Examination of the allele and haplotype richness (number of variants) in invasive S. invicta offers the simplest means of determining the minimum number of mated founder queens responsible for the establishment of the species in the USA. The highest estimates for Mississippi and the total US population, six and nine, respectively, correspond to the numbers of mtDNA haplotypes recovered. Data inferred for the most polymorphic nuclear gene, the sex-determination locus, suggest a minimum of four founders for either population, while allele richness at the most polymorphic microsatellite (Sol-42) is consistent with a minimum of three and five founders for the respective populations. These are almost certainly underestimates of the numbers of founders, given that they are limited by the polymorphism of the markers and that they assume every founder queen bore a unique haplotype and a set of three unique alleles per nuclear gene different from every other founder.
Results of computer simulations modelling the effects of founding on mtDNA haplotype richness are shown in . Given the haplotype data from the native range, the most likely number of founders bearing six haplotypes, the number currently found in Mississippi, is six or seven, depending on whether Formosa or the pooled Argentina samples are considered as the potential source and whether or not estimates of the native haplotype richness are corrected. In all cases, only founder group sizes from six to nine yield probabilities greater than 0.2 of carrying six unique haplotypes. The most likely number of founders bearing nine haplotypes, the number currently found throughout the USA, ranges from 10 to 17 (probabilities greater than 0.2). These probabilities probably underestimate the propagule size because additional losses of haplotypes may have occurred due to drift following the initial founder event; thus, they are best viewed as probabilities of the genetically effective numbers of founders.
Figure 1 Simulation-derived probabilities of six or nine mtDNA haplotypes being represented in different-sized groups of founder queens of S. invicta in the USA. Six haplotypes presently occur in Mississippi, whereas nine occur throughout the US range. Sources (more ...)
Likelihood curves for estimates of a, the number of remaining haploid founder lineages, obtained from coalescence-based CoNe simulations are shown for each nuclear gene for various colonization scenarios in figure S1 of the electronic supplementary material. Maximum-likelihood estimates of a derived from the combined nuclear data correspond to genetically effective founder group sizes that are remarkably similar to those obtained from the mtDNA founder simulations described above, when 10 generations between founding and sampling are assumed (). Thus, the nuclear simulations suggest a high likelihood of 8–10 founders of the Mississippi population, while the mtDNA simulations suggest a high probability of 6–9 founders for this single population (lower values are favoured in each case when the larger and more diverse source population is assumed). Also, the maximum-likelihood value of approximately 14 founders of the entire US population derived from the nuclear data is bracketed by the 10–15 queens representing the highest probabilities of founding this population based on the mtDNA simulations (assuming Argentina as the source in both cases). The maximum-likelihood estimates of founder number based on the nuclear simulations effectively double when the number of generations is assumed to be 20 rather than 10 (electronic supplementary material, figure S1), illustrating the sensitivity of the coalescence-based method to the assumed values of this variable. Nonetheless, the estimates are in all cases less than 30, and generally less than 20 founder queens. We note again that the results from the nuclear coalescence simulations may be underestimates of the actual founder numbers (they amount to the genetically effective founder numbers) because they do not account for any loss of lineages that occurred through drift following founding.
Figure 2 Single-gene maximum-likelihood values for the number of founder lineages remaining in invasive S. invicta in the USA (a) distinguished by the class of nuclear marker. Values are derived from the coalescent simulation program CoNe by assuming 10 generations (more ...)
The maximum-likelihood coalescence-based estimates of a from the 10-generation simulations are shown separately for each nuclear gene in . When Mississippi is designated as the colonizing population, there is no evident bias in the estimates by marker type, although the higher diversity microsatellites clearly display less variance than the lower diversity allozymes. When the entire US population is considered, the microsatellites generally yield higher estimates than the allozymes. The estimates derived from the sex locus fall roughly in the middle of the range of values from the traditional nuclear loci in all cases. This pattern would seem to validate this highly novel, indirectly assayed marker as being useful for inferring genetically effective founder numbers. Identical relative rankings of the single-gene a values were obtained in the 20-generation simulations.
In the event that early founder population growth was high and the number of founders relatively low, estimates of the genetically effective founder numbers obtained by the mtDNA and nuclear coalescence-based simulations may closely approximate the actual propagule size (Knowles et al. 1999
; Anderson & Slatkin 2007
). Otherwise, only a subset of the original founder lineages is expected to be represented in our samples, with the other original lineages having been lost through drift. The relationship between the number of lineages at founding and the number surviving to the time of sampling depends on specific features of the demographic history of the colonizing population; hence, it is important to examine this relationship under different demographic scenarios (Anderson & Slatkin 2007
). The results of our simulations in which founder group size and genetic composition, as well as population growth rate, were systematically varied to infer the probability of retaining the extant allele and haplotype richness in the USA are shown in (for simplicity, only the extreme cases of 9 and 20 founders are shown). When population growth rates are modest (r
≤0.5), probabilities of the extant numbers of variants being retained are often low (less than 0.5), even with 20 founders bearing three variants in excess of the extant number. However, with values of r
of 0.8 or higher, the probabilities rise above 0.5 for all markers when two or three excess variants are assumed in as few as nine founders. Even when no excess variants are assumed, growth rates of r
≥1 yield high probabilities that the extant numbers of variants are retained at most markers when the founder groups comprise 12 or 20 queens. Given the extraordinary reproductive potential of mature S. invicta
colonies (Morrill 1974
; Vargo & Fletcher 1987
) and historical records of rapid population expansion following the initial founding (Tschinkel 2006
), growth rates of r
≥1 (100% or more increase in the number of colonies per generation) would seem biologically realistic for the early colonizing population (see also Ficetola et al. 2008
). Thus, these simulations suggest that our estimates of the genetically effective number of mated founder queens may be quite close to the actual number, especially if the founder group bore a small number of variants in addition to those presently found in the USA at most markers. These results, based on empirically determined allele counts and frequencies from the native and introduced ranges of S. invicta
, are congruent with the findings of Anderson & Slatkin (2007)
based on simulated data.
Figure 3 Probabilities of the numbers of genetic variants extant at the most polymorphic markers in S. invicta in the USA being retained, based on the simulations of different scenarios of the size and genetic diversity of the founder group and of early population (more ...)
Given the effect of excess variants carried by the founder queens on the relationship between the genetically effective and actual founder numbers, it is worth revisiting the results of our mtDNA simulations of the impact of the founder group composition on haplotype richness. Considering Mississippi as the relevant introduced population, the probabilities of a propagule group from Formosa or the combined Argentina populations carrying two or more extra haplotypes become relatively high once 10 or 9 queens, respectively, comprise the group, a modest increase over the most probable numbers bearing six haplotypes (). Considering the entire USA as the relevant introduced population, relatively high probabilities are attained once the numbers of queens reach 16 or 14, respectively, again a modest increase over the most likely numbers bearing 9 haplotypes (). The revised figures shown in columns 2–4 of may be regarded as the best approximations of the actual numbers of mated founder queens based on the mtDNA data, whereas the unrevised figures in column 5 (obtained from ) are best viewed as approximations of the genetically effective numbers.
Table 2 Numbers of founder queens necessary to introduce extant numbers of mtDNA haplotypes or at least two in excess of extant numbers into the USA, based on simulations. (Data in the top part of the table are relevant to the Mississippi population, while data (more ...)
It is worth noting that estimates of either the actual or effective numbers of founders may be preferable, depending on the goals of an analysis. A sound estimate of the actual number may be desired, for instance, in evaluating the potential for the successful introduction of specific organisms via specific conveyance mechanisms, whereas an estimate of the genetically effective number would be more relevant to evaluating the loss of genetic diversity and its effects on the persistence and evolutionary potential of a colonizing population. For S. invicta
, the actual numbers are appropriately regarded as genetically independent ‘queen equivalents’. For reproductive queens of the monogyne form or newly mated queens of either form that undertook dispersal flights, these equivalents should be the same as the actual number of individual founders. For polygyne reproductive queens, nest-mates of which are closely related in the native range (Ross et al. 1996
), the equivalents may correspond more closely to the number of colonies from which the founder queens originated than to the number of individual queens.
The results of this study, based on large sample sizes, data from a number of highly informative genetic markers and relevant background biological information, provide the first robust estimates of the numbers of founder queens of S. invicta
responsible for colonizing the USA. Based on the data from the Mississippi population, our analyses suggest that 9–20 unrelated mated queens are likely to have comprised the initial founder group to colonize the USA at Mobile, Alabama, in the mid-1930s. Estimates based on the complete set of pooled US samples range marginally higher, with perhaps 15–30 queens involved in the colonization of the entire introduced range. The consistent differences between the estimates of founder number derived from the Mississippi and the total US samples in all of our analyses can be taken as support for the hypothesis that one or more secondary introductions of the ant into the USA occurred (see also Shoemaker et al. 2006
The congruence between the results based on the different classes of markers and different analytical approaches lends weight to the credibility of our estimates. Among the nuclear markers, the sex-determination locus stands out from the others with respect to the way that variability was assayed; allele counts and frequencies were inferred indirectly based on the proportions of queens producing atypical, diploid males, rather than directly by scoring individual genotypes. The mtDNA sequence data not only track a separate genome with a different mode of inheritance and effective population size than the other markers, but also these data were analysed using a completely different simulation method than the coalescent-based likelihood method used to analyse the nuclear data.