Linear methods to estimate kinships from genetic marker data for the construction of core sets in genetic conservation schemes

Three log-linear models were developed to improve the estimates of kinships between breeds (MEK) and of alike in state probabilities (AIS) using all marker data and all pairs of animals simultaneously. These models were developed to (i) increase accuracy of MEK, (ii) improve AIS estimates (especially compared to methods that simply take average allele frequencies) and (iii) to reduce the number of zero contributions of breeds to the core set where actual contributions are larger than zero. The models are: unweighted log-linear model (ULM), weighted log-linear model (WLM), where marker data is weighted to account for the amount of information per locus and weighted log-linear mixed model (WLMM), where the solution is restricted such that a maximum of one zero-contribution remains. These models were tested using simulated data from a tree-like phylogeny and compared with the results from the weighted least similarity, where the per locus probabilities of alleles AIS are taken from the similarities between the pair of populations with the minimum average similarity. An example using field data on 10 cattle populations in the Netherlands is discussed. Differences in accuracy between the four methods were small, although substantial differences in contribution of breeds to the core set were found. In terms of conserved variation WLM tended to be the most efficient, followed by WLMM. WLMM yielded the smallest number of zero contributions of breeds and provides a more conservative solution (i.e. fewer breeds will be erroneously excluded). It is argued that the small differences between the methods in accuracy of the MEKs may be due to the relatively well-behaving simulated data, and that the methods that use all information simultaneously (WLM and WLMM) may prove more robust when complications occur in field data.