• animal model;
  • evolutionary response;
  • genetic variability;
  • maternal effect;
  • pedigree;
  • quantitative genetics;
  • Soay sheep

Using a genealogy containing over 1800 dams and nearly 400 sires (estimated by genetic paternity techniques), combined with maximum likelihood procedures and an ‘animal model’, we have estimated the heritabilities, genetic correlations and variance components of three morphometric traits in the Soay sheep (Ovis aries) on St Kilda, Scotland. This approach allows heritabilities to be estimated in natural populations that violate the assumptions of offspring–parent regression methods. Maternal (or paternal) effects can also be estimated under natural conditions. We demonstrate that all the traits, body weight, hind leg length and incisor arcade breadth, have low but significant heritabilities. Body weight, the trait that experiences the strongest selection, had the lowest heritability but the highest additive genetic coefficient of variation. An evolutionary response to selection is predicted. When maternal effects were not taken into consideration heritabilities were over-estimated, although this effect was only significant in female offspring.