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.
A review of two different approaches for the analysis of growth data using longitudinal mixed linear models: Comparing hierarchical linear regression (ML3, HLM) and repeated measures designs with structured covariance matrices (BMDP5V)
