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Methods to estimate effective population size using pedigree data: Examples in dog, sheep, cattle and horse
© Leroy et al.; licensee BioMed Central Ltd. 2013
Received: 22 June 2012
Accepted: 30 November 2012
Published: 2 January 2013
Effective population sizes of 140 populations (including 60 dog breeds, 40 sheep breeds, 20 cattle breeds and 20 horse breeds) were computed using pedigree information and six different computation methods. Simple demographical information (number of breeding males and females), variance of progeny size, or evolution of identity by descent probabilities based on coancestry or inbreeding were used as well as identity by descent rate between two successive generations or individual identity by descent rate.
Depending on breed and method, effective population sizes ranged from 15 to 133 056, computation method and interaction between computation method and species showing a significant effect on effective population size (P < 0.0001). On average, methods based on number of breeding males and females and variance of progeny size produced larger values (4425 and 356, respectively), than those based on identity by descent probabilities (average values between 93 and 203). Since breeding practices and genetic substructure within dog breeds increased inbreeding, methods taking into account the evolution of inbreeding produced lower effective population sizes than those taking into account evolution of coancestry. The correlation level between the simplest method (number of breeding males and females, requiring no genealogical information) and the most sophisticated one ranged from 0.44 to 0.60 according to species.
When choosing a method to compute effective population size, particular attention should be paid to the species and the specific genetic structure of the population studied.
In population genetics, different tools are used to assess genetic diversity for conservation purposes and one of the most commonly used indicators is the effective population size (N e ) developed by Wright . N e is defined as the number of reproducing individuals, bred in an idealized population in which all individuals are of the same sex and selfing is permitted, and that leads to the same decrease of genetic diversity than the population being studied . However, several genetic diversity indicators have been proposed and the most classical ones are genetic drift through temporal changes in allele frequencies (variance of effective population size), increase in homozygosity (inbreeding effective population size), or the rate at which unique alleles are lost (eigenvalue effective population size) [3, 4]. Moreover, different information sources (demographic information, pedigree or molecular data) can be used to estimate N e . Therefore, when estimating N e , it is important to know precisely which process is ongoing and to have the information used to assess it .
where ΔIBD is the rate of IBD, classically estimated by the rate of inbreeding ΔF as ΔIBD, i.e. the evolution of the average coefficient of inbreeding F over time . However, recently, new methods have been proposed to compute ΔF from an approximate rooting of individual inbreeding coefficients based on pedigree knowledge (Equivalent complete generations, EqG) . Cervantes et al.  have also suggested using coancestry instead of inbreeding for IBD estimation.
All these methods do not differ only in terms of the indicator or force observed, but also in terms of the time scale investigated and the amount of available information. Moreover, they are more or less sensitive to the level of pedigree knowledge and to some parameters related to breeding conditions, such as the existence of population subdivisions or departure of the random mating hypothesis, which may lead to biased N e estimates. Depending on the context and the authors, one or several of these methods have been applied to domestic breeds [10–14] and captive animal populations [15, 16]. More specifically, the fact that in a number of breeds, no pedigree information is available, the simplest approximation of N e (computed on the basis of number of breeding males and females) has been used to classify the endangerment level of breeds by the European Association for Animal Production (EAAP), and the Food and Agriculture Organisation (FAO).
Our study aimed at comparing several methods used to estimate N e from pedigree data for a wide range of domestic animal populations. One hundred and forty breeds from four different species, i.e. dog, sheep, cattle and horse, were used. These include intensively selected breeds with large current population sizes, as well as endangered breeds benefiting from conservation programs. Six different methods for computing N e were compared in order to provide practical advice to breeders and stakeholders, for choosing endangerment thresholds according to species and for predicting N e accurately with more or less sophisticated methods.
Pedigree files for 60 dog, 40 sheep, 20 cattle and 20 horse breeds were extracted from French national data bases. For each species, breeds were chosen to represent a wide range of situations i.e. actual population size, endangerment status (28 populations among the sheep, cattle, and horse breeds studied have received financial support from the French government through subsidies for endangered breeds), breeding purpose (for example, selection for meat or milk), or geographical origin (local, imported or transnational populations).
In order to define the reference populations, generation intervals (T) were computed in the four pathways (see below), as the average age of parents when their useful offspring are born (i.e. offspring, which in turn become parents) over a 10 year period before a reference year (2005 for dog breeds (see ), and 2007 for sheep, cattle and horse breeds). Reference populations were defined as all the individuals (or only females for sheep and cattle breeds, given the small number of males raised in these species) with both parents known, born during a generation interval period before the reference year.
Methods used to estimate effective population size N e
Method based on sex ratio: Nes
Method based on the variance of progeny size: Nev
Method based on inbreeding rate between two successive generations: NeFt
The effective population size can then be computed using the formula N eFt = 1/2ΔF t .
Method based on coancestry rate between two successive generations: NeCt
Taking into consideration the average coefficient of coancestry (C), the preceding model can be applied using C t+1 , the average coefficient of coancestry between the animals in the reference population, and C t , the average coefficient of coancestry between the parents of this reference population, instead of Ft+1 and F t . Since the number of coancestry coefficients to be computed within a population of size n is equal to n(n -1)/2, computation of average coancestry can be very time-consuming in large populations. Therefore, when n(n -1)/2 is larger than 100 000, 100 000 pairs of individuals are sampled at random with C estimated as the mean value of the 100 000 computed coefficients.
Method based on individual inbreeding rate: NeFi
with n being the reference population size and the standard deviation of ΔF i .
Method based on individual coancestry rate: NeCi
where k is the number of coefficients computed (either n(n -1)/2 or 100 000) and is the standard deviation of ΔC ij .
All the pedigree analyses were performed using PEDIG software  and our own FORTRAN routine procedures.
where α i is the computation method, β j the species, and γ ij the interaction between computation method and species, all considered as explanatory fixed factors, and ε ijk is the error term following a distribution N(0,σ ij ). This model was chosen because when including breed as a random effect (here, breeds are considered as samples within each species) no significant effect was observed and because the model minimizes both Akaike Information (AIC) and Bayesian Information (BIC) Criteria (see Additional file 1: Table S1).
Finally, in addition to assessing ranges of N e values, we examined if ranking was similar with the different methods by performing for each species, a Principal Component Analysis (PCA), considering breeds as observations and the six methods as variables.
Results and discussion
Demographic and genealogical parameters
Genealogical parameters and effective population sizes for the 140 breeds studied averaged for each species
F IS %
Similar to the heterogeneity of pedigree knowledge, average IBD coefficients (average C and F) ranged from 0.2% (C and F in Comtois horse breed) to 9.1% (C in the Barbet dog breed). Pearson correlations between EqG and IBD coefficients were equal to 0.45 and 0.23 for F and C, respectively, while they were larger (r = 0.67) between F and C [see Additional file 3: Figures S1, S2, S3]. Differences between C and F, measured by the fixation index F IS , varied more or less according to species. Average F IS values were negative in cattle, sheep and horse breeds i.e. -0.45%, -0.37%, -0.1%, respectively and positive i.e. 1.37% (with P < 0.001) in dog breeds, underlining the existence of population substructure within most dog breeds.
Variance analysis of effective population size estimates
Depending on breed, species and method, N e values varied greatly i.e. between 15 (N eFt for the Saarloos Wolfdog breed) and 133 056 (N es for the Charolais cattle breed). When IBD rate was negative i.e. indicating a decrease in C or F between the last two generations, N eFt (four breeds) and N eCt (one breed) were not calculated.
Principal component analysis of effective population size estimates
Kendall correlations between methods used to estimate N e for each species
This study allowed us to analyse the specificities of each of the four included species with regards to the assessment of their effective population size estimated with different approaches.
Genealogical parameters were quite similar to previously reported results [10–13, 20–27], although for horse, pedigree knowledge was relatively low, because horse breeds’ pedigree were restricted to individuals belonging to each breed. We would also like to underline that the Pearson correlations between EqG and IBD estimators were moderate, indicating that the regression suggested by Nagy et al.  between pedigree knowledge and IBD is not straightforward.
The effective population sizes computed here were on average of the same magnitude as those reported in other studies using similar approaches for cattle [14, 20, 21], sheep [22, 23], or horse [11, 27]. For dog, previous studies [10, 24–26] applied inbreeding approaches to compute N e , with average values close to 100 (ranging from 17 to 1090), which is in agreement with our results.
In this data set, the largest populations concerned cattle as expected, given the high level of homogenization in this species due to intense selection. For instance, in France, out of 46 different cattle breeds, the main five breeds (namely, Holstein, Charolais, Limousine, Montbéliarde and Blonde d’Aquitaine) account for 80% of the total cattle stock (estimated to be 8 million cows; source: France Génétique Elevage, http://www.france-genetique-elevage.fr/). Among the six methods used to compute N e for cattle populations, those based on sex-ratio (N es ) and those taking into account variance of progeny size (N ev ) or directly measuring IBD increase produced very different results (Figure 1). This is explained by the wide use of artificial insemination (AI) in cattle (particularly in dairy cattle) with a small number of sires producing thousands of offspring, although cattle have a low prolificacy compared to dogs. Such a contrast was not observed for sheep because (among other reasons) AI is not as developed in sheep as in cattle and a ram cannot provide as many doses as a bull. For dog, the most striking result was the difference between methods based on coancestry C and those on inbreeding F evolutions, which is linked to the positive F IS values found for this species. Under panmixia, both C and F parameters are assumed to differ only by Δ IBD, the average coancestry of reproducers corresponding to the average inbreeding of the next generation. This is why, in random mating conditions at least, it is expected that C is larger than F, and thus that F IS is negative. This was not the case for most of the dog breeds (and some breeds of the other species) either because of the existence of subpopulations or of particular breeding practices such as a high frequency of mating between close relatives . As a consequence, when F was used instead of C to compute N e , on average, N e was divided by more than two in dogs. Indeed, it has been shown that if inbreeding is used as an estimator of population genetic diversity bias can occur because of population substructure [11, 29]. Such phenomena are often observed for dog breeds. Since all previous reports on N e of dog breeds were based on F coefficients, they must be largely underestimated. From a more general point of view, for a domestic or captive population with more or less substructure, the method based on coancestry is the most appropriate to compute N e .
Characteristics of the different methods used to compute effective population size N e
Indicator used to compute N e
Time period or number of generations taken into account
Theoretical sample size for a reference population of size n
change in allele frequency / heterozygosity loss
number of reproducers
change in allele frequency / heterozygosity loss
variance/covariance of progeny sizes
period or number of generations to be fixed
period or number of generations to be fixed
n x (n-1)
all known generations
all known generations
n x (n-1)
The issue of minimum viable population sizes is not new and it has been suggested to use N e thresholds of 50 and 500 for risks of extinction on the short or long runs, respectively . Although the existence of these “magic numbers” has been discussed and criticized, they do constitute an interesting tool for stakeholders . According to the FAO , a breed can be categorized as critical if the total number of breeding females is less or equal to 100 or the total number of breeding males is less or equal to 5, and endangered if the total number of breeding females is less or equal to 1000 or the total number of breeding males is less or equal to 20. Since pedigree information is not always available, i.e. for livestock breeds in developing countries or wild populations, the FAO has based its recommendations on sex ratio considerations (similar to those in the N es computation) to determine the level of endangerment of a breed. However, as underlined in our study and by Martyniuk , the FAO figures for breed risk-status do not provide a full picture of the level of genetic diversity.
Given the contrasted results obtained for cattle between the N es and the more sophisticated methods, we recommend choosing a higher threshold when considering endangerment level of cattle in comparison to other species, at least in breeds in which animals are mainly bred via AI. Comparing rankings of N e estimated with the method based on sex-ratio and the more sophisticated ones showed interesting results. In the comparison with the N eCi method, which does not suffer from bias linked to population substructure, sampling size or IBD decrease, the correlation ranged among species from 0.44 (cattle) to 0.60 (sheep). By contrast, correlations between N ev that takes variance of progeny size into account and N eCi were much larger and ranged ranging from 0.59 (dog) to 0.74 (horse). This indicates that, even if the number of reproducing males and females is a major explanatory factor for variation in effective population size, other parameters and, in particular, unbalanced progeny sizes may differ greatly according to breeds. Thus, caution must be taken when interpreting estimated effective population sizes.
According to the French law, a breed may receive financial support as an endangered breed, if it is considered as a French indigenous population and if the total number of females is below a threshold defined - by species - by the European Union (European Union Commission Regulation 445/2002 and 817/2002). As an example, the Clun Forest or the Finnish sheep breeds are not considered as endangered since they are not French. This explains why even if N e is estimated with the method based on demographic parameters (N es ), some breeds receive financial support although they have a larger N e than others which do not receive support. This discrepancy is even more pronounced with other methods that take into account other parameters impacting effective population size (Figure 2).
Among other methods to measure effective population size, molecular approaches may constitute an interesting option, especially if many markers are available. Indeed, methods based on linkage disequilibrium may provide interesting and original information since they can estimate the evolution of effective population size over former generations . When computing effective population size for the international Holstein breed, using between 3000 and 10 000 SNP and the linkage disequilibrium approach, de Roos et al.  reported N e values ranging from 64 to 90 according to country, which are of the same order of magnitude as those calculated in our study with the most sophisticated methods N eCi = 93 and N eFi = 91. However, it should be underlined that similar to the pedigree-based methods, the different molecular methods may give divergent results depending on the sampling strategy or the parameter used to compute N e (evolution of heterozygosity or variance of allele frequency over time, linkage disequilibrium,…) [35, 36]. Moreover, given the cost of genotyping, pedigree knowledge will continue to represent a valuable information source in the coming years in many cases.
In this study, we show that indicators of effective population size may follow different trends depending on the species studied and, in particular, on the genetic structure existing within the breed. Further studies are necessary to improve the accuracy of genealogical methods, for instance taking better account of heterogeneity in pedigree knowledge. Finally, it must be stated, that for conservation issues, socio-cultural background is at least as important as effective population size, and should, when possible, be taken into account when assessing the endangerment level of a given breed (e.g., ).
The authors would like to thank the breeding associations for the data provided, Hélène Hayes and Wendy Brand-Williams for linguistic revision.
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