Scaling maximal oxygen uptake to predict performance in elite-standard men cross-country skiers.

The purpose of this study was to: 1) establish the optimal body-mass exponent for maximal oxygen uptake (VO(2)max) to indicate performance in elite-standard men cross-country skiers; and 2) evaluate the influence of course inclination on the body-mass exponent. Twelve elite-standard men skiers completed an incremental treadmill roller-skiing test to determine VO(2)max and performance data came from the 2008 Swedish National Championship 15-km classic-technique race. Log-transformation of power-function models was used to predict skiing speeds. The optimal models were found to be: Race speed = 7.86 · VO(2)max · m(-0.48) and Section speed = 5.96 · [VO(2)max · m(-(0.38 + 0.03 · α)) · e(-0.003 · Δ) (where m is body mass, α is the section's inclination and Δ is the altitude difference of the previous section), that explained 68% and 84% of the variance in skiing speed, respectively. A body-mass exponent of 0.48 (95% confidence interval: 0.19 to 0.77) best described VO(2)max as an indicator of performance in elite-standard men skiers. The confidence interval did not support the use of either "1" (simple ratio-standard scaled) or "0" (absolute expression) as body-mass exponents for expressing VO(2)max as an indicator of performance. Moreover, results suggest that course inclination increases the body-mass exponent for VO(2)max.

Genetic heterogeneity of residual variance - estimation of variance components using double hierarchical generalized linear models.

BACKGROUND: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. RESULTS: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. CONCLUSIONS: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.