Genetic estimates of contemporary effective population size: what can they tell us about the importance of genetic stochasticity for wild population persistence?

Authors


Friso P. Palstra, Fax: (902) 494 3738; E-mail: fpalstra@dal.ca

Abstract

Genetic stochasticity due to small population size contributes to population extinction, especially when population fragmentation disrupts gene flow. Estimates of effective population size (Ne) can therefore be informative about population persistence, but there is a need for an assessment of their consistency and informative relevance. Here we review the body of empirical estimates of Ne for wild populations obtained with the temporal genetic method and published since Frankham's (1995) review. Theoretical considerations have identified important sources of bias for this analytical approach, and we use empirical data to investigate the extent of these biases. We find that particularly model selection and sampling require more attention in future studies.

We report a median unbiased Ne estimate of 260 (among 83 studies) and find that this median estimate tends to be smaller for populations of conservation concern, which may therefore be more sensitive to genetic stochasticity. Furthermore, we report a median Ne/N ratio of 0.14, and find that this ratio may actually be higher for small populations, suggesting changes in biological interactions at low population abundances. We confirm the role of gene flow in countering genetic stochasticity by finding that Ne correlates strongest with neutral genetic metrics when populations can be considered isolated. This underlines the importance of gene flow for the estimation of Ne, and of population connectivity for conservation in general. Reductions in contemporary gene flow due to ongoing habitat fragmentation will likely increase the prevalence of genetic stochasticity, which should therefore remain a focal point in the conservation of biodiversity.

Introduction

A fundamental contribution by evolutionary theory to conservation biology has been the development of a predictive framework for the fate of small populations. A population's extinction risk depends on both deterministic (natural selection, harvesting, etc.) and stochastic (e.g. environmental, demographic and genetic) processes. The latter are more pronounced at small population size, thereby potentially accelerating extinction processes often initiated by deterministic factors. Population size can also influence the level of genetic diversity (Frankham 1996): in small populations, random genetic drift, inbreeding and the resulting accumulation of deleterious mutations are all known to lead to loss of genetic variation (Frankham et al. 2003). These claims have a sound theoretical basis (e.g. Lynch et al. 1995) but in the wild it is less clear how often a link can be established between population size and extinction risk due to genetic factors.

One important genetic factor that may affect extinction risk is inbreeding depression. The relationship between inbreeding depression and population size has been demonstrated empirically under controlled conditions (laboratory: Frankham 2005; Swindell & Bouzat 2006c; Wright et al. 2007; animals in captivity: Ralls et al. 1979; Ballou & Ralls 1982; Boakes et al. 2007) as well as in the wild (Crnokrak & Roff 1999; Keller & Waller 2002). Inbreeding depression may be one factor leading to the relatively low mean fitness of small populations (Reed 2005). Fitness loss due to decreased population size has also been linked to increased extinction risk under experimental (e.g. Wright et al. 2007) and natural conditions (Newman & Pilson 1997; Saccheri et al. 1998; Nieminen et al. 2001). Studies of the impact of immigration on fitness in small and endangered populations provide additional evidence for population size affecting inbreeding depression (plants: Richards 2000; prairie chickens: Westemeier et al. 1998; wolves: Flagstad et al. 2003; Vila et al. 2003; song sparrows: Keller et al. 2001; and adders: Madsen et al. 1999). These lines of evidence thus suggest that inbreeding depression due to reduced population size can contribute significantly to extinction risk in the wild (Frankham 2005).

The empirical evidence for other genetic factors affecting population persistence is, however, less abundant. Small populations may be more susceptible than large populations to accumulation of deleterious mutations due to the decreased efficiency of natural selection: natural selection becomes effectively neutral when s < 1/2N (Wright 1943). While the theoretical basis for this relationship is well established (Lynch et al. 1995), strong empirical support for mutational meltdowns is thus far lacking (Gilligan et al. 1997; Woodworth et al. 2002). Purging, the selective removal of deleterious alleles when in homozygous state, has been suggested as a mechanism responsible for the scarcity of such evidence. Empirical evidence for purging is, however, also mixed (Swindell & Bouzat 2006b; Boakes et al. 2007) and most often comes from studies on plants (Byers & Waller 1999), where the opportunity for gene flow is relatively limited. Even under isolation, the beneficial fitness effects of purging appear to be limited (Boakes et al. 2007 but see Crnokrak & Barrett 2002). Importantly, immigration (even at very low levels) seems to be more efficient in countering inbreeding and may interfere with purging (Keller et al. 2001). Although biologically plausible, the prevalence of purging in natural (animal) populations therefore remains uncertain and difficult to predict (Leberg & Firmin 2008).

Loss of genetic diversity, and therefore quantitative trait heritability (‘evolutionary potential’), is often considered the most relevant evolutionary consequence of declining population size (Franklin 1980; Frankham et al. 2003). Although experiments under controlled conditions provide some support (Weber 1990; Weber & Diggins 1990; Swindell & Bouzat 2005; Swindell & Bouzat 2006a), in the wild the correlation between population size and evolutionary potential is generally weak. This may result from the complex relationship between variability in adaptive quantitative traits and neutral genetic diversity (Reed & Frankham 2001; Merila & Crnokrak 2001; Mckay & Latta 2002; Willi et al. 2006): while neutral genetic diversity decreases with population size following a sigmoid function (Frankham 1996), the heritability for quantitative traits decreases with population size only at very small population sizes (Willi et al. 2006). In addition, both the complex genetic architecture of most quantitative traits and the fact that the type of selection (Willi et al. 2006) will vary with the type of trait, e.g. morphological or life history (Mousseau & Roff 1987; Roff & Emerson 2006), make a strong correlation between neutral genetic and quantitative trait variation less likely. Nevertheless, based on reduced neutral genetic variation, Spielman et al. (2004) argued that threatened taxa would have an elevated extinction risk due to loss of evolutionary potential. These considerations, along with the realization that population connectivity tends to counter genetic stochasticity, suggest that concerns about the long-term evolutionary potential of small or declining populations may be less well founded than for instance, immediate concerns about inbreeding depression (Frankham et al. 2003).

Genetic diversity depends on a population's genetically effective size, Ne (Wright 1931), which refers to the size of an ideal population experiencing the same rate of random genetic change over time as the real population under consideration (Crow & Kimura 1970). Real biological systems do not adhere to idealized settings (Whitlock & McCauley 1999), and thus, effective sizes are typically much smaller than census sizes. For a wide range of demographic and reproductive scenarios, Ne/N is expected to be ~0.5 (Nunney 1991, 1993, 1996; Nunney & Elam 1994). Over longer terms, population size fluctuations can reduce Ne further (Wright 1938; Vucetich et al. 1997; Kalinowski & Waples 2002; Waples 2002a). Frankham (1995) reviewed (mainly demographic) estimates of the ratio of Ne to N in wild populations and reported a median value of 0.11, identifying fluctuating population size, unequal sex ratio and variance in reproductive success as the main factors responsible for the low Ne/N ratios. Life-history aspects and reproductive biology are thus very important determinants of Ne, but additional factors may also be important (Turner et al. 2006). This low ratio implies that populations may become sensitive to genetic stochasticity at levels where census population estimates would provide no such indications, although the consistency of Ne/N ratios in wild populations is uncertain (e.g. Hauser et al. 2002; Ardren & Kapuscinski 2003).

Concurrently, efforts to establish lower population size thresholds, at which the impact of genetic factors should be minimal, have suggested Ne = 50 to minimize inbreeding depression and Ne = 500 to maintain sufficient evolutionary potential (Franklin 1980; but see Lande 1988; Franklin & Frankham 1998; Lynch & Lande 1998). Estimating Ne can thus be an important tool in the assessment of the genetic vulnerability of endangered populations (Mace & Lande 1991). Although several demographic and genetic methods have been developed to estimate Ne (reviewed by Caballero 1994; Leberg 2005; Wang 2005), here we focus on the ‘temporal’ genetic method, which is based on the premise that temporal variance in neutral genetic allele frequencies is inversely proportional to the effective population size. The approach was pioneered by Krimbas & Tsakas (1971), and substantial statistical refinement has since then been achieved (Nei & Tajima 1981; Pollak 1983; Waples 1989, 1990a, b; Anderson et al. 2000; Wang 2001; Berthier et al. 2002; Laval et al. 2003; Wang & Whitlock 2003; Anderson 2005). Originally developed for species with discrete generations, the method has been extended to situations where generations overlap (Waples 1990a, b; Jorde & Ryman 1995; Waples & Yokota 2007) and importantly, for cases in which the assumption of complete isolation cannot be held valid (Wang & Whitlock 2003). The consequences of violating some of these assumptions have also been quantified (Waples & Yokota 2007).

Since Frankham's (1996) seminal review, an increased sophistication in molecular methods has been accompanied by a drastic increase in published genetic estimates of Ne (denoted inline image) and its ratio to census size (Ne/N). Concomitantly, awareness is growing that natural systems (as well as statistical models for estimating Ne) can have complicated features that need to be considered in detail when estimating effective population size (e.g. Wang & Whitlock 2003; Fraser et al. 2007a; Waples & Yokota 2007). Accounting for these factors is imperative for gaining a better understanding of both the magnitude of effective population size and its implications for conservation and evolution. Given that monitoring of Ne is strongly advocated in conservation and management programs (Schwartz et al. 1999; Leberg 2005; Schwartz et al. 2007), there is a need for an assessment of the consistency and reliability of estimates derived from these temporal methods, and their relevance for conservation.

The purpose of this review is threefold:

  • 1) Theoretical evaluations have shown that the estimation of inline image is sensitive to several potential sources of bias. Here we extend these theoretical concerns to natural populations, using empirical estimates derived from the temporal approach to quantify such biases. We focus on model selection and sample size, and make practical recommendations for future studies.
  • 2) Gene flow is known to affect processes of genetic stochasticity and thereby also Ne. We review the empirical literature on gene flow and effective population size, focusing on the effect of gene flow on Ne estimation, as well as considerations of Ne in the context of metapopulation dynamics.
  • 3) Finally, we compare temporal estimates of effective population sizes of wild populations available since 1995 with those compiled by Frankham (1995) and investigate whether populations of conservation concern are characterized by relatively low effective population sizes and/or Ne/N ratios. We quantify the genetic behaviour of populations as predicted by inline image, placing special emphasis on gene flow. We conclude with a discussion of the value and utility of the temporal approach to the estimation of effective population size in the context of conservation.

Data selection criteria

An extensive literature search located 83 studies reporting genetic estimates of Ne using the temporal method (see Table S1, Supplementary material). These came from a total of 65 species in diverse groups including amphibians, birds, crustaceans, fish, insects, mammals, molluscs, reptiles and plants. We considered estimates for wild populations only, ignoring those supplemented by supportive breeding. Five additional studies were located that provided temporal genetic data, yet had not estimated effective population size. After calculation of inline image, these were added to the data set, which thus includes 88 studies. Where multiple estimates applied to the same population, only estimates covering different time periods were considered. Furthermore, whenever species with overlapping generations were analysed by estimating the annual number of breeders (Nb), only estimates of Ne, derived from this value, were included in subsequent analyses. Using these selection criteria, a grand total of 780 temporal estimates of Ne and 251 estimates of the Ne/N ratio were available for subsequent analyses. Although a large component of these data pertain to salmonid fish (20% of studies; 40% of temporal estimates), we attempt to make general inferences and limit our conclusions to salmonids wherever appropriate. All statistical analyses were performed in s-plus 6.2 (Insightful).

Analytical considerations when estimating Ne

Indirect genetic approaches have the strong advantage that they can provide demographically inclusive Ne estimates and avoid some of the logistic difficulties associated with direct, ecological approaches of estimating Ne. They may suffer, however, from their own sources of biases, principally among them violations of the common assumption of closed populations characterized by discrete generations, and sample size effects. Here we focus on the last two factors, relegating the consequences of ignoring gene flow to the next section. In addition, we use empirical data to evaluate approaches for improving precision of Ne estimates.

The importance of accounting for age structure and demographics

Empirical studies have commonly applied models of estimating Ne that assume discrete generations to species with overlapping generations. Discrete model estimates of Ne over short-terms (roughly < 4 generations) are expected to be biased when applied to age-structured species with overlapping generations (Jorde & Ryman 1995; Waples & Yokota 2007), because genetic fluctuations among cohorts will often differ from those for the population as a whole (Jorde & Ryman 1995).

We used empirical Ne values to evaluate the extent of this bias by comparing all independent estimates reported with those that correctly accounted for the species’ life history only. We used the following criteria for inclusion in this subset. Estimates with discrete generation models were included when the species exhibited discrete generations, regardless of time span (n = 33). Discrete models applied to species with overlapping generations were used when temporal samples were spaced more than four generations apart (n = 50), when bias due to overlapping generations is expected to be insignificant (Waples & Yokota 2007). Ne estimates on age-structured populations covering shorter time spans (t < 4 generations) were included only if the analytical model (Waples 1990a, b; Jorde & Ryman 1995) took this into account (n = 60). This restricted data set, which may more accurately reflect effective population sizes for wild species, contained 143 temporal estimates, vs. a grand total of 304 estimates.

Our analyses reveal that Ne estimates that do not properly consider species’ biology generally tend to be biased downwards. A comparison of overall values (Table 1) shows that inline image tends to be larger for studies that applied an appropriate analytical model (inline image) than for all empirical estimates available (inline image, one-sided t-test, P < 0.001). This may partly be because the majority of estimates published to date are on fish, which are generally characterized by a life history with a type III survival curve (high fecundity and high juvenile mortality), for which temporal estimates derived from short time spans are particularly sensitive to downward bias (Waples & Yokota 2007). Similar differences in Ne are also observed when only considering estimates for marine fish, all of which are characterized by a type III survival curve (t-test, one-sided, P = 0.007, Wilcoxon one-sided rank test, Z = 2.0688, P = 0.02). These results reiterate that proper model selection is a very important consideration for the temporal approach.

Table 1.  Overview of empirical estimates of effective population size (inline image) and its ratio to census size (Ne/N) from published studies (n, see Table S1 for references) for different conservation categories. Average transformed parameter values ± standard deviation (SD) are presented as back-calculated untransformed values. Additionally given is the median value derived from untransformed parameter values. Values are given for all independent data points and for a more restricted data set, assumed to be relatively free of analytical model bias
Conservation categoryinline imageinline image
nAverage ± SDmediannAverage ± SDMedian
All data
Exploited 21521 ± 125 697  98.1.10−5 ± 7.7.10−51.9.10−5
Stable22689 ± 36  89 610.20 ± 0.090.16
Conservation 58116 ± 26 101 320.28 ± 0.150.20
All305104 ± 39 1041020.19 ± 0.110.16
Selected data only
Exploited  92085 ± 3221235  61.0.10−4 ± 1.0.10−42.3.10−5
Stable 94271 ± 62 265 330.18 ± 0.170.14
Conservation 35149 ± 31 175 260.27 ± 0.150.20
All140267 ± 65 251 640.16 ± 0.130.14

Sample size considerations for temporal Ne estimators

Sample size is known to affect not only precision, but also bias temporal estimators of Ne. This is because allele frequency shifts reflect not only random drift but also the sampling process (Waples 1989). All analytical variations of the moment-based method (Waples 1989, 1990a, b; Jorde & Ryman 1995) correct for the effect of sampling. Likelihood methods make no such explicit correction, but are expected to be more powerful, given that they make use of more of the information contained in the data, in particular when data contain many rare alleles. Although power for some of these methods has been evaluated through simulations (Berthier et al. 2002; Wang & Whitlock 2003), the potential of sampling-related bias in empirical studies remains relatively unexplored. Hence we examined the influence of sample size on bias in temporal inline image by applying a generalized linear model to the relationship of inline image with sample size.

We selected three different analytical methods commonly reported in the literature: the general moment-based approach, the pseudo-maximum likelihood method of Wang (2001) and the coalescent maximum-likelihood method of Berthier et al. (2002). Data for the three estimator methods were analysed separately, but only estimates assuming closed populations were considered. Studies are based on a large range of sample sizes and we report on correlations between inline image and sample size for all data combined, for the subset of Ne estimates obtained with samples sizes S < 50, and for those obtained with samples sizes S < 30.

We find that insufficient sampling may lead to (strong) bias in estimates of effective population size, in particular for methods that do not explicitly correct for sample size. Regardless of the estimator method, correlations between inline image and S are weak when all sample sizes are considered (Table 2). However, significant correlations are detected for the likelihood methods when considering smaller sample sizes (S < 50, S < 30). This suggests that they may be more sensitive to (downward) bias than the moment-based approach when dealing with small sample sizes. Moreover, extended regression analyses (Table 2) show that a general log-linear relationship provides the best fit between sample size and inline image.

Table 2.  Correlation between sample size (S) and effective population size estimates, for different groupings of sample size and three different analytical models. Given are the degrees of freedom (d.f.), correlation coefficient (r) and statistical significance (P) of linear regressions for nontransformed and log(Ne)-transformed data
Ne estimatorSNontransformed data, linearLog(Ne)-transformed data, linear
d.f.r2rPd.f.r2rP
Moment-basedAll1950.000.010.8811950.070.27< 0.001
< 501220.000.020.8531220.230.48< 0.001
< 30 510.010.070.625 510.220.480.002
Wang (2001)All1290.010.100.2711290.260.51< 0.001
< 50 860.090.290.007 860.250.50< 0.001
< 30 240.210.460.018 240.600.78< 0.001
Berthier et al. (2002)All 350.030.180.295 350.010.050.791
< 50 180.260.510.021 180.510.72< 0.001
< 30  3  3

Precision of temporal estimates of Ne

Besides the obvious importance of avoiding bias, increased emphasis is also placed on the precision of Ne estimators. This precision is suggested to principally benefit from increasing (1) sample size (2) number of marker loci and (3) number of generations between samples (Waples 1989; Waples 1990a; Luikart et al. 1998; Anderson et al. 2000; Berthier et al. 2002; Wang & Whitlock 2003). Estimate precision (95% confidence interval of inline image) is strongly determined by its own magnitude (linear regression model, n = 376, r = 0.91, P < 0.0001): large estimates of Ne are thus expected to be less precise than small estimates. We used empirical estimates based on microsatellite markers to assess the merit for improvement in estimate precision of sample size, number of marker loci (L), time span (t in generations), total number of alleles (Na), total number of independent alleles (Na-L) and locus variability (Na per locus). Analyses were conducted separately for moment-based estimators, Wang 2001) pseudo-maximum likelihood model and a third group consisting of other likelihood methods. Relationships between variables and estimator precision were investigated using generalized linear regression models. We examined the residuals of the regression of 95% confidence intervals onto Ne estimates as the dependent variable, in order to minimize the effect of estimate magnitude on its own precision.

The main improvements of precision for the temporal approach come from considerations of the genetic markers used. For each method considered, estimator precision improved with marker diversity (Table 3). In addition, the precision of the pseudo maximum-likelihood method of Wang (2001) also benefits from an increase in time span between samples. Neither number of loci or sample size appears to affect precision of Ne estimation significantly, at least within the variable ranges considered (2–19 microsatellite loci, 6.5–1058 samples per time point). With the current technical and analytical limitations, the most efficient approach to improve the precision of a temporal estimate of effective population size may therefore be to use more variable marker loci (Table 3).

Table 3.  Improving the precision of temporal estimates of effective population size. Given for three different methods of estimating Ne are correlations between precision and variables (factors) thought to improve precision. For each relationship the nature of the relationship, effect on precision (direction), the degrees of freedom (d.f.), correlation coefficients (r) and significance (P) are given.
Ne estimatorFactorRelationshipDirectiond.f.rP
Moment-basedNumber of (microsat) lociLinear1410.120.168
Sample sizeLinear1410.130.134
Time span (t in g)Linear1400.100.239
Number of alleles (Na)Linear+1250.260.004
Number of independent allelesLinear+1250.270.002
Allelic diversity (Na per locus)Linear+1250.37< 0.001
Wang (2001)Number of (microsat) lociLinear1010.270.007
Sample sizeLinear1010.000.976
Time span (t in g)Log-linear+1010.44< 0.001
Number of alleles (Na)Linear+ 700.130.283
Number of independent allelesLinear+ 700.150.196
Allelic diversity (Na per locus)Log-linear+ 700.300.010
Other likelihood methodsNumber of (microsat) lociLinear 640.300.014
Sample sizeLinear 640.070.554
Time span (t in g)Log-linear+ 640.090.485
Number of alleles (Na)Linear+ 520.000.975
Number of independent allelesLinear+ 520.080.570
Allelic diversity (Na per locus)Log-linear+ 520.300.026

These results are in line with expectations for likelihood approaches, which are well suited for analysing highly polymorphic data (Wang 2005). However, evaluations of the performance of the moment-based estimator (Waples 1989) suggest that more alleles per locus, or rather more rare alleles resulting in a skewed allele frequency distribution, will tend to exert an upward bias on Ne estimates, with an expected decrease in precision (wider confidence intervals). Binning of rare alleles has been suggested as a strategy to improve estimator accuracy (Waples 1990a, b), but simulations (Turner et al. 2001) show that estimate precision may suffer as a consequence. Empirical studies have reported mixed results of the binning strategy (Scribner et al. 1997; Shrimpton & Heath 2003; Brede & Beebee 2006). The simple availability of more alleles to measure drift (improving precision) may override the risk of reduced estimation accuracy (upward bias). Here, the estimator of Jorde & Ryman (2007), explicitly developed for data with many rare alleles, may be particularly useful. In summary, slightly different approaches can improve precision of different estimator methods. These should be considered seriously, given that confidence intervals themselves contain information relevant for conservation (Fraser et al. 2007a).

Effective population size of marine fish

The statistical concerns over analytical biases may be particularly relevant for effective population size estimation of (commercially exploited) marine fish species (Hauser et al. 2002; Turner et al. 2002; Hutchinson et al. 2003; Hoarau et al. 2005; Gomez-Uchida & Banks 2006), that are characterized by Ne/N ratios that are well below theoretical expectations (Nunney 1991, 1993, 1996) and empirical estimates for most other natural populations (Frankham 1995; this review). These species are generally characterized by type III survivorship curves, the biological consequences of which have been explored theoretically. Hedgecock (1994) suggested that extremely low Ne/N ratios may be due to a combination of high fecundity and high juvenile mortality, generating a very high variance in reproductive success which can depress Ne substantially. This idea has since been demonstrated to be theoretically plausible (Nunney 1996; Waples 2002b; Hedrick 2005), provided that a small number of families survive to produce offspring (Hedrick 2005). Such demographic trends will first need to be compatible with aspects of the species’ life history and reproductive behaviour (Poulsen et al. 2006). For example, empirical observations of the spawning behaviour of Atlantic cod (Gadus morhua) (Herbinger et al. 1997) do not support an extreme variance in family survival, required as a biological explanation for the reported low estimates of effective population size in this species (Hutchinson et al. 2003; Poulsen et al. 2006). Furthermore, these estimates are also difficult to reconcile with observations of high marker polymorphism, unless microsatellite mutation rates are generally much higher than currently believed (Poulsen et al. 2006).

We evaluated the scope for the ‘Hedgecock’ effect by comparing Ne/N ratios for species characterized by different survival curves. Since delineating survival curve types can be complicated, we combined type I and II (n = 24), considering species to be type III whenever they are characterized by relatively high fecundity (n = 78). We find that species with a type III survivorship curve exhibit significantly lower Ne/N ratios than species with either a type I or type II survivorship curves (type III: 0.18 ± 0.07 vs. type I + II: 0.32 ± 0.11, t-test one-sided, P = 0.019). These analyses did not consider marine fish estimates and confirm that a life history with very high fecundity and high mortality early in life can indeed result in a reduction in effective population size (Waples 2002b; Hedrick 2005). However, this reduction appears too small (~40%) to explain the extremely low Ne/N ratios observed in marine fish (Table 1), suggesting that additional reasons may exist for this pattern. For example, nonbiological factors such as human perturbation or commercial exploitation may act to further reduce Ne (Turner et al. 2006). The ultimate relevance of this explanation needs to be assessed by carefully considering other explanations that can be provided by sampling variance, violation of assumptions of applied analytical models and population structuring.

There are known problems in applying the temporal method in studies of species characterized by extremely large census sizes. First, a very large number of individuals may have to be sampled to obtain reliable estimates of Ne in cases where one can a priori expect this value to be very large (Nei & Tajima 1981). Second, many marine species are characterized by overlapping generations and age structure, and though analytical models are available to deal with this complication (Jorde & Ryman 1995), many studies have applied discrete generation models to such species. Our own analyses confirm that Ne estimates derived from analytical models compatible with the species’ biology can be substantially larger than those that did not. Studies on marine fish effective population sizes that have applied a model designed for overlapping generations tend to report slightly less extreme Ne/N ratios (e.g. Turner et al. 2002; Gomez-Uchida & Banks 2006; Saillant & Gold 2006) than those that did not. Some low Ne/N ratios (e.g. Hauser et al. 2002; Hoarau et al. 2005) should be relatively free from this bias, since they considered samples taken over comparatively long time spans. Future studies of marine fish Ne should attempt to harmonize analytical considerations and sampling with what is known of the species’ biology and demography. These considerations do not rule out the consequences of population structuring and metapopulation dynamics for marine effective population sizes (see below).

Recommendations for future studies

Adequate sampling is essential for an unbiased estimation of Ne with the temporal method, regardless of the estimator method (moment-based or maximum-likelihood). Although that statement seems trivial, a substantial part of the published Ne estimates may be subject to (some) downward bias due to small sample sizes. This potential bias appears less strong for moment-based methods than for likelihood methods. The main strength of likelihood methods lies in their ability to make more effective use of the information contained in data with many low frequency alleles, typical for microsatellites (Wang 2005). Our analyses, however, show that this improved power does not extend to samples characterized by small sizes (S < 50), a result that is consistent with sampling recommendations made for these analytical models (Anderson et al. 2000; Berthier et al. 2002; Laval et al. 2003; Wang & Whitlock 2003).

The important question is then how much should one sample in empirical studies. Sample size should be large enough to override effects of sampling variance when estimating Ne, that is, to maximize the signal-to-noise ratio (Nei & Tajima 1981). Temporal methods are well known to not be equally suitable for analyses of populations of all sizes, particularly for those that are very large (Waples 1989). Although many studies have recommended sample sizes of at least 50, many more may have to be sampled for large populations. Power analyses of the temporal method for detecting population bottlenecks (Luikart et al. 1999) reveal that even for moderately small effective population sizes (Ne~40 100), substantial numbers of loci and individuals (> 10 loci, S  > 45) may have to be surveyed. Using simulations, Ovenden et al. (2007) estimated that ~2000 sampled individuals are required to attain sufficient power to reliably estimate an effective size of 8000. Clearly, maximizing the ratio of S to Ne, rather than sample size itself, is important for the temporal approach (Nei & Tajima 1981). However, the ‘true’Ne is usually unknown for natural populations. Instead, we used generational census size as a proxy for Ne to estimate this ratio. For a subset of estimates (n = 30) on populations smaller than 105 individuals per generation, which were deemed relatively unbiased on the grounds of model selection and time span between temporal samples, we find the median S/N ratio to be ~0.10. Thus, while large sample sizes may be required for populations with large census size, small samples can be permissible when working with small populations and some low Ne estimates reviewed here undoubtedly reflect biological reality. Ultimately, the onus will be on researchers to justify their sampling design in the context of what is known of the species’ demography, and on journal editors to keep them to it.

Second, one should carefully consider the analytical model best compatible with the study species’ biology and life history. Our review confirms that inappropriate model consideration may often lead to downward bias (Waples & Yokota 2007). When a cohort analysis (Jorde & Ryman 1995) appears warranted (as will frequently be, when short time spans are studied), sampling should be optimized to ensure that individual cohorts contain sufficiently large sample sizes. For long-lived iteroparous species, this may imply collecting comparatively large sample sizes at any given point in time, on top of the demographic information required for this analytical approach. However, estimates derived from year-class approaches can provide information that applies directly to the time span sampled, thereby facilitating efficient genetic monitoring programs (Schwartz et al. 2007).

An alternative option is to increase the temporal span between samples, but this time span (> 4 generations) may be very long for some species, and this approach has its own drawbacks. First, in particular in studies with archived ‘ancient’ DNA samples, it is important to minimize technical artefacts, since these will likely exert a downward bias on inline image (see Poulsen et al. 2006). Perhaps more importantly, when no historical samples are available for comparison, the choice to wait until enough time has passed may be incompatible with the need for genetic information due to imminent conservation concerns. Here the temporal method may simply not be the best option for estimating effective population size: instead Ne estimators based on a single population sample may be more useful (Hill 1981; Bartley et al. 1992; Tallmon et al. 2004, 2008; Waples 2006). These estimators, however, suffer from the important drawback that they can currently not account for the effects of gene flow.

Finally, current genetic approaches for estimating Ne are poorly equipped to analyse populations with dynamic demographics. The cohort model of Jorde & Ryman (1995) assumes static age structure and population size, whereas many natural populations may be dynamic in this respect, especially those undergoing declines (i.e. of conservation concern). Although single sample genetic estimators may be less sensitive to this complication, some ecological methods may be better suited to evaluate the consequences of demographic instability for Ne. Analytical models have recently been developed that account for fluctuating age structure and population size, based on demographic and environmental stochasticity (Engen et al. 2005, 2007). These ecological models require no genetic data but are based on (detailed) demographic information. Comparative studies using direct ecological approaches and indirect genetic methods, in particular on closed systems (e.g. Kaeuffer et al. 2007), will likely increase our understanding of the behaviour of Ne in natural, dynamic populations.

Consequences of gene flow for inline image

It is a basic feature of population genetics theory that gene flow will override the effects of random genetic drift when m > 1/4Ne (Wright 1931). Empirical studies have since confirmed the importance of immigration in countering adverse genetic effects (e.g. Westemeier et al. 1998; Vila et al. 2003). Furthermore, under metapopulation scenarios where dispersal is mainly a function of local density, one would expect smaller populations to have higher immigration rates (Hanski & Gaggiotti 2004; Pulliam 1988), thereby possibly countering enhanced genetic drift. When ignored, gene flow can thus bias temporal estimates of Ne, the direction of bias depending on the relative magnitude and continuity of gene flow under natural conditions. Although the importance of confirming population isolation in the temporal approach was realized long ago (Nei & Tajima 1981), there is currently only one analytical model for jointly estimating contemporary gene flow and effective population size (Wang & Whitlock 2003). We used combined estimates derived from this model to examine the question of whether gene flow is more common into effectively smaller populations than into larger populations. The main assumptions of Wang & Whitlock's model are that immigration from a source population is constant over the time period considered and that the source population is infinitely sized (i.e. has temporally stable allele frequency distributions), even though simulations have shown that the model provides reasonably accurate results when this latter assumption is not met (Wang & Whitlock 2003).

We compiled a database of 93 joint estimates of Ne and m from published studies to test the null hypothesis that incoming gene flow is independent of population size. This hypothesis was rejected. There is a negative log-linear relationship between gene flow and population size, indicating that migration rate (m) may indeed be higher into smaller populations (r = 0.56, P < 0.001, Fig. 1a). This effect can be mainly attributed to data on anadromous fish (n = 33, r = 0.77, P < 0.001): without estimates from this group the null hypothesis could not be rejected. These relationships remain unchanged when over longer time scales (g > 5 only, r = 0.68, P < 0.01 for all data (n = 23); r = 0.93, P < 0.001 for anadromous fish only (n = 14)). Thus, even though variance around estimates of gene flow at low population sizes is often considerable, our analyses suggest gene flow as inferred in this model is generally higher into small than into large (salmonid fish) populations. As such, they lend some support the suggestion that neutral genetic diversity (and possibly effective population size) in small populations can be maintained by ongoing immigration (Ostergaard et al. 2003; Consuegra et al. 2005; Fraser et al. 2007b; Schmeller & Merila 2007; Watts et al. 2007). This conclusion, however, needs to be qualified by uncertainty about how biologically realistic the applied analytical model is.

Figure 1.

Gene flow and effective population size estimation. (a) Relationship between estimates of gene flow (m) and effective population size (NeOPEN) following Wang & Whitlock (2003). (b) Effect of considering gene flow on estimates of Ne as a function of genetic differentiation (FST) between focal and source populations. ΔNe represents (NeOPEN – NeCLOSED)/NeCLOSED, estimated from Wang & Whitlock (2003). Correlation coefficient given for salmonid data only (P < 0.001). See Table  S1 for references.

Continuous vs. incidental gene flow

A recurrent point, emphasized when applying this method, is the need for the proper knowledge of potential sources of gene flow into the focal population (Hoffman et al. 2004; Johnson et al. 2004; Fraser et al. 2007a). Potential biases, as well as recommendations for a biologically meaningful application of Wang & Whitlock (2003) approach, are discussed in detail by Fraser et al. (2007a). Among other things, uncertainty remains regarding the causes of the frequently observed large differences between Ne estimates assuming open (NeOPEN) or closed (NeCLOSED) populations. The effects of ignoring gene flow in analyses of effective population size depend chiefly on (1) whether gene flow is incidental (discontinuous) vs. systematic (continuous) throughout the period of study (Wang & Whitlock 2003) and more trivially on (2) the extent of genetic differentiation between the focal and the source populations (Wang & Whitlock 2003; Fraser et al. 2007a). A downward bias is expected to occur in NeCLOSED (gene flow ignored) when gene flow actually occurs on an incidental basis (i.e. discontinuous) and the extent of this bias is expected to be directly proportional to the genetic differentiation between focal and source populations. Alternately, when gene flow occurs continuously, estimating NeCLOSED is expected to bias inline image upward. Although the extent of this bias may perhaps be somewhat dependent on the extent of the genetic differentiation between the focal and source populations, in practice under continuous gene flow, both populations are expected to be little differentiated.

We evaluated the likelihood of the two scenarios (upward vs. downward bias) by comparing the relative change in effective population size estimates when considering gene flow (ΔNe = (NeOPEN – NeCLOSED)/NeCLOSED) with the extent of genetic differentiation from gene flow sources as a proxy for the type of gene flow (continuous vs. incidental) (based on 56 available estimates). Our analyses suggest that there is a strongly positive correlation between ΔNe and FST (r = 0.56, P < 0.001, Fig. 1b). This relationship becomes stronger when only considering anadromous salmonid fishes (r = 0.72, P < 0.001), arguably a group with large potential for gene flow due to their migratory life cycle (Stabell 1984; Quinn 1993). Within the salmonids, 29 of 31 estimates of ΔNe are < 0, indicating an upward bias in inline image under closed conditions (NeCLOSED). This could suggest that systematic, more or less ‘continuous’ incoming gene flow may generally be responsible for a reduction in the genetic drift signal. Consistent with this interpretation, the only positive estimates of Ne occur when populations are highly differentiated (FST > 0.08), expected only under conditions of very low and intermittent gene flow. Two studies on nonsalmonid species with an NeOPEN > NeCLOSED (Lacson & Morizot 1991; Lessios et al. 1994) reported temporal instability of population structure, possibly due to (incidental) intermittent gene flow or recolonization. Ultimately, this issue may only be resolved in experiments with different scenarios of gene flow, under conditions where focal Ne can be controlled for. Although the analytical model of Wang & Whitlock (2003) may not fully capture the potential complexity of gene flow in biological systems, these analyses reiterate that contemporary gene flow, whenever biologically plausible, needs to be accounted for in empirical studies (Fraser et al. 2007a). Paradoxically, considerations of gene flow in the temporal method may become more important as populations become effectively larger, since genetic drift will be weaker under such circumstances.

Effective population size of metapopulations

The discussion about which effective population size estimate (open or closed) reflects the ‘true’Ne may be confounded by the possibility that these estimates may actually apply to different levels in a metapopulation. Over longer terms, with constant gene flow, the local effective population size may reflect the genetic behaviour characteristic of a larger hierarchical level represented by a metapopulation (meta-Ne). Conversely, unrecognized population substructuring may also bias estimates of effective population size downward. Under biologically realistic scenarios, the most likely effect of population subdivision is a (substantial) reduction in (meta)Ne (Whitlock & Barton 1997; Nunney 1999; Wang & Caballero 1999; Whitlock 2004). Whenever variance in subpopulation or ‘deme’ productivity is larger than random, meta-Ne is expected to be smaller than the sum of local effective sizes (Whitlock 2004). This may particularly be true under scenarios of asymmetrical gene flow and unequal (sub)population sizes, which might be common in natural systems (Fraser et al. 2004; Consuegra et al. 2005; Manier & Arnold 2005; Fraser et al. 2007a, b; Hansen et al. 2007; Palstra et al. 2007). Under such conditions the reproductive contributions of individual demes will vary greatly, effectively acting to enhance the reproductive variance of individuals within demes, hence providing an alternative explanation for low Ne and Ne/N estimates. Conversely, the genetic behaviour of individual demes will strongly depend on their relative role in a metapopulation (Wang & Caballero 1999), that is, whether they function as relative sources or sinks. Gene flow can thus strongly influence the effective size of a (sub)population, with its disregard potentially leading to strong positive or negative biases in the estimation of Ne. We reiterate that researchers should not a priori assume population isolation (or unity) when estimating effective population size.

The ‘gene flow problem’ has received relatively little attention in the literature on temporal effective population size, but may have contributed to some extremely low estimates of effective population size in marine fishes (Hauser et al. 2002; Hoarau et al. 2005; Laurent & Planes 2007). For example Hoarau et al. (2005) have reported Ne/N ratios of ~10−5 in plaice (Pleuronectes platessa) in the North Sea, where population substructuring has been documented (Hoarau et al. 2002). Although the local population scale may be difficult to capture (Waples 1998), conclusions drawn from these studies may have been different if estimates were applied to that scale. Despite recent efforts using a combination of genetic and nongenetic approaches (e.g. Bekkevold et al. 2005; Ruzzante et al. 2006 for herring; Pampouli et al. 2006 for cod), population structure and dynamics remain poorly quantified for most marine systems. Increased knowledge of variance in habitat productivity (Saillant & Gold 2006) is required, as well as the extent to which gene flow (asymmetry) modulates this variance, since this will determine overall Ne. We need more empirical studies on metapopulation Ne (meta-Ne), in particular on closed systems where the number of populations or demes is known and can be sampled temporally. Under these conditions, one can start to disentangle the effects of processes operating at the metapopulation level (variance in gene flow and productivity among demes) from those acting within demes (individual reproductive variance and other biological aspects). Without such knowledge, it will remain challenging to attach biological significance to meta-Ne estimates, in particular those for marine fish.

Concluding, the extremely low Ne/N ratios for marine fish could reflect analytical biases, as well as real biological effects of (undetected) population structuring and life history. Although future studies may succeed in removing estimator bias, ultimately the practical value of precisely estimating very large Ne also needs to be considered. Very large Ne values would indicate that genetic stochasticity may be of minor importance, as such forming a poor guidance tool for conservation and management. Studying the context and process of natural selection in large populations may perhaps provide more useful avenues for predicting evolutionary responses to factors such as fisheries pressure and environmental changes (Conover & Munch 2002; Olsen et al. 2004; Poulsen et al. 2006; Hutchings et al. 2007).

Relevance of effective population size for conservation

A comparison of inline image based on conservation status

Threatened or endangered species have been shown to exhibit lower (neutral) genetic diversity than closely related nonthreatened taxa (Spielman et al. 2004). Threatened species may therefore be expected to exhibit relatively low effective population sizes. In addition, they may also be characterized by lower Ne/N ratios if deterministic factors, contributing to census declines, commonly act to reduce Ne to levels below biological expectations (Luikart et al. 1998; Turner et al. 2006). Increased demographic stochasticity at low census size may have similar effects by enhancing individual reproductive variance. Conversely, if environmental stochasticity is driving population declines, this may act to increase Ne/N ratios, since it affects all individuals in a population equally, thereby possibly reducing individual reproductive variance. Changes in biological interactions at low abundance (genetic compensation) would have a similar effect on Ne/N. Therefore we hypothesized that populations of conservation concern exhibited lower Ne values, and evaluated if they had lower Ne/N ratios relative to presumably stable populations. Hence we divided our data according to whether estimates correspond to populations of conservation concern or not, as well as to (formerly) commercially exploited populations.

Information on conservation status was collected from the respective publications: populations were assumed nonthreatened whenever there was no mention of conservation concerns. We only considered estimates assuming closed populations, but whenever multiple estimates were available for the same population-time period combination, we selected the estimator method deemed most appropriate for the particular species (we note here that different estimators usually gave similar point estimates). Importantly, we only considered estimates that were assumed to be free of bias due to inappropriate model selection (see above). Furthermore, we ignored Ne estimates of infinity, since they most likely reflect a lack of statistical power to estimate Ne (see Waples 1989), but we did include some Ne/N ratios larger than one. Applying these restrictive criteria, the data set for this analysis contained 143 estimates of Ne and 65 estimates of Ne/N, covering a wide range of phyla, but somewhat biased towards anadromous fish (see Appendix). The question of whether effective population size differs between these three (conservation, stable, exploited) categories was first addressed with nonparametric tests (Mann–Whitney U) conducted on the untransformed data. This analysis was then repeated with transformed data (logarithmic and arcsine-square root, respectively, for Ne and Ne/N) and the significance assessed with pairwise t-tests. Average transformed values are reported back-calculated to untransformed estimates to facilitate interpretation.

We find that populations of conservation concern were characterized by smaller effective sizes: Ne (conservation concern) = range 7–1160, inline image vs. Ne (nonconservation concern): range 19–8935, inline image (one-sided t-test, P = 0.0004), though the magnitude of the mean Ne estimate (267 ± 65) suggests that, in general, genetic stochasticity is not likely of immediate concern (Table 1, Fig. 2). Commercially exploited marine fish exhibited significantly larger effective population sizes (range 560–19 535, inline image) than the other two categories. Nonparametric tests gave similar results for the comparison of groups based on conservation concern (Mann–Whitney U-test, Z = 3.997, P < 0.0001) and when commercially exploited species are compared with stable species (Mann–Whitney U-test, Z = –2.4315, P = 0.015). Here we note that estimates for nonthreatened species were derived from (nonsignificant) longer time spans (one-sided t-test, P = 0.07), and can therefore, if anything, be expected to be smaller due to the effect of fluctuating population size (Wright 1938; Vucetich et al. 1997; Kalinowski & Waples 2002).

Figure 2.

Distribution of selected empirical estimates of (a) effective population size (inline image) and (b) the ratio of effective size to census size (inline image) for wild populations, sorted by different categories. Figures are based on 144 published inline image and 66 inline image values. See Table S1 for references.

Contrary to effective population size, Ne/N ratios did not differ among the two conservation categories (Fig. 2, Table 1). Ne/N ratios were slightly higher, but not significantly so (one-sided t-test, t = –1.386, P = 0.09), for populations of conservation concern than for presumably stable populations (0.27 ± 0.15 vs. 0.18 ± 0.17). Marine fish populations though were characterized by substantially lower ratios (1.0 × 10−4 ± 1.0 × 10−4) (one-sided t-test, t = –3.979, P = 0.001). Again, nonparametric tests on the untransformed data sets gave very similar results (Mann–Whitney U-tests; Z = –1.2899, P = 0.122 for the conservation/stable comparison and Z = –3.8121, P < 0.0001 for the exploited/stable comparison). Multigenerational ratios are often based on arithmetic mean census sizes, thereby incorporating the effect of fluctuating population size. Without those estimates, we find that Ne/N ratios are significantly higher for populations of conservation concern (0.36 ± 0.16, median 0.37, one-sided t-test, P = 0.039) than for presumably stable populations (0.18 ± 0.12, median 0.14), with results for exploited populations unchanged. When all estimates were considered, regardless of conservation status, the average Ne/N ratio is 0.16 (±0.13, median 0.14, n = 65) with, and 0.20 (±0.15, median 0.15, n = 52) without, the ratios based on the arithmetic mean census size. These results reflect the reducing effect of fluctuating population size on Ne/N (Wright 1943; Frankham 1995; Vucetich et al. 1997), perhaps especially for populations of conservation concern. Higher Ne/N ratios for this latter group may also imply that genetic compensation against reductions in Ne commonly operates at low census size (see below).

These estimates are slightly higher than those reported by Frankham (1995) (median value ~0.1), but not as high as expected theoretically (0.25–0.50; Nunney 1991, 1993, 1996). Frankham (1995) considered mainly demographic estimates, and genetic estimates can a priori be expected to provide lower values, since they should incorporate all demographic effects. Empirical studies that have made a direct comparison between demographic and genetic estimates generally confirm these expectations (Husband & Barrett 1992; Ardren & Kapuscinski 2003; Rowe & Beebee 2004; Schmeller & Merila 2007; Watts et al. 2007). Importantly, interpreting Ne/N ratios from published genetic estimates can be difficult (Waples 2005), as it is often not made explicit what generation of census sizes (N) the calculated effective sizes refer to. Inappropriate estimation of the corresponding census population size will introduce additional bias to Ne/N estimates. The general unavailability of census data in the literature precludes an evaluation of the magnitude and direction of this bias and therefore we recommend interpreting our ratios with some caution.

Ne/N ratios and population size

A ‘constant’ value of the Ne/N ratio, regardless of temporal fluctuations in population size, would have great practical value in conservation. However, temporal fluctuations in effective size and the Ne/N ratio are not uncommon within natural populations and can be larger than differences between populations (e.g. Miller & Kapuscinski 1997; Heath et al. 2002; Waples 2002a; Shrimpton & Heath 2003; Fraser et al. 2007b). Thus, Ne/N ratios cannot be assumed constant over time or population size. One theoretical explanation for an inverse relationship between Ne/N ratio and N is that the standardized variance in family size increases as N increases, and conversely, that this variance decreases as N decreases (Hedrick 2005). Such genetic compensation can be viewed as a buffering mechanism against genetic adversity at low N, operating at the intrapopulation level. Initially observed under controlled laboratory settings (Pray et al. 1996), indications of genetic compensation in the wild have also been documented in salmonid fishes (Ardren & Kapuscinski 2003; Araki et al. 2007; Fraser et al. 2007b) and damselflies (Watts et al. 2007). For salmonid fish, genetic compensation can be reconciled with aspects of their breeding ecology (Fleming 1996; Fleming 1998), such as precocious mature male parr (Jones & King 1952), that may have increased fertilization success at low breeding densities (e.g. Jones & Hutchings 2001; Jones & Hutchings 2002). Therefore, we compared Ne/N ratios to census population size (N), using empirical values reported in the literature, excluding ratios based on the arithmetic mean census size. We limited these analyses to salmonid fish (n = 28), since our main goal was to quantify potential density-dependent influences on Ne/N for similar mating systems.

We find that the ratio of Ne to N is indeed higher at lower census size (Fig. 3), thus suggesting that genetic compensation may be a real feature of natural (salmonid) populations. However, there are a few alternatives to consider. First, Ne/N ratio estimates for very large census populations may have been (additionally) reduced by the effects of population substructuring (see above). Importantly, these results may simply reflect a spurious negative correlation, caused by plotting a ratio against its denominator. Therefore we cannot currently conclude, based on these data, that genetic compensation is or is not a realistic aspect of salmonid or other populations. Many more studies are required on natural systems where variance in reproductive success can be directly measured and related to population density. The ultimate relevance of genetic compensation to conservation will hinge on appropriate knowledge of the biological and environmental factors that control intraspecific competition and reproductive success.

Figure 3.

Genetic compensation as an intrapopulation buffer against reductions in effective population size (Ne). Plotted are empirically derived ratios of Ne/N against harmonic mean census size (for N < 10000) for salmonid fish only. See Table S1 for references.

Does inline image predict genetic stochasticity?

The practical relevance of effective population size in conservation genetics is its predictive value for adverse genetic processes (Frankham et al. 2003). Since endangered species have smaller effective population sizes, one could expect them to be more sensitive to genetic stochasticity. This expectation, however, requires validation with empirical data, and here we do so by relating published Ne estimates to the amount of neutral genetic diversity (average multilocus heterozygosity ΔHe) and its rate of loss of over time (ΔHe). We did not consider number of alleles, despite their sensitivity to sudden population declines (Nei et al. 1975; Maruyama & Fuerst 1985; Luikart et al. 1998; Garza & Williamson 2001), because the theoretical relationship with effective population size is complicated by additional factors (Maruyama & Fuerst 1985).

It is worth noting that these genetic properties are related to different definitions of effective population size. Whereas genetic drift (and random loss of alleles) is determined by variance effective size(Ne(V)), loss of genetic diversity (heterozygosity) and inbreeding are predicted by inbreeding effective size (Ne(I)) (Kimura & Crow 1963). The former is a function of the sampling process (size of offspring generation), whereas the latter is determined by the size of the parental generation. These two forms of effective size are equal when population size is constant over time, but are offset in populations that drastically fluctuate in size (Crow & Denniston 1988).

Joint estimates of inline image and genetic metrics were selected from the literature using the following criteria. For each population, we only considered noninfinite temporal estimates for the longest time span covered. Whenever Ne was estimated using several different estimators, we selected the method considered most applicable. For the analyses of loss of genetic diversity (ΔHE), we included short-term (t < 4 generations) estimates, to increase the number of data points, but assessed consistency with a more restricted data set (t > 4 generations). Relationships between effective population size and genetic metrics were investigated using generalized linear regression models.

Importantly, theoretical predictions of genetic stochasticity based on Ne assume that the population under consideration is closed to gene flow. Ongoing gene flow can change the impact of genetic stochasticity, as well as influence inline image (see above), but is often assumed to be negligible. We simultaneously tested the validity of this assumption by conducting analyses with all data points and with only those that were obtained from isolated populations (i.e. those for which no potential sources of contemporary gene flow could be inferred from the information in published studies).

For the gene diversity analyses we only considered studies using microsatellite markers and estimated gene diversity as the average of (two) individual time point estimates. We compiled 86 combined estimates of Ne and He from a wide taxonomic range (26 isolated and 60 open populations). Analyses reveal that genetic diversity as measured by heterozygosity is strongly correlated with inline image when only closed populations are considered (log-linear, r = 0.73 P < 0.001, Fig. 4a). This correlation weakens, though remains significant, when all populations, including those considered open to immigration, are included in the analysis (log-linear, r = 0.34, P = 0.002, Fig. 4a).

Figure 4.

Genetic stochasticity as a function of effective population size. Given are the relationships between empirical estimates of Ne and (a) average multilocus heterozygosity (HE) and (b) generational rate of loss of genetic diversity over time (HT/HO). Shown are data points for isolated populations (black circles) and populations open to gene flow (open circles) along with the correlation coefficients when all points are considered jointly (following ‘Open’) or when only isolated populations are considered isolated (following ‘Isolated’). See text for additional information and sample sizes.

We compiled 126 individual population estimates of Ne and rate of loss of genetic diversity (HT/HO, calculated on a rate of decrease per generation basis), again from a wide range of organisms (for 32 isolated and 96 open populations). The second, more conservative data set only contained 59 combined estimates applying to time scales longer than 4 generations (21 isolated, 38 open populations). Loss of genetic diversity over time was evaluated by fitting a model of the expected rate of loss of heterozygosity, based on effective population size (inline image; Crow & Kimura 1970) to the observed temporal rate of change in genetic diversity.

inline image generally provides a good indication of the rate of relative loss of genetic diversity, provided that the populations considered are isolated. This is particularly so for small populations, where values of change in gene diversity can be seen to fluctuate widely (Fig. 4b). These findings are similar when only considering the more robust genetic estimates (t > 4 generations): the predictive value of inline image for rate of decrease in heterozygosity was highest for estimates of isolated populations in the more restricted data set (r = 0.78, P < 0.001). Genetic diversity therefore only appears to be lost substantially when populations are both small and isolated.

The main conclusion from these analyses therefore is that temporal estimates of Ne only provide relevant information on the neutral genetic processes they are theoretically expected to predict, when the focal population receives no immigrants. Effective population size correlated poorly with genetic diversity and its loss over time when ‘open’ estimates were considered: gene flow appears to uncouple Ne from genetic stochasticity. This can be due to its buffering effect on genetic stochasticity, or impact on Ne itself, or a combination of these two. This latter explanation may be most likely, since temporal approaches infer Ne from measures of genetic drift. Therefore, generally speaking, effectively small populations may be less susceptible to genetic stochasticity than expected.

On the other hand, there may be a common discrepancy between Ne(I) and Ne(V) in natural populations. The genetic metrics considered are predicted by Ne(I) (Kimura & Crow 1963), whereas temporal estimates reflect Ne(V). We attempted to correct for this by considering temporal estimates for longer time spans where Ne(I) and Ne(V) would be roughly similar. However, a population may only acquire equilibrium Ne (when Ne(I) and Ne(V) are the same) when the underlying demographic and ecological dynamics remain constant for a large number of generations (Kimura & Crow 1963; Crow & Denniston 1988; Wang & Pollak 2000). Our results may suggest that this is generally not true for natural systems, and highlight the difficulty with interpreting genetic processes under nonequilibrium conditions (Hutchison & Templeton 1999; Whitlock & McCauley 1999). Population declines may be common cause of such a discrepancy, complicating the practical value of temporal estimates for conservation. This is another reason for combining the temporal method with other approaches for estimating Ne that do reflect inbreeding effective size (Hill 1981; Bartley et al. 1992; Waples 2006; Tallmon et al. 2008), thus providing more complete insights into the genetic behaviour of natural populations.

Conservation implications

The main goal of empirical studies of contemporary Ne arguably is to assess evolutionary potential and vulnerability to genetic stochasticity, under the rationale that this parameter will be informative on these processes. Based on our review, the size of an average natural population (inline image ~260) indicates that we may often have to be concerned about the detrimental impact of genetic factors on population persistence. If one applies the most conservative thresholds for critical population size (Franklin 1980; Franklin & Frankham 1998), the majority of natural populations (~70% of published estimates with inline image < 500) appear to currently lack sufficient evolutionary potential for long-term adaptation. Additionally, a substantial part (~8% of all published estimates have inline image < 50) of natural populations may suffer from adverse effects of inbreeding depression, which is in accordance with studies based on fitness-related traits (Crnokrak & Roff 1999). This picture obviously becomes more dramatic when considering higher threshold values for Ne (e.g. Lande 1988): populations with contemporary effective sizes in the low thousands appear to be very uncommon (~7%). On the one hand, this may indicate that genetic stochasticity constitutes an important component of population persistence for the majority of wildlife. On the other hand, theoretical predictions of genetic stochasticity as a function of population size assume complete population isolation, but immigration and gene flow may be common attributes of natural systems. Therefore, concerns of genetic stochasticity may often be somewhat overblown, since predictions will only apply when populations are truly isolated.

Our findings are likely not based on a systematic bias in sampling natural populations: Ne tends to be smaller for populations of conservation concern, but these do not constitute the majority of published estimates (~25%). Publication bias, upward and downward, cannot, however, be discounted. The effective size of many ‘stable’ populations may be too large to enable estimation with ‘temporal’ genetic methods (using conventional sample sizes), but populations impacted by genetic stochasticity due to low Ne, may also generally become extirpated before they can be sampled (Frankham 2005). Furthermore, although a large component of empirical estimates are for salmonid fish, quantitative and qualitative patterns remain consistent when omitting these. Therefore, our reported values may indeed reflect sizes typical for wild populations. Hence, for an average population, concerns of immediate threats to population persistence due to inbreeding depression (Newman & Pilson 1997; Saccheri et al. 1998; Nieminen et al. 2001) may be comparatively small. Encouragingly, commonly applied sampling designs appear generally powerful enough to detect levels of Ne at which inbreeding depression starts to become severe (Luikart et al. 1999). As such, temporal methods will remain an important tool in genetic monitoring, provided that due consideration is given to the potential sources of bias discussed. Concerns about genetic stochasticity ultimately need to be framed in the context of what is known about the prevalence of gene flow in natural systems.

Our review confirms that genetic stochasticity will only become important when populations have become both effectively small and isolated from the beneficial effects of gene flow. Under these circumstances (neutral) genetic diversity can indeed decay quickly (Fig. 4, Srikwan & Woodruff 2000; Johnson et al. 2004). Intrapopulation biological mechanisms may operate to buffer against reductions in Ne when census sizes decline, but by themselves will not replenish genetic variation lost and, ironically, may also interfere with conservation efforts to increase effective sizes. Regardless, quantitative genetic variance is lost at a much slower rate than neutral genetic variation (Willi et al. 2006): a substantial amount of trait heritability and hence evolutionary potential may therefore still be maintained after populations have become effectively small. This maintenance will ultimately be of little protection against fitness losses due to inbreeding depression at small population size.

Population connectivity is perhaps a more important factor than Ne when one attempts to evaluate extinction risk due to genetic factors. Gene flow (at very low levels) can relieve inbreeding depression (e.g. Vila et al. 2003) and generally contribute to genetic diversity, even without strongly influencing local heterozygosity (Barton et al. 2002; Willi et al. 2006; but see Fig. 4). Our own analyses show that gene flow can uncouple Ne estimates from processes of genetic stochasticity, perhaps mainly due to a positive effect on local Ne itself. Genetic variance may generally be maintained at hierarchical levels higher than the local population, reemphasizing the importance of population connectivity. Surprisingly little still is known about the evolutionary dynamics of metapopulations (including its effective size, meta-Ne). Human-induced fragmentation can obliterate such crucial population connectivity. Although the genetic consequences of population fragmentation will vary per species (Ouborg & Vantreuren 1994; Mundy et al. 1997; Srikwan & Woodruff 2000; Henle et al. 2004; Schmuki et al. 2006; Vandergast et al. 2007), dispersal ability can influence subsequent local persistence (Hoehn et al. 2007). Where population fragmentation persists, gene flow potential can be further reduced due to population divergence as a consequence of (changes in) selection regimes underlying quantitative traits (Hendry 2004; Nosil et al. 2005) and/or enhanced genetic drift (Johansson et al. 2007; Willi et al. 2007a), which may ultimately result in selection against immigrants (Hendry 2004). This would limit the scope for genetic rescue (but see Willi et al. 2007b), making early detection of population fragmentation imperative. These considerations reemphasize the utility of establishing wildlife linkages as a conservation strategy (see also Nunney 2001).

In summary, the practical relevance of Ne as an indicator of the role of genetic stochasticity in population persistence will require that some important biases are dealt with in its estimation, as well as an increased understanding of the mechanisms by which genetic variance is maintained in metapopulations. Similar to its countering effect on genetic stochasticity within populations, gene flow may often have a strong influence on (estimating) local Ne: temporal genetic methods derive Ne from measures of genetic drift, itself forming one major component of genetic stochasticity. Paradoxically, although very little gene flow can confound temporal estimates of Ne, such low levels may hardly impact deterministic evolutionary processes. Researchers should be cautious in assuming that the focal population constitutes one single panmictic unit, since violation of this assumption implies that estimates may not apply to local scales (Nei & Tajima 1981), thereby complicating inferences of genetic stochasticity and evolutionary potential based on inline image. This uncertainty of scale reiterates that linking population genetic parameters with ecological and evolutionary processes is important (Waples & Gaggiotti 2006; Palsboll et al. 2007) but remains challenging. Such issues will, however, become less relevant with ongoing habitat fragmentation, where the evolutionary fate of endangered populations will progressively start to depend on local population size and less on connectivity (e.g. Johnson et al. 2004). Consequently genetic factors will likely become more important for population persistence and hence species extinction. Concluding, considering genetic stochasticity should remain an important focus in the conservation of biodiversity.

Acknowledgements

We thank Dylan Fraser, Laura Weir, Jeff Hutchings, Paul Bentzen and Joe Bielawski for valuable feedback and stimulating discussions on earlier drafts. The manuscript benefited from many thoughtful critiques and suggestions by Louis Bernatchez and three anonymous reviewers. This work was supported by NSERC (DER), DFO Academic Subvention Grant (DER), Dalhousie University Post-graduate Scholarship (FPP) and the Dr Patrick Lett Fund (FPP).

This study is an extension of Friso Palstra's PhD research in Daniel Ruzzante's laboratory. Friso Palstra is interested in elucidating mechanisms that shape the evolution and ecology of (aquatic) organisms and their relevance and application to conservation and management. Daniel Ruzzante is interested in conservation genetics, biodiversity and phylogeography of aquatic organisms.

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