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.