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Causes and short-term consequences of variation in milk composition in wild sheep.

Ecologists seek to understand the fitness consequences of variation in physiological markers, under the hypothesis that physiological state is linked to variability in individual condition and life history. Thus, ecologists are often interested in estimating correlations between entire suites of correlated traits, or biomarkers, but sample size limitations often do not allow us to do this properly when large numbers of traits or biomarkers are considered. Latent variables are a powerful tool to overcome this complexity. Recent statistical advances have enabled a new class of multivariate models-multivariate hierarchical modelling (MHM) with latent variables-which allow to statistically estimate unstructured covariances/correlations among traits with reduced constraints on the number of degrees of freedom to account in the model. It is thus possible to highlight correlated structures in potentially very large numbers of traits. Here, we apply MHM to evaluate the relative importance of individual differences and environmental effects on milk composition and identify the drivers of this variation. We ask whether variation in bighorn sheep milk affects offspring fitness. We evaluate whether mothers show repeatable individual differences in the concentrations of 11 markers of milk composition, and we investigate the relative importance of annual variability, maternal identity and morphological traits in structuring milk composition. We then use variance estimates to investigate how a subset of repeatable milk markers influence lamb summer survival. Repeatability of milk markers ranged from 0.05 to 0.64 after accounting for year-to-year variations. Milk composition was weakly but significantly associated with maternal mass in June and September, summer mass gain and winter mass loss. Variation explained by year-to-year fluctuations ranged from 0.07 to 0.91 suggesting a strong influence of environmental variability on milk composition. Milk composition did not affect lamb survival to weaning. Using joint models in ecological, physiological or behavioural contexts has the major advantage of decomposing a (co)variance/correlation matrix while being estimated with fewer parameters than in a "traditional" mixed-effects model. The joint models presented here complement a growing list of tools to analyse correlations at different hierarchical levels separately and may thus represent a partial solution to the conundrum of physiological complexity.