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Methods to estimate effective population size using pedigree data: Examples in dog, sheep, cattle and horse

Grégoire Leroy*, Tristan Mary-Huard, Etienne Verrier, Sophie Danvy, Eleonore Charvolin and Coralie Danchin-Burge

Genetics Selection Evolution 2013, 45:1  doi:10.1186/1297-9686-45-1

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Comment to article Genetics Selection Evolution 2013, 45:1

Felix Goyache   (2013-04-26 10:06)  SERIDA email

Comments on: Methods to estimate effective population size using pedigree data: Examples in dog, sheep, cattle and horse (Leroy et al. 2013)

Felix GOYACHE*, e-mail: fgoyache@serida.org
Juan Pablo GUTIERREZ**, e-mail: gutgar@vet.ucm.es
Isabel CERVANTES**, e-mail: icervante@vet.ucm.es

**SERIDA-Deva, Camino de Rioseco 1225, 33394 Gijon (Asturias), Spain
**Departamento de Produccion Animal, Facultad de Veterinaria, Avda. Puerta de Hierro s/n, 28040 Madrid, Spain

Leroy et al. [1] have recently published in Genetics Selection Evolution a comparison of six different methods used to estimate effective population size (Ne) from pedigree data: (a) method based on sex ratio (Nes) [2]; (b) method based on the variance of progeny size (Nev) [3]; (c) method based on inbreeding rate between two successive generations (NeFt) [4]; (d) method based on coancestry rate between two successive generations (NeCt); (e) method based on individual inbreeding rate (NeFi) [5]; and (f) method based on individual coancestry rate (NeCi) [6]. NeFi was actually computed using the modification proposed in Gutierrez et al. [7] that accounts for the fact that self-fertilization is not possible in real diploid populations. Comparisons of most of the methods tested by Leroy et al. [1] can be found elsewhere [5,6,8]. However, the objective of Leroy et al. [1] was not simply to identify the distinctive features of each method but ''to provide practical advice to breeders and stakeholders, for choosing endangerment thresholds according to species and for predicting Ne accurately with more or less sophisticated methods''. We would like to comment on this article.

Leroy et al. [1] intended to illustrate the properties of the six methods and their differences on an impressive number of genealogies, including 60 dog, 40 sheep, 20 cattle and 20 horse breeds. These genealogies include a wide number of genetic scenarios varying from populations with large current population sizes to endangered breeds subject to conservation programmes. The study by Leroy et al. [1] is relevant because it ruins the myth of the Ne thresholds under which a breed is considered to be at risk [9]. However, it does not derive clear recommendations for the methodology to be used, probably because the authors did not take the opportunity to comment some remarks concerning the methods based on individual increase in inbreeding or coancestry and reported in [5,6,8].

Certainly, Leroy et al. [1] considered that demographic estimates of Ne (Nes and Nev) are only acceptable in cases of virtually inexistent pedigrees: the number of reproducing males and females is a major explanatory factor for variation in Ne. However, sex ratio and unbalanced progeny sizes vary greatly among species and among breeds within species. Thus comparing the Ne values computed by using different genealogies is difficult. Furthermore, as pointed out by Cervantes et al. [8], Nev values ignore the fact that animals with the highest number of selected sibs are also the animals most likely to have their offspring selected.

Leroy et al. [1] discussed the advantages and concerns of the methods based on IBD increases between successive generations (NeFt and NeCt) in contrast to those based on individual increase in inbreeding or coancestry (NeFi and NeCi). Their discussion can be summarised as follows:
(i) NeFt and NeCt could be more flexible methods because they only need the values of inbreeding or coancestry of the parents and their offspring. The analyses can be carried out choosing arbitrary time lengths while computation of NeFi and NeCi would need to use the whole pedigree. Therefore, NeFt and NeCt would allow analysing the evolution of IBD probability during a variable number of years or generations and the comparison of values computed using genealogies with different pedigree depths
(ii) NeFt and NeCt can be affected by changes in mating policy, registration of new individuals or sampling effects over time, that could give biased or even negative Ne values while both NeFi and NeCi clearly overcome this problem [5,8].

The advantage of NeFi and NeCi summarised in the above point (ii) is clear and Leroy et al. [1] explain it from a technical point of view since the computation of the individual increase of IBD is based on the rooting of IBD coefficients by the pedigree depth (equivalent to discrete generations coefficients). However, regarding point (i) the statements by Leroy et al. [1] are not sufficiently clear and may lead to confusion for breeders and stakeholders when choosing methods for predicting Ne. Of course, both the methods based on IBD increases between successive generations (NeFt or NeCt) and those based on individual increase in IBD (NeFi or NeCi) use the whole pedigree known for the individuals belonging to an arbitrarily defined reference population. The difference lies in what the pedigree is used for: NeFt and NeCt compare the average inbreeding or coancestry between the parents and offspring belonging to the reference population trying to mimic a population renewal while NeFi and NeCi estimate the Ne of a given population considering it as ''renewed''. This intuitive explanation may help to understand why NeFt and NeCt are affected by sampling errors or changes in mating policies (point (ii) above). Moreover, the comparison of genealogies with different pedigree depths can also be done using NeFi or NeCi. Regarding NeFi, Cervantes et al. [8] stated that ''If the aim for estimating the effective population size is to ascertain the effect of changes in the mating policy, it would be recommendable to truncate the pedigree, thus considering as founders those animals which were used to establish the new mating policy. However, always make sure that the depth of the remaining pedigree is enough to achieve reliable estimates''. This simple approach i.e. truncation of the larger genealogies to the desired pedigree depths or time periods, may be extended to any scenario to compare Ne values computed in different populations within species and, therefore, to assess the effect of different mating policies. Indeed, a minimum pedigree depth is necessary to estimate reliable Ne values, but this limitation equally operates for NeFt and NeCt since the computation of Ft+1 and Ft is affected. If the truncation of the genealogies leads to very shallow pedigrees neither NeFi nor NeCi methods can be blamed for not producing sound Ne estimates. Even in such scenarios, methods based on individual increase in inbreeding or coancestry will never give negative or unacceptably high Ne values. The latter problem was not explicitly commented by Leroy et al. [1]. However, this may happen when the mating policy focuses on limiting the rate of inbreeding [10]. In such cases, if limiting inbreeding is done at the expense of average inbreeding coefficients, the distribution of the individual inbreeding coefficients in a reference population becomes bimodal, with most of these having high Fi values but some being very low, that bias upwards the results of the methods based on IBD increases between successive generations. NeFi and NeCi are free of this skewness since they operate on the average rates of inbreeding [10].

Furthermore, it is worth mentioning that computation of the standard error of the estimates of NeFi and NeCi can be done directly from the standard deviations of the individual increase in inbreeding or coancestry assessed [5,6]. This unique feature gives information on the confidence of the estimates of Ne obtained allowing comparison of different genealogies.

Finally, Leroy et al. [1], in agreement with Cervantes et al. [6], suggested that, given the precision of Ne estimates, coancestry-based methods should be preferable to methods based on the increase in inbreeding. Although time and computer consuming, coancestry-based methods were clearly superior to those based on inbreeding in the case of population substructure [6]. The case of the dog breeds analysed by Leroy et al. [1], in which the inbreeding-based methods largely underestimated Ne, clearly illustrate this fact and we do agree with the suggestion of Leroy et al. [1]. However, we also consider that NeCi is the most appropriate method to compute Ne when some population substructure exists, only if the objective is to modify this population substructure. Otherwise, the most informative estimator of the population scenario would be NeFi. The concept of effective size usually has an asymptotic meaning in a regular system and, therefore, can be used for predictive purposes, i.e. the risk status of a population. Note that, in the case of population structure, a sudden loss in subpopulations would make it impossible to further decrease average IBD and therefore the NeFi values could appropriately illustrate the risk of a given population when gene exchange between subpopulations is not possible.

Overall, we consider the paper by Leroy et al. [1] as extremely relevant in terms of clarification of the validity and interpretations of Ne values across populations. However, The paper does not give straightforward recommendations on the method to be used to compute Ne. Leroy et al. [1] concluded that the method chosen to compute Ne in a given genealogy depends on the particular scenario of the analysed population; Ne can be estimated even in the absence of pedigree data if it is assumed that neither Nes nor Nev reflect ''real'' genetic scenarios. In our opinion, some precisions on this issue would be useful to clarify concepts to newcomers in this field. Leroy et al. [1], using NeFt and NeCt methods, obtained 5 out of 280 negative estimates of Ne and remarked that this proportion is low. However, applying methods that may lead to such biased estimates of Ne can hardly be recommended. Based on the discussion we report here i.e. that the only concern mentioned by the authors is easy to overcome, in our opinion, the recent methods used to estimate Ne based on individual increase in inbreeding (NeFi) or coancestry (NeCi) have relevant features that make them particularly interesting for breeders involved in the management of non-experimental animal populations [5,6,7,8].



References



1. Leroy G, Mary-Huard T, Verrier E, Danvy S, Charvolin E, Danchin-Burge C Methods to estimate effective population size using pedigree data: Examples in dog, sheep, cattle and horse. Genetics Selection Evolution 2013, 45:1.

2. Wright S: Evolution in Mendelian populations. Genetics 1931, 16:97-159.

3. Hill WG: Effective size of populations with overlapping generations. Theor Pop Biol 1972, 3:278-289.

4. Falconer DS, Mackay TFC: Introduction to Quantitative Genetics. 4th edition. Harlow: Longman Group Ltd; 1996.

5. Gutierrez JP, Cervantes I, Molina A, Valera M, Goyache F: Individual increase in inbreeding allows estimating effective sizes from pedigrees. Genet Sel Evol 2008, 40:359-378.

6. Cervantes I, Goyache F, Molina A, Valera M, Gutierrez JP: Estimation of effective population size from the rate of coancestry in pedigreed populations. J Anim Breed Genet 2011, 128:56-63.

7. Gutierrez JP, Cervantes I, Goyache F: Improving the estimation of realised effective population sizes in farm animals. J Anim Breed Genet 2009, 126:327-332.

8. Cervantes I, Goyache F, Molina A, Valera M, Gutierrez JP: Application of individual increase in inbreeding to estimate realized effective sizes from real pedigrees. J Anim Breed Genet 2008, 125:301-310.

9. FAO: The State of the World's Animal Genetic Resources for Food and Agriculture. Rome: FAO; 2007.

10. Cervantes I, Meuwissen THE: Maximization of total genetic variance in breed conservation programmes. J Anim Breed Genet 2011, 128:465-472.

Competing interests

Felix GOYACHE, Juan Pablo GUTIERREZ and Isabel CERVANTES have developed some of the methods used and commented by Leroy et al.

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