Mini-symposium on Adaptive Dynamics on the occasion of Stefan Geritz'
PhD organized by the Section Theoretical Evolutionary Biology of the
Institute of Evolutionary and Ecological Sciences, EEW, RUL, in
collaboration with the project Population Dynamics of the NWO priority
program Non-Linear Systems.

Address: | Van der Klaauw Laboratory |

`grote collegezaal' (in the blue building) | |

Kaiserstraat 63, Leiden |

**10:00 - 11:00**- Hans Metz (EEW, RUL).
*From Population Dynamics to Adaptive Dynamics, and introduction for the uninitiated* **11:00 - 12:00**- Éva Kisdi (Department of Genetics, Eötvös University).
*Evolutionary Loitering and Branching in a Model for Asymmetric Competition* **13:00 - 14:00**- Mats Gyllenberg (Department of Mathematics, University of Turku).
*Adaptive Dynamics under Predation* **14:00 - 15:00**- Stefan Geritz (Department of Zoology, University of Maryland).
*The Adaptive Dynamics of Seed Size Evolution*

Addendum: Between 16:15 and 17:00 Stefan Geritz will defend his PhD entitled `The Evolutionary Significance of Variation in Seed Size' in the old Senate office, Rapenburg 73, Leiden.

NLS winterschool on Population Dynamics, Woudschoten, January 7-11 1998 Registration form at the end of the announcement. Please feel free to pass this message on to anyone you think would be interested in modelling population dynamics.

The school will be organised along the same lines as the 1996 Winterschool. Five speakers will each give five lectures on their field of expertise. In addition to these lectures all participants will give a short presentation of their own work and interest (two minutes, one transparancy). During the school some papers will be studied in small groups culmunating in a short plenary presentation of the findings.

The five speakers are:

Ulf Dieckmann (Vienna) | stochastic theory and adaptive dynamics |

Josef Hofbauer (Vienna) | deterministic dynamical systems in population |

dynamics and population genetics | |

Mous Sabelis (Amsterdam) | population ecology |

Mats Gyllenberg(Finland) | metapopulation dynamics |

Olof Leimar (Sweden) | behaviour and evolutionary dynamics |

The aim of this winterschool is to give (beginning) PhD students in population biology a better understanding of the way mathematics can be applied to appoach biological problems. Participants will be given a background in many relevant deterministic and stochastic mathematical and numerical modelling apoaches. There are now 55 participants from all over the world!

Summer School "Spatio-Temporal Patterns" will be held at Twente University, the Netherlands.

This course is intended for young researchers with a strong mathematical interest, and should provide them with a good overview of various approaches to understand patterns displayed by the space-time characteristics of physical, chemical, biological, ... phenomena. There will be five main lecturers, and each of them will lecture 6 hours. Their names, the title of their lectures and a short abstract are listed below.

Right at the beginning of the course, participants will be asked to present themselves, their background and scientific interests, in a ``3 minutes/1 overhead transparency'' presentation. We expect 30-40 participants.

Participants and lecturers will be lodged in hotel "de Logica". Prices are Dfl. 50,- per day for a double room and Dfl. 65,- per day for a single room. As the number of rooms is limited, we ask people to share a room as much as possible. The organisers cannot provide any financial support (neither for travel, bed and breakfast, nor for subsistence). We therefore have kept the admission fee as low as possible: Dfl. 100,-.

Applications (The application form is attached below) can be send to: M.Plekenpol@math.utwente.nl Admission is on the basis of arrival of the application.

The course is sponsored by MRI, the SWON-NWO program "Dynamical
Systems and Pattern Formation", .... and is organised by Odo
Diekmann, Arjen Doelman, Stephan van Gils and Ronald Meester.

The lecturers are:

Rick Durrett (Cornell) | Stochastic and Spatial Models |

Jean-Pierre Eckman (Geneva) | Some topics in the study of partial differential |

equations on the infinite line | |

Nick Ercolani (Tucson) | tba |

Satya Majumbar (Bombay) | Self-organised Criticality |

Yasumasa Nishiura (Sapporro) | Asymptotic and transient dynamics in pattern |

formation of nonlinear dissipative systems |

Fifth International Conference `Mathematical Population Dynamics
Zakopane, Poland, June 21-26, 1998. This conference will be an
interdisciplinary forum where applied mathematicians, statisticians,
engineers, computer scientists, biologists, epidemiologists,
biomedical scientists and ecologists can share their experiences.

Web site: http://www.cyf-kr.edu.pl/zakopane/index.html

Information: Mr. Jaroslaw Smieja, Department of Automatic
Control, Silesian Technical University, Akademicka 16, 44-101 Gliwice,
Poland.

E-mail:
JSMIEJA@peach.ia.polsl.gliwice.pl

Alcala First International Conference on Mathematical Ecology, Alcala de Henares (Madrid) Spain.

Plenary Lectures: **P.Auger** (University Claude Bernard Lyon 1,
France), **H.Caswell** (Woods Hole Oceanograplic Institution,
USA), **J.Cushing**, **T.G.Hallam** (University of Tennessee, USA),
**J.Horwood** (CEFAS Lowestoft, UK), **S.A.L.M.Kooijman** (Free
University Amsterdam), **S.Levin**, **F.Milner**, **D.Rand**,
**S.Rinaldi** (Politecnico di Milano, Italy).

**Summary** of the talk of Bas Kooijman bas@bio.vu.nl:*The
Dynamic Energy Budget model for structuring populations on the basis
of physiological processes*

The Dynamic Energy Budget (DEB) model consists of a set of simple, mechanistically inspired, rules for the uptake and use of substrates (food) by an individual organism. It specifies the key processes of feeding, assimilation, development, maintenance, growth, reproduction (or division) and ageing quantitatively, and is meant to apply to all organisms on earth. These processes can by specified realistically for animals, feeding on other animals, with only one internal reserve and structural body mass as state variables, while cumulated damage is required as third state variable to specify the aging process. Organisms, such as algae, which can be limited in their growth by several types of nutrients (and/or light), require more types of reserves. Organisms, such as plants, which use different organs for the uptake of different nutrients and light, also require more types of structural biomass. These extensions with respect to the simpler model for animals, follow naturally from the set of simple rules, and specify all energy and mass fluxes simultaneously, on the basis of the principle of homeostasis. These fluxes include dissipating heat, water, oxygen and carbon dioxide (among others). The theory, therefore, provides a fundamental basis for the coupling between energy and mass fluxes in organisms.

Since the DEB model relates substrate uptake to surface area and maintenance to volume of structural biomass, changes in shape are important in the specification of the key processes. The DEB model reduces to a very simple structure for 1D-isomorphs: organisms for which surface area is proportional to volume. It can be shown that organisms that divide into two parts at a fixed investment into maturation, such as microorganisms, behave approximately as 1D-isomorphs, irrespective of their actual changes in shape during growth. Several popular models for the growth of microorganisms turn out to be special cases of the DEB-model. The distinction between the individual and population level disappears for 1D-isomorphs, and physiologically structured population models reduce to unstructured ones, which can be represented as a simple set of ode's. This does not hold for organisms with big ratios between adult and neonate size.

The set of rules that specify the DEB-model imply the existence of a maximum body size for each species of organism, and classifies all its parameters into two categories: intensive parameters that do not depend on maximum body size, and extensive parameters that can be shown to be proportional to volumetric length. The rules, therefore, imply trends in parameter values, when species with different maximum body sizes are compared. These trends turn out to be realistic for many physiological and life history quantities that can be written as functions of parameter values, such as respiration rate, life span, maximum reproduction rate, etc. This property is of great help to reduce the number of parameters in the application of the DEB-model to specify the dynamics of food webs, for instance.

The DEB-model is simple enough to obtain some analytical results for populations in steady state, while some popular software packages can be used successfully to analyse the population dynamics in simple environments, such as the chemostat. It appears to be possible to obtain at least some of the rules on which the DEB-model is based from more detailed models on molecular kinetics. The DEB-model seems, therefore, usefull in linking physiological processes to population dynamics.

*Keywords*: Mass and Energy balances, homeostasis, body size scaling
relationships, multiple nutrient limitations.

*References*: Kooijman, S.A.L.M. (1993) Dynamic Energy Budgets in
Biological Systems, Theory and application in ecotoxicology. Cambridge
University Press.

**Special Sessions**

**P.Auger**, Lyon. Aggregation methods and
perturbations in population dynamics,

**B.W.Kooi**, Amsterdam.
Bioenergic modelling of ecosystems,

**J.L.Gouzé**, Nice.
Control theory applied to ecological problems,

**S.Tuljapurkar**, Los Altos. Do variable environments affect life
history trade-offs?

**J.Michalski**, Laussane. Food webs,

**
Jia Li**, Alabama. Mathematical modeling in infectious diseases,

**M.A. Zavala**, Princeton. Perspectives in modeling vegetation
dynamics,

**H. Heesterbeek**, Wageningen. Population ecological
effects of parasites,

**V.Kaitala**, Helsinki. Spatial
population dynamics: models and empirical testing,

**H.Malchow**,
Osnabtück, **J.Brindley**, Leeds, and **A.B.Medvinsky**,
Pushchino. Spatial, temporal and spatio-temporal structures in
oceanic plankton populations,

**M.Popescu**, Bucharest.
Stability and analysis in the dynamics of systems,

**E.Sánchez**, Madrid, and **O.Arino**, Pau. Structured Population
Dynamics: Comparison of individual and global models,

**T.Kostova**, Sofia. Structured population models: Behavior of
solutions: Analytical and numerical approaches.

**Summary** of the session organized by Hans Heesterbeek
J.A.P.HEESTERBEEK@cpro.dlo.nl : *Population ecological
effects of parasites*

It has been well-studied, both theoretically and by observation, that parasites and infectious agents can be important determinants of community structure and that they can regulate host population growth. Recently, there is renewed interest for ecosystem effects of infections in a number of important areas that all deserve more attention from mathematical modellers. Concrete examples are: 1. diseases in metapopulations (improved connectedness of sub-populations leads to increased spread of infections; implications both for nature management and for understanding dynamics of human infections such as measles); 2. the role of parasites in structuring foodwebs; 3. the role of infections in structuring spatial phenomena observed in stochastic spatial models; 4. the role of parasites in driving spatial genetic host diversity.

**Summary** of the session organized by Bob Kooi
kooi@bio.vu.nl : *Bioenergic modelling of ecosystems*

The classical Lotka-Volterra model has been altered in many ways to model food webs more realistically. The dynamics of the web is mathematically described as a set of coupled nonlinear ordinary differential equations. This makes application of the theory of nonlinear dynamics systems possible. Commonly used models for food chains have been studied intensively using bifurcation analysis. Various types of dynamic behaviours were described in the literature: point attractors, limit cycles and chaos. The chaotic behaviour includes boundary crises and global homoclinic and heteroclinic bifurcations. Nowadays computer packages are available to perform these bifurcation analyses. Application to a entire food web is, however, still cumbersome. Modelling a whole food web, including all sorts of complex ecological phenomena such as competition, omnivory would require a large number of parameters. Furthermore the obtained bifurcation diagrams may be difficult to interpret and there is always a danger to miss important bifurcation points. This hampers direct application of the theory of nonlinear dynamic systems.

To reduce the number of parameters, different methods can be applied. One might consider the use of aggregation techniques and body size scaling relationships across species. When time-scales differ greatly, singular perturbation techniques can be used. On the other hand, bifurcation theory could be used to classify the calculated bifurcations, in order to detect the intrinsic characteristics of food web dynamics.

In this session researchers are invited to contribute their views on
the issue of modelling communities. These models allow the
quantitative investigation of a number of hypotheses which have been
put forward to explain dynamic phenomena of ecosystems in nature (for
instance: the shortness of food chains). Also welcome are
contributions with application of these mathematical approaches to
real-life problems in e.g. conservation biology or ecotoxicology.

Web site: http://www.ciencias.alcala.es/depmat/aicme.htm

Information: Rafael Bravo de la Parra Departamento de Matematicas
Universidad de Alcala 28871 Alcala de Henares (Madrid) Spain,

E-mail:
aicme@mat.alcala.es

International Conference on Theory and Mathematics in Biology and Medicine Joint meeting of the European Society for Mathematical and Theoretical Biology (ESMTB) and the American Society for Mathematical Biology (SMB). Place: Amsterdam. Organising body: Dutch Society for Theoretical Biology (NvTB).

Application form Summer School "Spatio-Temporal Patterns" will
be held at Twente University, the Netherlands.

Last Name :

First Name :

Title :

Institute :

Postal address:

Country :

Email address :

Arrival : (date & time)

Departure : (date & time)

* please indicate your preferences to the following

Single room yes no (Dfl 65,- p.p. p.n. incl. breakfast)
Double room yes no (Dfl 50,- p.p. p.n. incl. breakfast)
Lunch regular vegetarian (Dfl 15,- per lunch)
Diner regular vegetarian (Dfl 35,- per diner)

Thu Dec 18 11:35:42 MET 1997