Maternal allocation of carotenoids increases tolerance to bacterial infection in brown trout.

Life-history theory predicts that iteroparous females allocate their resources differently among different breeding seasons depending on their residual reproductive value. In iteroparous salmonids there is typically much variation in egg size, egg number, and in the compounds that females allocate to their clutch. These compounds include various carotenoids whose functions are not sufficiently understood yet. We sampled 37 female and 35 male brown trout from natural streams, collected their gametes for in vitro fertilizations, experimentally produced 185 families in 7 full-factorial breeding blocks, raised the developing embryos singly (n = 2960), and either sham-treated or infected them with Pseudomonas fluorescens. We used female redness (as a measure of carotenoids stored in the skin) and their allocation of carotenoids to clutches to infer maternal strategies. Astaxanthin contents largely determined egg colour. Neither egg weight nor female size was correlated with the content of this carotenoid. However, astaxanthin content was positively correlated with larval growth and with tolerance against P. fluorescens. There was a negative correlation between female skin redness and the carotenoid content of their eggs. Although higher astaxanthin contents in the eggs were associated with an improvement of early fitness-related traits, some females appeared not to maximally support their current offspring as revealed by the negative correlation between female red skin colouration and egg carotenoid content. This correlation was not explained by female size and supports the prediction of a maternal trade-off between current and future reproduction

Observables and a Hilbert Space for Bianchi IX

We consider a quantization of the Bianchi IX cosmological model based on taking the constraint to be a self-adjoint operator in an auxiliary Hilbert space. Using a WKB-style self-consistent approximation, the constraint chosen is shown to have only continuous spectrum at zero. Nevertheless, the auxiliary space induces an inner product on the zero-eigenvalue generalized eigenstates such that the resulting physical Hilbert space has countably infinite dimension. In addition, a complete set of gauge-invariant operators on the physical space is constructed by integrating differential forms over the spacetime. The behavior of these operators indicates that this quantization preserves Wald's classical result that the Bianchi IX spacetimes expand to a maximum volume and then recollapse.Comment: 23 pages, ReVTeX, CGPG-94/6-3, UCSBTH-94-3