Summary: The aim of this note is to describe the program endog (v.3.0). The program handles pedigree information to conduct several demographic and genetic analyses including: (a) the individual inbreeding and average relatedness coefficients; (b) effective population size; (c) parameters characterizing the concentration of both gene and individuals origin such as the effective number of founders and ancestors, the effective number of founder herds; (d) F statistics and paired genetic distances for each subpopulation under study; (e) descriptors of the genetic importance of the herds in a population and (f) generation intervals. The program will help breeders and researchers to monitor the changes in genetic variability and population structure with limited costs of preparing datasets. The program, user's guide and example file can be downloaded free of charge from the World Wide Web at http://www.ucm.es/info/prodanim/Endog30.zip.

Summary: Computation of inbreeding rate (ΔF) must consider that inbreeding is delayed with one generation with respect to the idealized population when addressed using individual inbreeding coefficients. The expression relating inbreeding in generation t with inbreeding rate F_t = 1 – (1–ΔF)^t should be more correctly written in real animal populations as F_t = 1 – (1–ΔF)^t−1, as changes in allele frequencies occur in the equivalent co‐ancestries in the previous generation. This simple approach is tested on simulated and real pedigrees thus demonstrating that: (i) the adjusted individual increase in inbreeding becomes stable in populations under random mating while the unadjusted parameter does not; (ii) regression of the unadjusted parameter over generations in pedigrees under random mating is highly significant while after correction it is not significant; and (iii) the variance of the adjusted parameter is reduced with the generations.

Recently different studies have formalized the way in which it is possible to obtain coancestry coefficients from molecular information (Caballero and Toro 2002; Eding and Meuwissen 2001) by applying Malécot's (1948) definition of kinship to marker genes, though referring it to identity-by-state instead of identity-by-descent (Caballero and Toro 2002). The molecular coancestry between two individuals, i and j, is the probability that two randomly sampled alleles from the same locus in two individuals are identical by state. Because of its straightforward relationship with genealogical coancestry, this parameter has been shown to have interesting properties that may be used for conservation purposes (Eding et al. 2002; Toro et al., 2002; 2003). Moreover, molecular coancestry can be used to assess genetic diversity within and between populations (Eding and Meuwissen 2001). Using simulated data, Eding and Meuwissen (2001) showed that molecular coancestry has some interesting properties, namely that average kinship between populations becomes constant very quickly after population fission, causing between-population diversity to remain constant. This property allows researchers using molecular coancestry information to study the genetic relationships between populations (Álvarez et al. 2005; Caballero and Toro 2002; Fabuel et al. 2004).

The genetic structure of eight Spanish autochthonous populations (breeds) of beef cattle were studied from pedigree records. The populations studied were: Alistana and Sayaguesa (minority breeds), Avileña – Negra Ibérica and Morucha ("dehesa" breeds, with a scarce incidence of artificial insemination), and mountain breeds, including Asturiana de los Valles, Asturiana de la Montaña and Pirenaica, with extensive use of AI. The Bruna dels Pirineus breed possesses characteristics which make its classification into one of the former groups difficult. There was a large variation between breeds both in the census and the number of herds. Generation intervals ranged from 3.7 to 5.5 years, tending to be longer as the population size was larger. The effective numbers of herds suggest that a small number of herds behaves as a selection nucleus for the rest of the breed. The complete generation equivalent has also been greatly variable, although in general scarce, with the exception of the Pirenaica breed, with a mean of 3.8. Inbreeding effective population sizes were actually small (21 to 127), especially in the mountain-type breeds. However, the average relatedness computed for these breeds suggests that a slight exchange of animals between herds will lead to a much more favourable evolution of inbreeding. The effective number of founders and ancestors were also variable among breeds, although in general the breeds behaved as if they were founded by a small number of animals (25 to 163).

Inbreeding depression on female fertility and calving ease in Spanish dairy cattle was studied by the traditional inbreeding coefficient (F) and an alternative measurement indicating the inbreeding rate (DeltaF) for each animal. Data included records from 49,497 and 62,134 cows for fertility and calving ease, respectively. Both inbreeding measurements were included separately in the routine genetic evaluation models for number of insemination to conception (sequential threshold animal model) and calving ease (sire-maternal grandsire threshold model). The F was included in the model as a categorical effect, whereas DeltaF was included as a linear covariate. Inbred cows showed impaired fertility and tended to have more difficult calvings than low or noninbred cows. Pregnancy rate decreased by 1.68% on average for cows with F from 6.25 to 12.5%. This amount of inbreeding, however, did not seem to increase dystocia incidence. Inbreeding depression was larger for F greater than 12.5%. Cows with F greater than 25% had lower pregnancy rate and higher dystocia rate (-6.37 and 1.67%, respectively) than low or noninbred cows. The DeltaF had a significant effect on female fertility. A DeltaF = 0.01, corresponding to an inbreeding coefficient of 5.62% for the average equivalent generations in the data used (5.68), lowered pregnancy rate by 1.5%. However, the posterior estimate for the effect of DeltaF on calving ease was not significantly different from zero. Although similar patterns were found with both F and DeltaF, the latter detected a lowered pregnancy rate at an equivalent F, probably because it may consider the known depth of the pedigree. The inbreeding rate might be an alternative choice to measure inbreeding depression.