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Talk Abstract

On Fitness in Structured Metapopulation Models with an Application to Epidemics

On Fitness in Structured Metapopulation Models with an Application to Epidemics

**Mats Gyllenberg **

Member of the Research Council for Natural Sciences and Technology

Academy of Finland

Department of Mathematics

University of Turku

matsgyl@utu.fi

http://www.utu.fi/~matsgyl/

http://www.utu.fi/ml/sovmat/bio/

Fitness is usually defined as the long term exponential growth
rate *r(E)* of a phenotype in a given environment *E*.
In adaptive dynamics this concept of fitness is used for instance
to determine a criterion for successful invasion of a rare mutant:
Invasion will take place if and only if the fitness of the mutant
in the environment set by the resident is positive. If we try
to adapt this notion of fitness to metapopulations consisting
of local populations in different habitat patches we encounter
several difficulties. One is that even if the overall environment
defined by the equilibrium metapopulation state is constant,
the mutant experiences different conditions in different patches
and moreover, these conditions change within a patch as the
local resident population grows. It is therefore far from obvious
how to define fitness in a metapopulation.

In this talk I shall present a mathematical definition of
fitness which applies to a large class of structured metapopulation
models. Because infectious diseases can be modelled as metapopulations
with the hosts playing the role of patches, the results can
be applied to calculating *R*_{0} for epidemic
models. In addition, the dynamics of infectious diseases in
a metapopulation can be treated within this framework.