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| 4. The rise and fall of isolation by distance in the anadromous brook charr Salvelinus fontinalis Mitchill. | ||
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Les patrons géographiques de la diversité génétique dépendent des propriétés démographiques d’une espèce évoluant au sein d’un habitat donné. Comme pour beaucoup d’espèce l’environnement et les propriétés démographiques peuvent tous deux évoluer dans le temps, la structure de la diversité génétique ne correspond souvent pas à ce qui pourrait être prédit par un simple examen de leur habitat. Il est alors crucial de connaître la vitesse à laquelle les patrons d’organisation approchent leur état d’équilibre stable. L’omble de fontaine Salvelinus fontinalis (Salmonidae) occupe des patchs d’habitat (rivières) organisés linéairement le long des aires côtières et connait des mouvements marins d’ampleur limitée. Un patron constant d’isolement par la distance devrait donc être observé tout du long de laire de répartition de l’espèce. Cette aire de répartition s’est cependant, récemment déplacée vers le nord suite au retrait de la calotte glaciaire de l’est du Canada. Les populations nordiques sont donc présentes depuis moins longtemps et peuvent donc être encore en chemin vers l’équilibre migration-dérive. Nous avons documenté les variations temporelles des patrons d’isolement par la distance, de différenciation génétique et de richesse allélique le lon,g de 4992 km d’une côte linéaire sur la route probable de recolonisation post-glaciaire en nous basant sur les génotypes à six locus microsatellite de 2087 ombles de fontaine anadromes issues de 59 populations. Nous avons observé un déclin la richesse allélique concomitant d’une augmentation des niveaux de différenciation et d’un déclin du signal d’isolement par la distance dans les populations les plus récemment colonisées au nord. Suite à cette progression initiale vers l’équilibre, cependant, les patrons d’organisation ne se maintenaient pas parmi les populations du sud. À la place, la richesse allélique diminuait, les populations étaient de plus en plus différenciées, et l’intensité des patrons d’isolement par la distance diminuait à nouveau, suggérant une fragmentation accrue des populations les plus anciennes. Nous proposons que la perte des capacités de dispersion associées à l’expression de l’anadromie est responsable de cette fragmentation accrue des populations du sud. Cette étude démontre donc que les patrons d’organisation géographique de la diversité génétique ne dépendent pas uniquement des propriétés démographiques d’une espèce dans un habitat donné : l’évolution de l’aire de répartition et de la forme de dispersion ont également une importance majeure. Ces considérations d’ordre biogéographique mènent au constant que la fenêtre temporelle à l’intérieur de laquelle les patrons spatiaux de diversité génétique reflètent l’interaction à long terme d’une espèce avec son habitat peut être très réduite. Nos résultats introduisent donc une note de précaution quant à l’inférence de paramètres démographiques sur la seule base des patrons d’isolement par la distance. Plus généralement, ils argumentent pour une prise en compte plus générale d’une perspective biogéographique dans les études de génétique des populations.
Geographic patterns of genetic variation depend on a species’ demographic properties in a given habitat. Since both their environment and demographic properties evolve in time, many species will not fit the structure that would be predicted by a simple examination of their habitat. The rate at which patterns of genetic structure approach a stable equilibrium thus becomes pivotal in our understanding of spatial patterns of diversity. The brook charr Salvelinus fontinalis (Salmonidae) inhabits habitat patches (rivers) linearly organized along coastal areas and has limited movements at sea, such that a stable one-dimensional isolation by distance pattern should be observed over the whole range. The distribution range, however, recently shifted northward after the ice cap last retreated from eastern Canada, such that northern populations have been settled more recently and may still be on the process of reaching equilibrium. We investigated temporal variation in isolation by distance patterns, genetic divergence and allelic richness along 4992 km of a linear coast along the most likely northward postglacial colonization route of eastern Canada using individual genotypes of 2087 anadromous brook charr from 59 rivers at six microsatellite markers. We observed a decline in allelic richness, together with an increase in differentiation and a decrease in isolation by distance patterns in the most recently colonized populations in the North. Yet, after this initial rise towards equilibrium, spatial patterns did not stabilize among the most southern populations. Instead, allelic richness decreased, populations became increasingly divergent and isolation by distance patterns decreased in intensity again, suggesting increased fragmentation of older populations. We propose that the loss of dispersal capabilities associated with anadromy may be responsible for this increased fragmentation in the southern area of the range. This study thus demonstrated that geographic patterns of genetic variation depend not only on a species’ demographic properties in a given habitat: the evolution of the species range and the evolution of the form of dispersal are also of prime importance. When taking such biogeographic considerations into account, the temporal window within which geographic patterns of genetic diversity reflect the long-term interaction of a species with the habitat it inhabits may actually be narrow. Our results thus provide a cautionary note for the inference of demographic parameters from the sole isolation by distance patterns and, more generally, they call for the inclusion of a biogeographic perspective in population genetics studies.
With few exceptions (e.g. Whitlock 1992, Dybdahl 1994, Giles and Goudet 1997), population geneticists have considered that the current partitioning of genetic diversity in space reflects a species’ long-term interaction with the habitat it reproduces in. Theoretical results have been obtained for increasingly realistic models of populations, among which isolation by distance (thereafter IBD) models are widely used because they account for the common observation that dispersal capabilities of many species are limited in most habitats. Obviously, this model should result in the increase of genetic differences with geographic distance (Wright 1943). This pattern of increase has been analytically derived using asymptotic properties of the equilibrium, i.e. after sufficient time has elapsed for patterns to be established and stabilized (Sawyer 1977). This equilibrium pattern should be most obvious when dispersal occurs along a linear transect than across a two-dimensional area (Kimura and Weiss 1964) and has been included within inference frameworks designed to estimate demographic parameters such as Nσ2 or Nm, the products of effective population size N by either the mean square of parent-offspring distance σ2 (Rousset 1997) or by the fraction of a population replaced by migrants each generation m (Slatkin 1993). These methods are commonly used in the empirical literature of both plants and animals species (e.g. Neigel 1997, Bohonak 1999, Pogson et al. 2001 and references therein).
Such inferences, however, neglect that ecosystems are dynamic by nature (McArthur and Wilson 1967, Avise, 2000) and that species’ ranges expand and shrink, sometimes at a fast pace (Brown et al. 1996, Kirkpatrick and Barton 1997, Davis and Shaw 2001). The last ice age in particular was one of tremendous periodic shifts in the range of most northern temperate species (Hewitt 2000). During this period, species followed the ice border, successively advancing and retreating, such that one may question the assumption that the time scale of these fluctuations was very large relative to the time required for equilibrium patterns to establish. Indeed, although the latter is quantitatively poorly known (but see Sawyer 1976, Slatkin 1993, Hardy and Vekemans 1999 for IBD patterns), the geographic distribution of genetic diversity of many species still bears the footprint of recent natural disturbances they each experienced (reviewed in Hewitt 2000), thus providing empirical evidence that the rate of approach to equilibrium may be slow in comparison with the disturbance regime. This is problematic since contemporary spatial patterns of diversity should then be viewed as reflecting primarily past disturbances rather than current population dynamics and would therefore interfere with our understanding of the interaction between evolutionary processes and spatial patterns of genetic diversity. From a practical point of view, this is also of concern since reliable estimates of migration rates or dispersal distances are increasingly demanded as integral elements of applied management and conservation decisions.
Slatkin (1993) theoretically showed that in a species expanding its range instantaneously to a new bare habitat, the correlation between genetic and geographic distances should be first be low and then increase progressively until the pattern of increase reaches its stationary value. The pattern of increase should be most obvious in a one-dimensional habitat and be first attained at short geographic distances before the pattern spreads over larger geographic distances. The size of the region where IBD should be evident should increase with the parameter 
, where 
is the time since the foundation of the population, m is the fraction of migrants each generation and N is the subpopulation size. Thus, with small Nm values (low number of migrants each generation) and recent foundation (small
), the observed rate of increase of genetic differences with distance in recently settled systems may reflect foundation processes rather than contemporary demographic parameters, especially at wider geographic scales.
Empirical studies monitoring the evolution of spatial patterns of genetic diversity provide an important contribution to our understanding of the origin of geographic patterns of genetic diversity (Boileau et al. 1992, Whitlock 1992, Dybdahl 1994, Hossært-McKey et al. 1996, Giles and Goudet 1997). Yet, they remain rare in the literature, mainly because dealing analytically with spatial and temporal heterogeneity in demographic parameters is inherently difficult. Populations located at the expanding edge of a species’ range typically show a high occurrence of dispersing phenotypes (Thomas et al. 2001), low allelic richness (e.g. Taberlet et al. 1998, Frydenberg et al. 2002), while differentiation can be either decreased (e.g. Dybdahl 1994, Green et al. 1996, Comps et al. 2001, Wilcock et al. 2001, Bernatchez and Wilson 1998) or increased (Berlocher 1984, Johnson 1988, Whitlock 1992, McCauley et al. 1995, Ingvarsson and Giles 1999) depending on the dynamic of colonization (Slatkin 1977, Ibrahim et al. 1996, Austerlitz et al. 1997, 2000, Le Corre & Kremer 1998). Empirical data on the evolution of IBD patterns during the early settlement of a species in a new habitat remain even more scarce (but see Leblois et al. 2000, Barrai et al. 2001, Kinnison et al. 2002). A first approach relies on demographic estimates and colonization scenario to show that, would sufficient time have elapsed, IBD should have been apparent (e.g. Leblois et al. 2000, Kinnison et al. 2002). A drawback of this approach is that it relies entirely on the precision of demographic estimates and often cannot be disentangled from statistical impediments to detect an IBD signal. Indeed, the absence of a clear pattern of isolation by distance in species with restricted dispersal is typically taken as an indication that populations depart from equilibrium conditions, even if a precise knowledge of recent demographic events is lacking (e.g. Hellberg 1995, Baer 1998, Hutchison and Templeton 1999, Ehrich and Stenseth 2001). Using a second approach, other studies have compared IBD patterns among sets of populations of different ages (Green et al. 1996, Barrai et al. 2001) and ascribed differences in IBD patterns to their temporal evolution. This comparative approach requires a large amount of data and thus typically confines the comparison to a limited number of discontinuous sets of populations within a small portion of the species’ range (north vs. south of North America in Green et al. 1996, USA vs. Europe in Barrai et al. 2001). Furthermore, because habitat structure and migration patterns may eventually vary among sets of populations, it may also be difficult to control for several sources of additional variation when the number of samples is small. In sum, although empirical studies have provided important insights into the evolution of geographic patterns of genetic diversity, they have remained limited in scope by the number of populations surveyed, by the lack of knowledge on historical events and demography, and by uncertainties about the precise migration pattern of the species in a given habitat.
The present study is based on a nearly exhaustive sampling of all existing anadromous populations of the brook charr (Salvelinus fontinalis Mitchill), a salmonid fish inhabiting a linear coast associated with a temporal gradient of colonization. This gradient allowed a continuous investigation of the temporal evolution of IBD patterns over a homogeneous habitat in the native range of the brook charr. The brook charr is endemic to north-eastern North America, where the last Ice Age resulted in a 50 000-70 000 years long series of rapid northward and southward shifts of the whole biota (Hoccutt 1986, Pielou et al. 1991). These dramatic climatic oscillations came to an end no earlier than 18,000 years ago and the last northward shift in distribution followed the retreat of the Wisconsinian Ice Sheet from eastern Canada (11,000 YBP, Dyke and Prest 1987). Brook charr probably reinvaded eastern Canada northward from the single “Atlantic” glacial refugium (Danzmann et al. 1998) located off the Atlantic coast of New-England (Schmidt 1986). No paleontological data are available on the dynamic of recolonization, but marine movements of brook charr appear to be strictly restricted to the coastal fringe, suggesting that colonists had to closely follow the coastline and colonize rivers they now inhabit. The Gulf of Maine (USA) was freed of ice 13,000 years ago (Borns et al. 1985) and the lower north shore of St-Lawrence River (Province of Québec, Canada) 10,000 years ago (Denton and Terence 1980), so the minimum time span between colonization of both areas was 3,000 years. Furthermore, because brook charr populations had to follow their invertebrate prey, which in turn had to follow vegetational range shifts (de Vernal et al. 1993), they could not establish instantaneously, and the date of ice retreat therefore provides a maximum time frame within which the last colonization must have occurred. For instance, palynological studies indicate that modern vegetation only developed in western Labrador around 3,770 years ago (de Vernal and Hillaire-Marcel 1987). The South-North gradient thus also corresponds to a time gradient, whereby northern charr populations, putatively younger, were founded at least 3,000 years later than southern populations, and possibly as much as 9,230 years later. Although there seem to be no major physiological constraints to rare long-distance migration events as long as salinity and temperature conditions remain tolerable (salinity 26.9 ± 3.1ppt, temperature 10.4 ± 2.5ºC degrees, van de Sande, Curry and Whoriskey, unpublished manuscript), distances covered over a season by brook charr in the coastal zone are typically short (< 0.5 km, van de Sande, Curry and Whoriskey, unpublished manuscript). Because tolerable temperature and salinity conditions for brook charr are only found in the coastal fringe, distances swum towards the ocean in large open water masses are probably even more limited (White 1942, Besner and Pelletier 1991).
Taken together, the one-dimensional nature of coastal areas and the restricted movements of anadromous brook charr in this habitat suggest that isolation by distance should be apparent if time was sufficient for an IBD pattern to establish. Therefore, we first tested the null hypothesis of no correlation between coastal distance and genetic distances. Second, if equilibrium was reached all along the 4992 kilometers of coast, then no variation in the slope of the IBD relationship should occur along this south-north temporal gradient. Alternatively, if the effect of colonization was still perceptible, a lower IBD slope should be observed among the most recently settled populations. We thus tested the null hypothesis of no variations in the slope of IBD along the colonization gradient. Third, if colonization processes still prevail at the northern edge of the range, they should also translate into changes in the levels of genetic diversity and divergence. We thus also tested the null hypothesis of no spatial pattern in variation of intrapopulation genetic diversity and the extent of genetic divergence.
Two thousand and eighty seven anadromous brook charr were collected from 52 rivers along the Canadian Atlantic coast and seven rivers from Anticosti Island, Québec, Canada (mean N= 35.4, Table 1, Fig. 1), a sampling covering nearly 75 % of all important rivers inhabited by anadromous brook charr in the region (Ryther 1997). The brook charr occurs in coastal habitats as far south as North Carolina, USA (McCrimmon and Campbell 1969), but no anadromous movements (seasonal movements of fish between freshwater used at reproduction and by juveniles until the age of one or two years, and saltwater used at feeding stages, Power 1980) are currently known to occur south of the gulf of Maine, USA (Bigelow & Schroeder 1953). Therefore, samples were collected from one of the southernmost rivers where anadromous movements currently occur (Hunters’ Brook in Acadia National Park, Maine, USA, labeled kilometer zero) and spanned northward over 4992 km of coastline to the Lower North Shore of St-Lawrence River (Fig 1.). All fish were collected either in saltwater in river mouths, or in freshwater in the downstream section of the rivers, below any physical barrier to migration. Distances among river mouths were measured along the coastline on 1/250,000 topographic maps. No major stocking effort occurred for the species in coastal areas, such that all populations can be considered as native. Adipose fins were nonlethally removed and preserved in 95% ethanol for genetic analyses.
Total DNA was isolated using a standard phenol-chloroform protocol (Sambruck et al. 1989), and individuals were genotyped at six microsatellite loci (SFO-12, SFO-18, SFO-23, SFO-8, SSA-197 and MST-85) as described in Castric et al. (2001).
The number of different alleles per locus (A) was standardized to the smallest sample size (N=13, i.e. 26 alleles sampled) using a rarefaction method (Petit et al. 1998). Although our mean sample size was much higher (N=35.4), Petit et al. (1998) showed that their method provides an efficient way to directly compare estimates of allelic richness among populations with different sample sizes. Genetic diversity was quantified by the observed heterozygosity HO and the unbiased estimate of heterozygosity corrected for the sampling bias (HE, Nei 1987). Population means of genetic diversity in the present study were compared to those observed in Maine (USA) for populations strictly restricted to landlocked freshwater habitats (Castric et al. 2001) using the Student’s t test in Statview v.5.01. (SAS Institute Inc. 1998).
Departures from Hardy-Weinberg (HW) proportions were tested in each sample using an approximation of an exact test based on a Markov chain iteration implemented in the Genepop software package version 3.1 (Raymond and Rousset 1995). Multilocus values of significance for HW tests were obtained following Fisher’s method to combine probabilities of exact tests (Sokal and Rohlf 1995). Critical significance levels for multiple testing were corrected following the sequential Bonferroni procedure (α=0.05, k=59, Rice 1989). The extent of deviation from HW proportions was quantified by Weir and Cockerham’s (1984) estimator of FIS (f) at each locus in each river using Genetix 4.02 (Belkhir et al. 2000). We also tested whether the same loci consistently exhibited stronger deficits across all populations using Kendall’s concordance method (Sokal and Rohlf 1995 pp. 593).
Heterogeneity of allele frequencies across samples was tested with Genetix’s permutation procedure using 2 000 permutations in the global test and 30 000 permutations in the pairwise test to maintain the tablewide significance level at α=0.05 after sequential Bonferroni correction (k=1711 pairwise comparisons). Global population differentiation was estimated in Genetix by Weir & Cockerham’s (1984) FST estimator θ. A neighbor-joining phenogram based on Cavalli-Sforza and Edwards (1967) chord distance was constructed using Phylip 3.57c (Felsenstein et al. 1993) to depict the pattern of genetic relationships among populations. Support for the topology was estimated using 1000 bootstrap replicates.
Isolation by distance patterns were analyzed under Rousset’s (1997) regression-based framework. With finite variance of parental position relative to offspring position (σ2), a linear relationship is expected between FST/(1-FST) and distance between populations pairs (j) in a one-dimensional linear habitat: FST/(1-FST) ≈ A1/(4Nσ) + j/(4Nσ2ε), where N is effective subpopulation size, A1 is a constant dependent on the shape of the dispersal distribution (constant C0 in Sawyer 1977, equation 2.4) and ε is the distance among consecutive habitat patches. A permutation test implemented in Genetix 4.02 (2000 permutations) was used to test the significance of Mantel’s correlation coefficient between coastal distance and FST/(1-FST). We then tested whether isolation by distance was constant over geographic scales by computing the regression slope of FST/(1-FST) over coastal distance, successively including pairwise comparisons of populations separated by increasingly large distances and. That is, the slope at 100 km was obtained by including pairs of populations separated by 100 km or less, while all pairs at 200 km or less were included for the 200 km slope. All following analyses were performed using the mathematics computer language Maple® 6 (Waterloo Inc. 1999).
The evolution of isolation by distance patterns along the temporal colonization gradient was further investigated using a sliding window analysis based on Rousset’s (1997) inference framework described above. Because northward colonization most likely followed the coastline, latitudinal distribution measured along the coast was used as a surrogate for age of populations. A constant width window was slid along the coast, successively including different sets of populations from the southernmost population (population #1 at coastal kilometer 0) to the northernmost population (population #52 at km 4992). Since they were geographically isolated, samples from Anticosti Island were excluded from this analysis. The width of the window (600 km) was chosen as a compromise so as to be as narrow as possible while constantly including at least four populations over the main part of the range. In order to consistently compare values across geographic areas, sampling density was kept constant by resampling all possible sets of four populations within each window if it included more than four populations (final density =1 sample every 150 km) and by removing the window from the analysis otherwise. The slope and intercept of the least-square regression line of all possible four-population subsamples were computed within each 600 km window, and their mean over all possible combinations were plotted against the location of the southern end of the window (in kilometers). The window was then shifted by 10 km increment northward along the coast and computations of the mean slope and mean intercept were performed again with the populations now included in the new 600 km span. The slope provides an estimate of Nσ2 and should progressively increase in recent systems (more northern populations) evolving towards equilibrium (Slatkin 1993, see Rousset 1997 for the equivalence with Slatkin’s notation system). The intercept provides an estimate of A1/(Nσ) and is thus also dependent upon the shape of the distribution via the parameter A1. Leptokurtic dispersal distributions tend to be characterized by large A1, such that variations in the intercept can reveal variations in σ or variations in the shape of dispersal distances. The evolution of the slope and intercept along the coast was tested using a backward stepwise model simplification procedure available in Statview to determine whether a quadratic correlation explained significantly more variance than a linear correlation.
If colonization processes still prevail at the northern edge of the range and can be detected on isolation by distance patterns, they may also have left their footprint on the level of intrapopulation genetic diversity and on the extent of genetic divergence. This was tested by comparing linear and quadratic correlations between the standardized number of alleles and latitude following the coastline using the backward stepwise model simplification procedure available in Statview. The evolution of FST along the colonization gradient was investigated using the sliding window analysis described above for isolation by distance, and the existence of either a linear or a quadratic variation pattern was tested similarly. Because geographic variations in genetic diversity may compromise the use of the fixation index FST as an indicator of population differentiation (Whitlock & McCauley 1999, Hedrick 1999), a second analysis was run by standardizing FST estimates by the maximal theoretical value they could reach at a given level of diversity in a window: 1-HE.
High levels of allelic richness and genetic diversity were found at all loci (Table 2, Fig. 2). Thus, consistently more alleles were found within the anadromous than within the landlocked populations from Maine (Castric et al. 2001, t=6.086, P<0.0001). A globally significant heterozygote deficit was observed over the whole data set (FIS= 0.0817, P<0.0005). Kendall’s rank test provided evidence that several loci were consistently more affected than others (P=0.0057), thus suggesting that technical artifacts such as non-amplifying alleles (Callen et al. 1993) or small allele dominance (Wattier et al. 1998) at specific loci (SFO-8 and MST-85) may have contributed to the deficit. The rank correlation was however very weak (Kendall’s W= 0.05) and the deficit could be detected over all loci (P<0.0005 for all six loci, Table 2), suggesting that non-artifactual explanations had to be taken into account (Castric et al. 2002). Heterozygote deficits could also partly result from a Walhund effect in several rivers (e.g. Boula et al 2002), which would bias the estimation of genotype frequencies, but not that of alleles. Furthermore, because no spatial pattern was obvious in the distribution of deficits, the occurrence of heterozygote deficits in several samples is unlikely to affect any of our main interpretations and conclusions.
Significant heterogeneity of allele frequencies was observed among populations (P<0.0005). The global FST value was 0.1068, but this figure varied geographically (Fig. 3). Significant differences in allele frequencies were observed in 1695/1711 pairwise comparisons (99.1%) after sequential Bonferroni correction (final α=0.00323). As indicated by their clustering in the neighbor-joining phenogram (Fig. 4), geographically proximate populations tended to be genetically similar. With the exception of Anticosti Island populations, significant bootstrap values were restricted to the tip nodes, suggesting that no strong barrier to gene flow existed along the coast. In contrast, populations from Anticosti Island clustered together with strong statistical support (Bootstrap=86%), thus providing direct support to the hypothesis that the open waters act as a strong barrier to gene flow in anadromous brook charr. All further analyses were thus restricted to samples collected along the coast.
The genetic similarity of geographically proximate populations was further confirmed by the strong and highly significant correlation observed over the whole dataset between distance and genetic divergence (Fig. 5, Mantel’s test: r=0.5675, P<0.0005). The best-fit regression model had a slope of 3.37x10-5 km-1 and an intercept of 0.07743. The slope, however, varied as a function of the spatial scale at which the relationship was examined (Fig. 6). When considering only pairs of populations separated by less than 50 km, considerable variation in the value of the slope was found (range = -0.00111 to 0.00247). This was followed by a monotonous log-linear decrease of the slope with increasing spatial scale (Fig. 6).
There was considerable geographic variation in the regression slope of the IBD pattern, especially at latitudes less than 1500 km, where negative as well as positive values were observed (Fig. 7). However, values were centered on zero, suggesting the absence of any significant trend in IBD pattern at latitudes less than 1500 km. When excluding southern populations below 1500 km from the analysis, IBD slopes followed a quadratic pattern of variation (R2=0.703, P<0.0001) rather than the linear variation predicted if populations had been progressing monotonously towards equilibrium. The maximum slope was attained near population 30 at kilometer 3366. Similarly, geographic variation in the IBD intercept were quadratic rather than linear (R2=0.767, P<0.0001), thus suggesting that a minimal value for parameter A1/(Nσ) occurred at kilometer 2646 i.e. between populations 17 and 18 (Fig. 8). Commercial landings reveal no reduction in population size towards the north (Malouin 1996), such that increases in intercept may reveal higher A1 (such as produced by more leptokurtic dispersal distributions) or lower σ (such as produced e.g. by lower migration rates).
As for IBD slope and intercept, allelic richness and FST varied geographically, with a quadratic model capturing significantly more variance than a linear model (backward simplification procedure, Fig. 2, P=0.0032 and Fig. 3, P<0.0001 respectively). The number of alleles followed a bell-shaped pattern of geographic variation, with highest levels of diversity at intermediate latitude than either further north or further south. Thus, the least square parabola showed a maximum allelic richness at km 2945, i.e. in the Chaleur’s Bay near population 19 (Fig. 1, 2). The sliding window analysis revealed that FST also followed a quadratic pattern of variation, with lower values at intermediate latitudes (kilometer 2444, between populations 13 and 14) than either North or South (Fig. 4, backward simplification procedure, P<0.0001). Correcting for variation in intrapopulation diversity also provided a highly significant quadratic pattern of latitudinal variation (P<0.0001, data not shown), indicating that the different upper bounds possibly reached by FST with different levels of diversity were not responsible for this pattern.
Overall, our results provided evidence for important variation in geographic patterns of genetic diversity and structuring among anadromous brook charr populations in eastern Canada. Isolation by distance appeared to be the basic process shaping population genetic structure in this species. Yet, the comparative analysis also showed that contemporary patterns of IBD, allelic richness and genetic divergence were different in areas colonized at different times. This suggests that the time scale required for equilibrium patterns to settle may be of the same order of magnitude as that of demographic disturbances experienced by brook charr over a large portion of its range during postglacial times. Contrary to the expectation under a simple “equilibration” model, however, spatial patterns did not maintain constant once they had emerged. Indeed, variation in latitudinal patterns of genetic diversity was also apparent at the southern end of the range, where populations have been present for a longer period of time. We propose that anadromy as a form of dispersal has declined in the region that was first colonized following deglaciation, leading to increased fragmentation, which is now blurring the patterns that were initially shaped by drift and migration. Our results therefore indicate that the temporal window within which latitudinal patterns of genetic diversity reflect the species’ long-term interaction with its habitat may be narrow.
This study first provided insights into the biology of coastal migration of the brook charr. High levels of intrapopulation genetic diversity were also found compared to landlocked populations from Maine (Castric et al. 2001), indicating that the coastal habitat provides better opportunities for migration. Despite high connectivity in anadromous relative to freshwater populations, brook charr found in different rivers, even those separated by short distances, were genetically distinct, indicating that straying rates are low and/or homing is precise. This was most obvious in southern populations, where the regression curve predicted 24.8 alleles over the six microsatellite for the southernmost population (km 0). This low value was similar to levels found in lacustrine populations from Maine (Castric et al. 2001), thus suggesting that the loss of anadromy rendered populations as isolated as landlocked populations. The significant correlation observed between FST/(1-FST) and geographic distance together with the strong clustering of Anticosti populations also confirmed earlier direct observations of limited movements of brook charr in high salinity waters (White 1942). Such limited movements may be explained by the species limited tolerance for high salinity water, but more elaborate mechanisms may be invoked as well. The observation of repeated incursions of fish into non-natal rivers before entering their “home” river (Smith and Saunders 1958) may suggest that the potential for straying is greater than shown by the genetic differentiation and that the homing behavior is active and strong. Direct observations and experimental data, however, remain elusive (but see Keefe and Winn 1990). Field observations of fish repeatedly returning to spawn in the same spawning ground within a river (S. Lenormand and J. J. Dodson, unpublished data) and evidence for genetic distinctiveness of fish spawning on different spawning grounds within a same river system (Boula et al. 2002) provide further support for the hypothesis that homing can be precise down to very fine geographic scales.
Had only the biology of seaward migration been taken into account and assuming equilibrium conditions, then no pronounced variation in the spatial patterns of either allelic richness, population similarity or isolation by distance patterns would be expected. Yet, each of these patterns decreased with increased latitude. Because northern latitudes are also the most recently colonized regions along the temporal gradient, our data supports the hypothesis that colonization processes are still prevailing in shaping spatial patterns of genetic diversity among northern populations. In phylogeographic studies, gradients of genetic diversity are commonly observed as the result of sampling processes during colonization from southern glacial refugia (Hewitt 1996, Avise 2000), thus suggesting that mutation rates and/or subsequent migration are usually too low for equilibrium levels of allelic richness to recover. The effect of colonization on population differentiation is less straightforward because it depends on the number and origin of colonists (Slatkin 1977, Le Corre and Kremer 1998). Assuming that the pattern of migration operating at earlier times of colonization was comparable to that observed among contemporary populations, colonists would have been successively drawn from the most recent populations at every step of the process. With numerous colonists, the sampling effect should have been negligible and lower levels of divergence among populations would have been expected in recent compared to older populations (Good’s model of stepwise colonization in Slatkin 1993; Bernatchez and Wilson 1998). In contrast, with low number of colonists, a stepwise colonization would involve successive founder events and should thus lead to increased divergence in recently colonized populations (Le Corre and Kremer 1998). The general increase of divergence and decrease in allelic richness we observed in northern populations therefore suggests that founder effects may have prevailed at times of recolonization following deglaciation. Assuming constant N and σ across populations, the increased intercept of the IBD relationship (related to parameter A1/Nσ) in northern areas further indicates a leptokurtic distribution of dispersal distances during colonization (high A1). If so, the early dynamic of colonization of new areas would have been very different from the contemporary dynamic of migration. Contrasts between early colonization and subsequent migration dynamics have been proposed in other studies, especially for plant species where colonization occurs through seeds while subsequent gene flow primarily occurs through pollen (Combs et al. 2001). In salmonids, exponential demographic growth of salmonid populations is frequently reported after removal of barriers to migration (e.g. Bryant et al. 1999, Tremblay et al. 2000). Competition may thus quickly intensify following population founding, decreasing fitness of subsequent migrants compared to colonists (Nichols and Hewitt 1994, Davis and Shaw 2001).
Assuming that non-equilibrium dynamics had been the sole factor explaining the observed variation of latitudinal patterns of genetic diversity, then such patterns should have remained constant once established at equilibrium. Clearly, this was not the case, as all patterns were quadratic rather than linear. That is, following their initial increase allelic richness and the IBD slope decreased and the extent of population differentiation increased among southern populations. As the southernmost populations were progressing towards increased fixation, spatial patterns became blurred and varied randomly among them. Similar trends of decreased population connectivity at range margins have been observed in other taxa, including the green frog Rana pretiosa (Green et al. 1996) and the brown trout Salmo trutta (Bouza 1999) and have been interpreted as a lack of adaptation of the species to the marginal habitat. Why then have southern populations of anadromous brook charr evolved towards increased fragmentation? We propose two non-exclusive hypotheses for increased fragmentation among southern populations that involve the evolution of anadromy. Because individual growth is increased in the marine environment due to higher food availability, payoffs for switching between habitats may outweight the costs of physiological acclimations to a hyper- and a hypo-osmotic environment (Boula et al. 2002). As such, anadromy may firstly be strictly viewed at as form of seasonal migration driven by the productivity gradient between fresh- and saltwater. Because this gradient declines in intensity at temperate latitudes (Gross et al. 1988), selective pressures for anadromous behavior become weaker and eventually disappear. Thus far, the evolution of anadromy has mainly been interpreted in that perspective. Yet, because anadromous behavior also provides the opportunity to reproduce in a different river, it is also subjected to the forces driving the evolution of dispersal (reviewed in Clobert et al. 2001). Namely, habitat instability ranks among the most powerful forces selecting for dispersal (Gandon & Michalakis 2001), while a costly dispersal form should decline in frequency in a stable environment (Van Valen 1971, Olivieri et al. 1995 Fig. 3, Cody & Overton 1996). Assuming that the more southern habitat occupied by the brook charr in postglacial times can be considered as stable, theory predicts that anadromy should decrease among southern (and therefore older) populations. The rate of decrease may be slow (Paradis 1998) and depends on several parameters, including the fitness cost of dispersing (Olivieri et al. 1995), mutation rate, and the level of habitat fragmentation (Paradis 1998). To summarize, whatever the exact causes for the loss of anadromy among southern populations, our results clearly indicate that brook charr populations inhabiting different rivers at southern latitudes are becoming increasingly isolated one from each other, which is leading to a independent drift and thus progressive disruption of geographic patterns of genetic diversity observed among more northern (and younger) populations.
As pointed by Rousset (1997, 2001) but seldom taken into account in empirical studies (but see Hellberg 1995, Ruckelshaus 1998, Ehrich and Stenseth 2001), the estimation of demographic parameters from the slope of the IBD relationship is strongly affected by the spatial scale of observation. Thus, our results showed that the IBD slope first varied randomly until scales of 50 km were considered, then decreased monotonously. Similar fading of IBD at larger geographic scales has been observed in several species (Hellberg 1995, Johnson and Black 1998, Ehrich and Stenseth 2001) and has received various explanations. First, as genetic differences increased with geographic distances, FST may plateau if it reached its upper bound at large geographic distances. The mean expected heterozygosity was 0.72, such that the maximum theoretical FST value should be approximately 0.28 (Hedrick 1999). Because this value is much higher than the level of differentiation actually observed (FST = 0.11), a plateau seems unlikely to have been reached in this study. Second, the fading could reflect a non-equilibrium situation. The spatial scale over which isolation by distance signal should be apparent during the transitory period towards equilibrium in a one-dimensional array of populations depends upon the parameter
(Slatkin 1993). Thus, for recent systems (small τ values), IBD may be weak over large geographic scales and consequently remain undetected. Third, and non-exclusively, mutation may not remain negligible relative to migration when increasing geographic scales. Because mutations arise randomly in space, theory predicts that their effect should be similar to island migrations (Crow and Kimura 1970) and weakens the relationship between genetic and geographic distances. Regardless of the exact explanation for this scale-dependence, it is problematic since it is precisely the slope that is used in empirical studies to estimate Nσ2. Rousset (1997, 2001) advocates the use of prior independent estimates of σ to delimit the scale over which the linear relationship between FST/(1-FST) is expected to hold reasonably well. In cases where no such estimate is available and/or is difficult to obtain, we propose an investigation of the scale-dependence of the IBD slope as a possible alternative. We suggest that the maximum slope after random fluctuations at short distances have ceased (approximately 50 km in this study) would be most accurate and should be used to infer Nσ2 values because any bias would then be minimal.
In addition to scale-dependence, important latitudinal variation in IBD slope was observed even when controlling for scale of analysis and sampling density. As detailed above, those variations probably arise from spatial and temporal variations in migration parameters. New analytical methods, such as maximum likelihood frameworks (Beerli and Felsenstein 1999, Bahlo and Griffith 2000) may represent promising avenues to investigate the limitations imposed by spatial and temporal variations in migration parameters. The joint estimation of migration rates, speed of recolonization and decrease in the frequency of migrating phenotypes that would maximize the likelihood of observing the data may thus become possible in the near future.
Processes underlying spatial patterns of genetic diversity must be correctly identified and accurately understood since they may impact a species’ potential to respond to selection and to persist in the face of changing environments (Kirkpatrick and Barton 1997, Thomas et al. 2001). To that end, population genetics approaches have usually considered static systems, whereby spatial patterns of genetic diversity reflect a species’ ecological characteristics with little regard for their evolution through time. Although mathematically simplifying, the assumption of temporal stability may prove especially unwieldy in evolutionarily young systems, because it fails to capture the dynamic essence of spatial patterns of genetic diversity, as was exemplified in this study. Clearly then, traditional population genetic models assuming equilibrium are not always adequate to characterize young populations. Most attempts to characterize the genetic impacts of habitat fluctuations have concentrated on smaller geographic scales in the framework of extinction-recolonization dynamic in metapopulations (e.g. Slatkin 1977, McCauley 1993). At a wider geographic and temporal scale however, the availability of suitable habitat has also constantly fluctuated due to climatic changes driven by the rotation axis of the earth (Pielou 1991). Our results reinforce the view that a biogeographic perspective is essential in order to fully understand the evolution of geographic patterns of genetic variation such as isolation by distance.
We thank L. Papillon, S. Martin, R. St-Laurent, T. Gosselin, J. VandeSande, D. Courtemanche, R. A. Curry and F. Whoriskey (U. New-Brunswick), A. Gaudrault, J. Labonté, M. Dorais, J.P. Lebel (Société Faune et Parcs, Québec), M. Fournier (Société des Établissements de plein Air du Québec), J. McMillan (Department of Fisheries and Ocean, Nova-Scotia), B. Patterson (Club Le gourmet), R. Firth (Corporation de Gestion des rivières Matapédia et Patapédia), R. Kippen (Club Kegaska), R. Deroy (Pourvoirie de la Haute St-Jean), E.Tremblay and L. Leblanc (Kouchibouguac National Park, New-Brunswick), R. Cormier (ZEC de la rivière Bonaventure), J. Patterson (Corporation de Développement de la rivière Madeleine), C. Cyr (Destination Chic-Choc), J. Bouchard (Association Les Castillons), G. Lemieux (ZEC de la rivière Cap-Chat) for their help during sampling. Technical help in the laboratory by L. Papillon, S. Martin, C. Landry and M. Parent was instrumental all along this project and is gratefully acknowledged. V. C. thanks P. Duchesne for introducing him to Maple programming. Maple programs developed for the sliding window analysis are available upon request from the authors. We also thank J. Turgeon, D. Fraser, G. Perry and R. Leblois for critically reading previous versions of the manuscript. Funding for this study was provided by a Natural Science and Engineering Research Council (NSERC) strategic grant to L. B. This is a contribution to the research program of the Groupement Interuniversitaire de Recherche Océanographique du Québec (GIROQ).
Table 4-1 Anadromous brook charr samples collected. Geographic regions are based on coastal mophology.
|
Label |
Sample location |
Geographic region |
Coastal distance from km 0 |
Latitude N |
Longitude W |
N |
|
1 |
Hunter's brook |
Gulf of Maine |
0 |
|
|
40 |
|
2 |
Rivière Kennebecassis |
Bay of Fundy |
280 |
45° 19' 00" |
66° 08' 00 |
41 |
|
3 |
Dolan Brook |
Bay of Fundy |
345 |
45° 21' 00" |
65° 38' 00" |
33 |
|
4 |
Cornwallis River |
Bay of Fundy |
530 |
45° 06' 00" |
64° 21' 00" |
40 |
|
5 |
Acacia Brook |
Bay of Fundy |
786 |
44° 35' 00" |
65° 45' 00" |
25 |
|
6 |
Jordan River N.S. |
Bay of Fundy |
1086 |
43° 46' 00" |
65° 14' 00" |
29 |
|
7 |
Petite Rivière |
Atlantic Coast, N.-S. |
1166 |
44° 14' 00" |
64° 26' 00" |
29 |
|
8 |
West River St-Mary |
Atlantic Coast, N.-S. |
1406 |
45° 15' 00" |
62° 04' 00" |
24 |
|
9 |
Baddeck River |
Atlantic Coast, N.-S. |
1806 |
46° 05' 00" |
60° 52' 00 |
39 |
|
10 |
Clyburn Brook |
Atlantic Coast, N.-S. |
1886 |
46° 40' 00" |
60° 24' 00" |
30 |
|
11 |
McKenzies River |
Magdalen Shelf |
1956 |
46° 48' 25" |
60° 49' 35" |
30 |
|
12 |
South River |
Magdalen Shelf |
2126 |
45° 36' 00" |
61° 55' 00" |
38 |
|
13 |
Wallace River |
Magdalen Shelf |
2302 |
45° 49' 00" |
63° 31' 00" |
24 |
|
14 |
Black River |
Magdalen Shelf |
2522 |
47° 03' 00" |
65° 13' 00" |
15 |
|
15 |
Rivière Kouchibouguacis |
Magdalen Shelf |
2522 |
46° 47' 00" |
64° 54' 00" |
30 |
|
16 |
Cains Brook |
Magdalen Shelf |
2582 |
45° 41' 00" |
65° 02' 00" |
17 |
|
18 |
Rivière Tabusintac |
Magdalen Shelf |
2676 |
47° 20' 00" |
64° 56' 00" |
36 |
|
19 |
Rivière Jacquet |
Chaleur's bay |
2956 |
47° 55' 00" |
66° 01' 00" |
23 |
|
20 |
Rivière Matapedia |
Chaleur's bay |
2959 |
47° 58' 17" |
66° 56' 32" |
19 |
|
21 |
Rivière Patapedia |
Chaleur's bay |
2959 |
47° 51' 00" |
67° 23' 00" |
23 |
|
22 |
Rivière Restigouche |
Chaleur's bay |
2959 |
48° 04' 00" |
66° 20' 00" |
30 |
|
23 |
Rivière Nouvelle |
Chaleur's bay |
3019 |
48° 06' 14" |
66° 16' 58" |
30 |
|
24 |
Rivière Petite-Cascapedia |
Chaleur's bay |
3079 |
48° 09' 26" |
65° 51' 14" |
46 |
|
25 |
Rivière Bonaventure |
Chaleur's bay |
3110 |
48° 25' 16" |
65° 30' 15" |
50 |
|
26 |
Rivière Port Daniel |
Chaleur's bay |
3141 |
48° 10' 01" |
64° 57' 45" |
35 |
|
27 |
Rivière de l'A. à Beaufils |
Chaleur's bay |
3212 |
48° 28' 15" |
64° 18' 33" |
46 |
|
28 |
Ruisseau Murphy |
Chaleur's bay |
3251 |
48° 34' 19" |
64° 17' 42" |
31 |
|
29 |
Rivière St-Jean |
Gaspésie |
3286 |
48° 46' 08" |
64° 26' 51" |
35 |
|
30 |
Rivière York |
Gaspésie |
3301 |
48° 48' 57" |
64° 33' 18" |
19 |
|
31 |
Rivière de l'A. à Valleau |
Gaspésie |
3421 |
49° 05' 00" |
64° 33' 00" |
55 |
|
32 |
Rivière Grande Vallée |
Gaspésie |
3453 |
49° 14' 00" |
65° 08' 00" |
49 |
|
33 |
Ruisseau Manche d'Épée |
Gaspésie |
3476 |
49° 15' 00" |
65° 26' 00" |
57 |
|
34 |
Rivière Mont-Louis |
Gaspésie |
3499 |
49° 14' 00" |
65° 44' 00" |
42 |
|
35 |
Rivière Marsoui |
Gaspésie |
3525 |
49° 13' 00" |
66° 04' 00" |
21 |
|
36 |
Rivière Ste-Anne |
Gaspésie |
3558 |
49° 08' 00" |
66° 30' 00" |
15 |
|
37 |
Rivière Cap-Chat |
Gaspésie |
3578 |
49° 06' 00" |
66° 40' 00" |
28 |
|
38 |
Rivière Ste-Marguerite |
North Shore |
3958 |
48° 15' 49" |
69° 56' 47" |
50 |
|
39 |
Rivière des Escoumins |
North Shore |
3990 |
48° 20' 50" |
69° 27' 00" |
50 |
|
40 |
Rivière Laval |
North Shore |
4030 |
48° 46' 00" |
69° 03' 00" |
68 |
|
41 |
Rivière Godbout |
North Shore |
4158 |
49° 19‘ 00" |
67° 35‘ 0O" |
22 |
|
42 |
Rivière Trinité |
North Shore |
4188 |
49° 25' 05" |
67° 18' 16" |
50 |
|
43 |
Rivière du Calumet |
North Shore |
4214 |
49° 37' 00" |
67° 13' 00" |
48 |
|
44 |
Rivière Ile de Mai |
North Shore |
4264 |
49° 55' 38" |
66° 57' 50" |
50 |
|
45 |
Rivière Moisie |
North Shore |
4344 |
50° 16' 00" |
65° 56' 00" |
49 |
|
46 |
Rivière St-Jean |
North Shore |
4472 |
50° 17' 00" |
64° 20' 00" |
50 |
|
47 |
Baie-Johann-Beetz |
Lower North Shore |
4592 |
50° 17' 00" |
62° 48' 00" |
13 |
|
48 |
Rivière Washicoutai |
Lower North Shore |
4736 |
50° 13' 00" |
60° 52' 00" |
48 |
|
49 |
Rivière Watasheistic |
Lower North Shore |
4846 |
50° 24' 00" |
59° 50' 00" |
31 |
|
50 |
La Tabatière |
Lower North Shore |
4896 |
50° 50' 00" |
58° 59' 00" |
48 |
|
51 |
Rivière St-Augustin |
Lower North Shore |
4944 |
51° 12' 00" |
58° 35' 00" |
46 |
|
52 |
Rivière St-Paul |
Lower North Shore |
4992 |
51° 27' 00" |
57° 42' 00" |
41 |
|
A1 |
Rivère Bec-Scie |
Anticosti Island |
- |
49° 43' 00" |
64° 03' 20" |
30 |
|
A2 |
Rivière à la Loutre |
Anticosti Island |
- |
49° 37' 00" |
63° 48' 00" |
27 |
|
A3 |
Rivière Jupiter |
Anticosti Island |
- |
49° 28' 34" |
63° 35' 37" |
26 |
|
A4 |
Rivière Ferrée |
Anticosti Island |
- |
49° 09' 15" |
62° 42' 55" |
45 |
|
A5 |
Rivière Chaloupe |
Anticosti Island |
- |
49° 08' 00" |
62° 32' 00" |
32 |
|
A6 |
Rivière Patate |
Anticosti Island |
- |
49° 43' 00" |
62° 55' 00" |
24 |
|
A7 |
Rivière McDonald |
Anticosti Island |
- |
49° 45' 27" |
63° 03' 10" |
15 |
Table 4-2 Number of alleles (A) standardized to 26 alleles, expected (HE) and observed heterozygosity (HO), FIS estimate (f) and significance of the test for Hardy-Weinberg equilibrium (PHW). Overall significant P-values following Bonferroni correction are indicated in bold. 0 stands for PHW <0.0005
|
Sample |
1 |
2 |
3 |
4 |
5 |
6 | |
|
SFO-12 |
A |
4.99 |
5.52 |
4.50 |
3.83 |
4.36 |
2.96 |
|
HE |
0.646 |
0.671 |
0.704 |
0.692 |
0.642 |
0.423 | |
|
Ho |
0.600 |
0.725 |
0.645 |
0.590 |
0.792 |
0.310 | |
|
f |
0.072 |
-0.082 |
0.085 |
0.149 |
-0.24 |
0.27 | |
|
PHW |
0.4428 |
0.7701 |
0.0095 |
0.1223 |
0.959 |
0.0098 | |
|
SFO-18 |
A |
3.97 |
6.11 |
3.98 |
5.17 |
3.55 |
4.92 |
|
HE |
0.622 |
0.790 |
0.464 |
0.727 |
0.292 |
0.763 | |
|
Ho |
0.486 |
0.778 |
0.375 |
0.775 |
0.320 |
0.464 | |
|
f |
0.222 |
0.015 |
0.195 |
-0.067 |
-0.097 |
0.396 | |
|
PHW |
0.1313 |
0.5593 |
0.0069 |
0.8595 |
1 |
0.0007 | |
|
SFO-23 |
A |
6.33 |
10.47 |
9.21 |
12.41 |
6.34 |
9.54 |
|
HE |
0.702 |
0.898 |
0.864 |
0.913 |
0.771 |
0.883 | |
|
Ho |
0.649 |
0.925 |
0.633 |
0.947 |
0.640 |
0.607 | |
|
f |
0.077 |
-0.03 |
0.271 |
-0.038 |
0.173 |
0.316 | |
|
PHW |
0.3356 |
0.7886 |
0 |
0.3634 |
0.0231 |
0 | |
|
SFO-8 |
A |
6.79 |
14.27 |
7.74 |
8.57 |
6.11 |
12.28 |
|
HE |
0.688 |
0.942 |
0.790 |
0.796 |
0.779 |
0.917 | |
|
Ho |
0.737 |
0.868 |
0.471 |
0.686 |
0.840 |
0.846 | |
|
f |
-0.071 |
0.079 |
0.411 |
0.141 |
-0.08 |
0.079 | |
|
PHW |
0.7698 |
0.0468 |
0 |
0.006 |
0.857 |
0.0409 | |
|
SSA-197 |
A |
1.99 |
3.35 |
3.88 |
2.40 |
3.34 |
2.00 |
|
HE |
0.258 |
0.302 |
0.334 |
0.192 |
0.570 |
0.503 | |
|
Ho |
0.300 |
0.290 |
0.375 |
0.207 |
0.625 |
0.393 | |
|
f |
-0.164 |
0.042 |
-0.126 |
-0.08 |
-0.099 |
0.223 | |
|
PHW |
1 |
0.411 |
1 |
1 |
0.6749 |
0.21 | |
|
MST-85 |
A |
5.52 |
8.02 |
6.70 |
8.68 |
3.05 |
6.18 |
|
HE |
0.668 |
0.817 |
0.838 |
0.883 |
0.329 |
0.821 | |
|
Ho |
0.649 |
0.800 |
0.720 |
0.821 |
0.333 |
0.667 | |
|
f |
0.029 |
0.02 |
0.143 |
0.071 |
-0.014 |
0.191 | |
|
PHW |
0.5976 |
0.1338 |
0.0821 |
0.0807 |
0.6008 |
0.0316 | |
|
All |
A |
4.93 |
7.96 |
6.00 |
6.84 |
4.46 |
6.31 |
|
He |
0.598 |
0.737 |
0.666 |
0.700 |
0.564 |
0.718 | |
|
Ho |
0.570 |
0.731 |
0.537 |
0.671 |
0.592 |
0.548 | |
|
f |
0.05151 |
0.0235 |
0.20416 |
0.02844 |
-0.00707 |
0.26281 | |
|
PHW |
0.4812 |
0.0993 |
0 |
0.0241 |
0.7134 |
0 |
|
7 |
8 |
9 |
10 |
11 |
12 |
13 |
|
2.04 |
3.00 |
4.48 |
4.64 |
5.76 |
6.89 |
5.91 |
|
0.086 |
0.568 |
0.652 |
0.734 |
0.762 |
0.820 |
0.806 |
|
0.087 |
0.708 |
0.737 |
0.724 |
0.897 |
0.694 |
0.739 |
|
-0.011 |
-0.253 |
-0.132 |
0.014 |
-0.18 |
0.155 |
0.084 |
|
1 |
0.9836 |
0.5569 |
0.3935 |
0.9387 |
0.0387 |
0.2262 |
|
5.71 |
5.68 |
4.04 |
4.99 |
6.73 |
5.31 |
4.32 |
|
0.729 |
0.757 |
0.318 |
0.617 |
0.684 |
0.673 |
0.624 |
|
0.640 |
0.739 |
0.351 |
0.524 |
0.546 |
0.600 |
0.650 |
|
0.124 |
0.023 |
-0.105 |
0.154 |
0.206 |
0.11 |
-0.042 |
|
0.1667 |
0.563 |
1 |
0.2101 |
0.0034 |
0.1567 |
0.7182 |
|
9.20 |
10.45 |
12.25 |
7.89 |
10.49 |
11.76 |
11.70 |
|
0.884 |
0.902 |
0.917 |
0.796 |
0.911 |
0.925 |
0.916 |
|
0.889 |
0.864 |
0.889 |
0.750 |
0.846 |
0.865 |
0.750 |
|
-0.006 |
0.043 |
0.031 |
0.059 |
0.073 |
0.065 |
0.184 |
|
0.3721 |
0.3401 |
0.179 |
0.4825 |
0.1794 |
0.092 |
0 |
|
8.38 |
8.93 |
12.89 |
10.47 |
13.75 |
12.54 |
12.99 |
|
0.767 |
0.866 |
0.924 |
0.847 |
0.925 |
0.890 |
0.918 |
|
0.727 |
0.682 |
0.970 |
0.778 |
0.750 |
0.886 |
0.833 |
|
0.054 |
0.216 |
-0.051 |
0.083 |
0.192 |
0.005 |
0.094 |
|
0.3999 |
0.0023 |
0.8883 |
0.0158 |
0.1213 |
0.3899 |
0.0573 |
|
3.18 |
4.05 |
4.55 |
3.43 |
3.50 |
4.20 |
3.78 |
|
0.541 |
0.579 |
0.682 |
0.624 |
0.554 |
0.651 |
0.618 |
|
0.643 |
0.625 |
0.622 |
0.600 |
0.333 |
0.714 |
0.542 |
|
-0.193 |
-0.082 |
0.09 |
0.04 |
0.404 |
-0.098 |
0.126 |
|
0.873 |
0.7188 |
0.4227 |
0.3927 |
0.0061 |
0.8752 |
0.3536 |
|
7.00 |
6.41 |
7.02 |
5.93 |
7.94 |
9.37 |
7.55 |
|
0.863 |
0.813 |
0.809 |
0.620 |
0.825 |
0.900 |
0.749 |
|
0.300 |
0.696 |
0.737 |
0.552 |
0.800 |
0.886 |
0.583 |
|
0.665 |
0.147 |
0.09 |
0.111 |
0.031 |
0.016 |
0.225 |
|
0 |
0.1745 |
0.1189 |
0.2709 |
0.2325 |
0.4715 |
0.0251 |
|
5.92 |
6.42 |
7.54 |
6.23 |
8.03 |
8.35 |
7.71 |
|
0.645 |
0.747 |
0.717 |
0.706 |
0.777 |
0.810 |
0.772 |
|
0.548 |
0.719 |
0.718 |
0.655 |
0.695 |
0.774 |
0.683 |
|
0.16843 |
0.05972 |
0.045 |
0.08965 |
0.16691 |
0.02638 |
0.14362 |
|
0.0154 |
0.1052 |
0.3734 |
0.0157 |
0.0036 |
0.0052 |
0 |
|
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
|
5.77 |
4.84 |
4.69 |
5.03 |
4.81 |
4.25 |
5.55 |
6.31 |
|
0.775 |
0.748 |
0.731 |
0.725 |
0.678 |
0.590 |
0.772 |
0.792 |
|
0.867 |
0.800 |
0.824 |
0.851 |
0.694 |
0.522 |
0.737 |
0.714 |
|
-0.123 |
-0.071 |
-0.131 |
-0.176 |
-0.024 |
0.119 |
0.047 |
0.1 |
|
0.6674 |
0.7708 |
0.7885 |
0.0421 |
0.4665 |
0.0787 |
0.3758 |
0.2314 |
|
4.70 |
5.09 |
4.57 |
5.13 |
7.02 |
5.76 |
3.32 |
6.51 |
|
0.484 |
0.607 |
0.514 |
0.652 |
0.819 |
0.620 |
0.259 |
0.749 |
|
0.429 |
0.586 |
0.563 |
0.745 |
0.743 |
0.667 |
0.278 |
0.783 |
|
0.119 |
0.034 |
-0.098 |
-0.144 |
0.094 |
-0.077 |
-0.076 |
-0.046 |
|
0.0718 |
0.0395 |
0.8751 |
0.9586 |
0.2266 |
0.5344 |
1 |
0.1137 |
|
8.33 |
13.48 |
11.48 |
11.71 |
12.07 |
12.06 |
10.91 |
10.93 |
|
0.837 |
0.938 |
0.893 |
0.914 |
0.916 |
0.853 |
0.794 |
0.872 |
|
0.600 |
0.767 |
0.824 |
0.918 |
0.829 |
0.909 |
0.833 |
0.909 |
|
0.29 |
0.185 |
0.08 |
-0.005 |
0.097 |
-0.067 |
-0.052 |
-0.043 |
|
0.0586 |
0.034 |
0.3078 |
0.275 |
0.0251 |
0.9506 |
0.919 |
0.504 |
|
8.55 |
11.40 |
13.70 |
10.92 |
12.51 |
14.34 |
16.80 |
14.78 |
|
0.881 |
0.921 |
0.921 |
0.906 |
0.913 |
0.932 |
0.969 |
0.951 |
|
0.786 |
0.800 |
1.000 |
0.860 |
0.778 |
0.895 |
0.895 |
0.850 |
|
0.112 |
0.134 |
-0.088 |
0.051 |
0.15 |
0.041 |
0.078 |
0.109 |
|
0.2169 |
0.1234 |
1 |
0.0148 |
0.0945 |
0.4466 |
0.0466 |
0.0013 |
|
3.00 |
3.39 |
3.81 |
3.70 |
3.80 |
3.48 |
3.94 |
4.77 |
|
0.569 |
0.586 |
0.673 |
0.618 |
0.618 |
0.556 |
0.597 |
0.681 |
|
0.429 |
0.429 |
0.688 |
0.680 |
0.515 |
0.476 |
0.500 |
0.727 |
|
0.254 |
0.273 |
-0.022 |
-0.102 |
0.168 |
0.147 |
0.167 |
-0.07 |
|
0.2749 |
0.1049 |
0.5105 |
0.9061 |
0.2609 |
0.0139 |
0.2872 |
0.531 |
|
6.19 |
6.32 |
7.18 |
9.05 |
6.65 |
6.52 |
6.61 |
9.11 |
|
0.786 |
0.742 |
0.832 |
0.879 |
0.827 |
0.821 |
0.794 |
0.865 |
|
0.800 |
0.800 |
0.647 |
0.840 |
0.778 |
0.682 |
0.750 |
0.619 |
|
-0.018 |
-0.08 |
0.228 |
0.044 |
0.06 |
0.173 |
0.058 |
0.29 |
|
0.5514 |
0.8542 |
0.0421 |
0.3859 |
0.2797 |
0.0739 |
0.4718 |
0 |
|
6.09 |
7.42 |
7.57 |
7.59 |
7.81 |
7.73 |
7.85 |
8.74 |
|
0.722 |
0.757 |
0.761 |
0.782 |
0.795 |
0.729 |
0.697 |
0.818 |
|
0.652 |
0.697 |
0.757 |
0.816 |
0.723 |
0.692 |
0.665 |
0.767 |
|
0.12329 |
0.0941 |
0.01473 |
-0.01827 |
0.11018 |
0.05182 |
0.06702 |
0.04964 |
|
0.0637 |
0.0005 |
0.3152 |
0.0438 |
0.0032 |
0.0172 |
0.1373 |
0.0001 |
|
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
|
7.09 |
6.30 |
4.72 |
5.32 |
3.96 |
5.31 |
5.18 |
4.53 |
|
0.842 |
0.760 |
0.693 |
0.720 |
0.720 |
0.763 |
0.739 |
0.685 |
|
0.643 |
0.690 |
0.783 |
0.694 |
0.941 |
0.848 |
0.484 |
0.743 |
|
0.239 |
0.095 |
-0.132 |
0.036 |
-0.313 |
-0.113 |
0.349 |
-0.087 |
|
0.0201 |
0.1216 |
0.1094 |
0.345 |
0.9991 |
0.8492 |
0.0013 |
0.8549 |
|
4.93 |
6.09 |
5.38 |
4.21 |
3.47 |
3.54 |
5.08 |
3.97 |
|
0.652 |
0.726 |
0.659 |
0.731 |
0.407 |
0.562 |
0.776 |
0.706 |
|
0.552 |
0.607 |
0.581 |
0.674 |
0.429 |
0.578 |
0.548 |
0.833 |
|
0.156 |
0.166 |
0.119 |
0.079 |
-0.055 |
-0.028 |
0.297 |
-0.185 |
|
0.3384 |
0.1508 |
0.1417 |
0.1345 |
0.7746 |
0.5952 |
0.0006 |
0.9563 |
|
10.22 |
5.30 |
7.62 |
9.08 |
11.34 |
8.16 |
11.42 |
10.39 |
|
0.884 |
0.632 |
0.672 |
0.790 |
0.898 |
0.839 |
0.899 |
0.756 |
|
0.857 |
0.679 |
0.630 |
0.816 |
0.800 |
0.767 |
0.871 |
0.818 |
|
0.031 |
-0.075 |
0.062 |
-0.033 |
0.11 |
0.086 |
0.032 |
-0.084 |
|
0.2334 |
0.8785 |
0.0131 |
0.5844 |
0.156 |
0.1462 |
0.0282 |
0.9267 |
|
16.21 |
11.89 |
13.41 |
14.40 |
15.42 |
16.50 |
13.17 |
14.39 |
|
0.959 |
0.908 |
0.919 |
0.932 |
0.939 |
0.965 |
0.935 |
0.927 |
|
0.966 |
0.714 |
0.744 |
0.917 |
0.807 |
0.800 |
0.909 |
0.794 |
|
-0.007 |
0.217 |
0.193 |
0.017 |
0.143 |
0.173 |
0.028 |
0.145 |
|
0.553 |
0.0163 |
0 |
0.423 |
0 |
0 |
0.2058 |
0 |
|
3.44 |
4.20 |
3.62 |
3.90 |
4.74 |
4.26 |
5.17 |
3.38 |
|
0.635 |
0.630 |
0.581 |
0.665 |
0.733 |
0.735 |
0.766 |
0.602 |
|
0.517 |
0.846 |
0.552 |
0.617 |
0.686 |
0.733 |
0.821 |
0.727 |
|
0.188 |
-0.353 |
0.051 |
0.073 |
0.065 |
0.002 |
-0.074 |
-0.212 |
|
0.1102 |
0.9947 |
0.4426 |
0.2314 |
0.3791 |
0.5877 |
0.8562 |
0.9416 |
|
7.78 |
7.21 |
7.02 |
8.15 |
6.41 |
4.67 |
7.19 |
5.19 |
|
0.852 |
0.801 |
0.814 |
0.858 |
0.637 |
0.453 |
0.708 |
0.703 |
|
0.621 |
0.346 |
0.816 |
0.820 |
0.618 |
0.489 |
0.444 |
0.485 |
|
0.275 |
0.573 |
-0.003 |
0.045 |
0.031 |
-0.081 |
0.377 |
0.314 |
|
0 |
0 |
0.2773 |
0.1594 |
0.197 |
0.9118 |
0.0017 |
0.0055 |
|
8.28 |
6.83 |
6.96 |
7.51 |
7.56 |
7.07 |
7.87 |
6.97 |
|
0.804 |
0.743 |
0.723 |
0.783 |
0.722 |
0.720 |
0.804 |
0.730 |
|
0.693 |
0.647 |
0.684 |
0.756 |
0.713 |
0.703 |
0.680 |
0.733 |
|
0.14752 |
0.11761 |
0.0792 |
0.03715 |
0.04866 |
0.00505 |
0.147 |
0.00874 |
|
0.0021 |
0 |
0 |
0.3452 |
0.0613 |
0.1002 |
0 |
0.036 |
|
30 |
31 |
32 |
33 |
34 |
35 |
36 |
37 |
|
5.85 |
5.86 |
4.49 |
5.11 |
4.91 |
5.89 |
4.98 |
5.47 |
|
0.733 |
0.779 |
0.690 |
0.629 |
0.707 |
0.733 |
0.743 |
0.805 |
|
0.684 |
0.836 |
0.714 |
0.625 |
0.800 |
0.778 |
0.857 |
0.750 |
|
0.068 |
-0.074 |
-0.036 |
0.007 |
-0.134 |
-0.063 |
-0.16 |
0.07 |
|
0.2746 |
0.0534 |
0.525 |
0.5131 |
0.9518 |
0.1802 |
0.5862 |
0.3573 |
|
3.84 |
3.88 |
4.44 |
3.67 |
3.99 |
4.28 |
3.99 |
6.31 |
|
0.527 |
0.484 |
0.603 |
0.577 |
0.520 |
0.532 |
0.712 |
0.795 |
|
0.333 |
0.415 |
0.551 |
0.509 |
0.378 |
0.438 |
0.500 |
1.000 |
|
0.374 |
0.143 |
0.087 |
0.118 |
0.275 |
0.183 |
0.305 |
-0.267 |
|
0.0027 |
0 |
0.0061 |
0.1633 |
0.0207 |
0.58 |
0.0603 |
1 |
|
7.39 |
10.37 |
10.43 |
7.51 |
10.97 |
11.32 |
8.13 |
8.87 |
|
0.623 |
0.786 |
0.868 |
0.827 |
0.890 |
0.897 |
0.733 |
0.790 |
|
0.526 |
0.836 |
0.878 |
0.768 |
0.857 |
0.778 |
0.533 |
0.700 |
|
0.159 |
-0.065 |
-0.011 |
0.072 |
0.037 |
0.136 |
0.28 |
0.116 |
|
0.0151 |
0.8769 |
0.2113 |
0.1876 |
0.0802 |
0.0168 |
0.0146 |
0.1944 |
|
11.91 |
15.95 |
15.96 |
13.65 |
14.57 |
13.37 |
16.14 |
12.83 |
|
0.933 |
0.954 |
0.945 |
0.936 |
0.946 |
0.927 |
0.960 |
0.930 |
|
0.790 |
0.902 |
0.978 |
0.755 |
0.850 |
0.813 |
1.000 |
0.842 |
|
0.158 |
0.055 |
-0.036 |
0.195 |
0.102 |
0.128 |
-0.043 |
0.097 |
|
0.0371 |
0.1493 |
0.944 |
0.0063 |
0.0152 |
0.0192 |
1 |
0.1247 |
|
4.99 |
5.63 |
4.19 |
3.39 |
3.79 |
5.93 |
2.87 |
3.88 |
|
0.755 |
0.724 |
0.625 |
0.484 |
0.590 |
0.772 |
0.297 |
0.487 |
|
0.421 |
0.611 |
0.532 |
0.453 |
0.675 |
0.529 |
0.200 |
0.520 |
|
0.449 |
0.157 |
0.15 |
0.064 |
-0.146 |
0.321 |
0.333 |
-0.068 |
|
0.0042 |
0 |
0.1007 |
0.357 |
0.7823 |
0.0013 |
0.2031 |
0.7967 |
|
6.57 |
6.11 |
3.34 |
5.00 |
5.15 |
5.77 |
6.50 |
4.05 |
|
0.818 |
0.585 |
0.235 |
0.513 |
0.527 |
0.642 |
0.812 |
0.411 |
|
0.611 |
0.500 |
0.250 |
0.500 |
0.568 |
0.632 |
0.867 |
0.316 |
|
0.258 |
0.146 |
-0.066 |
0.026 |
-0.079 |
0.016 |
-0.071 |
0.237 |
|
0.0145 |
0.0369 |
1 |
0.3712 |
0.0738 |
0.6162 |
0.3844 |
0.0277 |
|
6.76 |
7.97 |
7.14 |
6.39 |
7.23 |
7.76 |
7.10 |
6.90 |
|
0.731 |
0.719 |
0.661 |
0.661 |
0.697 |
0.751 |
0.709 |
0.703 |
|
0.561 |
0.684 |
0.650 |
0.602 |
0.688 |
0.661 |
0.660 |
0.688 |
|
0.26095 |
0.05675 |
0.02777 |
0.07936 |
0.02493 |
0.10908 |
0.15339 |
0.00388 |
|
0 |
0 |
0.0241 |
0.0118 |
0.0002 |
0 |
0.051 |
0.1311 |
|
38 |
39 |
40 |
41 |
42 |
43 |
44 |
45 |
|
5.59 |
5.70 |
4.80 |
4.64 |
4.18 |
4.35 |
3.32 |
3.05 |
|
0.768 |
0.699 |
0.672 |
0.660 |
0.429 |
0.490 |
0.302 |
0.524 |
|
0.720 |
0.674 |
0.569 |
0.667 |
0.429 |
0.479 |
0.200 |
0.366 |
|
0.063 |
0.037 |
0.153 |
-0.011 |
0.001 |
0.021 |
0.341 |
0.304 |
|
0.2583 |
0.4502 |
0.0474 |
0.6579 |
0.717 |
0.2613 |
0.0003 |
0.0001 |
|
5.41 |
6.56 |
3.26 |
3.55 |
5.98 |
6.00 |
2.93 |
3.27 |
|
0.523 |
0.774 |
0.380 |
0.583 |
0.720 |
0.727 |
0.186 |
0.617 |
|
0.500 |
0.739 |
0.302 |
0.550 |
0.698 |
0.600 |
0.109 |
0.625 |
|
0.045 |
0.046 |
0.206 |
0.059 |
0.032 |
0.177 |
0.419 |
-0.013 |
|
0.4395 |
0.4304 |
0.002 |
0.3324 |
0.5638 |
0.0012 |
0.0004 |
0.5345 |
|
8.57 |
12.13 |
8.43 |
10.80 |
12.82 |
11.85 |
9.27 |
9.41 |
|
0.847 |
0.908 |
0.748 |
0.887 |
0.912 |
0.900 |
0.853 |
0.866 |
|
0.820 |
0.796 |
0.655 |
0.800 |
0.867 |
0.821 |
0.857 |
0.778 |
|
0.032 |
0.125 |
0.125 |
0.101 |
0.05 |
0.089 |
-0.004 |
0.103 |
|
0.0077 |
0.0099 |
0.0509 |
0.0415 |
0 |
0 |
0.4026 |
0.0891 |
|
12.70 |
11.45 |
9.37 |
10.14 |
12.42 |
9.96 |
9.53 |
12.13 |
|
0.927 |
0.890 |
0.856 |
0.800 |
0.922 |
0.881 |
0.859 |
0.920 |
|
0.917 |
0.694 |
0.746 |
0.667 |
0.875 |
0.544 |
0.696 |
0.889 |
|
0.011 |
0.222 |
0.129 |
0.17 |
0.051 |
0.386 |
0.192 |
0.035 |
|
0.3595 |
0.0134 |
0.0328 |
0.011 |
0 |
0 |
0.0059 |
0.2841 |
|
4.22 |
4.98 |
3.96 |
5.76 |
4.75 |
5.07 |
3.74 |
3.87 |
|
0.550 |
0.577 |
0.682 |
0.771 |
0.729 |
0.747 |
0.582 |
0.680 |
|
0.600 |
0.408 |
0.603 |
0.700 |
0.721 |
0.587 |
0.478 |
0.475 |
|
-0.093 |
0.295 |
0.116 |
0.094 |
0.011 |
0.216 |
0.18 |
0.305 |
|
0.7013 |
0.0615 |
0.129 |
0.0041 |
0.4076 |
0.0052 |
0.0386 |
0.0012 |
|
6.41 |
8.47 |
7.07 |
8.32 |
7.30 |
8.33 |
8.49 |
7.20 |
|
0.784 |
0.830 |
0.784 |
0.779 |
0.853 |
0.875 |
0.818 |
0.749 |
|
0.720 |
0.551 |
0.758 |
0.778 |
0.820 |
0.761 |
0.744 |
0.745 |
|
0.082 |
0.339 |
0.034 |
0.002 |
0.039 |
0.132 |
0.091 |
0.006 |
|
0.008 |
0 |
0.3934 |
0.6336 |
0.0092 |
0.0281 |
0.0073 |
0.2208 |
|
7.15 |
8.21 |
6.15 |
7.20 |
7.91 |
7.59 |
6.21 |
6.49 |
|
0.733 |
0.780 |
0.687 |
0.747 |
0.761 |
0.770 |
0.600 |
0.726 |
|
0.713 |
0.644 |
0.606 |
0.694 |
0.735 |
0.632 |
0.514 |
0.646 |
|
0.03091 |
0.1873 |
0.11356 |
0.08841 |
0.02703 |
0.19947 |
0.11476 |
0.0927 |
|
0.0075 |
0 |
0 |
0.0009 |
0 |
0 |
0 |
0 |
|
46 |
47 |
48 |
49 |
50 |
51 |
52 |
A1 |
|
3.57 |
5.00 |
3.52 |
5.13 |
5.44 |
6.17 |
5.92 |
4.44 |
|
0.306 |
0.652 |
0.551 |
0.610 |
0.640 |
0.783 |
0.772 |
0.797 |
|
0.220 |
0.833 |
0.354 |
0.600 |
0.553 |
0.773 |
0.718 |
0.750 |
|
0.282 |
-0.294 |
0.36 |
0.016 |
0.136 |
0.013 |
0.07 |
0.060 |
|
0.0014 |
0.9877 |
0 |
0.0118 |
0.1057 |
0.5616 |
0.1892 |
0.210 |
|
4.24 |
4.98 |
2.65 |
3.15 |
5.16 |
3.85 |
6.40 |
2.46 |
|
0.683 |
0.735 |
0.544 |
0.315 |
0.590 |
0.483 |
0.788 |
0.592 |
|
0.612 |
0.846 |
0.521 |
0.323 |
0.438 |
0.422 |
0.692 |
0.500 |
|
0.105 |
-0.158 |
0.043 |
-0.024 |
0.261 |
0.127 |
0.123 |
0.157 |
|
0.0558 |
0.9437 |
0.4534 |
0.6588 |
0.018 |
0.0887 |
0.0089 |
0.073 |
|
11.33 |
7.83 |
5.63 |
12.13 |
10.25 |
10.86 |
9.68 |
10.03 |
|
0.887 |
0.739 |
0.750 |
0.857 |
0.858 |
0.896 |
0.842 |
0.893 |
|
0.884 |
0.539 |
0.773 |
0.714 |
0.745 |
0.932 |
0.805 |
0.655 |
|
0.004 |
0.279 |
-0.031 |
0.169 |
0.133 |
-0.041 |
0.045 |
0.270 |
|
0.3647 |
0.1423 |
0.3822 |
0.1048 |
0.1481 |
0.7014 |
0.2975 |
0.000 |
|
11.48 |
7.00 |
9.79 |
11.24 |
14.26 |
12.84 |
14.99 |
6.06 |
|
0.897 |
0.855 |
0.827 |
0.877 |
0.940 |
0.907 |
0.937 |
0.793 |
|
0.723 |
1.000 |
0.750 |
0.567 |
0.875 |
0.810 |
0.731 |
0.759 |
|
0.195 |
-0.179 |
0.094 |
0.358 |
0.07 |
0.109 |
0.223 |
0.043 |
|
0 |
1 |
0.1294 |
0 |
0.0325 |
0 |
0.0019 |
0.213 |
|
4.22 |
3.00 |
2.54 |
2.42 |
4.15 |
3.90 |
3.03 |
1.26 |
|
0.694 |
0.582 |
0.301 |
0.502 |
0.607 |
0.495 |
0.220 |
0.128 |
|
0.714 |
0.692 |
0.313 |
0.484 |
0.646 |
0.476 |
0.158 |
0.133 |
|
-0.029 |
-0.2 |
-0.038 |
0.036 |
-0.064 |
0.038 |
0.285 |
-0.040 |
|
0.7141 |
0.7278 |
0.7261 |
0.5047 |
0.2001 |
0.5114 |
0.0559 |
0.101 |
|
7.07 |
2.83 |
5.39 |
6.70 |
6.66 |
6.99 |
6.74 |
6.54 |
|
0.820 |
0.301 |
0.741 |
0.812 |
0.767 |
0.811 |
0.804 |
0.814 |
|
0.698 |
0.083 |
0.792 |
0.690 |
0.583 |
0.850 |
0.677 |
0.897 |
|
0.15 |
0.732 |
-0.069 |
0.153 |
0.242 |
-0.048 |
0.161 |
-0.104 |
|
0.0139 |
0.0062 |
0.7912 |
0.1529 |
0.0072 |
0.7052 |
0.0014 |
0.830 |
|
6.98 |
5.11 |
4.92 |
6.80 |
7.65 |
7.44 |
7.79 |
5.13 |
|
0.714 |
0.644 |
0.619 |
0.662 |
0.734 |
0.729 |
0.727 |
0.669 |
|
0.642 |
0.666 |
0.584 |
0.563 |
0.640 |
0.710 |
0.630 |
0.616 |
|
0.05784 |
0.00236 |
-0.01189 |
0.15968 |
0.13693 |
0.00727 |
0.12247 |
0.082 |
|
0 |
0.6866 |
0.0672 |
0 |
0 |
0.085 |
0 |
0.020 |
|
A2 |
A3 |
A4 |
A5 |
A6 |
A7 |
Overall |
|
3.37 |
3.14 |
4.76 |
3.87 |
3.00 |
3.00 |
4.76 |
|
0.786 |
0.719 |
0.639 |
0.696 |
0.747 |
0.646 |
0.672 |
|
0.630 |
0.480 |
0.691 |
0.688 |
0.583 |
0.667 |
0.657 |
|
0.201 |
0.337 |
-0.081 |
0.013 |
0.223 |
-0.033 |
0.028 |
|
0.013 |
0 |
0.713 |
0.373 |
0.022 |
0.422 |
0 |
|
3.49 |
2.94 |
3.72 |
3.80 |
3.71 |
3.64 |
4.56 |
|
0.606 |
0.340 |
0.420 |
0.438 |
0.370 |
0.361 |
0.585 |
|
0.680 |
0.208 |
0.409 |
0.452 |
0.250 |
0.333 |
0.539 |
|
-0.126 |
0.392 |
0.026 |
-0.031 |
0.328 |
0.079 |
0.084 |
|
0.736 |
0 |
0.281 |
0.412 |
0.002 |
0.125 |
0 |
|
10.57 |
12.72 |
10.97 |
10.88 |
13.49 |
11.44 |
10.15 |
|
0.857 |
0.854 |
0.908 |
0.897 |
0.880 |
0.897 |
0.848 |
|
0.769 |
0.720 |
0.929 |
0.875 |
0.875 |
0.800 |
0.786 |
|
0.104 |
0.160 |
-0.023 |
0.025 |
0.006 |
0.111 |
0.074 |
|
0.031 |
0 |
0.548 |
0.208 |
0.307 |
0.033 |
0 |
|
13.51 |
12.56 |
12.09 |
7.23 |
8.64 |
7.84 |
11.96 |
|
0.611 |
0.888 |
0.861 |
0.922 |
0.858 |
0.828 |
0.890 |
|
0.480 |
0.720 |
0.923 |
0.852 |
0.792 |
0.786 |
0.802 |
|
0.217 |
0.193 |
-0.073 |
0.078 |
0.079 |
0.053 |
0.101 |
|
0.004 |
0 |
0.879 |
0.045 |
0.095 |
0.185 |
0 |
|
3.19 |
2.86 |
3.15 |
1.60 |
2.73 |
1.54 |
3.68 |
|
0.175 |
0.425 |
0.427 |
0.613 |
0.290 |
0.395 |
0.552 |
|
0.185 |
0.364 |
0.356 |
0.563 |
0.333 |
0.333 |
0.517 |
|
-0.057 |
0.147 |
0.168 |
0.083 |
-0.154 |
0.162 |
0.057 |
|
0.183 |
0 |
0.026 |
0.183 |
0.525 |
0.108 |
0 |
|
7.14 |
8.02 |
7.04 |
6.64 |
6.85 |
6.59 |
6.71 |
|
0.804 |
0.822 |
0.854 |
0.695 |
0.828 |
0.810 |
0.746 |
|
0.600 |
0.560 |
0.850 |
0.630 |
0.609 |
0.714 |
0.652 |
|
0.258 |
0.323 |
0.004 |
0.095 |
0.269 |
0.122 |
0.127 |
|
0.003 |
0 |
0.374 |
0.083 |
0.000 |
0.070 |
0 |
|
6.88 |
7.04 |
6.96 |
5.67 |
6.40 |
5.67 |
6.97 |
|
0.640 |
0.675 |
0.685 |
0.710 |
0.662 |
0.656 |
0.715 |
|
0.557 |
0.509 |
0.693 |
0.676 |
0.574 |
0.606 |
0.659 |
|
0.131 |
0.250 |
-0.012 |
0.049 |
0.136 |
0.080 |
0.087 |
|
0.001 |
0 |
0.653 |
0.083 |
0.001 |
0.059 |
0 |
Figure 4-1 Location of brook charr samples. Numbers refer to locations in Table 1. The southernmost population is labeled km 0 and is close to the southern limit of anadromous brook charr distribution. Distances were linearly measured along the coast in a northward direction to kilometer 4992.
Figure 4-3 Geographic variation in FST depicted using a sliding window analysis. A 600 km-wide window was shifted along the coast by 10 km increment. Each data point refers to the mean FST over all possible combinations of four populations within each window. Windows including less than four populations were discarded.
Figure 4-4. Neighbor-joining phenogram based on DCE distances depicting genetic similarities among populations. Population numbers refer to table 1. Nodes confidence values are percentage values over 1000 bootstrap replicates. Note the tight clustering with a high bootstrap value of 86% of Anticosti Island populations. Only bootstrap values over 50% are shown.
Figure 4-5. Isolation by distance relationship, where FST/(1- FST) was regressed over coastal distances.
Figure 4-6. Variation of the slope of the isolation by distance regression as a function of the spatial scale of observation. Slopes were computed by progressively including population pairs at increasing geographic distances. To better show initial fluctuations, only the 500 first km are shown.
Figure 4-7. Variation in the slope of the isolation by distance regression. A 600 km-wide window was shifted along the coast by 10 km increment. Each data point refers to the mean slope over all possible combinations of four populations within each window. Windows including less than four populations were discarded.
Figure 4-8. Geographic variation in the intercept of the isolation by distance regression revealed by the sliding window analysis.
Copyright Vincent Castric
| | | |
| 3. Heterozygote deficiencies in small lacustrine populations of brook charr Salvelinus fontinalis Mitchill (Pisces, Salmonidae) : a test of alternative hypotheses. |  | 5. Should I stay or should I go ? Individual inbreeding as a determinant of anadromy in coastal populations of Salvelinus fontinalis. |