Last modified: 2014-04-01

#### Abstract

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,

925-932

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