Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

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.

Seasonal reproduction leads to population collapse and an Allee effect in a stage-structured consumer-resource biomass model when mortality rate increases

“…Our model is identical to the model presented by Soudijn and de Roos [ 20 ], except for the fact that we assume the consumers to forage following a linear, type I instead of a type II functional response. Moreover, we analyse a scaled version of the model.…”

“…The model accounts for one shared resource R and one consumer population. Following [ 20 ] we assume that the consumer individuals are distinguished by their body size, denoted by s , and all consumer individuals are born with the same body size s b and can mature at any body size. The consumer population is thus divided into two stages: juvenile stage and adult stage.…”

“…Throughout the growing season juvenile biomass increases through somatic growth of juveniles at mass-specific rate and decreases through mortality at rate d j ( R ) and through maturation. Maturation of juveniles is modeled as in [ 18 , 20 ] by a resource-dependent per capita maturation rate γ ( ν j ( R ), μ ) (see [ 20 ] for its derivation and justification). Here μ is the stage-independent background mortality rate of the consumer and ν j ( R ) is the mass-specific, net-biomass production rate.…”

“…The exact form of the maturation rate is crucial for our current model to be a consistent approximation to the analogous fully size-structured version of the model, in which maturation of juveniles in each cohort occurs as a discrete event and new cohorts are formed at each reproduction event, because it ensures that the expected lifetime contribution of biomass per juvenile individual to the adult phase is the same in both models. Finally, this maturation rate ensures that the juveniles can only grow in body size and mature when they have positive net biomass productivity, that is when ν j ( R ) > 0, and takes into account that high mortality rate of juveniles may reduce the survival of juveniles till maturation [ 18 ], while also allowing juveniles to mature at any ages and body sizes [ 20 ].…”

A modelling exercise to show why population models should incorporate distinct life histories of dispersers

“…However, recently it has been argued that population ecology should shift its focus from formulating models at the population level to the level of individual organisms (Clark et al 2011;Topping et al 2015;Soudijn and Roos 2017); an argument echoed in the field of dispersal (Bonte et al 2012). Although ecological patterns can be observed at the population level, it is the behaviour and demographic changes of individuals that shape the dynamics of the population (Clark et al 2011;Soudijn and Roos 2017). So, in order to fully understand the effects of dispersal on natural systems, it is necessary to incorporate individual-level differences in dispersal behaviour in population models.…”