Speaker
Description
In 1926 Vito Volterra proposed his prey-predator model within his "Teoria Matematica della Lotta per la Vita" and gave an explanation to some biological oscillations observed in several natural contexts. Since then, several extensions of Volterra model have been considered, in the context of O.D.E. modeling, to explain the rich behavior of ecological prey-predator system. These models have been used widely and form the basis of most, if not all, of our current theory on population and community processes. And yet, these models completely ignore one of the most important processes in an individual's life history: development (A. M. de Roos and L. Persson, Population and Community Ecology of Ontogenetic Development, 2013). Development mechanisms regard how individual internal variables change in time, influencing vital parameters such as fertility and mortality and tuning the interaction of different populations. In particular, in the case of a prey-predator system, the size of an individual is crucial, because apart from its influence on fertility and mortality, it determines the predator ability to catch the prey, and the prey contribution to predator growth. The model we consider corresponds to Volterra model and is fully size-structured. We are interested in steady states, in their stability and in the existence of periodic solutions. The complexity of the model allows only partial analytical results, but we adopt a pseudo-spectral method to perform a thorough numerical exploration.