Non-semisimple Lie algebras with Levi factor \frak{so}(3), \frak{sl}(2,R) and their invariants

We analyze the number N of functionally independent generalized Casimir invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{% oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and \frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that for any dimension n >= 6 there exist Lie algebras \frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.Comment: 16 page

Leptin Affects Life History Decisions in a Passerine Bird: A Field Experiment

BACKGROUND: Organisms face trade-offs regarding their life-history strategies, such as decisions of single or multiple broods within a year. In passerines displaying facultative multiple breeding, the probability of laying a second clutch is influenced by several life-history factors. However, information about the mechanistic background of these trade-offs is largely lacking. Leptin is a protein hormone produced by white fat cells, and acts as a signal between peripheral energy depots and the central nervous system. In addition, leptin affects cells at all levels of the reproductive axis and plays a critical role in regulating the allocation of metabolic energy to reproduction. As such, it is possible that leptin levels influence the decision of whether or not to invest time and energy into a second clutch. Accordingly, we expect a treatment with exogenous leptin to result in an increased number of second broods. METHODOLOGY/PRINCIPAL FINDINGS: At a later stage during the first brood, female great tits were treated either with long-term leptin-filled cholesterol pellets (the experimental birds) or with pellets containing only cholesterol (the control birds). We found that leptin-treated females were significantly more likely to have a second brood and that the earlier females were more likely to lay a second clutch than the late females. CONCLUSIONS/SIGNIFICANCE: As both timing of first brood and treatment with leptin were important in the decision of having multiple broods, the trade-offs involved in the breeding strategy most likely depend on multiple factors. Presumably leptin has evolved as a signal of energy supply status to regulate the release of reproductive hormones so that reproduction is coordinated with periods of sufficient nutrients. This study investigated the role of leptin as a mediator between energy resources and reproductive output, providing a fundamentally new insight into how trade-offs work on a functional basis

Development of Secondary Woodland in Oak Wood Pastures Reduces the Richness of Rare Epiphytic Lichens

Wooded pastures with ancient trees were formerly abundant throughout Europe, but during the last century, grazing has largely been abandoned often resulting in dense forests. Ancient trees constitute habitat for many declining and threatened species, but the effects of secondary woodland on the biodiversity associated with these trees are largely unknown. We tested for difference in species richness, occurrence, and abundance of a set of nationally and regionally red-listed epiphytic lichens between ancient oaks located in secondary woodland and ancient oaks located in open conditions. We refined the test of the effect of secondary woodland by also including other explanatory variables. Species occurrence and abundance were modelled jointly using overdispersed zero-inflated Poisson models. The richness of the red-listed lichens on ancient oaks in secondary woodland was half of that compared with oaks growing in open conditions. The species-level analyses revealed that this was mainly the result of lower occupancy of two of the study species. The tree-level abundance of one species was also lower in secondary woodland. Potential explanations for this pattern are that the study lichens are adapted to desiccating conditions enhancing their population persistence by low competition or that open, windy conditions enhance their colonisation rate. This means that the development of secondary woodland is a threat to red-listed epiphytic lichens. We therefore suggest that woody vegetation is cleared and grazing resumed in abandoned oak pastures. Importantly, this will also benefit the vitality of the oaks