A Biomass Flow Approach to Population Models and Food Webs

Plastic energy allocation toward life-history functions in a consumer-resource interaction : Analyzing the temporal patterns of the consumer-resource dynamics

Various environmental alterations resulting from the current global change compromise the persistence of species in their habitual environment. To cope with the obvious risk of extinction, plastic responses provide organisms with rapid acclimatization to new environments. The premise of plastic rescue has been theoretically studied from mathematical models in both deterministic and stochastic environments, focusing on analyzing the persistence and stability of the populations. Here, we evaluate this premise in the framework of a consumer-resource interaction considering the energy investment towards reproduction vs. maintenance as a plastic trait according to positive/negative variation of the available resource. A basic consumer-resource mathematical model is formulated based on the principle of biomass conversion that incorporates the energy allocation toward vital functions of the life-cycle of consumer individuals. Our mathematical approach is based on the impulsive differential equations at fixed moments considering two impulsive effects associated with the instants at which consumers obtain environmental information and when energy allocation strategy change occurs. From a preliminary analysis of the non-plastic temporal dynamics, namely when the energy allocation is constant over time and without experiencing changes concerning the variation of resources, both the persistence and stability of the consumer-resource dynamic are dependent on the energy allocation strategies belonging to a set termed stability range. We found that the plastic energy allocation can promote a stable dynamical pattern in the consumer-resource interaction depending on both the magnitude of the energy allocation change and the time lag between environmental sensibility instants and when the expression of the plastic trait occurs.

Persistence and size of seasonal populations on a consumer-resource relationship depends on the allocation strategy toward life-history functions

The long-term ecological dynamics of a population inhabiting a seasonal environment is analyzed using a semi-discrete or impulsive system to represent the consumer-resource interaction. The resource corresponds to an incoming energy flow for consumers that is allocated to reproduction as well as to maintenance in each non-reproductive season. The energy invested in these life-history functions is used in reproductive events, determining the size of the offspring in each reproductive season. Two long-term dynamic patterns are found, resulting in either the persistence or the extinction of the population of consumers. In addition, our model indicates that only one energy allocation strategy provides an optimal combination between individual consumption and long-term population size. The current study contributes to the understanding of how the individual-level and the population-level are interrelated, exhibiting the importance of incorporating phenotypic traits in population dynamics.