Eco-evolutionary Model of Rapid Phenotypic Diversification in Species-Rich Communities

Abstract

Evolutionary and ecosystem dynamics are often treated as different processes -operating at separate timescales- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field experiment has explicitly shown that communities of competing plant species can experience very fast phenotypic diversification, and that this gives rise to enhanced complementarity in resource exploitation and to enlarged ecosystem-level productivity. Here, we build on progress made in recent years in the integration of eco-evolutionary dynamics, and present a computational approach aimed at describing these empirical findings in detail. In particular we model a community of organisms of different but similar species evolving in time through mechanisms of birth, competition, sexual reproduction, descent with modification, and death. Based on simple rules, this model provides a rationalization for the emergence of rapid phenotypic diversification in species-rich communities. Furthermore, it also leads to non-trivial predictions about long-term phenotypic change and ecological interactions. Our results illustrate that the presence of highly specialized, non-competing species leads to very stable communities and reveals that phenotypically equivalent species occupying the same niche may emerge and coexist for very long times. Thus, the framework presented here provides a simple approach -complementing existing theories, but specifically devised to account for the specificities of the recent empirical findings for plant communities- to explain the collective emergence of diversification at a community level, and paves the way to further scrutinize the intimate entanglement of ecological and evolutionary processes, especially in species-rich communities.

Fig 1. (Color online) Sketch of the model.

(A) Individuals of different species (different colors) compete for available resources in a physical space (two-dimensional square lattice), which is assumed to be saturated at all times. Each individual is equipped with a set of phenotypic traits that corresponds to a single point in the trade-off space. This is represented here (as a specific example) as an equilateral triangle (a “simplex” in mathematical terms) corresponding to the case of 3 coordinates which add up to 1 (e.g., fraction of the total biomass devoted to roots, leaves/stems and flowers, respectively [41]). For instance, a point close to vertex T¹ exploits better the limiting resource 1 (e.g. soil nutrients) than another one near vertex T², but is less efficient at exploiting resource 2 (e.g. light) than this latter one (see Methods). (B) Individuals die after one timestep, giving rise to empty sites; each of these is occupied by an offspring from a “mother” within its local neighborhood (consisting of 8 sites in the sketch for clarity, although we considered also a second shell of neighbors in the simulations, i.e. a kernel of 24 sites). The mother is randomly selected from the plants occupying this neighborhood in the previous generation, with a probability that decreases with the level of similarity/competition with its neighbors (see Methods). The implanted seed is assumed to have been fertilized by a conspecific “father” from any arbitrary random location, selected also with a competition-level dependent probability. The offspring inherits its phenotype from both parents; its traits can lie at any point (in the shaded region of the figure) nearby the the parental ones, allowing for some variation. For a given number of initial species S, two key parameters control the final outcome of the dynamics: β, characterizing the overall level of competition, and μ, representing the variability of inherited traits. We fix most of the parameters in the model (lattice size, individuals within the competition/reproduction kernel, etc.) and study the dependence on S, β and μ.

Fig 2. (Color online) Illustration of the emergence of rapid phenotypic diversification for a computational system of size 64 × 64 and 16 species (labeled with different colors).

(Top).Phenotypic diagrams measured at different evolution stages (1, 3, 10 and 100 generations, respectively) for different values of the two parameters: level of competition β (1 for the case of low competition and 10 for strong competition) and variation in inherited traits μ (0.1 for large variation and 0.025 for small variation). In all cases, phenotypic differentiation among species is evident even after only 10 generations. In the long term (100 generations) species diversification and specialization is most evident for small μ and large β; in this last case, different species (colors) can coexist for large times in the same region/corner of trade-off space. (Central). Complementarity diagrams representing the values of averaged local complementarity for all individuals of any species for small μ (0.025) and large β (10). Individuals with small complementarity (i.e. under strong competition with neighbors) disappear in the evolutionary process, while communities with high degrees of local complementarity are rapidly selected. (Bottom). Spatial distribution of species for different number of generations. As a result of the eco-evolutionary dynamics, anti-correlated patterns –in which neighboring plants tend to be different– emerge (note that colors represent species assignment and do not reflect phenotypic values).

Fig 3. (Color online) Measurements of different biodiversity indices.

(A)Phenotypic distances among species grow systematically during the eco-evolutionary process, reflecting a clear tendency towards species differentiation (same sets of parameter values as in Fig 2, S = 16). Differentiation is faster for relatively small values of trait variability μ and large values of the competitive stress β. (B) Phenotypic differentiation among and within species. While interspecies distances grow in time for all values of S and converge to similar values on the long term, intraspecific phenotypic variability is much larger on the long term for monocultures than for biodiverse mixtures. (C) Phenotypic similarity among close neighbors. Moran’s index (I) for β = 10 and different values of S as well as for β = 0 and for a random distribution (i.e. in the absence of spatial interactions). The value of I tends to 0 for random distributions, is positive for β = 0, and tends to small negative values for β ≠ 0. Whenever competition depends on the phenotypic values (i.e., β > 0) the system avoids close cohabitation of individuals of the same species. This negative spatial autocorrelation results in I < 0; in all cases, μ = 0.025. (D) Averaged local and relative complementarity in the community increase with time and reach larger values for more biodiverse communities. The phenotypic differentiation among individuals is greater both among close neighbors and at the global scale as the number os species S increases. In all plots, parameters are L = 64 and, unless it is specified, β = 10 and μ = 0.025; curves are averaged over at least 10³ runs; shaded light grey areas stand for times during which extinction tends to occur causing S to decrease (see S10 Appendix in S1 Text for details), while in dark grey ones the system tend to stabilize at a given final number of species.