Individual-based models for stage structured populations: formulation of “no regression” development equations

Abstract

Individual-based models describe the growth dynamics of a population by performing numerical simulations of the life histories of its individuals. The life of an individual is determined by the basic processes of development, reproduction and mortality. In this paper the model equations for the development process are stochastic difference equations with discrete time and describe the time evolution of the status of an individual, in terms of a physiological age. We address the formulation of development models, when "regression" effects (defined as negative development) on the status of an individual are forbidden; this is a natural assumption when the physiological age is defined in terms of an abstract non-decreasing indicator measuring the maturity or the percentage of development. Different stochastic models of the development process are presented, and their behaviours are analyzed by varying the stochasticity level, which takes into account the degree of intraspecific variability. Moreover, remarks on the choice of the time step are reported.

The effects of fecundity, mortality and distribution of the initial condition in phenological models

“…With the oviposition profile (2(b)) ( Figure 8) model (6) is in advance in the first part of the dynamics and delayed in the second part but the gap is, in general, smaller than in the previous case. In case of oviposition profile (2(c)), the dynamics of the model (7) is delayed with respect to that of model (6) (Figure 9), and the delay is up to approximately 10 days in the first part of the dynamics for the second larval generation.…”

“…We note that the first adult generation is equal for each fecundity formulation, while starting from the first eggs generation there are differences in the outcomes. In detail, with the oviposition profile (2(a)), the dynamics of the model (7) are in advance with respect to the ones of model (6) (Figure 7), and the gap is up to approximately 10 days on the second larval generation. With the oviposition profile (2(b)) ( Figure 8) model (6) is in advance in the first part of the dynamics and delayed in the second part but the gap is, in general, smaller than in the previous case.…”

“…In detail, with the oviposition profile (2(a)), the dynamics of the model (7) are in advance with respect to the ones of model (6) (Figure 7), and the gap is up to approximately 10 days on the second larval generation. With the oviposition profile (2(b)) ( Figure 8) model (6) is in advance in the first part of the dynamics and delayed in the second part but the gap is, in general, smaller than in the previous case. In case of oviposition profile (2(c)), the dynamics of the model (7) is delayed with respect to that of model (6) (Figure 9), and the delay is up to approximately 10 days in the first part of the dynamics for the second larval generation.…”

“…Note that in this case no temperature dependence is present. However, it is known that the eggs production is influenced by temperature, and in a different way with respect to (6). For this reason, we want to deal with a flux which depends on both temperature and physiological age.…”

“…Cumulative percentage of individuals entering in the four stages (eggs, larvae, pupae, adults). Light blue continuous line: model(6), fecundity equal to adult development. Blue dashed line: model(7), fecundity dependent on physiological age with the profile (2(a)).…”