Research School for Socio-Economic and
Natural Sciences of the Environment
Research School for Socio-Economic and
Natural Sciences of the Environment

Modelling population dynamics with Physiologically Structured Population Models (PSPM)

Date: 29 April 2018 - 04 May 2018
Location: Ede

Population models are increasingly important in today’s ecological research and provide an indispensable contribution to understanding the dynamics of, and links between, different levels of biological organization. Population models that recognize differences among individuals in survival, reproduction, growth, development, etc. as a function of size, age, or other life history states are particularly important. These so-called structured population models come in different forms, but all share the property that the dynamics of a population emerge from the life histories of the individuals within the population.

​Physiologically structured population models (PSPMs) constitute a subset of structured models in which both the life histories of individuals and the emerging population dynamics unfold in continuous time, and individual states may be continuous (e.g., size) or discrete (e.g., juveniles vs. adults). In this respect, PSPMs differ from matrix population models (in which both time and states are discrete) and integral projection models (in which time is discrete and states are continuous). Furthermore, PSPMs are particularly suited to account in detail for the interactions between individuals of the same and/or other populations and to describe individual life histories by bio-energetic models, such as in the Dynamic Energy Budget theory (DEB). This makes PSPMs a powerful tool for exploring the population- and community-level consequences of DEB.

Although PSPMs are less familiar to general ecologists than matrix models or integral projection models, they have been very successful in describing and explaining the mechanisms that drive dynamics of natural populations and communities. Moreover, PSPMs form a powerful tool for understanding how population and community dynamics emerge from individual life histories, and equally important, how population and community processes feed back to shape the life histories of individuals. This feedback loop between individual- and population-level processes often yields non-linear dynamics and can lead to counterintuitive results. However, it can also make the formulation and analysis of PSPMs intimidating at first.

The aim of this course is to provide participants with the conceptual background and technical skills to formulate and analyze PSPMs. In addition, a set of lectures will highlight some of the insights into population and community dynamics gained from the use of PSPMs. Participants will analyze PSPMs with the R-package ‘PSPManalysis’, which is a collection of numerical routines to perform demographic, equilibrium and evolutionary analysis of PSPMs. The PSPManalysis program makes it possible to:

  • Simulate ecological dynamics as a function of time
  • For linear problems: calculate population growth rate, expected lifetime reproductive output (R0), stable size/age-distributions, and sensitivity analysis
  • For non-linear problems: calculate population equilibrium as a function of a model parameter (bifurcation analysis)
  • For evolutionary problems: calculate evolutionary singular strategies (ESSs) for multi-dimensional traits, calculate pairwise invisibility plots (PIPs) and solve the canonical equation of adaptive dynamics.

Participants will get hands-on experience with using the variety of functions available in PSPManalysis, in addition to learning about their mathematical background. The main focus will be on existing PSPMs, but attention will also be given to the requirements for developing new PSPMs. In addition, participants will be encouraged to think about how to apply the techniques to their own research.

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