Does evolution design robust food webs ?

Theoretical works that use a dynamical approach to study the ability of ecological communities to resist perturbations are largely based on randomly generated ecosystem structures. In contrast, we propose here to asses the robustness of food webs drawn from ecological and evolutionary processes with the use of community evolution models. In a first part, with the use of Adaptive Dynamics theoretical framework, we generate a variety of diversified food webs by solely sampling different richness levels of the environment as a control parameter, and obtain networks that satisfactory compare with empirical data. This allows us to highlight the complex, structuring role of the environmental richness during the evolutionary emergence of food webs. In a second part, we study the short-term ecological responses of food webs to swift changes in their customary environmental richness condition. We reveal a strong link between the environmental conditions that attended food webs evolutionary constructions and their robustness to environmental perturbations. When focusing on emergent properties of our evolved food webs, especially connectance, we highlight results that seem to contradict the current paradigm. Among these food webs, the most connected appear to be the less robust to sudden depletion of the environmental richness that constituted their evolutionary environment. Otherwise, we appraise the “adaptation” of food webs, by examining how they perform after being suddently immersed in an environment of modified richness level, in comparison with a trophic network that experienced this latter environmental condition all along its evolution.

Vote budgets and Dodgson’s method of marks

We examine voting rules that are inspired by Dodgson’s method of marks (to be distinguished from the procedure that is commonly referred to as Dodgson’s rule) by means of two criteria. Each voter decides how to allocate a vote budget (which is common to all voters, and need not be exhausted) to the candidates. Our first criterion is a richness condition: we demand that, for any possible preference ordering a voter may have, there is a feasible allocation of votes that reflects these preferences. A (tight) lower bound on the vote budget is established. Adding a strategy-proofness condition as a second criterion, we recommend that the vote budget be given by the lower bound determined in our first result.