WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from

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Traits that are closely associated with fitness tend to have lower heritabilities (h2) than those that are not. This has been interpreted as evidence that natural selection tends to deplete genetic variation more rapidly for traits more closely associated with fitness (a corollary of Fisher's fundamental theorem), but Price and Schluter (1991) suggested the pattern might be due to higher residual variance in traits more closely related to fitness. The relationship between 10 different traits for females, seven traits for males, and overall fitness (lifetime recruitment) was quantified for great tits (Parus major) studied in their natural environment of Wytham Wood, England, using data collected over 39 years. Heritabilities and the coefficients of additive genetic and residual variance (CVA and CVR, respectively) were estimated using an "animal model." For both males and females, a trait's correlation (r) with fitness was negatively related to its h2 but positively related to its CVR. The CVA was not related to the trait's correlation with fitness in either sex. This is the third study using directly measured fitness in a wild population to show the important role of residual variation in determining the pattern of lower heritabilities for traits more closely related to fitness.

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-Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights with age were modelled through B-splines of age at recording. A total of thirteen analyses, considering different combinations of linear, quadratic and cubic B-splines and up to six knots, were carried out. Results showed good agreement for all ages with many records, but fluctuated where data were sparse. On the whole, analyses using B-splines appeared more robust against "end-of-range" problems and yielded more consistent and accurate estimates of the first eigenfunctions than previous, polynomial analyses. A model fitting quadratic B-splines, with knots at 0, 200, 400, 600 and 821 days and a total of 91 covariance components, appeared to be a good compromise between detailedness of the model, number of parameters to be estimated, plausibility of results, and fit, measured as residual mean square error. covariance function / growth / beef cattle / random regression / B-splines