Background

The separation of populations and their eventual speciation is a fundamental process and a driving force in evolution. However, a newly formed reproductive barrier is often incomplete. Hybridization and introgression between incipient species, or gene flow from one species’ gene pool into another by backcrossing, may still occur. Many cases of species hybridization, resulting from accidental introduction of foreign species into new environments, have been identified and documented [1,2,3]. Often the outcome of human activities, these systems provide an opportunity to dissect the mechanisms underlying the formation of reproductive barriers. Exploring the differences between populations and their environments in native and introduced ranges may reveal the factors responsible for genetic isolation, which would eventually result in irreversible speciation.

Here, we describe one such case study involving two invasive fire ant species. These species, thought to maintain genetic isolation in their native range [4,5,6], freely hybridize in their newly introduced range [7, 8]. Unlike other incidents of introduction resulting in admixture, the two species are parapatric in both the native and the introduced ranges. Furthermore, the fact that the two ranges are located thousands of kilometers apart, allows for clear distinction between the native and introduced populations under study. This makes it a unique system which can help to provide insights into the evolution of genetic isolation and speciation.

The red fire ant, Solenopsis invicta, and the black fire ant, S. richteri, are closely related species, native to South America. Both species were inadvertently introduced to North America in the early twentieth century [9,10,11], with S. invicta subsequently migrating to other countries worldwide [12, 13]. Since they were first detected in the USA, the fire ant species have been closely monitored and their spread across the southeast is well documented. Their life cycle, behavior, genetic makeup, population structure and invasion history are the subject of many publications, making these species, in particular S. invicta, amongst the most studied invasive species, and an excellent subject for demographic history analysis.

S. invicta and S. richteri’ display social polymorphism, with two distinct social colony structures – the monogyne (single queen) and the polygyne (multiple queens) forms. The social polymorphism is a Mendelian trait determined by a supergene of 13 megabases, and is marked by the gene gp-9 with monogyne queens always having gp-9BB genotypes and polygyne queens always having gp-9Bb genotypes [14,15,16]. The social structure of a colony greatly affects its size, longevity, and dispersion patterns [17, 18].

Population genetics analysis of microsatellite and mitochondrial genotypes of thousands of S. invicta colonies around the world were used to trace the place of origin of the introduced S. invicta populations to the Formosa region in northern Argentina [11, 13]. It was also established that all subsequent introductions of S. invicta across the globe originated in the introduced USA population. The population of origin of the introduced S. richteri is still unknown.

The number of S. invicta queens that were initially introduced to North America was estimated through the screening of haplotypes in mtDNA sequences, as well as genotypes of allozymes, microsatellites, and the complementary sex determination (CSD) locus in individuals sampled throughout the introduced range [19]. It was determined that to account for all of the allele variants, the original group that was introduced to USA consisted of 9–30 unrelated mated queens.

In the introduced range, admixture between S. invicta and S. richteri is prevalent [7, 8]. A hybrid zone was identified ranging from Georgia in the east through Alabama to central Mississippi [18, 20, 21]. This is not the case in the native range of South America, where admixture was found to be a rare occurrence [4], or not evident at all [4,5,6]. While extensive sampling of native colonies was conducted, no more than 26 nuclear genetic markers were used in testing for admixture between the species, which limits the power of the analysis to detect gene flow.

We used large scale population genomic data to study the demographic history of S. invicta and S. richteri. Our data include samples from both species in both native and introduced ranges. The hybrid zone was not included in the sampling because the admixture in the introduced range has been well established in previous studies [7, 8] . These genomic data allow for an explicit maximum likelihood test for historic gene flow between the S. invicta and S. richteri in their native range to determine if these species had indeed maintained genetic isolation since their separation. We also provide estimates for speciation times, population divergence times and historic and contemporary effective population sizes, including the founding S. invicta population in North America. This is the first demographic history study of these species that uses thousands of genomic markers, which allow population genetic model inference at high accuracy and provide the necessary statistical power to test for gene flow.

Results

We inferred the population structure and demographic history using RAD sequencing of population samples of S. invicta and S. richteri from nine localities in their native range in Argentina and their introduced range in the USA (Fig. 1; Additional file 1: Tables S1 and S2). Altogether, this dataset consists of 962,896,602 sequenced reads, 96 nucleotides long each, from 337 samples. After stringent quality filtering, the genotypes of between 6389 and 285,847 SNPs, representing between 161 and 337 individuals (depending on filtering parameters and analysis type) and a total of 16,648 aligned RADseqs were used in the different analyses (see Methods).

Fig. 1
figure 1

Distribution map of S. invicta and S. richteri across North and South America with marked sampling sites. S. invicta was sampled in three sites in its native range (Her, Ale, Elr) and in two sites in the introduced range (OgGA, PMS). S. richteri was sampled in two sites in its native range (BAA, LfL) and in two sites in the introduced range (BTN, FlNT). The area marked in purple shows the hybridization zone between S. invicta and S. richteri. Distribution is based on [13, 60,61,62,63] and https://www.aphis.usda.gov/plant_health/plant_pest_info/fireants/downloads/fireant.pdf. Sampled populations are: Herr - Herradura, Elr – El Recreo, Ale – Alejandra, PMS - Pascagoula, Mississippi, OgGA - Oglethorpe Co., Georgia, BAA - Buenos Aires, LfL - Las Flores, BTN - Benton Co., Tennessee FlTN - Flatwood, Tennessee

Full size image

Population structure

STRUCTURE [22, 23] is a Bayesian clustering method that assigns individuals to ancestry clusters. STRUCTURE analysis resulted in the identification of five distinct population clusters (Fig. 2). No further substructure was found for K > 5 (Additional file 1: Figure S1). In 76 of 100 STRUCTURE runs with K = 5, the four introduced populations were clustered into two separate clusters, one for each species. Two individuals of the introduced S. richteri population of Benton, Tennessee, had inferred ancestry belonging to both clusters, indicating possible hybrids. The two native S. richteri populations were assigned to a single cluster, while two of the native S. invicta populations (Alejandra and El Recreo) were assigned to a fourth cluster. Individuals of the third native S. invicta population, sampled in Herradura, were partially assigned to the cluster of the introduced S. invicta populations and partially to a separate, fifth cluster.

Fig. 2
figure 2

Structure analysis of the studied populations. Summary of 76 of 100 runs of STRUCTURE with K = 5. Each individual is shown as a vertical bar, colored in accordance to its inferred clustering. Individuals of eight of the nine populations are clustered according to species and range, with the exception of two individuals marked in red triangles. These are mapped to both introduced S. invicta and S. richteri clusters, probably due to hybrid ancestry. Individuals of Herradura population are mapped to a fifth cluster, and to a cluster shared with the introduced S. invicta ants

Full size image

The allocation of populations into clusters suggests that the polymorphism in the introduced S. invicta is a subset of the genetic variants found in the native Herradura samples, making the latter a possible population of origin of the former. This result is in line with the previous studies that identified the Formosa region, which includes Herradura, as the likely source of the introduced S. invicta [11, 13]. Unlike the pattern observed in the Herradura population, neither of the sampled native S. richteri populations share a cluster with the introduced populations, indicating that these are not the source population of the introduced S. richteri.

We calculated the genetic distances between each pair of populations, using the genetic differentiation measure of FST. The results can be found in Additional file 1: Table S3.

Reproductive isolation in the native range

We tested for historic and contemporary gene flow between the native S. invicta and S. richteri populations by comparing between two competing demographic history models. To this end, we used a full maximum likelihood analysis of coalescent models [24, 25] as implemented in the 3s software [26]. Based on the phylogenetic inference, the maximum likelihood scores of two possible demographic history models are compared. A null model that does not allow genetic flow between the two closely related species and an alternative model that does.

This analysis concluded with an insignificant difference between the likelihood scores of the two scenarios (ΔlnL = 0.06; p > 0.9). Consequently, the null model could not be rejected, indicating that there was no evidence of gene flow between the native S. invicta and S. richteri populations since their divergence from a common ancestral population.

Speciation times and population sizes

3s provided maximum likelihood estimates for the null model parameters, including effective population sizes and the time since the speciation of S. invicta and S. richteri. Since we used the sequence of an individual of a different Solenopsis species, Solenopsis fugax, as an out-group, the model provided an estimate to the speciation time of this species from the lineage leading to S. invicta and S. richteri. Estimates were also provided to the effective size of the populations of S. richteri and S. invicta, the effective size of the ancestral population of S. invicta and S. richteri and that of the ancestral population of all three Solenopsis species (Table 1). Using the mutation rate of 3.4*10− 9 bp/generation (95% confidence interval of 2.2*10− 9 – 4.9*10− 9) that was estimated for the honey bee [28, 29], we calculated that the speciation of S. invicta and S. richteri happened 1.9*105 (1*105–3.5*105) generations ago and the speciation of S. fugax from the lineage leading to S. invicta and S. richteri took place 2.5*106 (1.6*106–4*106) generations ago. See Fig. 3 for all estimated parameters.

Table 1 3s parameter estimates
Full size table
Fig. 3
figure 3

Population effective sizes and generations number since the two speciation events. The values were calculated using the mutation rate of 3.4*10− 9 with the 95% confidence level range of 2.2*10− 9 - 4.9*10− 9 over 3S’s estimates (Table 1). Marked in blue are the population effective sizes and to the left is the time line in generations number

Full size image

The estimates for the effective population sizes were similar between present-day populations of S. invicta and S. richteri, while the ancestral population of these two populations was found to be slightly smaller. The effective size of the ancestral population of the three Solenopsis species was found to be larger than the other populations by an order of magnitude, indicating a very diverse ancestral population. See Fig. 3 for the exact numbers.

Founder population of introduced S. invicta

We estimated the demographic and temporal parameters that define the history of S. invicta populations using Approximate Bayesian Computation (ABC) [30], as implemented in DIYABC v2.0.4 [31, 32]. Unfortunately, it was not possible to fit a similar model to the S. richteri populations (poor goodness of fit). This may be because we did not sample the source population of the S. richteri introduction.

An ABC analysis is often used to compare between multiple competing historic demographic models that differ in their scenarios. As many details in the history of S. invicta are already established, an alternative scenario is unnecessary. Rather, we concentrated on estimating the model parameters of population sizes and time of demographic events as depicted in Fig. 4.

Fig. 4
figure 4

Model of S. invicta demographic history. The model describes the population history starting with the divergence within the native populations and followed by the introduction to North America, which originated from the Herradura population. Populations: NN1 – native population of Herradura; NN2 – native population of Alejandra and El Recreo; NF – bottlenecked founder population in the USA; NI – contemporary population in the USA. Times: 0 – populations sampling; TI – introduction; TB – length of bottleneck for the introduced population; TD - divergence of the Herradura population from the Alejandra and El Recreo populations

Full size image

With a maximum posterior of 39 (95% credible interval of 14–139), the effective size of the founding population is quite low. The length of the bottleneck period of the introduced S. invicta (TB) is minimal and stands at 2 generations for the maximum posterior estimate, with 95% credible interval ranging between 0 and 16 generations. Combined with the small size of the founder population, this suggests a rapid increase in population size immediately following the introduction. It is in line with historic records in which the presence of the newly introduced fire ants was initially reported as a mere curiosity and quickly changed into a growing concern and even panic, as ant numbers exploded [18].

The effective population size of the Herradura population (NN1) is approximately two orders of magnitude larger than the second native population cluster (NN2) estimated at 1.2*107 and 2.5*105, respectively (95% credibility interval of 3.3*106–7.8*107 and 8.2*104–2*106, respectively).

In Fig. 5, we plotted the full posterior distributions of all model parameters. The numeric values of these distributions, including their 95% quantiles, are summarized in Additional file 1: Table S4. For parameters NI, TI and TD, the posterior density distributions are very similar to their prior density distributions, indicating that the analysis could not extract information from the given data. The first two parameters are directly linked to the recent introduction to the USA, and the rapid increase in population size that followed. The sudden shift in dynamics from the originally stabilized population in the native range may have resulted in poor representation of the introduced populations by their summary statistics. Nevertheless, a ‘goodness of fit’ analysis indicated that the observed genetic data are well explained by the model and its parameter posterior distributions (Additional file 1: Figure S4).

Fig. 5
figure 5

Demographic model parameters inferred for S. invicta populations. The prior and posterior density distributions are plotted in red and green, respectively. The maximum posterior estimate of each of the parameters is indicated above its plot. Parameters defined in Fig. 2

Full size image

Discussion

We explicitly tested two competing demographic history models and found that the reproductive barrier between two closely related species of fire ants was sustained for about 200,000 generations, and is still preserved in their native range of South America. The STRUCTURE analysis of 171 native samples seems to indicate low levels of introgression of S. invicta ancestry into the native S. richteri population in Las Flores population, but not in the Buenos Aires population. If hybrids are indeed formed on rare occasions, it may be that such incidents do not lead to detectable gene flow between the species. Alternatively, this may be noise in the STRUCTURE analysis. The latter explanation seems more likely because Las Flores is more distant from the S. invicta range than Buenos Aires.

A previous study conducted by Ross and Trager (1990) indicated that genetic isolation may be incomplete in the native range [4]. By analyzing six informative allozyme loci (out of 26 that were genotyped) in 100 samples of S. invicta and 57 samples of S. richteri, three samples were identified as possible hybrids. The results were inconclusive, but occasional admixture between S. invicta and S. richteri could not be dismissed. Neither could it be determined if the hybrid specimens, assuming it is what they were, are the product of one or many generations of admixture, and so the reproductive potential of native invicta-richteri hybrids was still unclear. Other studies that used less extensive sampling and more diverse, but still limited, genetic markers of mtDNA sequences and allozyme loci, could identify no signs of admixture [5, 6]. Our conclusion of genetic isolation between these species since they diverged is more powerful than the observation that admixture is not taking place at present time, and is consistent with a strong reproductive barrier. It makes the extensive admixture, observed in North America, even more intriguing. This suggests that the two diverging lineages of S. invicta and S. richteri were well on their way to complete speciation in South America, but have not reached the point of no return. Their introduction to the USA has resulted in the breakdown of barriers and reversal of this process.

Reproductive isolation between related species is maintained by endogenous (genetic) and/or exogenous (environmental) factors [33]. One explanation for the difference between the admixture patterns in the native and introduced ranges could be that the native populations that were the sources of the introductions are genetically compatible between the species but geographically separated, while the populations whose ranges overlap in South America, are incompatible. This explanation was previously proposed by Ross & Trager (1990) [4]. Since Formosa is located outside of the overlap region, this may well be the case. Another possibility is that the introduced populations have been released from certain exogenous factors, biotic or abiotic, that prevent admixture in the native range. Biotic factors may include parasites that affect mating and reproduction. One such factor is Wolbachia – an endosymbiotic bacterium that infects high proportion of insects [34], and manipulates their reproductive systems in ways such as the induction of cytoplasmic incompatibilities between infected and uninfected individuals. Such incompatibilities were found to hinder the admixture between two species of Drosophila [35]. As Wolbachia was detected in native populations of S. invicta and S. richteri, but not in the introduced populations [36] it is a strong option that was already pointed out before [6]. Another possibility is changes in the ants’ diet following their introduction to a new environment. Different foods might affect the chemical blend of pheromones the ants produce. In ants and in other insects, social interaction, which includes the identification of a potential sexual mate, relies heavily on chemical cues [37]. In fact, pheromonal differentiation is suspected to be the cause of reproductive isolation between many closely related insect species [38,39,40]. Moreover, diet was shown to affect the pheromonal profile and sexual desirability in fruit flies [41, 42].

We gave estimates of the number of generations since the two speciation events, which can be converted to years by multiplying them with the average generation time. The social polymorphism of S. invicta and S. richteri combined with overlapping generations and multiple nuptial flights throughout the year, make the length of a generation highly variable and difficult to pinpoint. Ross and Shoemaker (2008) have given an estimate of three to six years, based on the relative number of alates produced in different developmental stages of a colony [19]. They lean towards the higher end of this range, but maintain that a shorter generation time is more probable for the time following introduction, when their numbers were growing exponentially. Assuming an average generation time of six years, the speciation time between S. invicta and S. richteri can be estimated to be 1.1 (0.6–2.1) million years ago (MYA) and the speciation time of S. fugax and S. invicta and S. richteri to 15 (9.6–24) MYA. The high end of this estimate is just under the 25 million years (95% confidence interval of 18–32) inferred for the divergence of these lineages, based on Bayesian phylogenetic analysis and divergence dating using 27 fossil calibration points [43]. It should be noted that a phylogeny-based estimate is for the genetic distance between the two representative individuals whose sequences were analyzed, while the coalescent-based-estimate by 3s, is for the separation of the species (i.e. the formation of genetic isolation). By definition, the divergence between the representative individuals must predate the formation of reproductive barriers that led to speciation.

There is one parameter shared by the two different coalescent-based methods of DIYABC and 3s, which is the native S. invicta populations cluster, that of Alejandra and El Recreo. Both methods gave similar estimates for it (2.5*105 and 4*105 respectively). It is approximately two orders of magnitude smaller than DIYABC ‘s estimate of 1.2*107 given for the other native population cluster, the Herradura population. This suggests a much larger and more diverse population around Herradura in comparison to the southern population sampled at El Recreo and Alejandra. Of those three locations, Herradura is closest to Corrientes, which was highlighted as the most genetically diverse among the populations that were sampled across South America [44].

The effective population size of the S. invicta USA founder population (NF) was estimated at 39. While for diploid species the effective population size is \( \mathrm{Ne}=\frac{4\mathrm{NfNm}}{\mathrm{Nf}+\mathrm{Nm}} \) (Nf and Nm are the number of breeding females and males, respectively), for haplodiploid species, the reduced number of chromosomal copies in males results in \( \mathrm{Ne}=\frac{4\mathrm{NfNm}}{2\mathrm{Nf}+4\mathrm{Nm}} \) [45, 46]. This translates to a ratio of Ne = 1.5Nf for species in which the queen mates with a single male, as is the case with S. invicta [47]. Therefore, the founder population size maximum posterior estimate of 39 translates to 26 unrelated, singly-mated queens, which fits within the higher end of the 9–30 estimate range made by Ross and Shoemaker (2008). If we consider our entire 95% credible interval, then the number of founding S. invicta queens is between 10 and 93.

Conclusion

We described a unique study system in which the reproductive barrier between two closely related species is maintained for approximately 200,000 generations in their native range and breached in an introduced range. This setting allows sampling from clearly separate pure populations in the native range and admixing populations in the introduced range. Therefore, this is a powerful system for the study of the molecular basis of reproductive isolation, which is key to the process of speciation.

Methods

Population sampling

Samples were taken from nine ant populations: three S. invicta and two S. richteri populations in the native range in Northeastern Argentina; two S. invicta and two S. richteri populations in the introduced range in Southeastern USA. The specimens were identified by morphological characteristics by James Pitts as described before [48]. For each population, 23–51 diploid females were sampled, each from a different colony, totaling 337 individuals. See Fig. 1 and Additional file 1: Tables S1 and S2 for details.

Sequencing and processing

Seven restriction-site associated DNA (RAD) libraries were constructed from the sampled populations, with 31–68 individuals in each library. DNA was extracted from the samples and RAD libraries were constructed based on the protocols of Baird and colleagues [49] and Etter and colleagues [50], as described by Privman et al. (2018) [27]. Briefly, DNA was digested with PstI-HF enzyme (New England Biolabs) and ligated to one of 96 barcoded P1 adapters with 5 bp unique barcodes. The samples were multiplexed per lane of 100 bp single-end sequencing on an Illumina HiSeq 2000 or 4000 sequencer. A total of 962,896,602 reads, or RADseq, were sequenced, an average of 2,857,259 reads per sample, with the least number of reads for a sample being 197,598 and the most - 6,848,114. Library 3 averaged at the lowest number of reads of 1,628,368 reads per sample. Library 7 averaged at the highest number of reads of 3,335,288 reads per sample. See Additional file 1: Table S1 and S2 for details about samples, reads and sequencing depth.

The raw reads were initially processed using the Stacks pipeline [51, 52] and low quality reads were discarded. These were defined as reads in which the phred score drops below 10 (1:10 chance for a sequencing error), averaged over a sliding window of 14 bases. We mapped the reads to 44,102 distinct positions in a S. invicta reference genome (version Si_gnH; NCBI accession AEAEQ02000000; [27]) using Bowtie2 [53]. For each of the mappings, a maximum of two bases mismatch was allowed for its best hit. To maintain the uniqueness of the mapping, we removed alignments with the second best hit containing less than five bases mismatches. Additionally, we controlled for and filtered out reads mapped to what are suspected collapsed repetitive sequences in the reference genome assembly; these were identified based on excessive coverage and heterozygous genotype calls in whole-genome sequencing of 40 haploid S. invicta males sampled from Herradura and Alejandra [27].

We analyzed the mapped sequences for single nucleotide polymorphic sites (SNPs) using the Stacks pipeline and created a catalog containing 285,847 SNPs for the combined seven RAD libraries, with measured coverage of X16 on average. These SNPs were used to calculate the FST distances between the populations.

Population structure

We filtered the SNPs catalog further before its use in the population structure analyses. For each locus, we required genotype calls in at least 80% of the samples in each population (i.e. less than 20% missing data); a minimum of three reads made for a genotype call. Additionally, we required a minimal minor allele frequency (MAF) of 1%. This stringent filtering resulted in a collection of 16,759 high confidence SNPs. Finally, we removed samples with more than 30% missing data (i.e. loci without genotype calls), leaving 300 samples in the analysis.

We ran STRUCTURE over K (number of expected clusters) values of 2–9, 100 times for each K, with 100 different sets of 1000 SNPs randomly chosen out of the high confidence SNPs collection, a total of 800 separate runs. To avoid linked sites from affecting the analysis, we required a distance of at least 5000 bp between the selected sites. Multiple runs over various data subsets contributed to the robustness of the clustering inference and allowed us to use more SNPs than would be possible in a single run. We ran STRUCTURE for 1,100,000 MCMC repetitions and discarded the first 100,000 (burn-in period). All the other parameters were kept at default values. The results were analyzed using CLUMPAK [54]. The STRUCTURE analysis was repeated with all the SNPs in the Social chromosome removed, leaving 15,539 SNPs in the analysis. The results were largely unchanged, and they can be found in Additional file 1: Figure S2. We used the Evanno test [55] to identify the number of clusters K, which gave K = 4 (Additional file 1: Figure S3). However, we decided to present the results for K = 5 where the native and introduced S. richteri separated to two distinct clusters.

Populations demographic history

Full maximum likelihood test for gene flow using 3s

We tested the hypothesis that S. invicta and S. richteri have been maintaining complete genetic isolation in South America since their divergence. The alternative to this scenario is that these incipient species have had some form of gene flow between them, including isolated successful mating events (isolation with migration). We used 3s program, which is a coalescent-based maximum likelihood inference tool. The program analyses aligned sequences of three species, two that are closely related and a third which is used as an out-group, for the genealogical process of coalescence and migration. Based on this the maximum likelihood scores of two possible demographic history models are compared, a null model that does not allow genetic flow between the two closely related species and an alternative model that does.

In addition, 3s provides estimates for the times of the two speciation events and for historic and contemporary population effective sizes. Speciation times are inferred from the model parameter τ – the average number of substitutions per site since speciation. Effective population sizes are represented by the θ parameter. In diploid species, θ = 4μNe, where μ is the mutation rate and Ne is the effective population size. For a haplodiploid species, θ = 3μNe because of the ploidy ratio between males and females.

Using 3s, we investigated the demographic history of the closely related S. invicta and S. richteri species with the thief ant S. fugax as an out-group (genome assembly version Sf_gnA; NCBI accession QKQZ00000000; [27]). To give meaning to the chosen model parameter estimates of speciation times and effective population sizes, we used the mutation rate of another hymenopteran, the honeybee, which was estimated at 3.4*10− 9 (95% confidence interval of 2.2*10− 9 - 4.9*10− 9) mutations per site per generation. This mutation rate was calculated using direct measurement of two generations in three colonies and is similar to the mutation rate inferred for other insects [56, 57].

Genetic data set preparation

The program requires only a small number of individuals with a large number of loci to represent each species. We arbitrarily chose two S. richteri individuals from the populations of Las Flores and Buenos Aires (R1 and R2 respectively) and two S. invicta individuals from the populations of Alejandra and El Recreo (I1 and I2 respectively). All four chosen individuals were of the gp-9BB genotype of the social chromosome. Using Bowtie2, we aligned their RAD reads to the reference genome of S. invicta and to a fully sequenced S. fugax individual, allowing no gaps in the alignments. We retained only RADseq reads with no more than 4 mismatches compared to the S. invicta reference genome and RADseq reads with no more than 10 mismatches compared to the S. fugax genome. The mismatches cutoffs are based on the average of 95% sequence identity between S. invicta and S. fugax [27]. We also required unique mapping and only allowed alignments in which the second best hit has at least twice the number of mismatches as the best hit.

We assembled for each locus an alignment of three sequences composed of the sequences of the outgroup of S. fugax and one of following pairs of sequences at random: I1 and I2, R1 and R2 or R1 and I2. As the algorithm assumes no linkage disequilibrium (LD) between sites, we only allowed loci that were at least 2000 nucleotides apart. This produced 15,040 triplets of 96 bases long three-ways alignments, to be used as input for 3s software.

Execution

We ran 3s and calculated the maximum likelihood values for the two models using the Gaussian quadrature number of points = 16. To examine the robustness of the estimates we ran each of the models three times, with different seed values at each run. We used the likelihood scores and the parameter values that were obtained for the highest scoring run of each of the models and compared them in a Likelihood Ratio Test (LRT).

Demographic history of populations of S. invicta

Using approximate Bayesian computation (ABC), we estimated divergence times and population sizes of the three S. invicta population clusters identified by STRUCTURE, for the demographic history model depicted in Fig. 4. Instead of full Bayesian calculations of a likelihood function, DIYABC uses an approximate approach: it runs a series of coalescent simulations over a demographic history model, which includes an historic scenario and parameter prior distributions. The program estimates the posterior distributions for the model parameters based on how well the simulated data fit the observed genetic data (represented by their summary statistics).

Our STRUCTURE analysis found the two native S. invicta populations of Alejandra and El Recreo indistinguishable in term of their genetic polymorphism and so they were assigned to one population, while Herradura’s population was clustered separately. The introduced populations were also clustered together in one population. We formulated the demographic history model used for the ABC analysis with these three distinct population clusters.

Scenario construction

In the historic scenario, depicted in Fig. 4, the two native populations, NN1 and NN2, diverged from each other TD generations ago, prior to the introduction to the USA, which took place TI generations ago. As the introduced populations in the USA were found to originate from the region of Formosa (which includes Herradura), in our scenario the founder population, NF, is directly derived from population NN1, and their divergence time coincides with the time of introduction. The scenario also includes a population bottleneck effect after the introduction, which lasted for TB generations and concluded as the size of the population reached its contemporary size, NI.

Parameterization

Coalescent model parameters are either demographic, reflecting population effective sizes, or temporal, indicating the number of generations that had passed between events. We defined parameter priors of normal distributions with averages based on known life history of the fire ants. Prior distribution widths were set widely to allow DIYABC sizeable sampling range, encompassing all reasonable values of these parameters.

The introduction time of S. invicta predates sampling time by at least 80 years. Generation time for the fire ants, especially at the time they were dispersing throughout the newly introduced range, is hard to estimate. We therefore defined a prior of introduction time that ranges between 0 to 180 generations. Based on studies indicating that the original number of introduced S. invicta was small, we defined a prior for the effective population size that ranges between 1 and 500 individuals. The ants’ quick expansion in North America suggests a minimal time span of the population bottleneck. This allowed us to narrow the prior distribution of the bottleneck time between 0 and 40 generations. Not much is known about the effective sizes of the native and introduced populations or of the time of divergence between the native populations, and these parameter priors were kept at a wide distribution, which included many orders of magnitudes.

Choice of summary statistics

An ABC analysis depends on population summary statistics to reduce the high-dimensional genetic information and to evaluate the simulation results. A varied choice of summary statistics is therefore crucial. However, using too many would increase the dimensionality of the analysis, making the available observed data points too sparse in comparison [58]; a problem known as “the curse of dimensionality”.

The native NN1 and NN2 populations are presumed stable and well represented by their summary statistics. We therefore used all of the within-population summary statistics offered by DIYABC: the proportion of monomorphic alleles, mean and variance of gene diversity of polymorphic loci [59] and mean gene diversity across all loci. For the population NI, a newly established population, we only used the summary statistics of the proportion of monomorphic alleles and mean gene diversity across all loci.

We included between-populations summary statistics for pairs of populations that directly diverged from each other (NN1 & NN2 and NN1 & NI): the mean FST distance, the proportion of null FST distances [60], and mean and variance of non-null FST distances.

Genetic data set preparation

We subdivided the SNPs catalog to create a dataset to include only the S. invicta samples. The SNPs were filtered as described before, with the following modifications: we required that each locus has genotype calls in at least 90% of the samples of each population, a minimal MAF of 0.5%, and at least 5000 bp between SNPs. The reduced MAF threshold is meant to allow the DIYABC analysis to make use of the valuable information in the low frequency alleles. This resulted in 161 samples and 6389 loci that were used in the analysis.

Simulations and analyses

Running DIYABC coalescent simulations, we created 892,000 simulated data sets. Based on the 1% of the simulations that produced summary statistics closest to the observed data, the parameter posterior distributions were estimated and adjusted using a weighted linear regression in which the summary statistics were the independent variables. To measure the goodness of fit of the model [61], we randomly selected 10% of the adjusted simulated data sets, and compared them to the observed data in a PCA analysis of the summary statistics.