Samples from historical and contemporary lake trout populations were collected from Lake Huron (Parry Sound [PS]; sampled in 1958 and 1999) and Lake Superior (Isle Royale [IR] and Gull Island [GI]; both sampled in 1959 and 1995) (Fig. 1). A total of 303 individuals were analysed. Samples from historical populations were based on archival scale samples retained by management agencies. For archival data, sampling dates corresponded to times of minimum historical census sizes for Lake Huron (1958), and occurred two years before estimated historical minimum population size was reached for the Gull Island population (1961; [14]) (Fig. 1). Contemporary samples represented close spatial replicates of their historical counterparts (Fig. 1) and are considered as being remnant and historically self-sustained populations [14,15]. Those populations represent remnant populations that survived bottleneck [13].

We examined patterns of genetic variation at five dinucleotide microsatellite loci developed for other salmonids (Ogo1a [16]; Oneμ10 [17]; Scoμ19 [18]; Sfo1 [19]; and Ssa85 [20]). Microsatellite loci were selected for analysis due to their easy scoring in past and present populations (guidelines in [21]). Protocols are fully described elsewhere as well as care taken to avoid scoring error and artefacts in archival samples (e.g., allelic drop-out) [13].

Bottleneck testing was performed for each population using the M-ratio (hereafter M) method introduced by Garza & Williamson [8]. M represents the ratio of the number of alleles to total range in allele size. Computations were made for all loci, and average M computed across loci in each population. As other methods [4–7], this method allows for bottleneck testing based on a single sample. Hence, each population can be evaluated individually. Sampling at this level allows greater understanding of the evolution of M-ratios in temporarily replicated lake trout populations (Table 1), and if dramatic reductions in lake trout numbers that occurred in each lake impacted populations genetically over a period of 30–40 years (4–6 generations). Based on comparisons of genetics data used to compute M and known history of a given number of species, Garza & Williamson [8] reported that values of M lower than 0.7 indicated evidence of a bottleneck, whereas values greater than 0.8 indicated species with no bottleneck history. Values of M depended on several parameters such as the percentage of one-step mutation ${\Delta }_g(\mathrm{g}=1$; i.e., each mutation changes allele size by only one repeat unit; SMM model [22]), the size of alternate mutations Δ_g that are not one-step (g=2,3,…,n; two-phase model [23]), and Θ defined as four times the product of effective population size (N_e) and mutation rate (μ). These parameters are difficult to estimate in empirical samples, yet strongly influence the equilibrium value of the M-ratio. Hence, we tested each estimate of M under different evolutionary scenarios including (i) a two-phase model of mutations with proportions of non one-step mutations being 0.00 (SMM model), 0.05, 0.10, and 0.20; (ii) Δ_g varying from 2 to 4 (this latter value suggested by results obtained by Garza & Williamson [8] in simulations); and (iii) Θ being equal to 0.1, 1, 4, 10, 100 (a range that encompasses many realistic scenarios for natural populations). For each lake trout sample, a population at equilibrium is simulated 10 000 times for each combination of these parameters and simulated values of $M\left({\mathrm{M}}_{\mathrm{sim}}\right)$ were computed. The empirical estimate of M across polymorphic locus was then compared to the distribution of M_sim values to access significance (95% criterion). This procedure was replicated ten times and results report the average level of significance. For each population and for each combination of parameters, we obtained an average likelihood surface facilitating estimation of the extent to which populations had possibly been affected by a genetic bottleneck. Other tests attempting to evaluate existence of bottlenecks were not carried out on our data. For instance, the approach of Luikart et al. [5] requires more loci than available here, leading to inaccurate detection of reduction in population size. Beaumont's [6] method assumes a strict SMM that is not likely correct for the lake trout data.

Multilocus Hardy–Weinberg equilibrium was supported in each sample (results not shown). Significance of M-ratios as postulated based on previous literature [24], (i.e., M<0.7) indicate that four of six lake trout samples, including all contemporary samples, showed evidence of bottlenecks (Table 1). If the 0.7 threshold proposed in [8] was not reached for historical populations, estimates are very close to 0.7 indicating that low historical population sizes or other evolutionary events (e.g., coancestry and variance of reproductive success also affecting effective population size) had already demonstrably affected genetic diversity. No significant relationship between sample size and M was observed (r=0.14; p>0.1, 4 df).

Interpretations of M values for each population sample were not straightforward. Tests employing combinations of parameters (Θ), and different mutation models indicated that hypotheses of genetic bottlenecks were not universally supported across all parameter combination (cells in bold; Table 1). Without further information of effective population size allowing estimates of plausible ranges for Θ, or of information on mutational properties of the loci employed, (knowledge of δ and of the percentage of larger mutations; Table 1), it is difficult to know if each population was bottlenecked. Like for many species, any estimate of Θ is readily available for lake trout. Based on estimation made by Bernatchez & Wilson [25] on lake trout mitochondrial DNA (mtDNA) data, effective population of females was estimated to 42×10³ in Great Lakes. This estimate is rather low according to the values reported by those authors for a total of 42 freshwater and anadromous fish species (range 7×10²-−7×10⁶; scored 14^th on 42 species). Assuming a mutation rate of 0.02×10⁻⁶ [25], Θ could be estimated as roughly 33.6×10⁻². This estimate clearly ranged among values of Θ chosen for simulations (Table 1). For mutation models parameters encompassing δ=2 and δ=3, and for a percentage of larger mutations often up to 10% [i.e., for the majority of simulations (Table 1)], such values indicate that lake trout populations have very likely been influenced genetically by a bottleneck.

While plausible ranges of population parameters are consistent with occurrence of a bottleneck, it should be kept in mind that results reported in [25] are based on mtDNA data and cannot likely be transferred to microsatellite data. Because of maternal inheritance, mtDNA is more sensitive to bottleneck than other markers inherited from both parents (i.e., greater likelihood of drift owing to a four-fold lower expected evolutionary effective population size). A shift in the estimation of Θ due to bi-parentally inherited markers and to mutation rates more realistic for microsatellite loci is then possible. For instance, assuming a mutation rate of 10⁻⁴ classically used for microsatellite loci, and no change in other parameters leads to Θ=16.8. For such an estimate and any knowledge of mutation model, inference of bottleneck is not straightforward, particularly for δ=4 and for higher percentages of larger mutations (e.g., 0.1–0.2) (Table 1).

Without clear knowledge of the mutational patterns affecting loci, values of M may not be able to accurately infer population bottlenecks. In the lake trout case, better support for bottleneck can be made by comparing the likelihood surface across different population parameter values (for Θ) and mutation models. We found that bottlenecks were consistently indicated across a wider range of parameter values in contemporary samples than in archival historical samples, as indicated by the larger area of cells in bold in archival samples than in contemporary samples for a given mutation model (Table 1). Inferences were qualitative and not purely quantitative based on simple interpretation of M-values as proposed in [8]. This qualitative result indicates that bottlenecks can be inferred from genetics data using the M-ratio. However, inferences are best made using archival data as previously advocated in other fish studies, e.g., [26–29]. The value of the M-ratio method as a “single sample” method to detect bottleneck is likely to be limited without knowledge of mutation models, percentage of larger mutations, and a rough estimate of Θ. Number of loci probably plays a role [8], but the present study considered a number of loci that is very classically used in most empirical data. For example, archival population with higher M-values (IR59, PS58, M>0.7; Table 1) showed likelihood surfaces indicating that no bottleneck was evidence over a wide range of parameter combinations. The reverse was true for contemporary Lake Superior samples (IR95, GI95) that have the lowest M-ratios (Table 1). Similar explorations of likelihood surfaces should be produced for careful interpretation of M-values, particularly for species showing evidence of less stringent bottleneck than lake trout.