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Direct estimation of multivariate selection in these populations is beyond the scope of this study.
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However, reducing the potential for over-fitting by considering fewer variables in the multivariate selection process was more desirable in our opinion.
Cactus height and number of columns were considered as covariate in multivariate selection analyses (Lande and Arnold 1983; Brodie et al. 1995).
The mean phenotype evolves according to the multivariate Lande equation, where the multivariate selection gradient is (A10) In the gradual-change scenario, θ t = k t, the rate and the direction of environmental change is described by a speed vector k= k1,…, k n )′, which contains the rates of change in the optimum for each trait.
The multivariate version of Lande's equation is (3) where, for n traits, ′ is the vector of mean trait values (with ′ denoting transposition) and ′ is the multivariate selection gradient, which points in the direction of steepest ascent on the fitness landscape.
When all the variables in Table 3 were simultaneously considered in a stepwise multivariate selection procedure, age, sex, smoking and HDL cholesterol remained statistically significant predictors of CVD in the DPS cohort.
Factors were considered for the multivariate selection process only if P⩽0.25 in the univariate Cox analysis.
With multivariate selection procedures variables (i.e. gene expression ratios) are tested in combination to identify interactions between them.
Using multivariate selection analysis, we characterise directly the form and intensity of sexual selection acting on cuticular hydrocarbons, chemical compounds widely used in the selection of mates in insects.
In case variable selection is required, sample size is an important determinant of appropriate selection procedures, and we advise to rely mainly on prior expert knowledge and multivariate selection procedures.
Variables with significant effects (p<0.10) in univariate analysis were selected for step-wise selection in multivariate regression.
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