Abstract
Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.
Highlights
Seasonal reproduction is a common mode of reproduction, especially in the temperate zone (Vila-Gispert et al 2002; Felix et al 2011)
With seasonal reproduction, average biomass densities of a physiologically or size- structured population models (PSPMs) are reasonably well-represented by average biomass densities of the stage-structured biomass model that we derive
We investigated the effect of species body size and the number of juvenile stages in the stage-structured biomass model on the similarity of the dynamics of the stage-structured biomass model and the PSPM
Summary
Seasonal reproduction is a common mode of reproduction, especially in the temperate zone (Vila-Gispert et al 2002; Felix et al 2011). For the derivation of an expression for the maturation function γ that preserves the expected lifetime contribution of biomass by an individual to the adult stage from the PSPM, we assume a constant resource density that is high enough for the juvenile ingestion rate to exceed the maintenance requirements.
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