Theoretical Population Biology 85 (2013) 26–37 Contents lists available at SciVerse ScienceDirect Theoretical Population Biology journal homepage: www.elsevier.com/locate/tpb Caught in the middle: Asymmetric competition causes high variance in intermediate trait abundances Edwin van Leeuwen a,∗ , Rampal S. Etienne b a School of Biological Sciences, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK b Community and Conservation Ecology group, Centre for Ecological and Evolutionary Studies, University of Groningen, Box 11103, 9700 CC Groningen, The Netherlands article info Article history: Received 21 March 2012 Available online 8 February 2013 Keywords: Asymmetric competition Temporal variance Evolution Plant height Stochasticity Adaptive dynamics abstract In asymmetric competition between two individuals of the same or different species, one individual has a distinct advantage over the other due to a particular beneficial trait. An important trait that induces asymmetric competition is size (body size in animals, height in plants). There is usually a trade- off between fecundity and the trait that leads to competitive superiority (e.g. seed number vs seed size), enabling coexistence of populations with different trait values. These predictions on coexistence are based on classic deterministic models. Here, we explore the behaviour of a stochastic model of asymmetric competition where stochasticity is assumed to be demographic. We derive approximations for the temporal variance and covariance of the population sizes of the coexisting species. The derivations highlight that the variability of the population size of a species strongly depends on the stochastic fluctuations of species with higher trait values, while they are less influenced by species with lower trait values. Particularly, species with intermediate trait values are strongly affected resulting in relatively high variability. As a result these species have a relative high probability of extinction even though they have a larger population size than species with high trait values. We confirm these approximations with individual-based simulations. Thus, our analysis can explain gaps in size distributions as an emergent property of systems with a fecundity–competition trade-off. © 2013 Elsevier Inc. All rights reserved. 1. Introduction In nature, competition between organisms is often asymmet- ric, such that one organism has a distinct advantage over the other. Common examples of such interactions are interference competi- tion in animals, where the larger individual wins (Clutton-Brock and Albon, 1979; Clutton-Brock et al., 1979; Spiller, 1986; Car- roll and Salamon, 1995; Luiselli, 1996; Mitani et al., 1996; Mugabo et al., 2010; Nakayama and Fuiman, 2010) or scramble competition in plants, where taller individuals capture more light than smaller ones (Weiner, 1986; Weiner and Thomas, 1986; Weiner, 1990; Weiner and Damgaard, 2006). Furthermore asymmetric compe- tition is common in both interspecific (Connell, 1983; Schoener, 1983; Alatalo and Moreno, 1987; Dickman, 1988; Englund et al., 1992; Thompson and Fox, 1993) and intraspecific competition (Connell, 1983; Mugabo et al., 2010; Nakayama and Fuiman, 2010) and, thus, affects not only interactions within species, but also be- tween species. ∗ Corresponding author. E-mail address: edwinvanl@gmail.com (E. van Leeuwen). Predictions of theoretical studies on asymmetric competition include run-away evolution, where organisms evolve higher and higher trait values (e.g. height or bodymass) as a result of the competitive advantage (Maynard Smith and Brown, 1986; Abrams and Matsuda, 1994). The tendency to increase in size due to competitive advantage is also known as Cope’s rule (Cope, 1896; Hone and Benton, 2005). Run-away evolution can be prevented, however, if a trade-off exists such that high trait values are also associated with a disadvantage, such as high costs or lower fecundity (Parker, 1983; Abrams and Matsuda, 1994; Law et al., 1997; Kisdi, 1999; Jansen and Mulder, 1999; Bonsall et al., 2004). Asymmetric competition can then lead to an evolutionarily singular community, with one or more coexisting trait values. Kisdi (1999) showed, using adaptive dynamics (Metz et al., 1992; Geritz et al., 1997, 2004), that these evolutionarily singular communities are reachable through small mutational steps, i.e. a single species can evolve into multiple distinct, coexisting species. Two forms of asymmetric competition are usually distin- guished. In the first form, the competition kernel is skewed such that two organisms with similar trait values experience more com- petition than organisms with highly different trait values (Rum- mel and Roughgarden, 1985; Brown and Vincent, 1987; Taper and Case, 1992). This type of competition is to be expected when the 0040-5809/$ – see front matter © 2013 Elsevier Inc. All rights reserved. doi:10.1016/j.tpb.2013.01.008