Identifying conversion efficiency as a key mechanism underlying food webs evolution: A step forward, or backward?

Body size or mass is generally seen as one of the main factors which structure food webs. A large number of evolutionary models have shown that indeed, the evolution of body size (or mass) can give rise to hierarchically organized trophic levels with complex between and within trophic interactions. However, because these models have often very different assumptions, sometimes arbitrary, it is difficult to evaluate what are the real key factors that determine food webs evolution, and whether these models results are robust or not. In this paper, we first review the different adaptive dynamics models, especially highlighting when their assumptions strongly differ. Second, we propose a general model which encompasses all previous models. We show that our model recovers all previous models results under identical assumptions. However, most importantly, we also show that, when relaxing some of their hypotheses, previous models give rise to degenerate food webs. Third, we show that the assumptions made regarding the form of biomass conversion efficiency are key for food webs evolution, a parameter which was neglected in previous models. We conclude by discussing the implication of biomass conversion efficiency, and by questioning the relevance of such models to study the evolution of food webs.