How costly is clutch formation in the Audouin's Gull Larus audouinii?

During the Audouin's Gull's breeding season at the Ebro Delta in 1993, 24 fresh eggs from eight three-egg clutches (modal clutch-size) were collected at the peak of the laying period. Eggs were processed to obtain formalin-fixed yolks, which were halved and stained using the potassium dichromate method. Digitized images of the yolks were examined to assess the daily rates of yolk deposition. We used these data in combination with egg compositional analysis to build a model of energy demands during the formation of an average clutch in Audouin's Gull. To show how the different parameters of clutch formation affect the daily energy investment peak, we performed a simulation analysis in which the rapid yolk development (RYD) period, the follicle triggering interval (FTI), the laying interval (LI) and the albumen synthesis period (ASP) were allowed to vary simultaneously. In our sample, the mean RYD period was seven days with a range from six to eight days. There were no significant differences in yolk volume among eggs in a clutch, but albumen volume was significantly smaller in third eggs. According to our model the albumen synthesis of the a-egg coincides with the energy demand peak for clutch formation. This peak represents an increase by ca. 42% in female energy requirements. Values obtained from the simulation analysis showed that only the ASP of the a-egg and the RYD durations of the second and third follicles produced noticeable reductions in peak energy investment. We predict that in gulls, whose laying intervals seem to be kept constant, significant increases of the durations of the RYD periods of second and third eggs, or even significant reductions of yolk size of these eggs, may operate simultaneously to match the energy demands during clutch formation to the prevailing food conditions.     

The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.     

Turnover of plant lineages shapes herbivore phylogenetic beta diversity along ecological gradients

Understanding drivers of biodiversity patterns is of prime importance in this era of severe environmental crisis. More diverse plant communities have been postulated to represent a larger functional trait‐space, more likely to sustain a diverse assembly of herbivore species. Here, we expand this hypothesis to integrate environmental, functional and phylogenetic variation of plant communities as factors explaining the diversity of lepidopteran assemblages along elevation gradients in the Swiss Western Alps. According to expectations, we found that the association between butterflies and their host plants is highly phylogenetically structured. Multiple regression analyses showed the combined effect of climate, functional traits and phylogenetic diversity in structuring butterfly communities. Furthermore, we provide the first evidence that plant phylogenetic beta diversity is the major driver explaining butterfly phylogenetic beta diversity. Along ecological gradients, the bottom up control of herbivore diversity is thus driven by phylogenetically structured turnover of plant traits as well as environmental variables.