Towards consensus on how to measure neutral genetic diversity?

During the last two decades, animal breeders have become increasingly aware of the erosion of genetic diversity in livestock species and the need to stop this erosion. However, a consensus on how to measure genetic diversity is lacking, and this is very important for the acceptance of genetic diversity evaluations. Whilst genetic diversity might be measured in terms of phenotypic/adaptive differences, it is common to measure it in terms of neutral genetic differences between marker loci which measures genetic diversity for an undefined, hypothetical trait. This common use of marker-based diversity is probably due in part to the costs of phenotypic comparisons between breeds. Toro (2006) (J Anim Breed Genet 123: 289) argues, however, that adaptive variation can also be measured by genetic markers, e.g. markers linked to QTL, and he expects that the use of adaptive genetic diversity will increase in genetic diversity studies. I agree with the latter, but expect that markers linked to QTL or markers detecting selective sweeps will only explain a very limited fraction of the total genetic variation. Weitzman’s diversity (Thaon d’Arnoldi et al. 1998, Gen Sel Evol 30: 149–161). This implicitly uses λ = 0. Weitzman’s diversity stems from the evolutionary literature where between-species diversity is much more important than within-species diversity. This is probably why it neglects within-population diversity, just like all other genetic distance-based measures. For livestock breeds, this is clearly not acceptable. Expected heterozygosity (Eding and Meuwissen 2001, J Anim Breed Genet 118: 141–159; Caballero and Toro (2002) (Cons Genet 3: 289–299) which implicitly uses λ = 1. Hence, it gives equal weights to within and between population diversity, which makes a lot of sense. Ollivier and Foulley (2005) (Livest Prod Sci 95: 247–254) adjusted Weitzman’s diversity to include within-population diversity, which yielded an overall diversity measure that correlated highly with λ = 1. Piyasatian and Kinghorn’s (2003) (J Anim Breed Genet 120: 137–149) diversity measure which uses λ = 0.2. The choice of 5 times more weight to between-population diversity is somewhat arbitrary. The authors argue it reflects the speed of genetic change that can be made by natural/artificial selection across populations Total genetic variance of a hypothetical trait (Bennewitz and Meuwissen 2005, Genet Sel Evol 37: 315–337), which implicitly uses λ = 0.5. Allelic richness, i.e. the number of alleles at a locus, has been proposed as a measure of genetic diversity, but Caballero and Toro (2002) show that the maximization of measure (ii) also maximizes allelic richness. Weitzman (1992) (Quart J Econ 107: 363–405) gave four rules to which a sound diversity measure should adhere. Weitzman’s diversity (i) adheres, of course, to all four rules. Especially the 2nd and 3rd rule proved problematic for the above diversity measures. The 2nd rule is ‘if a population is removed, diversity should decrease’. Although this rule makes a lot of sense, criteria (ii), (iii) and (iv) do not adhere to this rule since they measure variance, and an estimate of variance can increase if data is removed. Eding et al. (2002) (Genet Sel Evol 34: 613–633) overcame this problem by using the core set approach, i.e. they measured the maximum variance that could be achieved in an optimal population, the core set, which was obtained by optimizing the contributions of the conserved populations. Hence, criteria (ii), (iii) and (iv) combined with the core set approach adhere to Weitzman’s 2nd rule. Weitzman’s 3rd rule ‘monotonicity in distance: if genetic distances increase, diversity should increase’. On the one hand this rule does not make sense: increased distance implies more inbreeding which results in loss of diversity (Caballero and Toro, 2002). On the other hand it makes sense: increased inbreeding makes the remaining variation more accessible (more extreme allele frequencies and more extreme genotypes). Due to its high weight on within-population diversity, measure (ii) does not adhere to Weitzman’s 3rd rule. This high weight, λ, of measure (ii) also leads to the following anomaly: preserving n endangered breeds separately yields the same GD as interbreeding the n populations into one big meta-population, and conserving the latter. From a conservation genetics point of view, the latter is clearly not an acceptable conservation strategy since the endangered breeds are not conserved. Thus, a criterion for genetic diversity that gives equal weight to within and between breed diversity is imperfect. Toro et al. (2006) argue for an intermediate value of λ since too much emphasis on between breed variation leads to the conservation of small, inbred lines, and too much emphasis on within breed variation leads to the conservation of large, often commercial, non-endangered breeds. This leaves measures (iii) and (iv) as qualified measures of diversity. Piyasatian and Kinghorn (2003) state that λ≈0.2 maximizes the response to across-population selection, but if the across-population distribution of genetic effects is more or less normal, the selection response is proportional to the total genetic standard deviation, and thus the total genetic variance measure (ii) is expected to maximize the selection response. All of this work was done before the 54 000 SNPs chip genotyping technology became available for cattle in January 2008 and similar SNP chips were developed for other species. How does this high-density genotyping affect our methods for measuring genetic diversity? Firstly, the above-mentioned methods become much more accurate. The accuracy of relationship estimates exceeds that of pedigree-based estimates, i.e. when all pedigree was available since the divergence of the breeds. Secondly, it enables us to measure genetic diversity per chromosome region instead of genome wide. Thus, we will be able to pinpoint breeds that are very different or contribute a lot of diversity in a particular chromosomal region. It may be possible to relate this to phenotypic differences between the breeds. Hence, it will bring us closer to the use of adaptive diversity as suggested by Toro (2006). Thirdly, it enables us to measure past effective population sizes and bottle necks (Tenesa et al., 2006, Genome Res 17: 520–526; Meuwissen and Goddard 2007, Genetics 176: 2551–2560). In conclusion, the proposed measures of genetic diversity mainly differ by the weight given to the between-population diversity versus the within-population diversity. Extreme weights, such as λ = 0 or 1, can lead to very different conservation decisions, favoring small inbred lines or large, non-endangered populations, respectively. In line with the tradition in the field of valuing genetic gain and genetic variance, ‘the total genetic variance of a hypothetical trait’ may well end up as the consensus criterion. However, genetic diversity/genetic uniqueness is only one of several motives for conserving a breed. The other main reasons are (Ruane 1999, J Anim Breed Genet 116: 317–323): (a) degree of endangerment, which is included in conservation decision-making by Simianer et al. (2003) (Ecol Econ 45: 377–392); (b) species to which the breed belongs; (c) adaptation to a specific environment; (d) possession of traits of current or future economic importance; (e) possession of unique traits that may be of scientific interest; (f) cultural and/or historical value of the breed. Any one of these motives can suffice to make a case for the conservation of a breed.