# Testing Hypotheses of Diversification in Panamanian Frogs and Freshwater Fishes Using Hierarchical Approximate Bayesian Computation with Model Averaging

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## Abstract

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## 1. Introduction

_{e}), mutation rate, and generation time create high variation in gene tree topologies and their depths (correlated with timing of their divergences; e.g., [11,19]), what appear as multiple divergence events may actually reflect the obscured signal of a single event [20]. Thus, comparing independent gene-tree depths and divergence time estimates can lead to erroneous inferences of multiple vicariance events.

## 2. Materials and Methods

#### 2.1. Taxon Sampling and Molecular Data

#### 2.2. Genetic Diversity and Neutrality

#### 2.3. Estimating Gene-Tree Depths Using Bayesian Dating

_{MRCA}s) and their Bayesian credible intervals for each species/lineage using BEAST version 1.8.2 [65]. BEAST runs (100 million generations, sampled every 4000; ‘burn-in’ = 10%) started from UPGMA (unweighted pair group method with arithmetic mean) tree topologies, employed HKY + Γ + I site models, and used coalescent constant size tree priors [66]. We evaluated the fit of different molecular clock models and investigated clock-likeness of the data by comparing results of strict-clock and relaxed-clock (uncorrelated lognormal model; [67]) runs on each dataset. Due to uncertainty over frog mtDNA mutation rates, we specified a range of 0.1–1.3% lineage

^{−1}Myr

^{−1}(per million years) in the frog runs spanning rates of protein-coding mtDNA gene evolution documented in a broader mtDNA dataset from one of our focal taxa [51]. This ‘frog rate’ spans Macey et al.’s [68] Mongolian toad (Bufo bufo) rate of 0.69% lineage

^{−1}Myr

^{−1}, which is commonly used to date patterns of herpetofaunal diversification [51]. Likewise, we specified a ‘fish rate’ of 0.17–1.4% lineage

^{−1}Myr

^{−1}in fish runs, a range spanning mutation rates estimated in 15 previous studies of teleost freshwater fish mtDNA (refs. in [69,70]). Rate ranges were supplied to the program as uniform priors. We summarized posterior distributions and ensured convergence and adequate effective sample sizes (all ESS >> 200) using Tracer version 1.5 (available at: http://beast.bio.ed.ac.uk/Tracer). In TreeAnnotator version 1.8.2, we summarized the posterior distribution of trees from each run by calculating a maximum clade credibility (MCC) tree annotated with median node ages from a sample of 5000 post-burn-in trees obtained using the ‘BEASTPostProc.sh’ script in PIrANHA version 0.1.4 [71].

#### 2.4. Tests for Synchronous Diversification

_{1}–M

_{4}), to compare using model averaging. Each model class consisted of one of two uniformly distributed priors on population divergence times (τ), ancestral population size (θ

_{A}), and daughter population size parameters (θ

_{D}; Table 2). Second, we obtained 5 million random (simulated) samples from each model class specified by a discrete uniform hyperprior distribution Pr(M

_{k}) = 1/4. We visually checked for efficient prior sampling by conducting principal components analysis on 1000 prior draws from each model class in R. Third, we obtained the ABC joint posterior distribution using the default summary statistic vector (D) from MTML-msBayes and rejection sampling to identify the 1000 closest Euclidean distances between the observed summary statistics (D*) for the data and D

_{i}calculated from 20 million random draws across all four priors (M

_{1}–M

_{4}). However, prior to rejection sampling, we rescaled the dispersion index of population divergence times Ω (=Var[τ]/E[τ]; the ratio of variance to the mean of the divergence times) and the mean assembly-wide divergence time, E[τ], from models with smaller upper θ

_{D}prior bound values (frog and fish M

_{1}, M

_{2}, and M

_{4}) to have the same coalescent units as the other model, M

_{3}[24]. Resulting estimates of Ω and E[τ] were weighted by Bayesian model averaging [24]. Last, we conducted hypothesis testing by comparing hyperposterior probability distributions of Ω estimates, to determine whether the data supported single or multiple diversification periods.

_{10}Bayes factors under the parameter thresholds above while accounting for prior support for the hypotheses, using B

_{10}“weight of evidence” criteria in Jeffreys [72] and Kass and Raftery [73]. We estimated mean assemblage-wide divergence times by converting model-averaged E[τ] estimates (in coalescent units of 4N

_{ave}generations) to absolute time (T

_{div}) using the equation T

_{div}= E[τ] × (θ

_{ave}/μ), where μ is the assumed mutation rate per site per generation and θ

_{ave}(per site) is the mean of the upper θ prior. Conversions used mutation rates equivalent to 0.7% lineage

^{−1}Myr

^{−1}and 0.785% lineage

^{−1}Myr

^{−1}, the median rates of uniform ‘frog rate’ and ‘fish rate’ priors used in our BEAST analyses. We assumed an average generation time of 1 year, which was also used in previous studies of our focal taxa ([51,52,54]; Michael J. Ryan, pers. comm.), and we acknowledge that divergence time estimates are sensitive to generation times. Shell and R scripts used during our MTML-msBayes analyses are accessioned in Mendeley Data [74].

## 3. Results

#### 3.1. Genetic Diversity and Neutrality

#### 3.2. Estimating Gene-Tree Depths Using Bayesian Dating

_{MRCA}s for each of the seven population-pairs were consistent across multiple BEAST runs, which had ESS values >500 for nearly all parameters. Results also were similar across strict-clock and relaxed-clock runs; however, we only present the results of the strict-clock analyses because 95% highest posterior densities (HPDs) of ‘ucld.stdev’ (standard deviation of the relaxed clock) abutted zero, indicating that the data could not reject strict clock models. The mitochondrial MCC time trees had variable gene-tree depths (Figure 3), and geometric mean t

_{MRCA}estimates (closer to peak likelihood values than the means) varied substantially across species/lineages, ranging from 1.71 Ma in A. coeruleopunctatus to 10.79 Ma in C. crassidigitus (Figure 4; frog geometric mean t

_{MRCA}range: 3.78–10.80 Ma; fish geometric mean t

_{MRCA}range: 1.71–4.88 Ma). Consistent with patterns of DNA polymorphism above, t

_{MRCA}s of the fish lineages exhibited less variation with a much narrower region of overlap in their coalescence times (1.92–5.57 Ma) as compared with that of the frog lineages (3.88–14.39 Ma), although the frog t

_{MRCA}s also overlapped substantially (Figure 4). Hereafter, geometric mean values are relied upon because they were closer to peak likelihood parameter estimates.

#### 3.3. Tests for Synchronous Diversification

_{10}= 1.14 for Ω < 0.01 versus Ω > 0.01; fish B

_{10}= 1.33 for Ω < 0.01 versus Ω > 0.01) as well as the asynchronous diversification model (frog B

_{10}= 0.88 for Ω > 0.01 versus Ω < 0.01; fish B

_{10}= 0.75 for Ω > 0.01 versus Ω < 0.01). Bayes factors were technically less than 1 for two or more divergences, but at best this provides very weak negative evidence for asynchronous divergence [72,73]. Likewise, posterior probabilities for the best-supported models were low (<0.5) and corresponding Bayes factors for synchronous diversification were weak, being approximately less than or equal to 1.

## 4. Discussion

#### 4.1. Comparative Phylogeography of Panamanian Frog and Fish Assemblages

_{MRCA}s for the taxon-pairs (Figure 4), strong peaks in the Ω posteriors near zero (Figure 5) and credible intervals including zero (Table 2), and peak-likelihoods and credible intervals of assemblage E[τ]. By contrast, Bayes factor model selection indicated that the data provide only a marginal accumulation of evidence in favor of synchronous diversification and against the null scenario of asynchronous diversification. The msBayes approach has been shown to correctly reject synchronous diversification using only mtDNA and summary statistics such as those used herein (e.g., [23,24,25]), and visual checks suggested that our priors were efficient samplers of the data (Figure S1). Moreover, we avoided the problem of overly broad or narrow τ priors (e.g., in [26,32]), which can cause ABC samplers to explore parameter space exceeding saturation effects on mitochondrial genes [24], by matching the upper bounds of these priors to empirical estimates from the data. As a result, we conclude that additional genetic data from unlinked loci or additional species, or improved methods for hABC or Bayes factor estimation, are needed to more confidently assess the timing and number of events at the WPI break in these taxa. Nevertheless, the much narrower credible intervals of our assemblage divergence times relative to the Bayesian gene-tree depths inferred in BEAST (Figure 3 and Figure 4) indicate that accounting for coalescent processes and changes in population sizes through time in our models yielded much more precise estimated divergence times across the WPI break than were previously available. Assuming that peaks in Ω and E[τ] contain one or multiple clusters of population divergence events, and acknowledging limitations and caveats of our mtDNA data (see Introduction and Section 4.2 below), we use our Bayesian assemblage E[τ] estimates to draw broad conclusions about the timing of diversification in these two assemblages and conduct hypotheses tests. We also discuss implications of our results for understanding the historical biogeography and diversification of Panamanian frog and freshwater fish species assemblages.

_{MRCA}s slightly older than that of E. pustulosus but younger than that of C. crassidigitus (Figure 3). In turn, C. crassidigitus (like C. talamancae) is considered more ecologically specialized, preferring wet forest habitat more so than its dry-forest congeners (i.e., C. fitzingeri; [42]). That the C. crassidigitus gene tree extends farthest backward in time thus seems to suggest this species experienced long-term isolation and persistence in preferred habitats, rather than an ability to tolerate climatic or vegetational shifts. However, whereas all the other frog species are egg-layers, Craugastor dirt frogs are direct-developing species that readily reproduce, and their local population sizes can therefore be notoriously large [82]. Given the direct relationship between N

_{e}and time to coalescence from coalescent theory, this contrast in life-history strategies would suggest that on one hand C. crassidigitus may have been superior at colonizing open niches or patches and spread throughout isthmian wet forest habitats more easily than the other taxa, while on the other hand its t

_{MRCA}estimate may also be inflated due to large ancestral N

_{e}[19].

_{MRCA}estimates for all three fish species/lineages fell within the predicted interval of diversification (Figure 3 and Figure 4). Peak posterior distributions from hABC model-averaging (e.g., Figure 5) also suggested that the focal fish species/lineages most likely diversified across the WPI break 1.36 Ma in the early Pleistocene, with Bayesian credible intervals ranging from early–late Pleistocene. This time period correlates best to the ‘Calabrian’ age (1.806–0.781 Ma; [83]), a time of 41-kyr periodicity of Pleistocene glaciations with drier and cooler-than-present conditions but less-extreme climatic oscillations than those following 800 ka [75,84]. Nevertheless, glacial periods vastly dominated the Calabrian to present, such that the Panama isthmus would have experienced many glacio-eustatic cycles but spent the majority of time since 1.8 Ma under glacial conditions with lowered sea levels and exposed continental shelf habitats. Eustatic sea-level curves give no convincing evidence that the oceans reached modern sea levels for any substantial period of time (e.g., >10–20 kyr) since the Calabrian, and the next eustatic sea-level highstand is not registered in the geological record until ~550–390 ka [76,81]. Geological patterns and processes are also consistent with decreased likelihood of fish dispersal across the WPI break zone since the Calabrian. In the break zone, the Pacific continental shelf becomes narrower (~0–40 km), tapering to the western Azuero peninsula coastline before being bisected by Cébaco and Coiba islands at the nearby Gulf of Montijo draining Soná peninsula (Figure 1). To evaluate the impact of lowered sea levels during Pleistocene glaciations on drainage connectivity in this area, we obtained a GIS model predicting paths of LGM paleo-drainages over modern bathymetry using ArcMap (courtesy of Peter J. Unmack, University of Canberra). The GIS model suggests that rivers draining to the west versus east of Soná peninsula did not anastomose over the continental shelf during the LGM (Figure 1), and possibly also preceding glaciations. Overall, our results combined with external environmental data suggest that a relatively stable geological setting at the Soná peninsula barrier has aided the historical isolation of drainage basins, maintaining fish lineage divergences at the WPI break during lower seas of the Calabrian to present.

#### 4.2. Caveats and Potential Limitations

#### 4.2.1. Mitochondrial DNA

#### 4.2.2. Migration and “Secondary Contact”

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Supplementary Methods

#### Appendix A.1.1. Taxon Sampling, Molecular Data, and Outgroup Details

_{MRCA}s in BEAST, tests for simultaneous diversification in MTML-msBayes, and our IMa2 analyses of community divergence. However, it was necessary to specify outgroup taxa in our analyses evaluating whether the data were consistent with predictions of the neutral model of molecular evolution [91]. To this end, we conducted MK tests, which test for deviations of the ratio of replacement (nonsynonymous fixed; RI) to synonymous fixed (SI) substitutions within species from that between species. Specifically, the SI:RI ratio from patterns of substitutions within one species (e.g., one of our focal population-pair datasets) is compared with that of the between-species patterns yielded from comparison to a close relative (e.g., a congeneric outgroup or sister species of one of our focal taxa). In the implementation of the MK test in DnaSP, substitution patterns in an intraspecific dataset are compared against the one or multiple sequences in an outgroup species dataset, and a non-significant difference between the two rations based on two-tailed Fisher’s exact tests is taken as evidence of neutrality. Next, we list outgroups used in MK tests for each population-pair dataset as well as references to studies used to determine the appropriate outgroups. We also provide GenBank accession numbers for outgroup sequences in parentheses, and all outgroup sequences were homologous to those of the focal taxon dataset. Based on phylogenetic analyses in Robertson et al. [54] and Robertson & Zamudio [53], we used one 16S-ND1 sequence of the congener Agalychnis saltator (GenBank GQ366296, [92]) in our MK test of the A. callidryas dataset. Based on phylogenetic analyses in Crawford et al. [42], we used 12 composite cytb-cox1 sequences of the congener Craugastor fitzingeri (GenBank DQ350193–198, DQ350236–241, [42]; EF635371, EF629419–423, EF629462, EF629458, EF629459, EF629455, EF629453, other studies cited in [42]) in our MK test of the C. crassidigitus dataset. Based on Robertson et al. [54], we used one composite sequence of 16S, tRNA-Leu, and ND1 genes from the congener Dendropsophus microcephalus (GenBank AY819503, [93]) as the outgroup in our MK test of the D. ebraccatus dataset. Based on Weigt et al. [51], we used one congeneric Engystomops petersi cox1 sequence from that same study (GenBank DQ120042) as the outgroup in our MK test of the E. pustulosus dataset. Based on McCafferty et al. [54], we used eight ATPase6/8 sequences from congener Andinoacara rivulatus (GenBank JX677777–784, [94,95]) as the outgroup sequences in our MK tests of the A. coeruleopunctatus dataset. Based on results in Bermingham and Martin [9] and Martin and Bermingham [55], we used composite ATP6/8, cox1 sequences from six individuals of the “type B” Pimelodella chagresi lineage (a cryptic species lineage discovered in that study; GenBank AF040388, AF040407–409, AF040412, AF040415, AF040484–489) as the outgroup sample in our MK test of the P. chagresi population-pair dataset. Last, based on Bermingham and Martin [9], we used composite ATP6/8, cox1 sequences from three individuals of the congener Roeboides meeki (GenBank AF040522–524 and AF040559–561 [9]) as the outgroup sample in our MK test of the R. occidentalis–R. guatemalensis population-pair dataset.

#### Appendix A.1.2. Supplementary MTML-msBayes Methods

#### Appendix A.2. Supplementary Results

#### Appendix A.2.1. Additional Genetic Diversity and Neutrality Results and Discussion

#### Appendix A.2.2. Additional MTML-msBayes Results and Discussion

_{2}mode Var[τ] = 3.89 × 10

^{−4}; model-averaging Var[τ] = 3.85 × 10

^{−4}, estimated from hyperparameter modes) and freshwater fishes (M

_{2}mode Var[τ] = 0.0015; model-averaging Var[τ] = 9.63 × 10

^{−5}, estimated from hyperparameter modes). However, variance of the modal τ values from model averaging was greater than that from the best-supported models.

Parameter | Description | Prior Distribution |
---|---|---|

A. Hyperparameters | ||

Ω | Dispersion index of divergence times, Var[τ]/E[τ] (ratio of variance to mean), across Y taxon/population-pairs | Set by Y, τ_{max}, and Ψ |

E[τ] | Mean multi-species (i.e., assembly-wide) divergence time across Y | Set by Y, τ_{max}, and Ψ |

Ψ | Number of distinct divergence times across Y | Discrete uniform [1, Y] |

S | Vector of mutation rate scalars to accommodate among-locus mutation rate heterogeneity | Gamma (with shape and scale parameters α and 1/α, respectively) |

α | Shape parameter of the gamma distribution | Uniform (1, 20) |

B. Parameters | ||

τ | Divergence time in units of 4N generations | Uniform (0.0, τ_{max}) |

θ = 4Nµ | Population size (mutation) parameter where N is average population size of two daughter populations, µ is the per-site mutation rate | Uniform (θ_{min}, θ_{max}) |

θ_{A} | Ancestral effective population size (mutation) parameter | Uniform (0.01, θ_{max} N_{anc-max}) |

θ_{A1}, θ_{A2} | Ancestral effective population size (mutation) parameters for daughter populations 1 and 2 over ancestral period (from time τ to τ_{B}) | Uniform (0.01, θ_{B1}), (0.01, θ_{B2}) |

θ_{B1}, θ_{B2} | Effective population size (mutation) parameters for daughter populations 1 and 2 over recent period (from time τ_{B} to 0.0, the present time) | Uniform (0.01 θ, 1.99θ), and where θ_{B2} = 2θ − θ_{B1} |

τ_{B1}, τ_{B2} | Times at which θ_{A1} and θ_{A2} experience exponential growth into populations with sizes of θ_{B1} and θ_{B2} | Uniform (0.0, τ), with τ_{B1} = τ_{B2} |

M = Nm | Effective migration rate, where m is the probability of symmetric migration between pairs of daughter populations | Uniform (0.0, M_{max}) |

r | Per-locus mutation rate scalar | fixed |

p | Per-locus ploidy and/or generation time scalar | p |

## References

- Avise, J.C.; Arnold, J.; Ball, R.M.; Bermingham, E.; Lamb, T.; Neigel, J.E.; Reeb, C.A.; Saunders, N.C. Intraspecific phylogeography: The mitochondrial DNA bridge between population genetics and systematics. Annu. Rev. Ecol. Syst.
**1987**, 18, 489–522. [Google Scholar] [CrossRef] - Avise, J.C. Phylogeography: The History and Formation of Species; Harvard University Press: Cambridge, MA, USA, 2000. [Google Scholar]
- Kidd, D.M.; Ritchie, M.G. Phylogeographic information systems: Putting the geography into phylogeography. J. Biogeogr.
**2006**, 33, 1851–1865. [Google Scholar] [CrossRef] - Soltis, D.E.; Morris, A.B.; Jason, M.; McLachlan, S.; Manos, P.S.; Soltis, P.S. Comparative phylogeography of unglaciated eastern North America. Mol. Ecol.
**2006**, 15, 4261–4293. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bagley, J.C.; Johnson, J.B. Phylogeography and biogeography of the lower Central American Neotropics: Diversification between two continents and between two seas. Boil. Rev.
**2014**, 89, 767–790. [Google Scholar] [CrossRef] [PubMed] - Arbogast, B.S.; Kenagy, G.J. Comparative phylogeography as an integrative approach to historical biogeography. J. Biogeogr.
**2001**, 28, 819–825. [Google Scholar] [CrossRef] - Hickerson, M.J.; Carstens, B.C.; Cavender-Bares, J.; Crandall, K.A.; Graham, C.H.; Johnson, J.B.; Rissler, L.; Victoriano, P.F.; Yoder, A.D. Phylogeography’s past; present; and future: 10 years after Avise. 2000. Mol. Phylogenet. Evol.
**2010**, 54, 291–301. [Google Scholar] [CrossRef] [PubMed] - Bermingham, E.; Avise, J.C. Molecular zoogeography of freshwater fishes in the south-eastern United States. Genetics
**1986**, 113, 939–965. [Google Scholar] [PubMed] - Bermingham, E.; Martin, A.P. Comparative mtDNA phylogeography of Neotropical freshwater fishes: Testing shared history to infer the evolutionary landscape of lower Central America. Mol. Ecol.
**1998**, 7, 499–517. [Google Scholar] [CrossRef] [PubMed] - Sullivan, J.; Arellano, E.; Rogers, D. Comparative phylogeography of Mesoamerican highland rodents: Concerted versus independent response to past climatic fluctuations. Am. Nat.
**2000**, 155, 755–768. [Google Scholar] [CrossRef] [PubMed] - Avise, J.C. Gene trees and organismal histories: A phylogenetic approach to population biology. Evolution
**1989**, 43, 1192–1208. [Google Scholar] [CrossRef] [PubMed] - Edwards, S.V.; Beerli, P. Perspective: Gene divergence; population divergence; and the variance in coalescence time in phylogeographic studies. Evolution
**2000**, 54, 1839–1854. [Google Scholar] [CrossRef] [PubMed] - Hey, J.; Machado, C.A. The study of structured populations—New hope for a difficult and divided science. Nat. Rev. Genet.
**2003**, 4, 535–543. [Google Scholar] [CrossRef] [PubMed] - Kuo, C.H.; Avise, J.C. Phylogeographic breaks in low-dispersal species: The emergence of concordance across gene trees. Genetica
**2005**, 124, 179–186. [Google Scholar] [CrossRef] [PubMed] - Irwin, D.E. Local adaptation along smooth ecological gradients causes phylogeographic breaks and phenotypic clustering. Am. Nat.
**2012**, 180, 35–49. [Google Scholar] [CrossRef] [PubMed] - Zink, R.M.; Barrowclough, G.F. Mitochondrial DNA under siege in avian phylogeography. Mol. Ecol.
**2008**, 17, 2107–2121. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kubatko, L.S.; Carstens, B.C.; Knowles, L.L. STEM: Species tree estimation using maximum likelihood for gene trees under coalescence. Bioinformatics
**2009**, 25, 971–973. [Google Scholar] [CrossRef] [PubMed] - Heled, J.; Drummond, A.J. Bayesian inference of species trees from multilocus data. Mol. Boil. Evol.
**2010**, 27, 570–580. [Google Scholar] [CrossRef] [PubMed] - Hudson, R.R. Gene genealogies and the coalescent process. Oxf. Surv. Evol. Boil.
**1990**, 7, 1–44. [Google Scholar] - Riddle, B.R.; Hafner, D.J. A step-wise approach to integrating phylogeographic and phylogenetic biogeographic perspectives on the history of a core North American warm desert biota. J. Arid. Environ.
**2006**, 66, 435–461. [Google Scholar] [CrossRef] - Beaumont, M.A.; Zhang, W.; Balding, D.J. Approximate Bayesian computation in population genetics. Genetics
**2002**, 162, 2025–2035. [Google Scholar] [PubMed] - Hickerson, M.J.; Stahl, E.; Takebayashi, N. msBayes: A pipeline for testing comparative phylogeographic histories using hierarchical approximate Bayesian computation. BMC Bioinform.
**2007**, 8, 268. [Google Scholar] [CrossRef] [PubMed] - Hickerson, M.J.; Stahl, E.; Lessios, H.A. Test for simultaneous divergence using Approximate Bayesian Computation. Evolution
**2006**, 60, 2435–2453. [Google Scholar] [CrossRef] [PubMed] - Hickerson, M.J.; Stone, G.N.; Lohse, K.; Demos, T.C.; Xie, X.; Landerer, C.; Takebayashi, N. Recommendations for using msBayes to incorporate uncertainty in selecting an ABC model prior: A response to Oaks et Al. Evolution
**2014**, 68, 284–294. [Google Scholar] [CrossRef] [PubMed] - Huang, W.; Takebayashi, N.; Qi, Y.; Hickerson, M.J. MTML-msBayes: Approximate Bayesian comparative phylogeographic inference from multiple taxa and multiple loci with rate heterogeneity. BMC Bioinform.
**2011**, 12, 1. [Google Scholar] [CrossRef] [PubMed] - Leaché, A.D.; Crews, S.C.; Hickerson, M.J. Two waves of diversification in mammals and reptiles of Baja California revealed by hierarchical Bayesian analysis. Boil. Lett.
**2007**, 3, 646–650. [Google Scholar] [CrossRef] [PubMed][Green Version] - Barber, B.R.; Klicka, J. Two pulses of diversification across the Isthmus of Tehuantepec in a montane Mexican bird fauna. Proc. R. Soc. Lond. B Boil. Sci.
**2010**, 277, 2675–2681. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bell, R.C.; MacKenzie, J.B.; Hickerson, M.J.; Chavarría, K.L.; Cunningham, M.; Williams, S.; Moritz, C. Comparative multi-locus phylogeography confirms multiple vicariance events in co-distributed rainforest frogs. Proc. R. Soc. Lond. B Boil. Sci.
**2011**, 279, 991–999. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dolman, G.; Joseph, L. A species assemblage approach to comparative phylogeography of birds in southern Australia. Ecol. Evol.
**2012**, 2, 354–369. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bagley, J.C.; Johnson, J.B. Testing for shared biogeographic history in the lower Central American freshwater fish assemblage using comparative phylogeography: Concerted, independent, or multiple evolutionary responses? Ecol. Evol.
**2014**, 4, 1686–1705. [Google Scholar] [CrossRef] [PubMed] - Smith, B.T.; Harvey, M.G.; Faircloth, B.C.; Glenn, T.C.; Brumfield, R.T. Target capture and massively parallel sequencing of ultraconserved elements for comparative studies at shallow evolutionary time scales. Syst. Boil.
**2013**, 63, 83–95. [Google Scholar] [CrossRef] [PubMed] - Oaks, J.R.; Sukumaran, J.; Esselstyn, J.A.; Linkem, C.W.; Siler, C.D.; Holder, M.T.; Brown, R.M. Evidence for climate-driven diversification? A caution for interpreting ABC inferences of simultaneous historical events. Evolution
**2013**, 67, 991–1010. [Google Scholar] [CrossRef] [PubMed] - Bagley, J.C. Understanding the Diversification of Central American Freshwater Fishes Using Comparative Phylogeography and Species Delimitation; Brigham Young University: Provo, UT, USA, 2014. [Google Scholar]
- Oaks, J.R. An improved approximate-Bayesian model-choice method for estimating shared evolutionary history. BMC Evol. Boil.
**2014**, 14, 150. [Google Scholar] [CrossRef] [PubMed] - Oaks, J.R.; Linkem, C.W.; Sukumaran, J. Implications of uniformly distributed; empirically informed priors for phylogeographical model selection: A reply to Hickerson et al. Evolution
**2014**, 68, 3607–3617. [Google Scholar] [CrossRef] [PubMed] - Papadopoulou, A.; Knowles, L.L. Species-specific responses to island connectivity cycles: Refined models for testing phylogeographic concordance across a Mediterranean Pleistocene Aggregate Island Complex. Mol. Ecol.
**2015**, 24, 4252–4268. [Google Scholar] [CrossRef] [PubMed] - Overcast, I.; Bagley, J.C.; Hickerson, M.J. Improving approximate Bayesian computation tests for synchronous diversification by buffering divergence time classes. BMC Evol. Boil.
**2017**, 17, 203. [Google Scholar] - Savage, J.M. The origins and history of the Central American herpetofauna. Copeia
**1966**, 1966, 719–766. [Google Scholar] [CrossRef] - Savage, J.M. The enigma of the Central American herpetofauna: Dispersals or vicariance? Ann. Mol. Bot. Gard.
**1982**, 69, 464–547. [Google Scholar] [CrossRef] - Savage, J.M. The Amphibians and Reptiles of Costa Rica: A Herpetofauna between Two Continents, Between Two Seas; University of Chicago Press: Chicago, IL, USA, 2002. [Google Scholar]
- Vanzolini, P.E.; Heyer, W.R. The American herpetofauna and the interchange. In The Great American Biotic Interchange; Stehli, F.G., Webb, S.D., Eds.; Plenum Press: New York, NY, USA, 1985; pp. 475–487. [Google Scholar]
- Crawford, A.J.; Bermingham, E.; Polania, C. The role of tropical dry forest as a long-term barrier to dispersal: A comparative phylogeographical analysis of dry forest tolerant and intolerant frogs. Mol. Ecol.
**2007**, 16, 4789–4807. [Google Scholar] [CrossRef] [PubMed] - Wang, I.J.; Crawford, A.J.; Bermingham, E. Phylogeography of the pygmy rain frog (Pristimantis ridens) across the lowland wet forests of isthmian Central America. Mol. Phylogenet. Evol.
**2008**, 47, 992–1004. [Google Scholar] [CrossRef] [PubMed] - Graham, A.; Dilcher, D. The Cenozoic record of tropical dry forest in northern Latin America and the southern United States. In Seasonally Dry Tropical Forests; Bullock, S.H., Mooney, H.A., Medina, E., Eds.; Cambridge University Press: Cambridge, UK, 1995; pp. 124–145. [Google Scholar]
- Piperno, D.R.; Pearsall, D.M. The Origins of Agriculture in the Lowland Neotropics; Academic Press: San Diego, CA, USA, 1998. [Google Scholar]
- Coates, A.G.; Obando, J.A. The geologic evolution of the Central American isthmus. In Evolution and Environment in Tropical America; Jackson, J.B.C., Budd, A.F., Coates, A.G., Eds.; University of Chicago Press: Chicago, IL, USA, 1996; pp. 21–56. [Google Scholar]
- Cronin, T.M.; Dowsett, H.J. (Eds.) Pliocene climates. Quat. Sci. Rev.
**1991**, 10, 115–296. [Google Scholar] - Zeh, J.A.; Zeh, D.W.; Bonilla, M.M. Phylogeography of the harlequin beetle-riding pseudoscorpion and the rise of the Isthmus of Panama. Mol. Ecol.
**2003**, 12, 2759–2769. [Google Scholar] [CrossRef] [PubMed][Green Version] - Perdices, A.; Bermingham, E.; Montilla, A.; Doadrio, I. Evolutionary history of the genus Rhamdia (Teleostei: Pimelodidae) in Central America. Mol. Phylogenet. Evol.
**2002**, 25, 172–189. [Google Scholar] [CrossRef] - Perdices, A.; Doadrio, I.; Bermingham, E. Evolutionary history of the synbranchid eels (Teleostei: Synbranchidae) in Central America and the Caribbean islands inferred from their molecular phylogeny. Mol. Phylogenet. Evol.
**2005**, 37, 460–473. [Google Scholar] [CrossRef] [PubMed] - Weigt, L.A.; Crawford, A.J.; Rand, A.S.; Ryan, M.J. Biogeography of the túngara frog; Physalaemus pustulosus: A molecular perspective. Mol. Ecol.
**2005**, 14, 3857–3876. [Google Scholar] [CrossRef] [PubMed] - Robertson, J.M.; Zamudio, K.R. Genetic diversification; vicariance; and selection in a polytypic frog. J. Hered.
**2009**, 100, 715–731. [Google Scholar] [CrossRef] [PubMed] - Robertson, J.M.; Duryea, M.C.; Zamudio, K.R. Discordant patterns of evolutionary differentiation in two Neotropical treefrogs. Mol. Ecol.
**2009**, 18, 1375–1395. [Google Scholar] [CrossRef] [PubMed] - McCafferty, S.S.; Martin, A.; Bermingham, E. Phylogeographic diversity of the lower Central American cichlid Andinoacara coeruleopunctatus (Cichlidae). Int. J. Evol. Boil.
**2012**, 2012, 780169. [Google Scholar] [CrossRef] [PubMed] - Martin, A.P.; Bermingham, E. Regional endemism and cryptic species revealed by molecular and morphological analysis of a widespread species of Neotropical catfish. Proc. R. Soc. Lond. B
**2000**, 267, 1135–1141. [Google Scholar] [CrossRef] [PubMed][Green Version] - Bussing, W.A. Geographic distribution of the San Juan ichthyofauna of Central America with remarks on its origin and ecology. In Investigations of the Ichthyofauna of Nicaraguan Lakes; Thorson, T.B., Ed.; University of Nebraska, Lincoln: Lincoln, NE, USA, 1976; pp. 157–175. [Google Scholar]
- Bussing, W.A. Freshwater Fishes of Costa Rica, 2nd ed.; Editorial de la Universidad de Costa: Rica San José, Costa Rica, 1998. [Google Scholar]
- Crawford, A.J.; Smith, E.N. Cenozoic biogeography and evolution in direct developing frogs of Central America (Leptodactylidae: Eleutherodactylus) as inferred from a phylogenetic analysis of nuclear and mitochondrial genes. Mol. Phylogenet. Evol.
**2005**, 35, 536–555. [Google Scholar] [CrossRef] [PubMed] - Picq, S.; Alda, F.; Krahe, R.; Bermingham, E. Miocene and Pliocene colonization of the Central American Isthmus by the weakly electric fish Brachyhypopomus occidentalis (Hypopomidae; Gymnotiformes). J. Biogeogr.
**2014**, 41, 1520–1532. [Google Scholar] [CrossRef] - Hasegawa, M.; Kishino, H.; Yano, T. Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J. Mol. Evol.
**1985**, 22, 160–174. [Google Scholar] [CrossRef] [PubMed] - Nei, M. Molecular Evolutionary Genetics; Columbia University Press: New York, NY, USA, 1987. [Google Scholar]
- Swofford, D.S. PAUP*: Phylogenetic Analysis Using Parsimony (*and Other Methods); Version 4.0a; Sinauer: Sunderland, MA, USA, 2002. [Google Scholar]
- McDonald, J.H.; Kreitman, M. Adaptive protein evolution at the Adh locus in Drosophila. Nature
**1991**, 351, 652–654. [Google Scholar] [CrossRef] [PubMed] - Librado, P.; Rozas, J. DnaSP v5: A software for comprehensive analysis of DNA polymorphism data. Bioinformatics
**2009**, 25, 1451–1452. [Google Scholar] [CrossRef] [PubMed] - Drummond, A.J.; Suchard, M.A.; Xie, D.; Rambaut, A. Bayesian phylogenetics with BEAUti and the BEAST 1.7. Mol. Boil. Evol.
**2012**, 29, 1969–1973. [Google Scholar] [CrossRef] [PubMed] - Kingman, J. The coalescent. Stoch. Process. Their Appl.
**1982**, 13, 235–248. [Google Scholar] [CrossRef] - Drummond, A.J.; Ho, S.Y.W.; Phillips, M.J.; Rambaut, A. Relaxed phylogenetics and dating with confidence. PLoS Boil.
**2006**, 4, e88. [Google Scholar] [CrossRef] [PubMed][Green Version] - Macey, J.R.; Schulte, J.A., II; Larson, A.; Fang, Z.; Wang, Y.; Tuniyev, B.S.; Papenfuss, T.J. Phylogenetic relationships of toads in the Bufo bufo species group from the Eastern Escarpment of the Tibetan Plateau: A case of vicariance and dispersal. Mol. Phylogenet. Evol.
**1998**, 9, 80–87. [Google Scholar] [CrossRef] [PubMed] - Waters, J.M.; Burridge, C.P. Extreme intraspecific mitochondrial DNA sequence divergence in Galaxias maculatus (Osteichthys: Galaxiidae); one of the world’s most widespread freshwater fish. Mol. Phylogenet. Evol.
**1999**, 11, 1–12. [Google Scholar] [CrossRef] [PubMed] - Burridge, C.P.; Craw, D.; Fletcher, D.; Waters, J.M. Geological dates and molecular rates: Fish DNA sheds light on time dependency. Mol. Boil. Evol.
**2008**, 18, 624–633. [Google Scholar] [CrossRef] [PubMed] - Bagley, J.C. PIrANHA. Justincbagley/PIrANHA: PIrANHA version 0.1.4 [Data Set]. Zenodo
**2017**. [Google Scholar] [CrossRef] - Jeffreys, H. Theory of Probability, 3rd ed.; Clarendon: Oxford, UK, 1961. [Google Scholar]
- Kass, R.E.; Raftery, A.E. Bayes Factors. J. Am. Stat. Assoc.
**1995**, 90, 773–795. [Google Scholar] [CrossRef] - Bagley, J.C.; Hickerson, M.J. Data for: Testing hypotheses of diversification in Panamanian frogs and freshwater fishes using hierarchical approximate Bayesian computation with model averaging [Data Set]. Mendeley Data
**2018**. [Google Scholar] [CrossRef] - Lambeck, K.; Esat, T.M.; Potter, E.K. Links between climate and sea levels for the past three million years. Nature
**2002**, 419, 199–206. [Google Scholar] [CrossRef] [PubMed] - Miller, K.G.; Kominz, M.A.; Browning, J.V.; Wright, J.D.; Mountain, G.S.; Katz, M.E.; Sugarman, P.J.; Cramer, B.S.; Christie-Blick, N.; Pekar, S.F. The Phanerozoic record of global sea-level change. Science
**2005**, 310, 1293–1298. [Google Scholar] [CrossRef] [PubMed] - O’Dea, A.; Lessios, H.A.; Coates, A.G.; Eytan, R.I.; Restrepo-Moreno, S.A.; Cione, A.L.; Collins, L.S.; de Queiroz, A.; Farris, D.W.; Norris, R.D.; et al. Formation of the Isthmus of Panama. Sci. Adv.
**2016**, 2, e1600883. [Google Scholar] [CrossRef] [PubMed][Green Version] - Montes, C.; Cardona, A.; Jaramillo, C.; Pardo, A.; Silva, J.C.; Valencia, V.; Ayala, C.; Pérez-Angel, L.C.; Rodriguez-Parra, L.A.; Ramirez, V.; et al. Middle Miocene closure of the Central American seaway. Science
**2015**, 348, 226–229. [Google Scholar] [CrossRef] [PubMed] - Nores, M. The implications of Tertiary and Quaternary sea level rise events for avian distribution patterns in the lowlands of northern South America. Glob. Ecol. Biogeogr.
**2004**, 13, 149–161. [Google Scholar] [CrossRef] - Smith, S.A.; Bermingham, E. The biogeography of lower Mesoamerican freshwater fishes. J. Biogeogr.
**2005**, 32, 1835–1854. [Google Scholar] [CrossRef][Green Version] - Hearty, P.J.; Kindler, P.; Cheng, H.; Edwards, R.L. A +20 m middle Pleistocene sea-level highstand (Bermuda and the Bahamas) due to partial collapse of Antarctic ice. Geology
**1999**, 27, 375–378. [Google Scholar] [CrossRef] - Crawford, A.J. Huge populations and old species of Costa Rican and Panamanian dirt frogs inferred from mitochondrial and nuclear gene sequences. Mol. Ecol.
**2003**, 12, 2525–2540. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gibbard, P.L.; Head, M.J.; Walker, M.J.C. The Subcommission on Quaternary Stratigraphy. Formal ratification of the Quaternary System/Period and the Pleistocene Series/Epoch with a base at 2.58 Ma. J. Quat. Sci.
**2010**, 25, 96–102. [Google Scholar] [CrossRef] - Gibbard, P.; van Kolfschoten, T. The Pleistocene and Holocene epochs. In A Geologic Time Scale 2004; Gradstein, F.M., Ogg, J.G., Smith, A.G., Eds.; Cambridge University Press: Cambridge, UK, 2004; pp. 441–452. [Google Scholar]
- Arbogast, B.S.; Edwards, S.V.; Wakeley, J.; Beerli, P.; Slowinski, J.B. Estimating divergence times from molecular data on phylogenetic and populations genetic timescales. Annu. Rev. Ecol. Syst.
**2002**, 33, 707–740. [Google Scholar] [CrossRef] - Nielsen, R.; Beaumont, M.A. Statistical inferences in phylogeography. Mol. Ecol.
**2009**, 18, 1034–1047. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wakeley, J. Inferences about the structure and history of populations: Coalescents and intraspecific phylogeography. In The Evolution of Population Biology; Singh, R.S., Uyenoyama, M.K., Eds.; Cambridge University Press: Cambridge, UK, 2004; pp. 193–215. [Google Scholar]
- Xue, A.T.; Hickerson, M.J. The aggregate site frequency spectrum for comparative population genomic inference. Mol. Ecol.
**2015**, 24, 6223–6240. [Google Scholar] [CrossRef] [PubMed][Green Version] - Xue, A.T.; Hickerson, M.J. Multi-DICE: R package for comparative population genomic inference under hierarchical co-demographic models of independent single-population size changes. Mol. Ecol. Resour.
**2017**, 17, E212–E224. [Google Scholar] [CrossRef] [PubMed] - Peterson, B.K.; Weber, J.N.; Kay, E.H.; Fisher, H.S.; Hoekstra, H.E. Double digest RADseq: An inexpensive method for de novo SNP discovery and genotyping in model and non-model species. PLoS ONE
**2012**, 7, e37135. [Google Scholar] [CrossRef] [PubMed][Green Version] - Kimura, M. The Neutral Theory of Molecular Evolution; Cambridge University Press: Cambridge, UK, 1983. [Google Scholar]
- Faivovich, J.; Haddad, C.F.B.; Baêta, D.; Jungfer, K.-H.; Álvares, G.F.R.; Brandão, R.A.; Sheil, C.; Barrientos, L.S.; Barrio-Amorós, C.L.; Cruz, C.A.G.; et al. The phylogenetic relationships of the charasmatic poster frogs, Phyllomedusinae (Anura, Hylidae). Cladistics
**2010**, 26, 227–261. [Google Scholar] [CrossRef] - Wiens, J.J.; Fetzner, J.W., Jr.; Parkinson, C.L.; Reeder, T.W. Hylid frog phylogeny and sampling strategies for speciose clades. Syst. Boil.
**2005**, 54, 778–807. [Google Scholar] [CrossRef] [PubMed] - Musilová, Z.; Říčan, O.; Janko, K.; Novák, J. Molecular phylogeny and biogeography of the Neotropical cichlid fish tribe Cichlasomatini (Teleostei: Cichlidae: Cichlasomatinae). Mol. Phylogenet. Evol.
**2008**, 46, 659–672. [Google Scholar] [CrossRef] [PubMed] - Musilová, Z.; Říčan, O.; Janko, K.; Novák, J. Phylogeny of the neotropical cichlid fish tribe Cichlasomatini (Teleostei: Cichlidae) based on morphological and molecular data, with the description of a new genus. J. Zool. Syst. Evol. Res.
**2009**, 47, 234–247. [Google Scholar] [CrossRef]

**Figure 1.**Map of the study area. The western Panama isthmus (WPI) break zone is shaded gray, and major physiographic features including the continental divide, peninsulas, and mountain ranges are shown over a digital elevation layer; GC, Golfo de Chiriquí; GM, Golfo de Montijo. Paleo-bathymetric river paths modeled assuming a 135 m eustatic sea level drop during the Last Glacial Maximum using ArcMap (ESRI, Redlands, CA, USA; courtesy of Peter J. Unmack, University of Canberra) are shown with the −135 m bathymetric contour (dashed line) as a reference.

**Figure 2.**Geographical locations of WPI phylogeographic breaks registered in different species/lineages of Panamanian (

**A**,

**B**) frogs and (

**C**,

**D**) freshwater fishes evaluated in this study. Map features and lines are identical to those in Figure 1.

**Figure 3.**BEAST maximum clade credibility (MCC) time trees for all seven focal species/lineages split across the WPI break. Tip labels are sequence codes used or modified from the original studies, colored according to geographical position east versus west of the break zone. Horizontal bars show 95% highest posterior densities (HPDs) for node ages, numbers along nodes are mean node ages, and numbers at bar tips are upper 95% HPD values for truncated bars. Scale bars: 1 million years.

**Figure 4.**Comparison of divergence time estimates for species/lineages, and species assemblages, diverged across the WPI break. Species/lineage gene-tree depths (t

_{MRCA}s) from BEAST [65] are shown as geometric means (dots) and 95% HPDs, with regions of overlap in coalescence times shaded gray. Estimated times of assemblage co-divergences (E[τ]) are shown as modal peak posterior estimates (diamonds) and 95% HPDs from approximate Bayesian computation (ABC) model averaging in MTML-msBayes [25].

**Figure 5.**Hierarchical approximate Bayesian computation (hABC) results. Joint hyperposterior probability distributions of the mean divergence time, E[τ] (left x-axis, coalescent time; right x-axis, absolute time), and the dispersion index of divergence times, Ω, from MTML-msBayes [25] are presented for (

**A**) frogs and (

**B**) freshwater fishes based on ABC model-averaging across model classes. Inset graphs show the posterior densities of Ω from each analysis.

**Figure 6.**GIS sea-level model for lower Central America. This map is based on the 250 m NASA Shuttle Radar Topographic Mission digital elevation model and shows predicted eustatic sea levels in the study area potentially resulting from highstands of +50 m (light blue), +100 m (blue), and +250 m (dark blue) above present sea level (a.s.l.), relative to current elevation. The approximate WPI break zone is mapped in red.

**Table 1.**List of taxa used to examine temporal diversification patterns across the western Panama isthmus.

Taxon | mtDNA Genes | Length (bp) | n_{total} (West/East) | π | Ti/Tv | % div | Source |
---|---|---|---|---|---|---|---|

Frogs | |||||||

Agalychnis callidryas | 16S, ND1 | 1149 (118, 1031) | 28 (16/12) | 0.0337 | 11.373 | 8.0 | Robertson & Zamudio (2009) |

Craugastor crassidigitus | cytb, cox1 | 1353 (714, 639) | 13 (5/8) | 0.0645 | 14.55 | 13.9 | Crawford et al. (2007) |

Dendropsophus ebraccatus | ND1, tRNAs | 1877 | 18 (11/7) | 0.0245 | 12.04 | 5.9 | Robertson et al. (2009) |

Engystomops pustulosus | cox1 | 564 | 15 (2/13) | 0.0139 | 31.67 | 4.6 | Weigt et al. (2005) |

Freshwater Fishes | |||||||

Andinoacara coeruleopunctatus | ATP6/8 | 842 | 10 (2/8) | 0.0093 | 20.77 | 2.4 | McCafferty et al. (2012) |

Pimelodella chagresi | ATP6/8, cox1 | 1471 (842, 629) | 14 (6/8) | 0.0210 | 12.19 | 3.5 | Bermingham & Martin (1998) |

Roeboides occidentalis–R. guatemalensis | ATP6/8, cox1 | 1493 (842, 651) | 11 (8/3) | 0.0311 | 10.36 | 6.4 | Bermingham & Martin (1998) |

**Table 2.**Prior model classes and results of tests for synchronous diversification using ABC model averaging in MTML-msBayes.

Prior | P(τ) | P(θ_{D}) | P(θ_{A}) | P(M_{k}|D)^{1000} | Ω Mode | Ω 95% HPDs |
---|---|---|---|---|---|---|

WPI frogs (Y = 4) | 0.0036 | [0.000, 0.0565] | ||||

M_{1} | ~U(0, 1.75) | ~U(0, 0.1) | ~U(0, 0.25) | 0.2666 | – | – |

M_{2} | ~U(0, 1.75) | ~U(0, 0.1) | ~U(0, 0.5) | 0.4990 | – | – |

M_{3} | ~U(0, 1.75) | ~U(0, 0.4) | ~U(0, 0.25) | 0.0000 | – | – |

M_{4} | ~U(0, 0.875) | ~U(0, 0.1) | ~U(0, 0.25) | 0.2344 | – | – |

WPI fishes (Y = 3) | 0.0017 | [0.000, 0.0423] | ||||

M_{1} | ~U(0, 0.8) | ~U(0, 0.1) | ~U(0, 0.25) | 0.3124 | – | – |

M_{2} | ~U(0, 0.8) | ~U(0, 0.1) | ~U(0, 0.5) | 0.3766 | – | – |

M_{3} | ~U(0, 0.8) | ~U(0, 0.4) | ~U(0, 0.25) | 0.0000 | – | – |

M_{4} | ~U(0, 0.4) | ~U(0, 0.1) | ~U(0, 0.25) | 0.3110 | – | – |

_{k}) run for each of two analyses of Y population-pairs used to test for synchronous diversification across the western Panama isthmus (WPI) break. Prior models had varying τ, θ

_{D}, and θ

_{A}prior distributions, P(x) for random variable x, but assumed zero post-divergence migration. Approximate posterior probabilities, P(M

_{k}|D)

^{1000}, of each model are given based on 1000 accepted simulated draws from 20 million random draws from the four prior models, with that of the best-supported model underlined. Modal Ω hyperparameter estimates and their 95% highest posterior densities (HPDs) from model averaging over all four prior models are given in the first row of each section. Abbreviations: M, model class (candidate prior); P, probability (density); U, uniform distribution.

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**MDPI and ACS Style**

Bagley, J.C.; Hickerson, M.J.; Johnson, J.B.
Testing Hypotheses of Diversification in Panamanian Frogs and Freshwater Fishes Using Hierarchical Approximate Bayesian Computation with Model Averaging. *Diversity* **2018**, *10*, 120.
https://doi.org/10.3390/d10040120

**AMA Style**

Bagley JC, Hickerson MJ, Johnson JB.
Testing Hypotheses of Diversification in Panamanian Frogs and Freshwater Fishes Using Hierarchical Approximate Bayesian Computation with Model Averaging. *Diversity*. 2018; 10(4):120.
https://doi.org/10.3390/d10040120

**Chicago/Turabian Style**

Bagley, Justin C., Michael J. Hickerson, and Jerald B. Johnson.
2018. "Testing Hypotheses of Diversification in Panamanian Frogs and Freshwater Fishes Using Hierarchical Approximate Bayesian Computation with Model Averaging" *Diversity* 10, no. 4: 120.
https://doi.org/10.3390/d10040120