The evolution of density-dependent dispersal in a noisy spatial population model A ´ da ´m Kun and Istva ´n Scheuring Kun, A ´ . and Scheuring, I. 2006. The evolution of density-dependent dispersal in a noisy spatial population model.  Oikos 115: 308  320. It iswell-known that dispersal is advantageous in many different ecological situations, e.g. to survive local catastrophes where populations live in spatially and temporally heterogeneous habitats. However, the key question, what kind of dispersal strategy is optimal in a particular situation, has remained unanswered. We studied the evolution of density-dependent dispersal in a coupled map lattice model, where the population dynamics are perturbed by external environmental noise. We used a very flexible dispersal function to enable evolution to select from practically all possible types of monotonous density-dependent dispersal functions. We treated the parameters of the dispersal function as continuously changing phenotypic traits. The evolutionary stable dispersal strategies were investigated by numerical simulations. We pointed out that irrespective of the cost of dispersal and the strength of environmental noise, this strategy leads to a very weak dispersal below a threshold density, and dispersal rate increases in an accelerating manner above this threshold. Decreasing the cost of dispersal increases the skewness of the population density distribution, while increasing the environmental noise causes more pronounced bimodality in this distribution. In case of positive temporal autocorrelation of the environmental noise, there is no dispersal below the threshold, and only low dispersal below it, on the other hand with negative autocorrelation practically all individual disperses above the threshold. We found our results to be in good concordance with empirical observations. A ´ . Kun (kunadam@ludens.elte.hu), Dept of Plant Taxonomy and Ecology, Eo ¨tvo ¨s Lora ´nd Univ., Pa ´zma ´ny P. se ´ta ´ny 1/C, HU-1117 Budapest, Hungary.  I. Scheuring, Dept of Plant Taxonomy and Ecology, Hungarian Academy of Sciences and Eo ¨tvo ¨s Lora ´nd Univ., Pa ´zma ´ny P. se ´ta ´ny 1/C, HU-1117 Budapest, Hungary. Dispersal is one of the most important life-history traits  it influences the dynamics and persistence of popula- tions, the distribution and abundance of species, the level of genetic diversity and community structure (reviewed by Dieckmann et al. 1999, Ferrie `re et al. 2000, Clobert et al. 2001). Dispersal is costly for the individual (Hanski 1998), but it can give evolutionary benefit for several reasons. Dispersal helps avoiding kin competition (Ronce et al. 1998, Gandon and Michalakis 2001, Lambin et al. 2001, Perrin and Goudet 2001) and prevents inbreeding (Hamilton and May 1977, Motro 1991, Gandon and Michalakis 2001, O’Riain and Braude 2001, Perrin and Goudet 2001). Furthermore it can be evolutionary favourable if the environment varies both spatially and temporally (McPeek and Holt 1992); dispersal then helps populations to escape local cata- strophes (Olivieri et al. 1995, Gyllenberg and Metz 2001, Metz and Gyllenberg 2001, Parvinen et al. 2003). To make the model analytically tractable, theoretical investigations of the evolution of dispersal rates gener- ally use two important assumptions. First, it is fre- quently assumed that dispersal is unconditional (i.e. a constant fraction of individuals disperse, regardless of the local population density and/or the environmental Accepted 2 June 2006 Subject Editor: Veijo Kaitala Copyright # OIKOS 2006 ISSN 0030-1299 OIKOS 115: 308  320, 2006 308 OIKOS 115:2 (2006)