Modelling population dynamics
with
Physiologically Structured Population Models (PSPM)

Concepts, formulation and analysis of PSPMs

To be announced

Scope

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.

The following references provide background and examples of PSPMs:
• De Roos, A. M., and L. Persson. 2001. Physiologically structured models – from versatile technique to ecological theory. Oikos 1:51–71.
• De Roos, A. M., and L. Persson. 2002. Size-dependent life-history traits promote catastrophic collapses of top predators. PNAS 99:12907–12912.
• De Roos, A. M., and L. Persson. 2013. Population and Community Ecology of Ontogenetic Development. Princeton University Press, Princeton.
• Persson, L., K. Leonardsson, A. M. De Roos, M. Gyllenberg, and B. Christensen. 1998. Ontogenetic Scaling of Foraging Rates and the Dynamics of a Size-Structured Consumer-Resource Model. Theoretical population biology 54:270–293.

Tentative programme

Every day will consist of a mix of lectures and Labs. Exercises will be carried out in R.
Day 1: General introduction to physiologically structured population models.
Day 2: Consumer-resource models.
Day 3: Tri-trophic models. Social activity in the afternoon.
Day 4: Emergent community effects and ontogenetic niche shifts.
Day 5: Synthesis.
A more detailed program will become available soon.

Travel grants and participation fee waivers for PhD candidates and postdocs

We are offering a number of grants for a waiver of the participation fee and/or travel support to PhD candidates and postdocs that would like to participate in this course. All PhDs and postdocs can apply for a fee-waiver grant, but only those coming from outside the Netherlands can apply for a travel grant. To apply for the grants, the applicant should submit a 1-page motivation letter in which (s)he:
a) Indicates his/her relevant prior theoretical knowledge and experience regarding dynamic models in ecology in general and/or regarding PSPMs in specific;
b) States what (s)he aims to achieve with this course and how it contributes to his/her research project; and
c) Includes a statement from his/her PhD / postdoc supervisor in which the support of the application is expressed and the added value of this course in the training programme of the applicant is indicated.
In addition, if one would like to apply for a travel subsidy, a travel itinerary with expected travel expenses needs to be included as a separate file in the application. Both the 1-page motivation letter and the travel itinerary can be uploaded when registering your participation at the bottom of this website, or they can be sent to office.pe@wur.nl directly.

Grants will be awarded on the basis of the criteria mentioned above, and in order of receipt of the 1-page motivation letter. A limited number of grants is available, so register your participation and submit the motivation letter soon to maximise your chances.

General information

Fees ¹

Generally, the following fees apply for this course, but note that the actual fees may be somewhat different for the next edition of this course.

¹ The course fee includes accommodation, all meals, coffee/tea/water, and course materials. It does not include beverages in the bar
² The Early-Bird Fee applies to anyone who REGISTERS AT LEAST 4 WEEKS PRIOR TO THE START OF THE COURSE

More information

Dr Lennart Suselbeek (PE&RC)
Phone: +31 (0) 317 485426
Email: lennart.suselbeek@wur.nl

Amber Heijboer MSc (PE&RC)
Phone: +31 (0) 20 525 7451
Email: a.heijboer@uva.nl

Registration

At this moment, this course is not scheduled yet. However, if you register your interest in this activity below, we will inform you as soon as the course is scheduled and registration of participation is opened.