A central model in theoretical ecology considers the competition of a range of species for a broad spectrum of resources. Recent studies have shown that essentially two different outcomes are possible. Either the species surviving competition are more or less uniformly distributed over the resource spectrum, or their distribution is “lumped” (or “clumped”), consisting of clusters of species with similar resource use that are separated by gaps in resource space. Which of these outcomes will occur crucially depends on the competition kernel, which reflects the shape of the resource utilization pattern of the competing species. Most models considered in the literature assume a Gaussian competition kernel. This is unfortunate, since predictions based on such a Gaussian assumption are not robust. In fact, Gaussian kernels are a border case scenario, and slight deviations from this function can lead to either uniform or lumped species distributions. Here, we illustrate the non-robustness of the Gaussian assumption by simulating different implementations of the standard competition model with constant carrying capacity. In this scenario, lumped species distributions can come about by secondary ecological or evolutionary mechanisms or by details of the numerical implementation of the model. We analyze the origin of this sensitivity and discuss it in the context of recent applications of the model.
Competitive exclusion Gaussian kernel Clumped distribution Niche model Lotka–Volterra
This is a preview of subscription content, log in to check access.
C.L. and E.H-G. acknowledge support from project FISICOS (FIS2007-60327) of MEC and FEDER and NEST-Complexity project PATRES (043268). K.H.A was supported by the Danish research council, grant no. 272-07-0485
Ackermann M, Doebeli M (2004) Evolution of niche width and adaptive diversification. Evolution 58(12):2599-2612PubMedGoogle Scholar
Baptestini EM, De Aguiar MAM, Bolnick DI, Araújo MS (2009) The shape of the competitition and carrying capacity kernels affects the likelihood of disruptive selection. J Theor Biol. doi:10.1016/j.tbi.2009.02.023PubMedGoogle Scholar
Barabás G, Meszéna G (2009) When the exception becomes the rule: the disappearance of limiting similarity in the LotkaVolterra model. J Theor Biol 258(1):89–94CrossRefPubMedGoogle Scholar
Case TJ (1981) Niche packing and coevolution in competition communities. Proc Natl Acad Sci U S A 78(8):5021–5025CrossRefPubMedGoogle Scholar
Chesson P, Kuang JJ (2008) The interaction between predation and competition. Nature (456):235–238Google Scholar
Doebeli M, Dieckmann U (2000) Evolutionary branching and sympatric speciation caused by different types of ecological interactions. Am Nat 156(4):77–101CrossRefGoogle Scholar
Doebeli M, Blok HJ, Leimar O, Dieckmann U (2007) Multimodal pattern formation in phenotype distributions of sexual populations. Proc R Soc Lond B 274(1608):347–357CrossRefGoogle Scholar
Haccou P, Iwasa Y (1995) Optimal mixed strategies in stochastic environments. Theor Popul Biol 47:212–243CrossRefGoogle Scholar
Hernández-García E, Pigolotti S, Lopez C, Andersen KH (2009) Species competition: coexistence, exclusion and clustering. Phil Trans R Soc A 367:3183–3195CrossRefPubMedGoogle Scholar
Johansson J, Ripa J (2006) Will sympatric speciation fail due to stochastic competitive exclusion? Am Nat 168(4):572–578CrossRefPubMedGoogle Scholar
Kubo T, Iwasa Y (1996) Phenological pattern of tree regeneration in a model for forest species diversity. Theor Popul Biol 49:90–117CrossRefGoogle Scholar
Lawson DJ, Jensen HJ (2007) Neutral evolution in a biological population as diffusion in phenotype space: reproduction with local mutation but without selection. Phys Rev Lett 98:098102CrossRefGoogle Scholar