Phill Watts, Marine and Freshwater Biology Research Group, The Biosciences Building, School of Biological Sciences, Liverpool University, Crown Street, Liverpool, L69 7ZB, UK. Tel.: +44(0)151 7954384. Fax: +44(0)151 7954404. E-mail: firstname.lastname@example.org
1Effective population sizes (Ne) and migration rates (m) are critical evolutionary parameters that impact on population survival and determine the relative influence of selection and genetic drift. While the parameter m is well-studied in animal populations, Ne remains challenging to measure and consequently is only rarely estimated, particularly in insect taxa.
2We used demographic and genetic methods to estimate Ne and m in a fragmented population of the endangered damselfly Coenagrion mercuriale to better understand the contrast between genetic and field estimates of these parameters and also to identify the spatial scale over which populations may become locally adapted.
3We found a contrast between demographic- and genetic-based estimates of these parameters, with the former apparently providing overestimates of Ne, owing to substantial underestimation of the variance in reproductive success, and the latter overestimating m, because spatial genetic structure is weak.
4The overall Ne of sites within the population network at Beaulieu Heath, the largest C. mercuriale site in the UK, was estimated to vary between approximately 60 and 2700.
5While Ne was not correlated with either the total numbers of adults (N) or the area of habitat, this parameter was always less than N, because of substantial variance in reproductive success. The ratio Ne/N varied between 0·006 and 0·42 and was generally larger in smaller populations, possibly representing some ‘genetic compensation’.
6From a simple genetic model and these data on Ne and m, it seems that populations of C. mercuriale have the potential to respond to localized spatial variation in selection and this would need to be considered for future genetic management of this endangered species.
Effective population sizes (Ne) and dispersal rates are fundamental evolutionary parameters that determine the spatial variation in allele frequencies as well as the efficacy of selection in shaping genomic architecture (Slatkin 1973, 1985; Nagylaki & Lucier 1980; Adkison 1995). Migration permits gene flow and re-colonization following local extinction and, accordingly, quantifying dispersal rates has received widespread attention (Slatkin 1985; Clobert et al. 2001; Hanski 2003), but field estimates of Ne, the focus of this study, have been largely neglected. The concept of Ne was introduced by Wright (1931) to predict the genetic properties of a finite population that meets the assumptions of random mating, constant population size and nonoverlapping generations (the Wright–Fisher model) (Fisher 1930; Wright 1931). In the absence of significant migration, selection or mutation, the allele frequencies of this ‘idealized’ population will vary among generations due to random sampling of gametes during reproduction; the amount of this genetic drift being inversely proportional to population size. Natural populations seldom conform to the Wright–Fisher model and various factors reduce the number of reproductively successful individuals (i.e. Ne) below that of the total adult census (N) (Frankham 1995). This has widely recognized consequences for species’ conservation because it is Ne and not N that determines levels of inbreeding and the rate of loss of genetic diversity, which are important correlates of population persistence (Saccheri et al. 1998; Spielman, Brook & Frankham 2004) and future evolutionary potential (Franklin 1980).
Numerous demographic- and genetic-based methods have been developed to calculate Ne (reviewed by Nunney & Elam 1994; Wang & Caballero 1999; Wang 2005) yet it remains challenging to quantify. For example, there are manifest difficulties associated with acquiring accurate estimates of population fluctuations, sex ratio and variance in mating success (VMS), which are the principal factors that determine Ne. The corollary is that most estimates of Ne are based on the frequencies of genetic markers in populations, as these are a retrospective measure of all processes that determine the successful breeders (but not the relative significance of each demographic factor). Of the genetic methods formulated to estimate Ne, such as the extent of temporal variation in allele frequencies (Nei & Tajima 1981; Waples 1989; and others), linkage disequilibrium (Hill 1981) or heterozygote excess (Pudovkin, Zaykin & Hedgecock 1996), the first is believed to have the greatest precision and is the most frequently employed.
For species existing as a dynamic network of partially connected patches (captured by the metapopulation paradigm, see Hanski 2003 for review) several issues may complicate estimation of Ne. First, the original genetic methods developed to calculate Ne assume that populations are closed and this is often invalid; migration limits genetic divergence and this biases estimates of Ne if not taken into account. For this reason, new techniques have been derived that are able to jointly estimate Ne and immigration rates (m) (Vitalis & Couvet 2001; Wang & Whitlock 2003) and there are now several examples of the application of these techniques to characterize vertebrate populations (Wilson, Hutchings & Ferguson 2004; Jehle et al. 2005). Second, the effect of spatial genetic structure should be examined, as the Ne of a structured population is a function of the amount of subdivision. For instance, under an island model (populations exchange equal numbers of migrants) Ne = nNeS/(1 – FST), where n is the number of subpopulations, NeS is the effective population size of the subpopulations and FST is the standardized variance in gene frequencies among populations (Wright 1943; Wang & Caballero 1999). Accordingly, with increasing spatial structure it is possible for the Ne of a metapopulation to be greater than that of a random mating population of equivalent total size (Nichols, Bruford & Groombridge 2001). The alternative view that subdivision can reduce Ne (Whitlock & Barton 1997) highlights the point that the overall Ne of a structured population depends on the particular metapopulation dynamics.
With increasing population fragmentation through anthropogenic habitat modification, predicting the long-term population viability of poorly known species from their life history and other ecological characteristics is clearly important. The parameters Ne and m certainly impact on population survival per se; however, they also inform on the relative influence of random genetic drift, gene flow and selection (Slatkin 1973, 1985; Nagylaki & Lucier 1980; Adkison 1995). Hence, their quantification can be indicative of the potential for adaptive divergence among populations, an understanding of which affords a better practice of species’ conservation that is able to recreate contemporary evolutionary patterns and processes that is preferable to static preservation (Crandall et al. 2000; Stockwell, Hendry & Kinnison 2003). Invertebrates in particular are poorly studied, and this is particularly true for analyses of Ne in insect populations (see also Thompson, Watts & Saccheri 2007). This deficiency is alarming as they form a dominant functional group in many ecosystems, and some 800 species are in the IUCN (2006) red list data book (excluding the least concern category).
In this paper we (1) quantify adult population sizes (N), Ne and m in a fragmented population matrix of the endangered damselfly Coenagrion mercuriale (Charpentier, 1840) (Odonata: Zygoptera). We (2) contrast genetic and demographic methods of estimating the latter two parameters, (3) examine whether there are simple correlates of Ne, such as habitat size or the numbers of adults per se, and (4) use estimates of Ne and m to assess whether local C. mercuriale populations are more likely to be influenced by the action of selection or genetic drift. We find that Ne is always less than the population census (N), likely because of variance in family size, and that the ratio Ne/N varies considerably with population size. Making accurate estimates of m in weakly differentiated systems remains challenging. These results are discussed with respect to conservation of C. mercuriale.
Materials and methods
Coenagrion mercuriale is one of Europe's most threatened damselflies, listed on Annex II of the EC Habitats Directive and Appendix II of the Bern Convention and protected within Europe as a whole and by specific legislation in several countries. Within the UK a combination of poor dispersal capability (Hunger & Röske 2001; Purse et al. 2003; Watts et al. 2004a, 2007; Rouquette & Thompson 2007a) and loss and fragmentation of its specific habitat has caused extinction of many populations, perhaps as many as 38% over the last 21 years (Purse 2001). Nevertheless, several large populations of this species remain in the UK, including one on Beaulieu Heath where habitat management has prevented population decline so far.
description of study site and field work
C. mercuriale was sampled from Beaulieu Heath (50°47·8′N, 01°29·9′W) in southern England, UK. This site (4·6 × 3·7 km), isolated from other colonies by more than 4 km of woodland and heath, is a matrix of a large central ‘population’ and four satellite colonies (Fig. 1). For convenience during sampling, the central site was divided into seven areas, which are not separate (but appear semi-isolated where the habitat narrows) except where they are bisected by a road. Therefore, for this analysis, the central area was divided into an east and west population (Fig. 1). The area of suitable C. mercuriale habitat at each site was taken from recent surveys (Daguet 2006).
C. mercuriale emerges from May until the end of July, with a peak during June (Purse & Thompson 2003). To estimate population size, we undertook capture–mark–recapture (CMR) between 11 June and 14 July 2002. Adults were searched for every day (09.30–16.00 h) except during poor weather when they are not active. All unmarked, mature damselflies were caught, marked and re-observed using standard methods described previously (Rouquette & Thompson 2007a), with the position of every encounter geo-referenced using a differential GPS.
demographic estimates of adult population, Ne and rates of migration
Daily population sizes were calculated using a full Jolly–Seber model (Jolly 1965; Seber 1973) that makes a number of assumptions, including that animals are unaffected by being marked, marks are not lost, marked animals become mixed within the population and there is an equal probability of catching classes of animals (i.e. different sexes, age classes, marked and unmarked animals). Deviations from these assumptions are minimal, for example marks are not lost as they were written in indelible ink and removal of a single leg for genetic analyses (see below) does not affect fitness in damselflies (Fincke & Hadrys 2001). However, female damselflies were encountered less often than males at breeding sites despite an even sex ratio (Rouquette & Thompson 2007b), so we calculated population size using male CMR data only and then doubled this estimate to account for the more cryptic females. Our sampling did not take place over the full flight season of C. mercuriale. Estimates of the daily numbers of adult damselflies present when CMR was not undertaken were made from the trend in logistic growth (or decline) based on the available increasing (or declining) daily population estimates and assuming zero adults on the first (or last) date that C. mercuriale were sighted in England (6 May and 25 September in 2002, D.K. Jenkins pers. comm.). Censuses on 23 June, 4 July and 6 July were lower than expected from the trend in daily population size, probably because poor weather reduced capture efficiency, and were replaced with expected sizes from the trend in logistic growth or decline. Dividing the sum of all daily censuses by the average life span (mean time between first and last captures in days) provided a total adult population estimate (N).
Ecological estimates of Ne were calculated using the approximation Ne ≈ 8N/(Vkf + Vkm + 4), where Vkf and Vkm are the respective VMS for females and males (Falconer & Mackay 1996) and the population meets the assumptions of a Wright–Fisher model, which are given in the Introduction; using lifetime mating success data (Purse & Thompson 2005) we estimated Vkf and Vkm of C. mercuriale to be 7·4 and 13·5 (Watts et al. 2007). Immigration rates (m) are the proportions of animals recorded moving into a site different to that in which they were first captured (Table 1).
Table 1. Numbers of adult damselflies, C. mercuriale, caught, recaptured and observed moving between separate study sites during a CMR study on Beaulieu Heath, UK during 2002. See Fig. 1 for locations of sample sites
No. of observed immigrant damselflies
genotyping and genetic data analysis
Full details of DNA extraction and genotyping are described elsewhere (Watts et al. 2004a). DNA was extracted from single legs that were removed from between 47 and 192 damselflies per sample during 2002 and 2004 (Fig. 1), which represents a single generation interval as C. mercuriale is semivoltine in the UK. We observed no significant effect of our sampling upon recapture rate (D.J. Thompson unpublished). Every individual was genotyped at 14 unlinked microsatellite loci: LIST4-002, LIST4-024, LIST4-034, LIST4-037, LIST4-062, LIST4-063, LIST4-023, LIST4-030, LIST4-031, LIST4-035, LIST4-042, LIST4-060, LIST4-066 and LIST4-067 (Watts et al. 2004c; Watts, Thompson & Kemp 2004b).
Every population and the entire sample was tested for departure from expected Hardy–Weinberg equilibrium (HWE) conditions using the randomization procedure (5000 randomizations) implemented by fstat ver. 2·9·3 (Goudet 1995). This software was used to calculate expected heterozygosities (He) and the level of genetic differentiation, FST (Weir & Cockerham 1984), throughout the study area, with 95% confidence intervals (95% CI) for FST made by bootstrapping over loci.
Temporal methods to estimate Ne are based on the premise that the magnitude of temporal fluctuations in allele frequencies is directly related to Ne. Recent statistical improvements on the original temporal methods (e.g. Berthier et al. 2002; Wang & Whitlock 2003) present a variety of techniques with which Ne may be estimated. It is beyond the scope of this paper to examine all of these, so we compared (1) Waples's (1989) original method with (2) moment and (3) maximum-likelihood (ML) estimators derived by Wang & Whitlock (2003) as the former is still widely used and the latter two methods were developed to estimate Ne and immigration rate (m) jointly, but may be applied to calculate Ne of a closed population (note that Waples’ method assumes that the population is isolated, a condition which is not met in this study; Table 1). Wang & Whitlock's methods estimate Ne and m of a focal population under the assumption that immigrants are provided by an infinitely large source, but are robust to deviations from this model and may be applied to a source comprising one or more finite subpopulations. Here, source populations consisted of the pooled Beaulieu Heath genotypes after those of the focal population had been removed. NeEstimator ver. 1·3 (Peel, Ovenden & Peel 2004) was used to calculate Ne according to Waples (1989) and MNe ver. 2·3 (Wang & Whitlock 2003) was used to calculate Ne according to the moment and maximum-likelihood estimators of Wang & Whitlock. Ninety-five per cent confidence intervals are calculated for the moment and ML methods of Waples (1989) and Wang & Whitlock (2003), respectively.
Because many studies are limited to a single sampling season, estimates of Ne were made using Hill's (1981) LD method, implemented by NeEstimator (Peel et al. 2004), to provide some guide to its reliability. Nonrandom associations between alleles at different loci (linkage disequilibrium, LD) may arise through selection, migration, assortative mating and genetic drift. At neutral loci the degree of LD within an isolated Wright–Fisher population is determined by genetic drift, such that the extent of association between alleles provides an estimate of Ne (Hill 1981).
Under a stepping-stone model of dispersal, which is appropriate for C. mercuriale (Watts et al. 2004a, 2007), several models of gene flow and selection (Slatkin 1973; Nagylaki & Lucier 1980; and others, reviewed by Slatkin 1985; Adkison 1995) can be used to assess the potential for local population adaptation. Briefly, adaptation is expected when two conditions are fulfilled. First, there is a ‘characteristic length’ of spatial variation in allele frequencies due to gene flow and selection (lc) that is defined by lc = σ/√s, where σ is the standard deviation of dispersal distances and s is the strength of selection, and local adaptation cannot occur if the direction of selection varies at distances less than lc (Slatkin 1973, 1985). Second, Nagylaki & Lucier (1980) demonstrated that the relative importance of selection and genetic drift can be captured by the single parameter where m is the migration rate, s is the strength of selection and Ne is the effective population size. If the first condition is met, then local adaptation occurs when β >> 1, but not if β << 1 as selection is overwhelmed by the effects of genetic drift. This approach is discussed in detail by Adkison (1995). We estimated lc using demographic and genetic estimates of dispersal distances (σ = 118 and 176 m, respectively, Watts et al. 2004a) and β, again using demographic- and genetic-based estimates of Ne and m [calculated using Wang & Whitlock's (2003) maximum-likelihood method]. Both lc and β were calculated for a range of selection coefficients (s) that varied from 0·1 to 0·0001 to describe the influence of strong to weak selective pressure.
The total Beaulieu Heath population was estimated to be approximately 39 913 individuals (Table 1). Numbers of damselflies per site, taken as a percentage of the total census according to the relative proportions of marked individuals (Table 1), varied from c. 400 at BAG to nearly 20 000 at BHE (Table 2); there is a significant correlation (ρ = 0·902, P = 0·014) between N and the area of habitat, although with fewer adults at BAG and HAT than expected given their areas (Fig. 2). Variance in reproductive success generates an Ne/N ratio of 0·32 that, for example, reduces the Ne of BAG and BHE to c. 130 and 6330, respectively (see Table 2 for details of other sites).
Table 2. Estimates of the total numbers of adults (N) and effective population sizes (Ne) (±95% CI) of C. mercuriale at six sites on Beaulieu Heath, assuming that each population is isolated. Ne was estimated using several methods: E, ecological data on variance in reproductive success (Falconer & Mackay 1996); L(WW), likelihood (Wang & Whitlock 2003); M(WW), moment (Wang & Whitlock 2003); LD, linkage disequilibrium (Hill 1981); M(Wp), moment (Waples 1989). Estimates of Ne were made for 2002 (above) and 2004 (below) samples separately using the LD method (see Methods for details)
In line with previous CMR studies (Hunger & Röske 2001; Purse et al. 2003; Watts et al. 2004a; Rouquette & Thompson 2007a), C. mercuriale are sedentary, with just over 75% of adults moving less than 100 m and 95% of adults found within 300 m of their initial mark position (cumulative distance moved over all recaptures). The rate of intersite dispersal is low, involving just five individuals (< 0·12% of the recaptures) that all moved to neighbouring areas. No immigration or emigration was recorded at ROU or HAT (Table 1) that are 2·2 and 1·2 km from BHW, respectively. Thus, immigration rates vary from zero (ROU, HAT) up to a maximum of c. 0·01 at the smallest site BAG where the single immigrant has a large influence on this parameter (Table 3).
Table 3. Joint estimates of the effective population sizes (Ne) and immigration rates (m) of six C. mercuriale populations calculated using several methods: E, direct ecological observations; L(WW), likelihood (Wang & Whitlock 2003); M(WW), moment (Wang & Whitlock 2003)
Ten of the 168 sample-locus comparisons had a significant heterozygote deficiency compared with expected HWE conditions (P < 0·05 with a sequential Bonferroni correction applied for k = 14 multiple tests per site, Rice 1989) (data not shown); four (LIST4-037, LIST4-042, LIST4-060 and LIST4-067) of these were present in the large BHE (2004) sample, while three (LIST4-034, LIST4-060 and LIST4-066) deficiencies occurred in the small GRE (2004) sample. Three locus-sample combinations had a significant (P < 0·05, k = 14) excess of heterozygotes. Departure from random mating within sites is minimal and all loci were retained for the analyses. The total Beaulieu Heath sample significantly deviates from expected HWE (P = 0·0002) and is therefore subdivided, consistent with low migration rates. Average He was similar over all samples, varying from 0·55 (GRE, both samples) up to 0·58 (BHE 2004). While the level of genetic differentiation among populations is weak (FST = 0·005), the CIs exclude zero (±95% CI = 0·002, 0·009).
Full details of the estimates of Ne using the different methods are presented in Tables 2 and 3. Under the assumption of a single population, Ne could not be derived using genetic data for some samples, notably ROU where only the LD method (Hill 1981) provided a finite value (Table 2). Total population sizes (N) and ecological estimates of Ne were always greater than the corresponding genetic estimates of Ne. In many instances, larger populations tend to have correspondingly larger Ne, but there are exceptions such as the HAT population that has a smaller Ne than GRE. All temporal genetic methods produced reasonably similar estimates of Ne for each population, which varied from c.40 at BAG up to 372 at BHE (although only two samples per method had finite upper 95% CIs). Estimates of Ne made using the LD method were mostly similar between generations within site (except at BAG and BHW) and demonstrated a moderate agreement with the temporal methods, but with the LD method always generating larger estimates of Ne; this discrepancy increases with N. LD-derived estimates of Ne varied from c.40 at BAG up to several thousand at BHE, with half of these estimates having finite upper CIs (Table 2).
For joint estimation of Ne and m, the values of Ne produced by the ML estimator (Wang & Whitlock 2003) yielded similar, but always lower, results to those made assuming population isolation. Moreover, the ML method generated estimates of Ne for all six populations, with narrower CIs (and finite upper CIs for four populations). All ML estimates of Ne are less than 250 except at ROU, which is an order of magnitude greater (Ne = 2709). It appears therefore that when Ne and m are jointly estimated the ML method outperforms the moment estimator, which either produced (apparently) inflated estimates of Ne (which at GRE was larger than N) or did not resolve a value for this parameter (three populations) (Table 3). There was no correspondence between any of the genetic or ecologically derived rates of immigration (m), with the former tending to be very high and with wide CIs (possibly except at ROU) and the latter very low (Table 3).
Except at ROU, the Ne/N ratios are all less than 1. When these values are plotted against population size, two features are evident. First, the ratio Ne/N tends to decline as N increases (where Ne was estimated using the likelihood method of Wang & Whitlock (2003) that jointly estimates Ne and m). Second, there is greater variability to these ratios in smaller populations (Fig. 3). Thus, Ne/N in small C. mercuriale populations falls between 0·04 and 0·42 and in the two large colonies (c. 20 000 individuals) from 0·006 up to 0·018. Consequently, there is no general relationship between genetically derived estimates of Ne and either N or the habitable area (Fig. 2).
As C. mercuriale are relatively sedentary (σ = 118–176 m, Watts et al. 2004a), populations may respond to spatial variation in selection, for s = 0·01 (or more) that occurs over distances of c. 1·2–1·8 km (or less if the strength of selection is greater), i.e. potentially among sites within the Beaulieu Heath population matrix. Assuming that the combination of the demographic estimate of migration and average genetic estimate of Ne provide the best estimates of these parameters (see Discussion for reasons) then, similar to above, the pattern of variation in the parameter β over a range of selection coefficients predicts that local adaptation among populations within Beaulieu Heath may occur when the strength of selection is of the order of s = 0·01 or greater. For selection coefficients less than s = 0·01, the effects of genetic drift are expected to outweigh those of selection (Table 4).
Table 4. Predicted influence of the relative influence of selection and genetic drift for C. mercuriale on Beaulieu Heath; conditions where genetic drift prevails are highlighted in bold. Estimates of the parameters lc and β are made for average effective population sizes (Ne) and migration rates (m) that were calculated using genetic or demographic techniques (see Methods for details) and also genetic or demographic methods of estimating dispersal distance (σ) (described by Watts et al. 2004a)
Method of estimation
Selection coefficient (s)
σ = 176 m
17 600 m
σ = 118 m
11 800 m
Ne = 113; m = 0·3655
Ne = 349; m = 0·0028
Ne = 113; m = 0·0028
Despite its evolutionary significance there are still few demographic estimates of Ne in animal populations, and fewer studies that jointly estimate Ne and m. We employ ecological and genetic methods to provide the first estimates of Ne and m in an endangered insect. The main results of this study are (1) substantial discrepancies between methods of estimating of Ne; (2) Ne is lower than the adult census, particularly in large populations; and (3) C. mercuriale populations are potentially able to respond to selection at small spatial scales.
effective population size
Ne is a convenient summary parameter that links demographic and population genetic processes. Demographic estimates of Ne are expected to be imprecise due to the inherent difficulties associated with fieldwork and also because they are based on predicted consequences of complex population processes. Like many other studies our ecological estimates of Ne incorporated one factor (VMS) only, so it is not surprising that they are greater than genetic estimates of Ne (Table 2). Our analysis indicates that VMS is an important determinant of Ne, reducing Ne to a third that of the adult population; examination of Banks & Thompson's (1985) data in the congener Coenagrion puella produces a similar Ne/N ratio of 0·26. These values may be typical for other odonates, where substantial variation in mating success is common (Fincke 1982; Michiels & Dhondt 1991; Stoks 2000; Fincke & Hadrys 2001). Captive Bicyclus anynana (Lepidoptera) populations had an Ne/N ratio of c. 0·6 (Brakefield et al. 2001), twice that estimated for Coenagrion sp., but we can only speculate whether this discrepancy reflects taxonomic differences or a contrast between natural and artificial environments. As genetic estimates of Ne encompass all factors affecting reproductive success they should provide more accurate estimates than demographic ones. However, many of the genetic-based estimates of Ne did not have a finite upper 95% CI, so it is possible that the genetic point estimates of Ne are not precise. A potential source of imprecision for this and many studies may be the small sampling interval (here, a single generation), such that there is a greater effect of sampling relative to drift. None the less, if we accept there is a consistent difference between genetic and ecological estimates of Ne, then it is relevant to ask: what processes reduce the genetic estimates Ne below their ecological counterparts? Rouquette & Thompson (2007b) uncovered an equal sex ratio in C. mercuriale populations and our sampling covered a single generation, so the principal factor must be greater VMS than predicted. This is intuitive as VMS was estimated from one component of overall VMS, lifetime mating success (Purse & Thompson 2005), and other factors, such as variation in fecundity and egg viability, sperm competition and survivorship of offspring (Fincke & Hadrys 2001), will increase VMS further; this discrepancy was observed also in natterjack toads (Rowe & Beebee 2004). To provide context to the magnitude of these processes, variance in family size (Vk, averaged over both sexes) would have to be at least an order of magnitude greater to make our demographic and genetic estimates of Ne comparable (Vk between c. 100 and 660 to generate Ne/N ratios of 0·06–0·006, respectively). Disentangling the importance of these processes remains a nontrivial, but significant challenge to understanding components of fitness.
Few studies estimate Ne using single generation samples, possibly because of a perceived imprecision associated with the LD method (e.g. Frankham 1995; Ardren & Kapuscinski 2003). England et al. (2006) found that the LD method was biased when sample sizes were smaller than the Ne, likely because of linkage disequilibrium caused during sampling. With this in mind we note that while the LD and temporal estimates were reasonably congruent, they were not significantly correlated. To some extent this is expected as alternative methods of estimating Ne determine this parameter over different time-scales: the LD method infers short- to medium-term (depending on the extent of linkage among markers) mean Ne, and temporal methods estimate an average over the sampling period. Encouragingly, the LD method provided estimates of Ne that were consistent among generations within sites, with narrow CIs in the small populations. However, the method was imprecise (compared with temporal methods) at the larger sites, presumably because the signal of LD is genuinely weaker or larger sample sizes reduced sampling effects (see England et al. 2006). Further evaluations of the LD method would be useful as it has the clear benefit of providing single generation estimates of Ne.
Estimates of Ne differed between temporal methods, similar to other studies (e.g. Rowe & Beebee 2004). Simulations suggest that moment-based estimates are biased upwards, particularly when genetic drift is strong (Berthier et al. 2002; Tallmon, Luikart & Beaumont 2004). This was not observed when populations were assumed to be isolated (Table 2) but was evident under the more appropriate model that estimated Ne and m jointly (Table 3). In the absence of methods to jointly estimate Ne and m, there were two pragmatic options to meet the assumption of closed populations when estimating Ne: (1) consider a particularly isolated site, or (2) assume that migration is unimportant. Given the former, estimates of Ne may reflect the demographics of atypical populations rather than the dynamic processes characteristic of most populations. With respect to the latter, we find that using an unbiased ML estimator and the model that (appropriately) accounts for immigration generated consistently lower values of Ne with narrower 95% CIs (cf. Tables 2 and 3), compatible with increased precision. Although the ML estimates do not differ significantly between models of isolation and immigration (they possess overlapping CIs) it is evident that overlooking the effect of migration upwardly biases estimates of Ne, which is consistent with the predicted short-term consequences of gene flow (Wang 2005).
Principally following Frankham's (1995) review there has been substantial interest in quantifying the range of Ne/N across taxa and under different demographic and environmental conditions. In C. mercuriale, this ratio varies from 0·006 to 0·4 that is lower than most values reported by Frankham (1995) for insects (17 studies), except the seaweed fly Coelopa frigida (Ne/N = 0·0047 and 0·0009); subsequent estimates of Ne/N in insect populations varied between 0·098 and 0·491 (mean = 0·21) for a beetle (Ingvarsson & Olsson 1997). Thus, there are still too few data to evaluate whether certain insect taxa or life histories have characteristic Ne/N ratios. Frankham (1995) reported a mean Ne/N of 0·1 for animals and this value has become a ‘rule of thumb’ to predict population genetic properties in the absence of specific data. Although the extent to which this value is an artefact is unclear (e.g. Waples 2002), our data indicate that the general use of this value will be misleading as the ratio Ne/N varies substantially among populations within a species (Fig. 3). This pattern, also reported for vertebrates (Ardren & Kapuscinski 2003; Rowe & Beebee 2004; Jehle et al. 2005), is indicative of heterogeneity in the factors that determine the successful breeding population that leads to a reduction in the rate of genetic erosion in smaller populations termed ‘genetic compensation’. Ardren & Kapuscinski (2003) suggested this to be a consequence of a reduction in VMS in smaller populations, though we are not aware of any ecological studies that have tested this hypothesis.
effect of population subdivision
A feature of population structure is its effect on Ne compared with a panmictic population of equivalent size. For example, if all subpopulations contribute equally to the next generation then the overall metapopulation Ne may be increased by a factor of 1/(1 – FST) (Wright 1943; Wang & Caballero 1999). Two comments are appropriate. First, the level of population subdivision at Beaulieu Heath is weak (FST = 0·005, see Results), implying that it has little impact on Ne. Second, this (island) model may be inappropriate as there are substantial differences in size and immigration rates among sites. None the less, using a different approach, Nichols et al. (2001) concluded that population subdivision may help retain diversity. Conversely, Whitlock & Barton (1997) argued that patterns of extinction–recolonization and interpopulation reproductive variance will tend to increase the loss of genetic diversity in metapopulations. On the one hand, substantial reproductive variance among Beaulieu Heath subpopulations points to an overall reduction in Ne, yet this variance among sites (Fig. 3) can be interpreted as implying that fewer individuals in the large populations would be ‘wasted’ if they existed in smaller subpopulations.
Ecological estimates of dispersal may be biased downwards because of limited spatio-temporal sampling (Koenig, van Vuren & Hooge 1996) or movement by unsampled life stages (Mallet 1986; Wilson et al. 2004). Conversely, field surveys will overestimate gene flow when immigrants fail to reproduce. Our data apparently are in line with the former (Table 3), but it should be emphasized that: (1) the CMR fieldwork was intensive; (2) pre-reproductive movement by C. mercuriale is considered unlikely (Watts et al. 2004a); and (3) studies at other sites confirm that the dispersal capability of adult C. mercuriale is less than the spatial scale of the Beaulieu Heath metapopulation (Hunger & Röske 2001; Purse et al. 2003; Watts et al. 2004a; Rouquette & Thompson 2007a). We cannot exclude the possibility of ‘temporal’ migration, whereby larvae delay metamorphosis for a year and recruit to a different cohort (i.e. one that is not its own generation) (see Watts et al. 2005), nor some unrecognized movement. However, the discrepancy between demographic- and genetic-based estimates of m arises because the latter method produces estimates that are far too large to be realistic. Inflated estimates of migration rates using this and related methods have been observed by other studies that jointly estimated Ne and m (Wilson et al. 2004; Jehle et al. 2005) and are a likely consequence of weak spatial genetic structure (Wang & Whitlock 2003).
C. mercuriale populations are liable to fine-scale genetic differentiation (Watts et al. 2004a, 2005, 2006). While high values of FST are relatively easy to interpret in terms of barriers to dispersal, where spatial structure is weak it can be difficult to disentangle contemporary gene flow from the residual historic component. Low values of FST among the Beaulieu Heath sites may indicate high reproductive success of the few migrants (failure to breed would accelerate population divergence) or episodic migration that was not observed during the temporal confines of our single season of CMR. Clearly, the former is speculative; however, nonequilibrium genetic structure is commonly suggested to confound analyses of spatial genetic structure. Here, nonequilibrium conditions seem likely, as the number of effective migrants (Nem) estimated from Wright's (1931) approximation FST ≈ 1/(4Nem + 1) is at least an order of magnitude greater than that calculated using genetic and demographic estimates of the parameters Ne and m (cf. Table 3).
implications for conservation
Present conservation policy for C. mercuriale in the UK is based on habitat restoration and subsequent management, but will this be sufficient to ensure long-term viability? An adult census at Beaulieu Heath, a reasonable indicator of population health (O’Grady et al. 2004), reveals a large and presumably vigorous population, yet Ne is substantially less than this. Quantifying Ne is important as it determines the rate of loss of genetic diversity. As it is difficult to measure, identification of factors that influence or correlate with Ne, such as the habitat area (e.g. Shrimpton & Heath 2003 for salmonids), would be useful for conservation management. However, at least for C. mercuriale on Beaulieu Heath, Ne is not a simple function of either N or the area of suitable habitat (Fig. 2). We did observe that sites varied by an order of magnitude in their population densities from c. 4200 ha−1 at ROU down to c. 240 and 380 ha−1 at BAG and HAT, the two sites with the lowest Ne. While this indicates that these latter two sites are suboptimal, there is presently no significant reduction in gene diversity (He) at present. Projecting forward, the isolated ROU site should be capable of maintaining reasonable levels of variability because of its large Ne. By contrast, there should be some concern for the other isolated colony HAT which has the lowest Ne (= 59) and the highest rate of genetic erosion. Connectivity between BAG, GRE, BHE and BHW may limit loss of diversity, depending upon the reproductive successes of migrants. Guidelines to maintain Ne > 50 to minimize the immediate effects of inbreeding and ensure short-term survival and Ne > 500–5000 to permit adaptation to future environmental conditions (Franklin 1980; Lande 1995), apparently raise concern for the long-term survival of the Beaulieu Heath metapopulation (see Table 3) and, moreover, as it is the strongest C. mercuriale population in the UK, the remaining other UK colonies that almost certainly have lower Ne.
Certain insect populations may persist in the face of extremely low genetic diversity (e.g. Joyce & Pullin 2003), including C. mercuriale (Watts et al. 2006), so it is possible that in some species typified by generally low Ne/N ratios, a lack of genetic diversity per se has less impact on population survival than extrinsic factors such as habitat loss and environmental fluctuations. Alternatively, these studies may simply serve to highlight the lack of correspondence between diversity at neutral genetic markers and adaptive traits (Reed & Frankham 2001). An increasing number of studies have uncovered inbreeding in wild populations (Keller & Waller 2002), but for most natural populations we can only speculate on whether low Ne has led to inbreeding depression. Where inbreeding is suspected some type of genetic augmentation may be advised, but an uncritical addition of migrants may reduce fitness through hybridization of genomes that are adapted to different conditions. Thus, in any attempt to limit diversity loss in small C. mercuriale populations by translocations, a key issue would be to identify the potential for local adaptation. With this in mind, a simple model predicts that populations of C. mercuriale separated by as little as 1·8 km (or less, depending upon the strength of selection) could be locally adapted in response to spatial variation in selection coefficients of s = 0·01. While this may seem counter intuitive – small Ne should limit effectiveness of selection – a rapid response to selection has been demonstrated in a species with small Ne (Koskinen, Haugen & Primmer). Of course, this is conjecture at present, as we have neither characterized any adaptive traits, nor spatial variation in strength and direction of selection. Without quantifying fitness components we cannot predict for how long a population will remain viable or indeed whether it would benefit from introduction of new genetic material. Habitat management is undoubtedly a key component of population survival for insects, but we must further examine the relationship between Ne and m and fitness components in natural populations if we are to do more than speculate about the possible benefits or costs of genetic restoration for insect populations with low genetic diversities.
C. mercuriale is protected under Schedule 5 of the Wildlife & Countryside Act (1981). All work was carried out under licence from English Nature. We are grateful to the NERC (grant no. NER/A/S/2000/01322) who provided the funds which enabled the work to proceed. We thank all those involved in the CMR studies for their help. Ian Harvey wrote the program that performed the scaling procedure that estimated the VMS.