A cohort projection method to follow deb-structured populations with periodic reproduction

Bob W. Kooi and Sebastiaan A. L. M. Kooijman 2020. A cohort projection method to follow deb-structured populations with periodic reproduction. Ecol. Mod,.: subm

Abstract

The need to follow structured populations, as opposed to unstructured ones, is well-recognized. The most detailed category of population models are the individual-based population models (IBMs), also called agent-based population models (ABMs). The required computational effort is roughly proportional to the number of individuals in the population, which is a problem if this is large, and their mathematical analysis is impossible. A less detailed method is the continuous-time partial differential equation (pde) method, where changes in the i-states of individuals are specified by a set of ordinary differential equations (ode's) and the population p-states as pde's. Their mathematical analysis and computational methods are generally complex. Matrix discrete-time population models (MPMs) are much simpler in all respects and can be used if individuals depend on time only and don't change too much from one time step to the other. The more recent Integral Projection Models (IPMs) are intermediary between pde's and MPMs, where the elements of the projection matrix are obtained by integrating the ode's that specify the changes in states of individuals. We here introduce a new class of models, the Cohort Projection Models (CPMs), which are intermediary between pde's and IPMs. CPMs follow of cohorts of similar individuals and changes in their istates in continuous time using ode's. The latter can depend on time, but also on i-states. The cohorts are followed in generations in a Lagrangian way, on the assumption that seasonal cycles synchronize reproduction events among cohorts and all eggs that are produced by the population are the same. Feedback from the environment can be included via specification of food dynamics that accommodates competition. Temperature follows a specified trajectory. This allows a projection of p-states, from one reproduction event to the next, a projection map, which properties can be studied using nonlinear dynamics theory, such as existence and stability of fixed points and, thereby, the long-term dynamics of the population. We demonstrate this using Dynamic Energy Budget (deb) models for changes in i-states. The Add-my-Pet (AmP) collection has deb parameters for over 2000 animal species, which were estimated from empirical data. CPMs are meant to match the relative simplicity of MPMs with the realism of deb models. We wrote Matlab code that extracts parameters and traits from the downloadable software AmP collection package and runs the analysis of CPMs.

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