here could have been reached over the period since eastern Ontario was colonized (i.e., 1500– 2000 generations; Karrow and Calkin 1985; Holman 1995). Further, if populations are replenished through high levels of migration, as our data suggest, frequent fluctuations in population size (characteristic of amphibians in general; Pechmann et al. 1991; Meyer et al. 1998) may not have a significant long-term effect on effective population size. For example, assuming an average mutation rate of 10%3 (e.g., Dallas 1992; Weber and Wong 1993), effective population sizes examined here range from 170 to )7000. Such large effective population sizes may permit the maintenance of equilibrium conditions by buffering populations from the effects of demographic stochasticity, particularly if bottlenecks are not prolonged. We confidently interpreted a pattern of equilibrium among populations within regions, whereas divergence between populations separated by ) !100 km may still reflect the relative importance of drift over gene flow (Hutchinson and Templeton 1999, case IV). This pattern may also simply reflect the effect of geography, particularly if regional groups are separated by habitat that is relatively unfavorable to dispersal, or it may be due to the high rate of mutation in microsatellite mark-


ers. Isolation by distance is often not detected in studies where population samples are few or the geographic scale is large (e.g., Comes and Abbott 1998; Peterson and Denno 1998; Latta and Mitton 1999). However, our study demonstrates that equilibrium conditions may be found in northern regions if enough data are collected and the proper scale is examined. Reconciling longer-term, contemporary gene flow and recent migration rates: Given the pattern of equilibrium among regional populations, estimating gene flow at this scale is biologically meaningful (Templeton 1998). Comparing longer-term gene flow (defined as averaged gene flow between populations over the past n generations at which populations were at equilibrium) with recent migration is valuable as it may provide confidence in historical estimates (if congruent patterns exist). Alternatively, if confidence in the Nm estimates is justified, differences in the geographic pattern of Nm vs. m, as estimated here, may be used to examine the effect of recent natural or anthropogenic changes to the landscape. In this sense, the hierarchical temporal approaches to examining patterns of gene flow and migration or gene flow with direct estimates of dispersal are highly complimentary. Migration rates between some pairs of R. catesbeiana populations were often asymmetrical and large, reflecting direct estimates of dispersal in ranid frogs that suggest seasonal movement over a scale of kilometers (e.g., Marsh and Trenham 2001; Pilliod et al. 2002). Assuming some of the direct estimates of dispersal translate into gene flow, breeding aggregations separated by only a few kilometers may often not represent independent populations. This conclusion is supported by our results from the Bayesian analysis of population structure that suggest that many populations separated by up to tens of kilometers are not genetically distinct. The grouping of Madawaska breeding aggregations together in the Bayesian analysis of population structure also explains the instability of some of the posterior probabilities of m. Because these breeding aggregations are not genetically independent, the posterior probability of an individual being assigned as a hybrid from this region may be split among these aggregations. Wherever Bayesian analysis of population structure suggested that breeding aggregations share a common origin, there were high values of m and high gene flow, although directional likelihood estimates of gene flow were relatively low in some instances. In many cases the proportion of individuals assumed to have originated in their source population was approximately two-thirds, which is the minimum proportion of nonmigrants allowed in BAYESASS (Wilson and Rannala 2003). In these cases, migration is likely underestimated. Estimates of m cannot be interpreted the same as those of Nm, the latter being a measure of allelic establishment whereas the former reflects dispersal (although it may also reflect the offspring of recent migrants). Despite the high levels of migration detected


J. D. Austin, S. C. Lougheed and P. T. Boag

here, our values may still be underestimates if dispersal in R. catesbeiana is biased in favor of females as is suggested by microsatellite data (Austin et al. 2003). Most samples in the present study, including some with high migrant values, were heavily biased in favor of calling males due to the timing and method of sampling (see materials and methods). Anthropogenic influences: With R. catesbeiana, an important consideration is the impact of anthropogenic dispersal confounding estimates of gene flow. The success of introduced R. catesbeiana across the globe (e.g., Telford 1960; Lanza 1962; Green 1978; Gasc et al. 1997; Hedges 1999) attests to the species’s ability to adapt to novel environments. However, the propensity of introduced R. catesbeiana to compete with native conspecifics is not known. If frequent anthropogenic dispersal occurs, introduced genotypes (assuming no selective barriers exist) should erase patterns of isolation by distance. However, empirical evidence from other species suggests that individuals introduced into established populations are typically more likely to disperse or may have lower fitness than residents (Endler 1977 and references therein; Anderson 1989; Reinert and Rupert 1999). Results from the FCA (also the Bayesian estimate of population structure) highlighted one location within the Madawaska region (MC) as having a strong influence on the global pattern of genetic variance due to the high frequency of private and globally rare alleles. Given its proximity to neighboring samples these private alleles may be recently introduced from elsewhere in the range. No other populations for which we estimated gene flow had evidence of introduced alleles (specifically, high frequencies of novel alleles), suggesting that unless anthropogenic dispersal is occurring frequently at fine geographic scales it is likely not a major factor within the populations studied here. Discriminating between anthropogenic and natural influences on gene flow is an increasingly important aspect of evolutionary (to eliminate its impact on interpreting natural processes) and conservation studies (in terms of anthropogenic disturbance to the landscape; e.g., Westerbergh and Saura 1994; Dawson et al. 1996; Fleischer et al. 2001; Mohanty et al. 2001; Church et al. 2003). Conclusion: Gene flow is high among sampled R. catesbeiana breeding aggregations that are interpreted to be at or near equilibrium, on average in excess of four individuals per generation. Even directional likelihood estimates of Nm were often greater than one migrant per generation. There was also large variance in the amount of gene flow and dispersal among pairs of populations representing similar geographic distances, likely reflecting the importance of landscape effects on shaping genetic structure. Given our results, gene flow appears to be an important cohesive force in this species. Our ability to test for violations of major assumptions prior to estimating, and the availability of sophisticated methods for calculating, Nm should lead to increased

confidence in interpreting the evolutionary role of gene flow vs. selection in maintaining “species boundaries.” We thank the Ontario Ministry of Natural Resources (OMNR) and St. Lawrence Islands National Park for providing samples from their population-monitoring programs. J. Brown assisted greatly with the operation of MIGRATE. This article was greatly improved by the comments of two anonymous reviewers. P. Beerli, A. Bohonak, D. Hutchinson, R. Petit, R. Rousset, M. Sillanpaa, and G. Wilson graciously answered our many queries. Financial support was provided by the OMNR, National Sciences and Engineering Research Council of Canada (NSERC) operating grants to P.T.B. and S.C.L., an NSERC Postgraduate Scholarship, and a Province of Ontario Graduate Scholarship to J.D.A. Additional funding for fieldwork was provided by the American Museum of Natural History—Theodore Roosevelt Memorial Fund and the Mountain Equipment Co-op Environment Fund.

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