Among specific genes that may affect economically important traits in sheep, the β-lactoglobulin (LGB) locus has been extensively studied. Polymorphism has been detected in several breeds, but studies of the effect of LGB alleles on milk production traits have given conflicting results. Some found that LGB polymorphism significantly affects milk yield (Bolla et al. 1989; Herget et al. 1995; Fraghì et al. 1996), fat and protein content (Garzon & Martínez 1992; Giaccone et al. 1997; Kukovics et al. 1998), only fat content (Pirisi et al. 1998) and cheese yield and composition (Di Stasio et al. 1997; Rampilli et al. 1997). However, other studies failed to detect any effect of the gene on milk production traits (Barillet et al. 1993; Recio et al. 1997). These inconsistencies, similar to those reported for dairy cattle, can be explained by breed differences, population size, frequency distribution of the genetic variants and a failure to consider relationships among animals (Sabour et al. 1996).

Moreover, both the production data considered and the methods used for statistical analysis could be further causes of conflicting results (Ng-Kwai-Hang, 1997). Investigations of the relationships between milk protein polymorphism and milk production usually consider accumulated yields for standardized lactation lengths, assuming that environmental effects average out over a lactation. Such an assumption is not always valid, because there can be marked effects peculiar to individual test day (TD) measures that may not average out (Jamrozik & Schaeffer, 1997). The direct modelling of TD measures offers the advantage of a more accurate removal of environmental variation from phenotypic observations (Stanton et al. 1992). However, particular attention to the temporal dependence of the covariance structure among TD is required. In TD analysis performed by mixed linear models a simple covariance structure, known as compound symmetry, is usually assumed. This structure assumes an equal variance for all TD and an equal correlation between all pairs of TD within each lactation. An initial drawback of this assumption arises because of the heterogeneity of variance throughout lactation. Moreover, since TD values within a lactation are a sequence of repeated measures taken on the same experimental unit (Van der Werf & Schaeffer, 1997), measures close in time are likely to be more highly correlated than measures far apart in time. All these potential patterns of correlation and variation may combine to produce a complicated structure of covariance among TD that, when ignored, may result in inadequate analysis or incorrect conclusions (Littel et al. 1998). In particular, there can be marked differences in the estimates of the fixed factors considered in the analysis; such a bias is enhanced when the data structure is highly unbalanced, as in the case of studies on relationships between milk protein polymorphisms and milk production traits.

A possible solution can be found in the property of mixed linear models to assume different (co)variance structures in order to find the one that best fits experimental data. The aim of the present study was to test the possible influence of the statistical model used on the results when the relationships between β-lactoglobulin polymorphism and milk production traits in dairy ewes were analysed. With this aim in view, TD measures were directly modelled with mixed linear models and the effects of alternative (co)variance structures on fixed factors estimates were compared.