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Population bottleneck and effective size in Bonamia ostreae-resistant populations of Ostrea edulis as inferred by microsatellite markers

Genetic variability at five microsatellite loci was analysed in three hatchery-propagated populations of the flat oyster, Ostrea edulis. These populations were part of a selection programme for resistance to the protozoan parasite Bonamia ostreae and were produced by mass spawns, without control of the genealogy. Evidence for population bottlenecks and inbreeding was sought. A reduction in the number of alleles, mainly due to the loss of rare alleles, was observed in all selected populations, relative to the natural population from which they were derived. Heterozygote excesses were observed in two populations, and were attributed to substructuring of the population into a small number of families. Pedigree reconstruction showed that these two populations were produced by at most two spawning events involving a limited number of parents. Most individuals within these populations are half or full-sib, as shown by relatedness coefficients. The occurrence of population bottlenecks was supported by estimates of effective number of breeders derived by three methods: temporal variance in allelic frequencies, heterozygote excess, and a new method based on reduction in the number of alleles. The estimates from the different methods were consistent. The evidence for bottleneck and small effective number of breeders are expected to lead to increasing inbreeding, and have important consequences for the future management of the three O. edulis selected populations.


Introduction
The effective population size (N e ) is a critical parameter to monitor for the management of genetic resources, because it determines the rate of increase in inbreeding (∆F ), hence the rate of loss of genetic variability in a population (∆F l 1\2N e ) (Crow & Kimura, 1970). Conservation programmes are often based on captive breeding, which, if based on a small number of founders and breeders, can cause an increase in the inbreeding coefficient and a subsequent decrease in fitness known as inbreeding depression (see for instance Backus et al., 1995).
In the case of aquatic species and especially marine bivalves, improvements in hatchery technology in the past decade have allowed aquaculture broodstocks to be kept as closed populations, without input of individuals from other wild or captive populations. Moreover, aquatic animals can have very high fecundity but variable fertilities, and there is evidence that hatchery seed may come from only a few successfully spawning individuals (Gaffney et al., 1992). Estimates of N e for cultivated species suggest that closed aquatic broodstocks are small populations in which random drift can be important (Sbordoni et al., 1986 ;Hedgecock & Sly, 1990 ;Hedgecock et al., 1992). The direct assessment of effective size requires measurement of many demographic parameters that are difficult to carry out in natural populations. Many different indirect methods have been used to evaluate N e , based on genetic variability at marker loci. Several studies have focused on estimating N e indirectly from temporal changes in allelic frequencies in finite populations (Pollack, 1983). This temporal method has been shown to be robust and well suited to the study of small captive populations (Waples, 1989), and particularly of aquaculture broodstock (Hedgecock & Sly, 1990 ;Hedgecock et al., 1992). Hill (1981) has developed a statistical method for estimating effective population size from data on linkage disequilibrium among gene loci. However, this method requires prior knowledge of linkage relationships among loci, and may produce a large standard error if only a small number of loci are considered (Hill, 1981). Finally, Pudovkin et al. (1996) have developed a method to estimate the effective numbers of breeders, based on the heterozygote excess in a progeny born from a small number of parents ; this heterozygote excess is caused by differences, due to binomial sampling errors, in allelic frequencies between male and female parents.
A reduction in the effective population size following a population bottleneck is correlated with a decrease in heterozygosity and a loss of rare alleles (Wright, 1931). Nei et al. (1975) even predicted that during a bottleneck allele diversity would decrease faster than heterozygosity. However, the evolution of the actual number of alleles at a locus has not been used to estimate effective size. We developed a method, modelling the reduction in the number of alleles in a population as a function of the sample size, which can be used to estimate the effective number of founders in a population that has undergone a bottleneck.
In this paper we investigate effective size and inbreeding in three hatchery-maintained populations of Ostrea edulis selected for resistance to Bonamia ostreae, a widespread protozoan parasite that has endangered the flat oyster O. edulis in France, the Netherlands, Spain, Denmark, England and Ireland, and in North America (see review in Naciri-Graven et al., 1998). Our purpose is to assess a posteriori the effect of bottlenecks and a small effective number of breeders on the genetic variability in the three selected O. edulis populations. We also compare estimates of N e obtained from temporal variance in allelic frequencies, heterozygote excess and reduction in number of alleles. Microsatellites markers have been chosen as the molecular tool to investigate these issues ; not only are they suitable for genetic diversity studies (Jarne & Lagoda, 1996), but their high polymorphism makes them particularly adapted to studies dealing with relatedness and kinship assessment (Queller et al., 1993 ;Blouin et al., 1996).

(i) Biological material
Three different hatchery populations of Ostrea edulis, namely S85, S89W and S89I, have been developed since 1985 and 1989 respectively. These populations have shown a significant increase in ' resistance ' to Bonamia ostreae (Naciri-Graven et al., 1998). Fig. 1 shows the relationship between the populations. The first generation (G1) of S85 and S89W\S89I and the second generation (G2) of S85 were produced in 1985, 1989 and 1990 respectively. All populations were derived from wild animals from Quiberon Bay (Brittany, France), an area where B. ostreae is known to be endemic. The first generation of S85 was divided in three different groups that were reared in different locations in Brittany (namely Paimpol, Quiberon and La Trinite! ) ; the three groups were not subsequently mixed for the production of the G2. S85-G1, S85-G2, S89I-G1 and S89W-G1 have been produced by mass spawning : around 100 animals were placed in a raceway, and larvae were collected over a short period of time (1-3 days). Such a technique does not allow for pedigree management because the number and the identity of the animals that actually spawn is unknown.
All animals still alive in 1995 from S85-G2, S89I-G1 and S89W-G1 (67, 38 and 52 animals respectively) were sampled. These were the last generations produced by mass spawning and were used as parents in a biparental crossing experiment in 1995 (Naciri- Graven et al., 2000). A sample of 49 individuals recruited in Quiberon Bay in 1993 was used as a control wild population, representative of the wild population from which the founders of the selected lines were drawn. For all animals sampled, a piece of gill or mantle tissue was collected by biopsy and stored either in 100 % ethanol at room temperature, or dried at k80 mC.

(ii) DNA extraction and microsatellite amplification
After removal of the ethanol, 400 µl of 5 % Chelex, 30 µl of TE buffer (Tris 0n01 mM, EDTA 1 mM) and 10 µl of Proteinase K (10 mg\ml, Boehringer-Mannheim) were added to each sample, which was then incubated at 55 mC for 4 h. The samples were then boiled for 15 min, vortexed for 30-60 s and centrifuged at 8000 rpm for 5 min. The supernatant was collected for storage at k20 mC and the Chelex beads were discarded.

(iii) Analysis of genetic parameters
Standard descriptors of the genetic variability were calculated for each locus in each selected population and the control : the number of alleles (N a ), allelic frequencies, observed heterozygosity (H ! ) and unbiased expected genic diversity (H exp l (1kp# i ) 2N\(2Nk1), (Nei, 1978) where N is the sample size and p i the frequency of the i th allele). Departures from Hardy-Weinberg equilibrium were estimated by calculations of Wright's Fis according to Weir & Cockerham (1984). The null hypothesis, Fis l 0, was tested by bootstrapping over alleles. Calculations were performed using the program Genetix (Belkhir et al., 1996).
Genetic relatedness, r, between each pair of individuals within each selected population and the control, was calculated according to Queller & Goodnight (1989) using the software Relatedness developed by these authors. r was computed as follow : where x indexes individuals in the data set, k indexes loci and l indexes allelic position (1 or 2 for a diploid individual). The variables used here can be defined as follow : P x is the frequency within the current x individual of the allele found at x's locus k and allelic position l ; P y is the frequency of that same allele in the selected line from which x comes ; and P* is the frequency of the allele in the Quilberon population, used here as a baseline population.
The mean relatedness value r was computed for each selected population (r )& , r )*I , r )*W ) and the Quiberon population (r Q ) ; standard errors were estimated by jackknifing over loci. Differences between mean relatedness were tested by a t-test. Groups of related individuals were identified by UPGMA clustering, using (1kr) as a measure of genetic distance. This technique has proved useful for identifying family relationships. For instance, Blouin et al. (1996) used relatedness estimates and UPGMA clustering to recover without misclassifications the true family relationships among the offspring of four sets of Fig. 2. Estimation of the number of founders in a selected strain, from the reduction in the number of alleles in comparison with a control population. The number of founders is estimated by (i) calculating using successive bootstrapping the number of alleles in 1000 subsamples of size p from a population of size N (1 p N ), (ii) calculating the number of alleles (N a ) in the selected strain, (iii) estimating the mean size of a subsample of the control population that would have the same allelic richness N a . In this particular example, the control population (N l 49) has a total number of alleles of 19. The selected population has 12 alleles, which is the allelic diversity of a subsample of 12 individuals from the control population. An estimate of the number of founders for this selected strain is therefore 12 (95 % CI : 9n1-15n7).
independent maternal half-sibs in the mouse, Mus musculus, using 10 microsatellite loci.
On the basis of the presence of alleles shared between individuals, tentative pedigrees were reconstructed for the different selected populations. These putative pedigrees were then compared with the UPGMA clustering. This moreover provides a first estimate of the number of founder parents.

(iv) Estimation of the effecti e numbers of founders
In the absence of genealogical information, we used different methods to estimate the number of founders at the origin of each selected population, including one that we developed for this study.
(a) Temporal ariance in allelic frequencies (Waples, 1989) Allelic frequencies and an estimate of temporal variance in allelic frequency, F, which is standardized to compensate for differences among loci in initial allelic frequencies, were calculated. According to Hedgecock et al. (1992), we used Pollack's (1983) estimator for F, F k . An estimator of the harmonic mean effective population number over the time interval is : where F is the population mean, estimated by the mean of F k across the different loci, weighted by the number of alleles ; and t is the number of generations in the time interval between the initial sample of S ! individuals and the second sample of S t individuals.
The Quiberon population was used as the initial sample ; the number of generation was 2 for S85-G2 and 1 for both S89I-G1 and S89W-G. In addition, in order to estimate the effective size and the effect of drift in the control population, N k was estimated for the Quiberon population using two samples from different years (animals recruited in 1989 and in 1993, considered to be separated by 2 generations). Standard errors for N k were calculated by using a χ# approximation (Waples, 1989). Calculations were performed with the program EPS, provided by D. Hedgecock and V. Chow (Bodega Marine Laboratory, UC Davis).
(b) Heterozygote excess (Pudovkin et al., 1996) H ! being the observed heterozygosity in the progeny, and H exp being the expected heterozygosity under Hardy-Weinberg equilibrium, Pudovkin et al. (1996) showed that an estimate of the number of breeders, N eb , which in our case is equivalent to the effective size N e , is where D l (H ! kH exp )\H exp . Confidence intervals were obtained by jackknifing over loci.

(c) Reduction in the number of alleles
We developed a simple method to estimate the effective number of breeders in a population that had undergone a bottleneck, if samples from this population before and after the bottleneck are available, based on the reduction in the number of alleles. The basic idea is to model bottlenecks of various intensities in a population of known allelic composition, and estimate the number of alleles in the population immediately following this bottleneck. From a population of N individuals of known genotypes, a sample of size p is drawn, and the number of alleles in that sample is computed. The mean and variance of the number of alleles for a given sample size p are calculated by doing 1000 successive samplings. It is then possible to graphically represent the expected number of alleles (N a ) as a function of the size of a subsample of the population (N i ). Using this algorithm, the curves N a l f (N i ) were constructed for each locus for the Quiberon population. They were modelled by : Parameters C and k were estimated using the nlin procedure from the SAS software. If N a is the number of alleles in a selected population, then we can determine N i from (3). This can be used as an estimate of the effective number of founders (and 95 % confidence interval) for each selected population (see Fig. 2).
population. Allelic frequencies for the different populations are given in the Appendix. The mean number of alleles by locus ( pstandard deviation) is 19n8p2n2 significantly in the control, and is reduced in all the selected populations : 12n8p2n2 alleles\locus in S85-G2 (P 0n05), 9n4p0n9 for S89I-G1 (P 0n01) and 5n4p0n5 for S89W-G1 (P 0n01). This reduction in allele number is due in large part to the loss of alleles that were at low frequency in the control population.
In the control population the mean frequency of the alleles that are not shared with S85-G2 is 0n025p0n019 vs 0n068p0n054 for the alleles present both in the control and in S85-G2 (P 0n001) ; similarly, these frequencies are 0n033p0n028 vs 0n076p0n058 for S89I-G1 (P 0n001) and 0n037p0n039 vs 0n076p0n062 for S89W-G1 (P 0n01). The mean observed heterozygosity level is lower in S85-G2 (H ! l 0n716p0n087) than in the control (H ! l 0n840p0n089 ; P 0n001). On the contrary, the mean heterozygosity level in S89I-G1 (H ! l 0n859p 0n143) and S89W-G1 (H ! l 0n969p0n051) are respectively not significantly different from (P l 0n40), and significantly higher than (P 0n001), that of the control.
The Fis values are given in Table 2. The control population shows a slight overall heterozygote de- ficiency (Fis l 0n082, P 0n001) which seems to be due mainly to OeduH15. S85-G2 shows a slightly higher heterozygote deficiency (Fis l 0n104, P (c) Fig. 3. UPGMA clustering based on relatedness values for strains S89W (3a), S89I (3b) and S85 (3c). Individuals (indicated by a three-digit identification number) are circled with different line width and shading according to the proposed pedigree (see Table 3 for genotypes and text for details) for S89W and S89I, and subpopulation of origin (Qui, Quiberon ; Pa, Paimpol ; Tri, Trinite! ) for S85. A question mark (?) indicates that the pedigree is not fully resolved. Individual F360 (S89W) that does not cluster with his full-sib group of origin is indicated with an arrowhead. 0n001). On the other hand, both S89I-G1 and S89W-G1 show heterozygote excesses (Fis l k0n074, P 0n05 and Fis l k0n239, P 0n001, respectively).

(ii) Relatedness estimates
The mean relatedness value increases from the Quiberon population to S89W-G1 : r Q l k0n022 p0n001, r )& l 0n150p0n026, r )*I l 0n239p0n028 and r )*W l 0n325p0n033. All the coefficients are significantly different from one another at the α l 0n001 level.
The results of the UPGMA grouping are presented in Fig. 3. Population S89W-G1 clusters in two different groups. The putative parents can be inferred from the individual genotypes for each of these groups, and are given in Table 3. A very likely hypothesis is that S89W-G1 is constituted by two biparental half-sib families that share one parent. O. edulis is a brooding oyster : the male gametes are released in the seawater and filtered by the female, and fertilisation takes place inside the female's shell. Given this reproductive biology, the results suggest that the population issued from a single spawning event involving one female and two different males. The proposed pedigree is listed for each individual on the UPGMA tree. The clustering reflects perfectly the family structure, with only one misclassified individual (F360). S89I-G1 also clusters in three main groups. By analyzing individual genotypes, and based on shared alleles (data not shown), two of these clusters can be attributed to two independent half-sib families ; in each of these families, the majority of the individuals can be attributed to a single full-sib group. For each of these families, the genotypes of the common parents and of one other parent are given in Table 3 (respectively C and M, and D and N, for each family group). At least two other parents must have contributed to each of the families to account for the existing allelic richness, but their genotypes remain uncertain due to the small sample size. On the basis of these reconstructed genotypes, the individuals that form the intermediate cluster can be attributed to a single full-sib family CxD. Therefore two individuals drawn at random from S89I-G1 can be either full-sib, half-sib or unrelated. The proposed pedigrees are listed for individuals on the UPGMA tree. Again, the clustering is a good image of the family structure. This family structure gives us a first estimate of the number of parents of at least 8.
The situation is different for S85-G2 : due to subsequent mixing of genotypes between the first and second generation, and possibly to a greater number of founders (see below), it is difficult to identify groups of related individuals or family structure. On the UPGMA tree we listed the subpopulation (Quiberon, Paimpol, Trinite! ) to which each individual belongs. These subpopulations share the same grandparents (G0), but G1 individuals were not mixed for the production of the G2 (see Fig. 1). The UPGMA clustering is not very informative, although the ends of the nodes tend to cluster individuals from the same subpopulation. Because of a small number of indi-viduals in the Trinite! subpopulations, subsequent relatedness analyses were conducted only for the Quiberon and Paimpol subpopulations (respectively 35 and 28 individuals), still using allelic frequencies in the wild Quiberon sample as a baseline. The mean relatedness values within the Paimpol subpopulation (r l 0n374p0n010) is significantly higher than within the Quiberon subpopulation (r l 0n134p0n008, P 0n001).

(iii) Estimation of the number of founders at the origin of the selected populations
Estimates of the number of founders are given in Table 4. Although we already determined that S89W-G1 derived from exactly 3 parents, we made the calculation for this population as a way of testing for the accuracy of our methods.
In the case of S89I-G1 and S89W-G1, the estimates of the effective number of parents are consistent for the different loci and the different methods, even though the heterozygote excess methods gives the lower estimates. The mean ( pstandard deviation) of all estimates is 8n3p1n4 for S89I-G1 and 4n2p1n6 for S89W-G1. These values are concordant with the estimate that we previously derived from the pedigree reconstruction attempt. A narrower confidence interval was found for the heterozygote excess method, but for S89W-G1 the confidence interval does not include 3. With this exception, each confidence interval includes the estimates derived from the pedigree reconstruction.
No pedigree information could be used for S85-G2 and the heterozygote excess method is not applicable. The other two methods give concordant multilocus estimates ; the mean of all estimates is 18n7p2n2. Results are consistent across loci with the exception of OeduT5, which gives a higher estimate (27n7) and a broader confidence interval (17n4-64n8) through the reduction in the number of alleles method.
Effective size in the wild Quiberon population was estimated through the temporal variance in allelic frequencies method, and we found N e l 464, with a negative value as the upper bound of the confidence N k , N eb and N i are estimates of effective size N e according to the following methods respectively : temporal variance in allele frequencies (Waples, 1989), heterozygote excess (Pudovkin et al., 1996) and reduction in the number of alleles (this study). F is the estimate of the variance in allelic frequencies between the selected population and the control population, D is the mean heterozygote excess (H ! kH exp )\H exp . CI, confidence interval ; na, not applicable. See text for details of calculation.
interval, which was interpreted as infinity according to Waples (1989).

(i) Usefulness of microsatellites for genetic ariability management in the selected populations
This study demonstrates the usefulness of highly polymorphic markers such as microsatellites for answering the numerous questions related to a selection programme. With only five markers we were able to assess the genetic variability within the selected populations, determine the number of families and reconstruct pedigrees a posteriori. However, a larger number of markers would be necessary to identify with more accuracy the parents of S89I-G1 and the number of families in S85-G2.
There is evidence, especially from the number of alleles, that the selected populations have been subjected to bottlenecks. As predicted (Nei et al., 1975), bottlenecks have a stronger and more immediate effect on allelic diversity than on heterozygosity. Whereas heterozygosity is still high, the number of alleles in the selected populations is significantly reduced compare with the control population, and this is due in large part to the loss of rare alleles. All selected populations showed departure from expected Hardy-Weinberg equilibrium, but in two opposite directions. Heterozygote excess was seen in both S89I-G1 and S89W-G1, and can be correlated with sampling bias of alleles because of a very small number of founders and non-random mating. A temporary increase in heterozygosity level has been shown to occur in the generation immediately following a bottleneck, due to allelic evening out (Maruyama & Fuerst, 1985 ;Hedgecock & Sly, 1990 ;Leberg, 1992), as seen in S89W-G1. On the contrary, S85-G2, which may have undergone two successive bottlenecks, showed a deficit in heterozygotes over all loci compared with Hardy-Weinberg expectations. Pervasive heterozygote deficiencies at marker loci (mostly allozymes) have often been reported for marine bivalve populations (see for instance Gaffney, 1994), but the origin of these deficiencies is still under debate (technical artefacts, functionally null alleles, selection, aneuploidy, Wahlund effect, etc.). In S85-G2, only two microsatellite loci taken individually showed heterozygote deficiencies (OeduH15 and OeduJ12). Different hypotheses, which are not mutually exclusive, can be put forward to account for the observed heterozygote deficiencies : (a) the population is in equilibrium, and deficiencies at OeduJ12 and OeduH15 are due to null alleles, which could also explain the heterozygote deficiency in the control population at OeduH15 ; (b) the population is substructured, since the different G1 subpopulations were kept separate for the production of the G2 (see Fig. 1), creating the possibility of differentiation (through founder effect and drift) between the G2 subpopulations, and hence a possible ground for Wahlund effect ; and (c) inbreeding level is increasing.

(ii) Estimation of effecti e size
The other aim of this study was to obtain and compare different estimates of the effective size of bivalve hatchery populations, as a predictor of the rate of loss of neutral variation. Our estimates indicated that the effective size of the selected O. edulis populations is very low, between 3 and 20 at the most.

(a) Assumption of the models
The different methods for estimating the effective size -temporal variance in allelic frequencies (1), heterozygote excess (2) and reduction in the number of alleles (3) -are based on a number of assumptions : (a) no (or negligible) mutation (1, 3), (b) no immigration from neighbouring subpopulations (1 to 3), (c) neutrality of alleles studied (1 to 3), (d) random mating (2), and (e) random sampling in the population (1 to 3). In addition, methods 1 and 3 require data for at least two samples drawn at different times whereas method 2 requires data from a single cohort only. Assumptions (b) and (c) are obviously fulfilled in our study.
Mutation. Mutation rate for a microsatellite sequence is expected to be higher than for other random or coding sequences (Jarne & Lagoda, 1996). However, no data are available on the mutation rate of the loci used in this study. Some alleles are found at a relatively high frequency in a selected population and are not found in the control population. This is the case for instance for allele OeduU2-212 ( frequency of 0n211 in population S89I-G1), or for allele OeduT5-146 ( frequency of 0n147 in S89W-G1). This could be due to a mutation in one of the founding parents ; alternatively, this could be explained by drift in the selected populations and sampling bias in the control population. In S89W-G1, where all the putative parents ' genotypes could be inferred, no alleles were seen in the progeny that could not be traced back to one of the parents. We will assume that in our study (limited sample size, limited number of generations), microsatellite alleles are not affected by mutation.
Random mating. Pudovkin et al. (1996) noted that the heterozygote excess that would be seen in the progeny of a small number of parents could be reduced or even cancelled if the union of gametes is not at random, because of the Wahlund effect. There is evidence from the pedigree reconstruction that S89I-G1 and S89W-G1 were not produced by random mating of the putative parents. We expect, then, that the heterozygote excess method will underestimate the effective number of parents compared with the direct estimation obtained through pedigree reconstruction (especially for S89W-G1). This could account for the lower estimates obtained with this method.
Random sampling. Method 1 depends on random sampling, and therefore on reliable estimates of allelic frequencies in a closed population at different points in time. Here, the wild Quiberon Bay population departs from an ' ideal ' control in that it was not sampled at t l 0 but was sampled at time t, (i.e. at the same time as the selected populations). With a small t, the values for N k given in Table 4 could be interpreted as the mean number of parents for both the selected population and the control, across t generations (Hedgecock et al., 1992). In our case, since the estimated effective size for the control population is 1 to 2 order of magnitude higher than that of the selected populations, drift can be considered to be limited in the control population, and N k can be taken as a reasonable estimate of the effective size of the selected populations.
(b) Comparison of the methods N e values are traditionally estimated from the increase in the inbreeding rate of population (N eI ) and from the variance of allele frequencies (N eV ). In this paper, we used both methods. N eV was estimated using the temporal variance method (Pudovkin et al., 1996), the method based on the reduction of the number of alleles and the method based on departure from Hardy-Weinberg equilibrium. The estimate of N e based on the calculation of genetic relatedness can be assimilated to N eI . Although in a population of constant size the two parameters N eV and N eI are equivalent, in a population that changes size very frequently N eI and N eV can differ greatly. In this paper, the different estimates of N eV are very congruent, and no discrepancy was found between N eV and N eI when estimates have been obtained (S89I and S89W). This might be attributed to the small number of bottlenecks (1) experienced in each of these two populations.
All three numerical methods, as well as pedigree reconstruction when applicable, give estimates of effective population size of the same order of magnitude. The confidence interval is larger for the reduction in the number of alleles method and narrower for the heterozygote excess method. As it stands, the method based on the reduction in the number of alleles can be used instantly to estimate the effective size of cohort produced from a subsample of a larger population. It is also straightforward and easy to compute. Non-random mating in the subsample should have little effect, but loss of genetic diversity through drift will. It might be useful, then, to estimate N e by comparing two samples that are close in time, whereas the temporal method relies on the assumption that all the variance in allelic frequencies is due to drift, and an important number of generations between samples is generally needed for a precise estimate of N e (Waples, 1989). Possible extensions of our programme could include the effect of sampling variation among the individuals and loci, of allele-frequency profiles in both samples, of heterozygosity level, and the reliability and power of this estimate compared with the other methods. For instance, for the same total number of alleles, the profile of the curve N a l f(N i ), as defined in Section 2, will be very different when all the alleles have equal frequency or when there is a large number of rare alleles. The control population has more rare alleles at OeduT5 than at the other loci and this could explain the discrepancy found at this locus in the estimate of N e in S85-G2 and S89W-G1.

(c) Low N e : N ratios
The effective sizes of the selected populations were found to be very small : between 15 and 20 for S85, around 8-10 for S89I and 3 for S89W. This is much smaller than the number of animals that were actually reared together in the tank during each mass spawning experiment (around 100). Such strong founder effects (and correlated important genetic changes) have often been reported in hatchery populations of O. edulis and other bivalves. For instance, Saavedra & Guerra (1996) collected over 5 days the spawn from 120 flat oysters, and estimated the effective number of parents to be around 3n5 (see also Alvarez et al., 1989 ;Hedgecock et al., 1992 ;Gaffney et al., 1992). Among marine bivalves, however, the flat oyster is particularly sensitive to founder effects, and an important reduction in effective size can be observed as soon as the first generation. Saavedra & Guerra (1996) suggest that this might be due to the flat oyster's life cycle, and to the fact that, in contrast to the cupped oyster Crassostrea gigas for instance, there is no synchronicity in sexual maturation and gamete release.
Similarly, the estimate of N e in the control population is far smaller than might be assumed from the abundance of flat oysters, even in populations that might be depressed by disease. In France, the remaining stock is estimated to be in the thousands, especially in Brittany (H. Grizel, personal communication). The order of magnitude of the discrepancy between census size and calculated N e (ratio N e : N lower than 10 −$ ) is similar to that previously reported by Saavedra (1997) for a flat oyster population from Spain. Such a discrepancy has already been noted for other marine bivalves (Hedgecock et al., 1992 ;Hedgecock, 1994). A proposed hypothesis was that bivalves have a large variance in reproductive success, V k , reducing effective population numbers to a small fraction of breeding numbers (see also Li & Hedgecock, 1998).

(iii) Consequences for the selection programme
Small effective size and high relatedness have numerous consequences for the selection programme that deal mainly with inbreeding management. Biparental crosses had been made using some of these individuals in 1995, before these results were obtained. The pedigree information is now available for both S891 and S89W. All the individuals within S89W-G1 are at least half-sibs, and any biparental cross within this population will lead to a family with an inbreeding coefficient f of at least 0n125 (Falconer & McKay, 1996). When crossing the S89I-G1 to itself, this will happen in approximately half the cases. We can expect a decrease in performance in the offspring as soon as the G2, as regards both survival (Ibarra et al., 1995) and growth (Beattie et al., 1987). The offspring performances are expected to vary depending on the degree of kinship of the parents, and Naciri- Graven et al. (2000) have observed negative correlations between growth performances of the offspring and relatedness of their parents.
Biparental crosses will allow precise control of genealogy and inbreeding level. In order to avoid the increase in inbreeding level, it is probably wise to stop crosses within S89W and S85 Paimpol subpopulation. On the other hand, it is possible to drive the selected populations towards inbred lines and select for a better hybrid value, as there seems to be a high potential for heterosis in marine bivalves (Hedgecock et al., 1995, and particularly in these flat oyster selected lines (Baud et al., 1997 ;Naciri-Graven et al., 1999, 2000.
We wish to thank all the staff members of the various laboratories for their help in maintenance and sampling, especially C. Ledu, P. Phe! lipot, S. Heurtebise and A.-G. Martin. We also thank D. Hedgecock for helpful comments and proof-reading of the manuscript and, together with V. Chow, for providing the program EPS for N e calculation. The manuscript has been improved by helpful remarks from three anonymous reviewers. This work was supported by grants from the French State, and the Brittany, the Pays de la Loire and the Poitou-Charentes Regions.