Preemptive spatial competition under a reproduction–mortality constraint Andrew Allstadt a , Thomas Caraco a,Ã , G. Korniss b a Department of Biological Sciences, University at Albany, Albany, NY 12222, USA b Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute,110 8th Street, Troy, NY 12180-3590, USA article info Article history: Received 21 August 2008 Received in revised form 23 December 2008 Accepted 17 February 2009 Available online 27 February 2009 Keywords: Invasion analysis Phenotypic evolution Propagation–mortality constraint Spatial competition abstract Spatially structured ecological interactions can shape selection pressures experienced by a population’s different phenotypes. We study spatial competition between phenotypes subject to antagonistic pleiotropy between reproductive effort and mortality rate. The constraint we invoke reflects a previous life-history analysis; the implied dependence indicates that although propagation and mortality rates both vary, their ratio is fixed. We develop a stochastic invasion approximation predicting that phenotypes with higher propagation rates will invade an empty environment (no biotic resistance) faster, despite their higher mortality rate. However, once population density approaches demographic equilibrium, phenotypes with lower mortality are favored, despite their lower propagation rate. We conducted a set of pairwise invasion analyses by simulating an individual-based model of preemptive competition. In each case, the phenotype with the lowest mortality rate and (via antagonistic pleiotropy) the lowest propagation rate qualified as evolutionarily stable among strategies simulated. This result, for a fixed propagation to mortality ratio, suggests that a selective response to spatial competition can extend the time scale of the population’s dynamics, which in turn decelerates phenotypic evolution. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction A number of empirical studies demonstrate neighborhood scaling of competitive effects. The count and species-identity of a sessile organism’s nearest neighbors can directly impact the focal individual’s growth or energy allocation (Benjamin, 1993; Cain et al., 1995; Stoll and Prati, 2001; Purves and Law, 2002; Callaway et al., 2003), indirectly influencing demographic performance. Other studies report direct effects of neighborhood composition on mortality or fecundity (Rees et al., 1996; Miriti, 2006). Interestingly, several analyses addressing spatially detailed inter- actions suggest that the competition is preemptive (Holway, 1998; Arenas et al., 2002; Connolly and Muko, 2003). That is, an occupied location cannot be acquired by an individual of the same or other species (other phenotype) until the current occupant’s mortality opens the location (Platt and Weis, 1985; Yurkonis and Meiners, 2004; Ra ´ cz and Karsai, 2006). Most theories for spatial competition discriminate between exclusion and coexistence of different species (Durett and Levin, 1998; Bolker et al., 2003; Snyder and Chesson, 2003). Within a population, spatially localized competitive interactions can gov- ern the relative abundance of different genotypes (phenotypes) (Ma ´ gori et al., 2005; Wei and Krone, 2005; Caraco et al., 2006; Yasi et al., 2006; Boots and Mealor, 2007); competition between phenotypes drives the population’s evolution. Our study focuses on preemptive competition between phenotypes subject to antagonistic pleiotropy between reproductive effort and mortal- ity; we apply a basic lesson of life-history theory (Emlen, 1984; Stearns, 1992; Roff, 2002) to pairwise spatial competition. We organize the paper as follows. First, we describe an individual-based model for locally structured competition be- tween phenotypes; each phenotype is characterized by a propagation rate and a mortality rate. In the same section, we develop a novel quantitative prediction from a mean-field approximation to our model. Next, we constrain feasible pheno- types according to a life-history invariant analyzed by Charnov (1993); any increase in propagule-production rate (reproductive effort) implies the same proportional increase in mortality rate. In Section 3, we develop a simplified stochastic invasion model invoking local neighborhood densities to predict invasion success. The fourth section reports results drawn from simulation of the individual-based model. The combined analyses predict that selection driven by spatial competition should favor phenotypes with reduced mortality (despite their lower propagation). The Discussion summarizes and generalizes our results. 2. Spatial competition model Our individual-based model envisions different phenotypes competing locally for the same open sites. In most cases, a ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology 0022-5193/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2009.02.012 Ã Corresponding author. Tel.: +1518 442 4343; fax: +1518 442 4767. E-mail addresses: andrew.allstadt01@albany.edu (A. Allstadt), caraco@albany.edu (T. Caraco), korniss@rpi.edu (G. Korniss). Journal of Theoretical Biology 258 (2009) 537–549