The studbook of the Andalusian horse comprising a total of 75,389 individuals (6318 of them classified as Carthusians) was analysed in order to ascertain the genetic history of the breed and, specially, to evaluate its genetic variability and the influence of the Carthusian strain in the breed. Although there is no possible way to identify studs acting as Nucleus in the breed, there is a high concentration of genes and individuals' origin. The effective number of studs producing grandfathers was of 10.6. The equivalent number of founders was 1948.5 individuals (370.5 Carthusians). The effective number of founders was 39.6 and the effective number of ancestors 27. Only 6 ancestors were necessary to explain 50% of the genetic variability of the breed. The average values of inbreeding and average relatedness for the whole Andalusian horse population were, respectively, 8.48% and 12.25%. The same values for the Carthusian strain were higher (9.08% and 13.01%) even thought the generation interval for the strain was larger than that for the whole population (12.43 versus 10.11 years). In any case, inbreeding in Andalusian horse breed seems to have a remote origin and linked to the Carthusian individuals. The total contribution of the Carthusian founders to the populations accounted for up to 87.64% of the population. In turn the Carthusian ancestors explained 80.46% of the genetic variability of the breed. No differentiation was found between Carthusian and non-Carthusian reproductive individuals using genealogical F ST (0.000026). It can be concluded that the distinction between Carthusian and non-Carthusian individuals within the Andalusian horse breed does not have genetic support. The unbalanced use of the Carthusian individuals with lower average relatedness values for reproduction is proposed to preserve the genetic variability of the breed. D

We introduce a simple method to estimate effective population size from increase in coancestry (Δc(jk)) for all pairs of individuals j and k in a reference subpopulation. An increase in pairwise coancestry for any pair of individuals j and k can be defined assuming that a hypothetical mating between them would give an individual with an inbreeding coefficient equal to c(jk), where c(jk) is the coancestry coefficient between the individuals j and k. The equivalent measure to discrete generations value (g(jk)) corresponding to the individual jk can be computed by averaging discrete equivalents generations of its parents (g(j) and g(k)). The mean increase in coancestry for all pairs of individuals in a reference subpopulation can be used to estimate a realized effective population size based on coancestries that would provide information on the effective size of a population under random mating. Performance of the new parameter was tested on simulated and empirical (horse) populations with different mating strategies and population structures. The routines needed to compute the introduced parameters have been included in a new version of the program ENDOG.

-We present here a simple approach to obtain reliable estimates of the effective population size in real world populations via the computation of the increase in inbreeding for each individual (delta F i ) in a given population. The values of delta F i are computed as t-root of 1 À (1 À F i ) where F i is the inbreeding coefficient and t is the equivalent complete generations for each individual. The values of delta F computed for a pre-defined reference subset can be averaged and used to estimate effective size. A standard error of this estimate of N e can be further computed from the standard deviation of the individual increase in inbreeding. The methodology is demonstrated by applying it to several simulated examples and to a real pedigree in which other methodologies fail when considering reference subpopulations. The main characteristics of the approach and its possible use are discussed both for predictive purposes and for analyzing genealogies.effective size / increase in inbreeding / overlapped generation / genetic contribution

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