Effective population sizes in cattle, sheep, horses, pigs and goats estimated from census and herdbook data

Accurate measures of effective population sizes (N-e) in livestock require good quality data and specialized skills for their computation and analysis. N-e can be estimated by Wright's equation N-e = 4MF/(M + F) (M, F being sires and dams, respectively), but this requires assumptions which are often not met. Total census sizes N-c of livestock breeds are collated globally. This paper investigates whether estimates of N-e can be made from N-c; this would facilitate conservation monitoring. Some N-e methodologies avoid the assumptions of Wright's equation and permit measurement, rather than estimation, of N-e. Those considered here employ, respectively, linkage disequilibrium (LD) of single-nucleotide polymorphisms (yielding N-e(LD)), and genealogical analysis (rate of increase of inbreeding, DF), yielding N-e(DF). Considering breeds of cattle, sheep, horses, pigs and goats for which N-c and either N-e(LD) or N-e(DF) are known (totals of 203 breeds and 321 breeds, respectively), proportionality has been investigated between N-c and these measures of N-e. N-e(LD) was found to increase with N-c, significantly in sheep and horses, less so in cattle, but not at all in pigs. N-e(DF) was correlated with log(10)(N-c) in cattle, sheep and horses (53, 56, 43 breeds, respectively). N-e(LD) was correlated in cattle (73 breeds) and pigs (31 breeds) with the log10 transformation of N-e as calculated by Wright's equation. Further verification and refinement are needed, particularly of census data, but credible predictions of N-e are obtainable by applying the following multipliers to log10(N-c): cattle 17.61, sheep 97.72, horse 70.78. For cattle and pigs, multiplying log10(N-e(Wright)) by, respectively, 40.69 and 60.09, also gives credible predictions. Such census-based estimates of N-e could in principle be generated by non-specialists and are likely to be suited to audits of conservation activity when financial resources or availability of data are limiting. The ratio N-e/N-c varied among species with an overall median value of 0.03, less than a tenth of that typically observed in wild mammals. Characteristics were also investigated of a distinct herdbook-based methodology, namely the development of Wright's equation to take into account variances of progeny numbers to yield what has been termed here N-e (Hill). Comparison of these values with N-e (Wright) could help to identify breeds with breeding structures conducive or inimical to genetic conservation. However, N-e(Hill) requires breed-specific values for these variances, and this restricts its applicability.