Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Evolutionary dynamics of site-selection
Kalle Parvinen

Last modified: 2014-04-01


In the site-based framework of deriving population models from
first principles (e.g., Sumpter and Broomhead, 2001),
individuals first settle randomly into sites, and therefore the
number of individuals in a site follows a Poisson distribution.
The reproductive success of individuals depends on the number
of individuals in their site. For example, in pure contest
competition, one individual is chosen for reproduction and has
b offspring, whereas in pure scramble competition
reproduction (resulting in b offspring) is possible only in
sites of size 1. All newborn individuals emigrate and
constitute the population in the next time-step. This framework
has been used as a mechanistic underpinning for various
discrete-time population models, such as the Skellam (contest
competition) and Ricker (scramble competition) models
(Brännström and Sumpter, 2005).

The settlement of individuals into sites is not necessarily random. Nonaka et al. (2013) assumed that individuals' preference of sites is a linear function of the number of individuals present in the site, and investigated how the coefficient of the linear function evolves by natural selection. Here we take a more mechanistic approach, and assume that all individuals encounter sites at random, and can then decide whether or not to settle in that site, or continue searching. The strategy of an individual is thus a vector consisting of probabilities to settle in an encountered site occupied by different number of individuals. We use adaptive
dynamics (e.g. Geritz et al 1998) to investigate how the vector-valued site-selection strategy evolves, and observe that it can
evolve to an evolutionarily singular, uninvadable strategy. We investigate how such a strategy depends on model parameters. In a specific case, the resulting discrete-time population model can be expressed analytically, which provides a mechanistic underpinning of a new discrete-time population model. Furthermore, we observe that evolutionary suicide (Ferriére 2000, Parvinen 2005) is one potential outcome of the evolutionary dynamics of site-selection.

D.J.T. Sumpter and D.S. Broomhead (2001) Relating individual
behaviour to population dynamics Proc. R. Soc. London B 268,

Å. Brännström and D.J.T. Sumpter (2005) The role of competition
and clustering in population dynamics. Proc. R. Soc. London B
272, 2065-2072

E. Nonaka, K. Parvinen and Å. Brännström (2013)
Evolutionary suicide as a consequence of runaway selection for greater aggregation tendency
J. Theor. Biol 317, 96-104

S.A.H. Geritz, É. Kisdi and G. Meszéna and J. A. J. Metz (1998)
Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree
Evol. Ecol. 12, 35-57

R. Ferriére (2000)
Adaptive responses to environmental threats: evolutionary suicide, insurance, and rescue
Options, IIASA, Laxenburg, Austria (Spring 2000) 12-16

K. Parvinen (2005)
Evolutionary suicide
Acta Biotheoretica 53, 241-264