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

Accurate measures of effective population sizes (Ne ) in livestock require good quality data and specialized skills for their computation and analysis. Ne can be estimated by Wright's equation Ne =4MF/(M+ F) (M, F being sires and dams, respectively), but this requires assumptions which are often not met. Total census sizes Nc of livestock breeds are collated globally. This paper investigates whether estimates of Ne can be made from Nc ; this would facilitate conservation monitoring. Some Ne methodologies avoid the assumptions of Wright's equation and permit measurement, rather than estimation, of Ne . Those considered here employ, respectively, linkage disequilibrium (LD) of single-nucleotide polymorphisms (yielding Ne (LD)), and genealogical analysis (rate of increase of inbreeding, DF), yielding Ne (DF). Considering breeds of cattle, sheep, horses, pigs and goats for which Nc and either Ne (LD) or N e(DF) are known (totals of 203 breeds and 321 breeds, respectively), proportionality has been investigated between Nc and these measures of Ne . Ne (LD) was found to increase with Nc , significantly in sheep and horses, less so in cattle, but not at all in pigs. Ne (DF) was correlated with log10(Nc ) in cattle, sheep and horses (53, 56, 43 breeds, respectively). Ne (LD) was correlated in cattle (73 breeds) and pigs (31 breeds) with the log10 transformation of Ne as calculated by Wright's equation. Further verification and refinement are needed, particularly of census data, but credible predictions of Ne are obtainable by applying the following multipliers to log10(Nc ): cattle 17.61, sheep 97.72, horse 70.78. For cattle and pigs, multiplying log10(Ne (Wright)) by, respectively, 40.69 and 60.09, also gives credible predictions. Such census-based estimates of Ne 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 Ne /Nc 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 Ne (Hill). Comparison of these values with Ne (Wright) could help to identify breeds with breeding structures conducive or inimical to genetic conservation. However, Ne (Hill) requires breed-specific values for these variances, and this restricts its applicability.