Effects of correlated interactions in a biological coevolution model with individual-based dynamics

Abstract

Abstract. Models of biological coevolution have recently been proposed and studied, in which a species is defined by a genome in the form of a finite bitstring, and the interactions between species i and j are given by a fixed matrix with independent, randomly distributed elements M ij . A consequence of the stochastic independence is that species whose genotypes differ even by a single bit may have completely different phenotypes, as defined by their interactions with the other species. This is clearly unrealistic, as closely related species should be similar in their interactions with the rest of the ecosystem. Here we therefore study a model, in which the M ij are correlated to a controllable degree by means of a local averaging scheme. We calculate, both analytically and numerically, the correlation function for matrix elements M ij and M kl versus the Hamming distance between the bitstrings representing the species. The agreement between the analytical and numerical calculations is excellent for correlations of limited range, but explainable differences arise for correlation ranges that are a significant fraction of the length of the bitstring. We compare long kinetic Monte Carlo simulations of coevolution models with uncorrelated and correlated interactions, respectively. In particular, we consider the probability density for the lifetimes of individual species. The species-lifetime distribution is close to a power law with an exponent near −2 over eight decades in time in both uncorrelated and correlated cases. The durations of quasi-steady states and power spectral densities for the diversity indices display noticeable differences. However, some qualitative features, like 1/f behaviour in power spectral densities for the diversity indices, are not affected by the correlations in the interaction matrix.

Effects of evolutionary changes in prey use on the relationship between food web complexity and stability

“…Some evolutionary food web models have described speciation and extinction processes (e.g., Caldarelli et al 1998;Drossel et al 2001Drossel et al , 2004Quince et al 2005;Rossberg et al 2008), but did not assume evolutionary processes within the population. A number of recent studies have used individual-based models or simulations of digital organisms to examine the evolution of complex food webs (e.g., Christensen et al 2002;Anderson and Jensen 2005;Sevim and Rikvold 2005;Bell 2007;Laird and Jensen 2007;Rikvold 2007). These models incorporated population genetics processes, but most of the models (e.g., Anderson and Jensen 2005;Sevim and Rikvold 2005;Bell 2007;Laird and Jensen 2007;Rikvold 2007) assumed asexual reproduction, and thus could not represent sexually reproducing species whose gene frequencies change via population genetics processes.…”

“…In several studies, quantitative genetic models have been used (e.g., Yamauchi and Yamamura 2005), but these models assumed fixed genetic variances and did not reproduce the patterns predicted by more mechanistic models that assumed explicit multilocus trait determination (Nuismer and Doebeli 2004). A number of recent studies have incorporated individual-based models or simulations of digital organisms to examine the evolution of complex food webs (e.g., Christensen et al 2002;Anderson and Jensen 2005;Sevim and Rikvold 2005;Bell 2007;Laird and Jensen 2007;Rikvold 2007). These models included population genetics processes; however, most (e.g., Anderson and Jensen 2005;Sevim and Rikvold 2005;Bell 2007;Laird and Jensen 2007;Rikvold 2007) assumed asexual reproduction, in which the definitions of species are arbitrary and the change of gene frequencies within a species cannot be represented.…”

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

“…The tanglednature model is an individual-based model, originally introduced by Hall and co-workers [17] and later simplified by Rikvold and Zia [20]. In the simplified models [18][19][20][21][22]30], the population evolves stochastically in discrete, non-overlapping generations. In these models, each individual of species I gives rise to F offspring with a reproduction probability P I before it dies.…”

“…Several models to bridge ecological and evolutionary time scales have been suggested, such as the tanglednature model [15][16][17], simplified versions of that model [18][19][20][21][22], the Webworld model [23][24][25][26], the scale-invariant model [27], and others [28,29]. More concretely speaking, these are population dynamics models with additional rules for the introduction and extinction of species.…”

“…However, the model captures the aspect that the number of mutant species accessible from a given community is limited [35]. Models to overcome this problem have also been proposed, and it is confirmed that the phenotypic correlation does not qualitatively alter the long-term fluctuations [21]. Each simulation run was started with a single, randomly chosen species (producer species for Model B) with a population size of 100 individuals.…”