Phylogeography of Petrolisthes armatus, an invasive species with low dispersal ability

Theoretically, species with high population structure are likely to expand their range, because marginal populations are free to adapt to local conditions; however, meta-analyses have found a negative relation between structure and invasiveness. The crab Petrolisthes armatus has a wide native range, which has expanded in the last three decades. We sequenced 1718 bp of mitochondrial DNA from native and recently established populations to determine the population structure of the former and the origin of the latter. There was phylogenetic separation between Atlantic and eastern Pacific populations, and between east and west Atlantic ones. Haplotypes on the coast of Florida and newly established populations in Georgia and South Carolina belong to a different clade from those from Yucatán to Brazil, though a few haplotypes are shared. In the Pacific, populations from Colombia and Ecuador are highly divergent from those from Panamá and the Sea of Cortez. In general, populations were separated hundreds to million years ago with little subsequent gene flow. High genetic diversity in the newly established populations shows that they were founded by many individuals. Range expansion appears to have been limited by low dispersal rather than lack of ability of marginal populations to adapt to extreme conditions.

The population-genetic constitution of marine invasive species in their native range is increasingly being studied in efforts to determine the source of invasions into new areas (reviews in refs 1-5). Less attention has been focused on the insights that such studies can provide regarding the relationship between genetic structure within the species range and invasive properties. Both factors are related to dispersal ability, which, in turn, is dependent on the degree to which propagules can spread and to the capacity of a species to adapt to varying physical and biological environmental factors. A species may be unable to invade a certain area because it cannot reach it, or it may not do so because it cannot survive there. Its native populations will also be isolated from each other to the degree that propagules cannot overcome barriers within its native range. Such barriers can either hinder dispersal physically, or be environments that exceed the tolerance of propagules. Thus, native population structure and invasiveness should be related. Ultimately, the question is one regarding the factors that determine species ranges.
Mayr 6 suggested that limits to range expansion are set by intraspecific gene flow. Populations at the range margin are unable to adapt to local conditions (and thus progressively invade new areas) because of the influx of genes from the species centre. Kirkpatrick and Barton 7 constructed models that supported this proposal. Their reasoning would lead to the conclusion that species with high levels of genetic structure are more likely to expand their ranges. Existing data from invasive species, however, have indicated the opposite, i.e. that species with high rates of gene flow in their native range are more likely to expand to new areas. Bohning-Gaese, et al. 8 found that in warblers of the genus Sylvia ability to disperse -as measured by capacity for long-distance flight-overwhelmingly explained the size of species ranges. In the marine realm, a meta-analysis by Gaither, et al. 9 found that the best predictive variable of whether a species would become invasive is the inverse of genetic structure in its native range. Species with low pairwise (but not global) F ST values between their native populations were more likely to be invasive. Thus, intraspecific phylogeography, of interest in any species, takes an additional dimension when the species is invasive, because it also addresses the basic biogeographical question of the factors that determine range expansion.
An invasive species with a wide native geographic range is the porcelain crab Petrolisthes armatus (Gibbes), a marine, crab-like anomuran decapod. This species has the largest geographical distribution of any neotropical porcellanid. In the Atlantic its range extends from central Florida and Bermuda to southern Brazil on the Results Phylogenetic Analyses. Although intraspecific gene genealogies are said to be better represented by networks than phylogenetic trees because ancestral haplotypes may still exist in the sample 40 , the split in Petrolisthes armatus from the eastern Pacific and the Atlantic cannot be more recent than the completion of the central American Isthmus, and thus their common ancestor could not be younger than 3 MY. Our purpose of reconstructing a phylogeny was to identify and date major clades within the species. For this reason, we employed a conservative approach of collapsing every node that did not receive adequate support in both our Maximum Likelihood and the two Bayesian analyses. This mostly meant that we preserved all nodes supported by >70% of the bootstrap iterations in RAxML, because this program produced much lower clade support than either MrBayes or BEAST. The mtDNA phylogeny of P. armatus from concatenated 16S and COI sequences (Figs 1 and 2) revealed that Atlantic haplotypes are monophyletic. All three approaches provided high support for one clade on the seaboard of the United States (which we will name the "NW Atlantic" clade) and for a second clade with all haplotypes from Bermuda, and from all southern locations (the "SW Atlantic" clade). All three approaches also provided high support for a separate eastern Atlantic clade. There was, however, one discrepancy between the topology produced by BEAST, on the one hand, and by RAxML and MrBayes on the other. Whereas RAxML and MrBayes showed the Atlantic clade as a tritomy, BEAST showed the eastern Atlantic clade to be reciprocally monophyletic sister of the SW Atlantic clade with a posterior probability of 95%. According to estimates from BEAST, these two clades were separated 3.1 million years ago (MYA) [95% HPDs (Highest Posterior Density) 1.7 to 4.8 MYA], whereas, if assumed to be part of the tritomy, the estimated age of their most recent common ancestor would be the same as the age of the Atlantic clade, 3.5 MYA (95% HPDs 2.0 to 5.4 MYA). Given the 95% HPDs, these differences are not significant. The geographic separation of the NW and SW Atlantic clades is not absolute. Two haplotypes at Colombia belong to the NW Atlantic clade, and four haplotypes at South Carolina belong to the SW Atlantic clade (Figs 1 and 3). These phylogeographically "oddball" haplotypes by and large are not related to potential recolonization after the 2010 cold spell that is thought to have decimated the populations of P. armatus in the NW Atlantic. Only six haplotypes at South Carolina ( Fig. 1), were collected in November 2012, whereas the rest were captured long before this time.
Whereas the NW Atlantic clade shows little geographic partitioning, with haplotypes from the two sides of Florida and from South Carolina mixed, the SW Atlantic clade displays phylogeographic structure. Haplotypes from Brazil are closely related to each other (Fig. 3), and appear to be ancestral to haplotypes from all other localities in the southern clade (Caribbean and Bermuda), except for three haplotypes in Bermuda, which form a monophyletic entity, nested among the Brazilian haplotypes (Fig. 1). The separation between Brazilian and Caribbean subclades is dated by BEAST as having occurred 2.5 MYA (95% HPDs 1.4 to 3.9 MYA). The Caribbean clade contains a subclade composed of the majority of haplotypes from Colombia, Panamá, Yucatán and Belize, with a few haplotypes from Venezuela, South Carolina, Trinidad and Bermuda. This clade was estimated to be 1.7 MY old (95% HPDs 0.9 to 2.7 MYA), and is nested within a polytomy that contains haplotypes from the Southeast Caribbean and from Bermuda. The small sample of African populations shows little phylogeographic structure (Figs 1 and 4). Haplotypes from three locations in the Gulf of Guinea are closely related to each other, but more distantly related to two haplotypes from Sierra Leone.
In the eastern Pacific (Fig. 2), haplotypes from Isla Puná and Salinas at the coast of Ecuador, and those from Colombia form a monophyletic unit with an estimated age of 1.8 MY (95% HPDs 0.7 to 3.5 MYA). However, the phylogeny of haplotypes from Panamá, Costa Rica and the Gulf of California is unresolved. Nevertheless the southern Pacific clade is separated from the rest of haplotypes by 33 mutations (Fig. 5). Given these phylogenetic 79 divisions, analyses of population genetics were conducted within each of the three regions, the western Atlantic, the eastern Atlantic and the eastern Pacific.
Population genetics. Hierarchical analysis of molecular variance (AMOVA) comparisons between clades (or geographically distant populations) illustrates the population genetic effect of population subdivision and few migrant haplotypes (Table 1). In the western Atlantic the gene genealogy suggested the existence of a barrier between Florida and Yucatán. Most of the variation (58%) was found on either side of the suspected barrier to genetic exchange, which is unsurprising given that these barriers were suggested by the phylogenetic analysis. Despite the existence of individuals of the northern clade in the South and vice-versa, and despite high F ST values between populations in the same region, F CT values between regions were high and significant. In the eastern Atlantic, the distance between Sierra Leone and the Gulf of Guinea may constitute a barrier to gene flow.  Accordingly, 65% of the variation was between the population in Sierra Leone, on the one hand, and the populations in Cameroon, Nigeria and São Tomé, on the other; the F CT value was high, but, because of small sample size in Sierra Leone, not significant. In the eastern Pacific 69% of the variation was explained by the separation of populations South and North of Panamá, but, once again, the F CT value was not significant.    With the exception of immediately adjacent populations, pair-wise F ST values between populations in the western Atlantic were large and highly significant (Table 2), which, under Wright's 41 island model would indicate a lack of gene flow over larger distances, assuming equilibrium between migration and genetic drift. Isolation by distance (IBD) analysis found a significant relationship between genetic dissimilarity and geographic distance, whether the two variables were measured in a linear (r = 0.506, p < 0.0001), or in a logarithmic (r = 0.541, p < 0.0004) scale. In contrast to the western Atlantic, genetic discontinuities between the populations in the eastern Pacific were mostly governed by the suggested barrier to gene flow between the coast of Colombia and the coast of Panamá. F ST values between populations between these two areas were large and significant, whereas within each area -despite long geographic distances between Panamá and the Sea of Cortez-they were indicative of gene flow between distant populations. Correlations between genetic and geographic distance in the eastern Pacific were not significant in either a linear (r = 0.0496, p = 0.331) or a logarithmic (r = 0.0978, p = 0.263) scale. Very small and non-significant F ST values between the Gulf of Guinea populations (Sierra Leone, with only two haplotypes was not included) indicated that P. armatus in this area is genetically uniform between Nigeria, Cameroon and São Tomé ( Table 2). In the Isolation by Distance analysis the Mantel correlation coefficient was high (r = 0.9849), but because of the small number of populations and low sample size, not significant (p = 0.1644).

Between regions
F ST statistics cannot distinguish between genetic similarity due to recent separation from similarity due to high gene flow. We employed a coalescent approach in IMa2 to date the time of the initial separation of populations and to estimate the magnitude and direction of subsequent gene flow. Based on the assumption that West Atlantic and eastern Pacific populations were separated for a minimum of 3 MY, and seeing that the average HKY 42 distance (the model of DNA evolution used by IMa2) between their concatenated haplotypes is 4.04%, we have calibrated estimated times of divergence and migration between populations on the assumption that the 1718 bp fragment experiences a substitution rate per lineage of 7.5-15 mutations per MY. In comparisons between the population at Georgia and the rest of the samples (for which only a 499 bp fragment of COI-HL was available), we used the divergence in this DNA fragment between West Atlantic and Pacific populations of 5.02% to set the substitution rate prior for this fragment as 2-5 mutations per lineage per MY. Posterior probabilities of successful runs in IMa2 are supposed to rise to a peak at particular values of each parameter, then drop back down. In some pairwise comparisons, despite many chains, wide priors and long runs, posterior probabilities rose to a plateau and remained there, so that no unique value could be assigned to the relevant parameters. In the western Atlantic, times of initial separation estimated by IMa2 between populations (Table 2) ranged from tens of thousands to >2 million years. The most recent separations were between populations at South Carolina and Georgia, and between Georgia and East Florida, suggesting that the recently established northern populations may have been due to recent transfers. Obviously, given the recent introduction of P. armatus into Georgia and South Carolina, the estimates of separation of centuries to millions of years ago do not correspond to the actual time of transportation   of individuals. These estimates of IMa2 are for the separation of the mixture of haplotypes transported into these localities relative to haplotypes in the rest of the species range. That populations at Georgia and South Carolina were the result of massive transfer, rather than having been started from a few individuals was also supported by their high genetic variability (Table 3). Both nucleotide and haplotype diversity in these populations were amongst the highest of all sampled populations with N > 10. Thus, the IMa2 results from the invaded localities reflect past history of the mixture of invaders. Estimates from the rest of the populations, however, are more likely to reflect population history. According to IMa2 estimates, the population of Petrolisthes armatus in Bermuda, the geographically most isolated locality in the western Atlantic, has been separated from all other localities 1.6 × 10 5 to 2.1 × 10 6 years ago ( Table 2) and has received little gene flow since then, except from Trinidad and the coast of Colombia (Table 4). The four haplotypes of the SW Atlantic clade found in South Carolina (Figs 1 and 3) were interpreted by coalescence as having arrived from Bermuda, as well as Venezuela and Yucatán (Table 4). To the extent that the analysis of the shorter COI-HL fragment can be trusted, there has also been some gene flow from the founder haplotypes of Georgia into Bermuda ( Table 4). The separation of the population in eastern and western Florida from populations that belong to the southern Caribbean clade has also been >10 5 years ago ( Table 2). The split between populations on the two coasts of Florida was estimated as much more recent. Gene flow between the two Florida populations has been relatively high, whereas gene flow into southern populations was not significantly different from 0 (Table 3). However, there has been asymmetrical gene flow from the Caribbean coast of Colombia, as also seen in the phylogenetic analysis (Figs 1 and 3). All estimated times of separation of populations within the SW Atlantic clade were in the order of 10 5 years, except for those involving Brazil; the latter were more than a million years old with the exception of more recent isolation from Yucatán and Venezuela (Table 2). Most migration rates between Brazil and populations of the SW Atlantic clade were also not significantly different from 0 ( Table 3). The contiguous Atlantic coasts of Panamá and Colombia registered both by F ST values (Table 2) and by IMa2 estimates (Table 3) as containing a single, panmictic population. Populations at Yucatán and the Caribbean coast of Colombia appeared as exchanging a high number of propagules. Interestingly, the two NW Atlantic clade haplotypes found in Colombia (Figs 1 and 3) did not contribute to migration rates significantly different from 0 in IMa2.
In the eastern Pacific, estimated times of isolation between the population in the Sea of Cortez and any other population (including the one in Panamá) was >1.5 × 10 6 years ( Table 2). Despite their geographic proximity, but in agreement with their distant phylogenetic affinity, populations on the coast of Panamá and of Colombia were also estimated to have been initially separated >2 × 10 6 years ago, longer than the isolation between populations at Panamá and the two localities at the coast of Ecuador (Salinas and Isla Puná). The most recent separation is  between the Colombian and the Isla Puná populations. Rates of migration were generally not significantly different from 0, except for asymmetrical gene flow, from the population at Isla Puná to Salinas and from the coast of Colombia into Isla Puná (Table 3). In contrast to the pattern seen in the western Atlantic, populations on the coasts of Nigeria, Cameroon and on the island of São Tomé contained haplotypes that mostly differ by only one mutation (Fig. 5), resulting in estimates of small F ST values and recent separation ( Table 2). Gene flow appeared to be along a North to South axis with a lower rate from São Tomé into Nigeria. Estimated migration in the opposite direction was not significantly different from 0.

Discussion
Genetic structure of Petrolisthes armatus is characterized by deep phylogenetic divisions (i.e. clades) and large divergence between populations within the same clade. Clearly, this is a species with low ability to disperse, either within the western Atlantic or within the eastern Pacific, although our limited sample from the eastern Atlantic indicates higher genetic connectivity between the more closely spaced samples in this region. The degree of structuring within the West Atlantic and East Pacific is evident in the mtDNA phylogeny, in F ST values and in the coalescent analysis. Yet a few errant haplotypes of one clade found in the region mainly inhabited by the other, along with the coalescence estimates of gene flow subsequent to initial separation, attest to infrequent long distance genetic exchange. What barriers and mechanisms of gene flow could account for the observed patterns?
Patterns of spread of genes between sedentary marine populations are obviously a function of the dispersal abilities of the species relative to potential barriers to planktonic transfer. The 12 to 19 day planktonic larva of Petrolisthes armatus 21,22 is conducive to high population structure, but it is not so limiting, as to be the entire explanation for the deep divisions seen in this species. Other tropical species in the same regions, which in the laboratory complete their planktonic cycle in approximately the same period of time, such as the sea urchin Echinometra lucunter with a larval life of 19 days 43 , and the sponge Cliona delitrix with a larval life of about 10 days 44 , show much less genetic structure within the Caribbean. Only the sea anemone Nematostella vectensis 45 , the gorgonian Gorgonia ventalina 46 and the barnacle Chthamalus proteus 47 show evidence of such high population differentiation between local populations. Shulman and Bermingham 48 calculated that if larvae were transported as passive particles, it would take only 13 generations for genes of a species with a larva that stays in the plankton for two weeks to traverse through stepping stones the entire Caribbean following the main Caribbean Current, given average current vectors [49][50][51][52] . It is unlikely that P. armatus is lacking stepping stones, as, in addition to our  sampled localities, it is also found in the Greater and the Lesser Antilles 10 . The lack of long-distance dispersal indicated by the high population structure, therefore, is more likely due to local retention of larvae, which appears to be a characteristic of this species 37,38 . The tendency of larval retention, however, cannot be absolute in a species of such a wide range, so barriers to gene flow must also be present to account for the phylogeographic divisions. An obvious such barrier is the Isthmus of Panamá, the timing of which we have used to date all other separations between populations. A multitude of lines of evidence has indicated that the final closure of the Isthmus, after a 12 MY process of narrowing water connections, occurred at approximately 3 MYA 53 . Some authors 54,55 have agreed that there were water connections until this time, but they presented their conclusions so as to imply that there may have been previous interruptions of gene flow between the eastern Pacific and the western Atlantic 56,57 . Whether the water connections had narrowed at instances prior to 3 MYA bears little relevance to the phylogenetic reconstruction of P. armatus, because among five sister clades in the genus Petrolisthes with representatives on either side of the Isthmus of Panamá, eastern Pacific and Atlantic populations of P. armatus have diverged the least 29,58,59 , and are thus most likely to have been the most recently separated. This, however, does not necessarily mean that the trans-isthmian split was contemporaneous with the final isthmus closure, because it could have pre-dated it by any length of time. Our use of wide priors in the split between the Pacific and the Atlantic clades in the BEAST reconstruction has resulted in an estimated date of 3.5 MYA, which seems reasonable for a species with wide environmental tolerances, such as P. armatus. Based on this, we have estimated the split between western and eastern Atlantic clades at 3.1 MYA. The barrier that separated populations at these two regions was undoubtedly the long distance between American and African coasts. Scheltema 60 estimated that, based on the speed of currents, larvae of marine organisms would require between 9 and 28 weeks to cross the contemporary tropical Atlantic. This distance barrier also accounts for distinct amphi-Atlantic clades in other porcellanids 29 , sea urchins 61, 62 and fishes [63][64][65][66] . Given the short length of larval life of Petrolisthes, the puzzle is not how the separation happened, but rather how the original colonization was effected. The only explanation for the expansion of P. armatus to the coast of Africa is that this species can occasionally raft, possibly on mangrove roots, on which adults and juveniles are frequently found. We can only speculate about ocean circulation in the Pliocene, but modern-day currents between the coast of Brazil and the coast of Africa 67, 68 are conducive to rafting transport; Ascensión may have been a stepping stone.
The barrier that could account for the presence of two clades in the Caribbean, one predominantly on the coast of Florida, the other from Yucatán to south Brazil, is less obvious. The population at Yucatán shows the lowest nucleotide diversity among all sampled localities ( Table 3), suggesting that effective population size may be smaller. Richards, et al. 69 found that a population of the brittle star Ophiothrix suensoni in the Gulf of Honduras was genetically isolated from populations in the rest of the Caribbean, which they attributed to larval entrapment arising from the Mesoamerican gyre 70,71 . A similar explanation was offered by Jackson, et al. 72 for the isolation of populations of the Nassau Grouper, Epinephelus striatus in this area. However, our sample from Yucatán was from the northern side of the peninsula and, given that in Petrolisthes armatus there is significant isolation by distance in the western Atlantic, the geographic separation of the two clades may be due to distance alone. Although larval entrapment in the Yucatán area could be the reason haplotypes in this area are so similar to each other, the F ST values between the Yucatán population and populations on the coast of Colombia and Panamá are significant but relatively small (Table 2), so this population is not completely closed. There is no need to postulate a barrier between Yucatán and Florida, because the large genetic distance between them could simply be a reflection of more gradual differentiation between stepping stone populations off the Gulf of México shores, which were not sampled. What remains elusive is the original barrier that may have caused the differentiation of the NW and SW Atlantic clades. It is also difficult to explain why Bermuda was colonized only by the SW Atlantic clade. Presumably, the original colonization resulted from rafted individuals, carried by the Gulf Stream, which occasionally throws off cold rings that reach Bermuda 49 . The Gulf Stream, however, flows by the east coast of Florida, but we found no evidence of the existence of the NW Atlantic clade in Bermuda. Either the frequency of haplotypes of the northern clade in Bermuda is lower than ~0.07, so that it could not be detected with a sample of 14 individuals, or the colonization of Bermuda by southern haplotypes was a chance event that has not been repeated. The two haplotypes of the NW Atlantic clade in Colombia and the four haplotypes of the southern clade in South Carolina were interpreted by coalescence as being the result of migration, not of incomplete lineage sorting. To the extent that this reconstruction is correct, their ancestors must have arrived through the Antilles, because no such odd haplotypes were detected in any other sampled locality. The average vector of currents on the eastern side of the Antilles is from South to North 50 , so any movement in the opposite direction would likely be due to local tidal currents and wind. Populations of P. armatus on the eastern and western coasts of Florida appear to be connected by gene flow uncharacteristically high for this species. That organisms with higher capacity for dispersal than P. armatus show more pronounced genetic breaks on the two sides of the peninsula 73-77 suggests human transport of this crab between these areas, similar to that responsible for the recent establishment of populations in Georgia and South Carolina. Haplotypes at the coast of Brazil in the MrBayes and BEAST phylogenetic reconstruction formed a monophyletic clade but they did not do so in RAxML. Nevertheless, the isolation of Brazilian populations is obvious in the high F ST values and low estimates of migration in IMa2 (we consider the apparent migration from Georgia an artefact of the short COI-HL sequences). Isolation of Brazilian marine populations of other species from their conspecifics in the Caribbean is usually attributed to the fresh-water plume of the Orinoco and the Amazon 43,62,78,79 ; however, given the wide salinity tolerance of P. armatus, the isolation of its Brazilian populations may be due to the extensive mud habitat off the coast of Guyana and Surinam 80 .
In the eastern Pacific, the monophyletic clade composed of haplotypes at the coasts of Ecuador and Colombia, highly differentiated from those at Panamá and the Sea of Cortez, is unusual. No other organism sampled genetically to date displays this genetic break between populations at Colombia and Panamá 81 . There is ample rocky habitat between Ecuador and Panamá, and there is little in patterns of ocean circulation to suggest that larvae could not spread through stepping stones [82][83][84] . It will be interesting to find out whether other eastern Pacific species of Petrolisthes show a similar genetic discontinuity.
The newly established populations of Petrolisthes armatus in South Carolina and in Georgia are of particular interest, because they have earned the title of invasive species for this crustacean 1, 18-20 . Our data clearly show that these populations were initiated by the movement of individuals from Florida. Their haplotype and molecular diversity is as high as that of native populations, a frequent characteristic of invasive populations when they are established by a large number of propagules 1, 85-87 . Transfer of large numbers of the oyster Crassostrea virginica from the Gulf of México to the Chesapeake Bay during the early 1960s to replace oyster stocks infected with "MSX" disease has been associated with invasions by crustaceans inhabiting oyster beds from the Gulf to the Atlantic seaboard of the United States 88 ; the same may have been true for introductions into Georgia and South Carolina. A large number of recently introduced founders, however, confounds the detection of evolutionary processes within the populations with the mark left by the genetic constitution of haplotypes that founded them. This is particularly true when there are multiple invasions from different sources 89,90 . At the time that our samples were taken at Georgia and South Carolina, a maximum of 22 years had elapsed since P. armatus was noticed in these areas. Despite the obvious tendency of this species to form deep genetic divisions between its populations over time, ~250 generations have apparently not been enough for haplotypes to sort themselves to the degree that coalescence can correctly infer the history of isolation and migration. Comparisons of the Georgia population with those from the native range are further complicated by their being based on a short fragment of mtDNA, which is less likely to conform to the infinite sites mutation model assumed by the IMa2 algorithm. Population density of P. armatus in Georgia and South Carolina fluctuates widely 91 , as it also does in its native range 92,93 , but the species appears well-established in areas occupied after its range shift 91 . P. armatus was present-though not as abundant-in South Carolina, even after the 2010 cold snap 20 , which suggests that larvae as well as adults are able to tolerate temperate temperatures. It is apparently too early to tell whether local adaptation in this marginal environment will permit the species to expand its range farther north.

Conclusions
With sufficient variation, pronounced genetic structure is expected to allow local adaptation 6,7 . Local adaptation is expected to promote range expansion 94,95 . Petrolisthes armatus, according to our mtDNA data, is a species characterized by high structure, although this structure may need thousands or millions of generations before it becomes established so that local adaptation can ensue. The signature of natural obstacles to migration remains in the genetics of both the newly established and the old populations. Two major barriers are identified by the phylogeny, the separation of Atlantic and Pacific populations by the completion of the Isthmus of Panamá, and the almost contemporaneous separation of two clades on the opposite shores of the tropical Atlantic. The subsequent separation of the North and South clades in the western Atlantic and a similar break in the eastern Pacific do not lend themselves to obvious explanations as to their causes, but further support the conclusion that dispersal in P. armatus is limited. The recent range expansion from Florida to the northern Atlantic seaboard of the United States is most likely due to human transportation of oysters, but the ability of the species to survive in the new habitats shows that it possesses the necessary plasticity to tolerate new physical and biotic environments. Thus, the range limits of this species are more likely set by species characteristics related to low ability to disperse, rather than by narrow physiological tolerance. Given these characteristics, any subsequent spread of this invasive species is likely to be caused by human mediation.

Material and Methods
Collections. We collected, or obtained from museums, 276 individuals of Petrolisthes armatus from both sides of the Atlantic and from the eastern Pacific (Fig. 6). All specimens from the Atlantic seaboard of the United States were collected before the extremely cold winter of 2010 (which is assumed to have caused high mortality of Petrolisthes armatus in this area 20  DNA extraction and sequencing. DNA was extracted from chelipeds or walking legs using the DNeasy ® Blood & Tissue Kit (Qiagen), following the manufacturer's protocol for animal tissues. A 530 bp fragment of the ribosomal 16S rDNA was amplified using primers 16Sar-5′ (CGCCTGTTTATCAAAAACAT) and 16Sbr-3′ (CCGGTCTGAACTCAGATCACGT) 96 , and was trimmed to 508 bp in the alignment. A 640 bp of Cytochrome Oxidase I (COI) was amplified using primers COIf-5′ (CCTGCAGGAGGAGGAGAYCC) and COIa-3′ (AGTATAAGCGTCTGGGTAGTC) 96 , and was trimmed to 532 bp in the alignment. A second 680 bp COI fragment was amplified using primers LCO1490 (GGTCAACAAATCATAAAGATATTGG) and HCO2198 (TAAACTTCAGGGTGACCAAAAAATCA) 97 , and was trimmed to 678 bp in the alignment. We refer to the first COI fragment as COI-af and to the second as COI-HL. Double-stranded amplifications were performed in 25 ml volume reactions containing 5 µl of Taq buffer (5×), 2.5 µl of dNTP mix (8 mM), 1.2 µl of each primer (10 µM), 2.5 µl of MgCl 2 (25 mM), 0.2 µl of GoTaq ® Flexi DNA Taq Polymerase (Promega), 1 µl of DNA template, and 11.4 µl of ddH 2 O. Thermal cycling conditions consisted of an initial denaturation step at 96 °C for 3 min, followed by 30 cycles of 95 °C for 1 min, 50 °C for 1 min, and 72 °C for 1 min. An extension step at 72 °C for 5 min followed the last cycle. Amplifications that resulted in unique PCR products were cleaned using the ExoSap-IT ® kit (USB Corporation) following the manufacturer's protocol. Samples that amplified multiple products were purified by cutting the band of the appropriate molecular weight out of a 2% low-melt agarose gel after electrophoresis in 1× TAE buffer. PCR products were recovered by incubating the sample at 70 °C for 10 min, and then at 45 °C for 60 min after adding 1 µl of GELase ™ (Epicentre Biotechnologies). Clean PCR products were cycle-sequenced in both directions using the BigDye ® Terminator v. 3.1 Cycle Sequencing Kit, and electrophoresed in an Applied Biosystems ® 3130 Genetic Analyzer. DNA from one individual of Petrolisthes robsonae was also sequenced to be used as outgroup in the phylogenetic analyses. Sequences were aligned by eye using BioEdit 98 100 , was used to select the model of nucleotide substitution that best fit each DNA region. These models were TIM3+I (I = 0.92) for 16S, GTR+I+G (I = 0.74, α = 1.29) for COI-af, and TIM+I+G (I = 0.18, α = 0.14) for COI-HL. The three fragments of each individual were concatenated and subjected to partitioned phylogenetic analysis after removal of redundant haplotypes, with the appropriate model applied to each partition.
Maximum Likelihood (ML) phylogenetic reconstruction was conducted in RAxML v. 8.2.6 101 , applying a GTR model with different values of α for each partition, as indicated by jModelTest2, and using the options for rapid bootstraps and automatic halting. Support values for the nodes were estimated from 456 bootstraps. Bayesian reconstruction was conducted in two Bayesian algorithms, MrBayes v.3.2.2 102 and BEAST v. 1.8.2 103 , using as priors the models indicated by jModeltest2, but letting the programs estimate the parameters. Mr. Bayes was run in 4 chains and for 6 × 10 7 steps, which allowed the average standard deviation of split frequencies to fall below 0.01, and the potential scale reduction factor to be equal to 1.00. Convergence was also determined in multiple runs, which produced the same topology. Node credibility values were determined by sampling every 600 th tree after discarding 25,000 trees as a burnin. BEAST results came from eight separate runs of different numbers of steps, combined in Logcombiner v. 1.8.2 taking every 10 th tree and a burnin of 10% per run, for a total of 26,085 trees. Tracer v. 1.6 verified that Effective Sample Size (ESS) of all estimates of the combined runs exceeded 200.
In addition to reconstructing the phylogeny, BEAST was used to estimate date of divergence between major clades. For this purpose, the separation between Atlantic and Pacific haplotypes was given an offset of 3 million years (MY) in a Lognormal Uncorrelated Relaxed clock. This is the generally accepted date of the completion of the Central American Isthmus 53, 59, 104 . However, as there are claims that only "narrow, shallow, and transient channels" connected the Caribbean with the Tropical Pacific as of 13 MYA (million years ago) 54 , the priors for this calibration point were set as uniform, ranging from 0.2 to 10 100 MY. RAxML and BEAST analyses were run on the CIPRES Science Gateway 105 . A median-Joining network 106 of haplotypes in the same geographic region was constructed in PopArt v.1 (http://popart.otago.ac.nz) to visualize relationships between haplotypes and geography within subclades in which the ancestral sequences may still be present in the populations 40 .

Population genetic analyses.
For the purposes of population genetic analyses, 4 samples from the Pacific shore of Costa Rica were pooled with those from the adjacent coast of Panamá, and 3 samples from Belize were pooled with those from Yucatán. All analyses were based on the full concatenated sequences of 16S, COI-af and COI-HL except for those involving the invasive Georgia population, for which only sequences from COI-HL were available. Haplotype and molecular diversity 107 and sequence-based pairwise F ST (Φ ST ) values were calculated in Arlequin 3.5.1.2 108 using Tamura and Nei 109 distances. Analysis of Molecular Variance (AMOVA) 110 was also carried out with this program, with significance determined in 10,000 reshufflings of haplotypes between populations. For a coalescent analysis, intended to determine times of separation of populations and subsequent direction of gene flow, we used IMa2 v. 2.0 111 . In the MCMC mode of this program we used geometric heating with 60 chains and a burnin of 5 hours. The runs were continued until an ESS of >200 was obtained for each parameter. L mode, intended to determine whether gene flow was significantly different from 0 and significantly different in each direction, was run for 3 × 10 7 steps. The uniform prior for mutation rate per lineage was estimated from assuming that divergence between Atlantic and Pacific populations of P. armatus reflects separation of 3 MY. The prior of the substitution rate was given a range equal to the mean and distributed symmetrically on either side of the mean. Comparisons between populations were made in pairwise fashion in separate runs. For Isolation by Distance analysis, Mantel 112 correlations between Φ ST and geographic distance by sea we employed IBDWS 113 with 10 4 iterations.