Carrying capacity in a heterogeneous environment with habitat connectivity.

A large body of theory predicts that populations diffusing in heterogeneous environments reach higher total size than if non-diffusing, and, paradoxically, higher size than in a corresponding homogeneous environment. However, this theory and its assumptions have not been rigorously tested. Here, we extended previous theory to include exploitable resources, proving qualitatively novel results, which we tested experimentally using spatially diffusing laboratory populations of yeast. Consistent with previous theory, we predicted and experimentally observed that spatial diffusion increased total equilibrium population abundance in heterogeneous environments, with the effect size depending on the relationship between r and K. Refuting previous theory, however, we discovered that homogeneously distributed resources support higher total carrying capacity than heterogeneously distributed resources, even with species diffusion. Our results provide rigorous experimental tests of new and old theory, demonstrating how the traditional notion of carrying capacity is ambiguous for populations diffusing in spatially heterogeneous environments.

Negative plant-soil feedback predicts tree-species relative abundance in a tropical forest.

The accumulation of species-specific enemies around adults is hypothesized to maintain plant diversity by limiting the recruitment of conspecific seedlings relative to heterospecific seedlings. Although previous studies in forested ecosystems have documented patterns consistent with the process of negative feedback, these studies are unable to address which classes of enemies (for example, pathogens, invertebrates, mammals) exhibit species-specific effects strong enough to generate negative feedback, and whether negative feedback at the level of the individual tree is sufficient to influence community-wide forest composition. Here we use fully reciprocal shade-house and field experiments to test whether the performance of conspecific tree seedlings (relative to heterospecific seedlings) is reduced when grown in the presence of enemies associated with adult trees. Both experiments provide strong evidence for negative plant-soil feedback mediated by soil biota. In contrast, above-ground enemies (mammals, foliar herbivores and foliar pathogens) contributed little to negative feedback observed in the field. In both experiments, we found that tree species that showed stronger negative feedback were less common as adults in the forest community, indicating that susceptibility to soil biota may determine species relative abundance in these tropical forests. Finally, our simulation models confirm that the strength of local negative feedback that we measured is sufficient to produce the observed community-wide patterns in tree-species relative abundance. Our findings indicate that plant-soil feedback is an important mechanism that can maintain species diversity and explain patterns of tree-species relative abundance in tropical forests.

Plant-soil feedbacks promote coexistence and resilience in multi-species communities.

Both ecological theory and empirical evidence suggest that negative frequency dependent feedbacks structure plant communities, but integration of these findings has been limited. Here we develop a generic model of frequency dependent feedback to analyze coexistence and invasibility in random theoretical and real communities for which frequency dependence through plant-soil feedbacks (PSFs) was determined empirically. We investigated community stability and invasibility by means of mechanistic analysis of invasion conditions and numerical simulations. We found that communities fall along a spectrum of coexistence types ranging from strict pair-wise negative feedback to strict intransitive networks. Intermediate community structures characterized by partial intransitivity may feature "keystone competitors" which disproportionately influence community stability. Real communities were characterized by stronger negative feedback and higher robustness to species loss than randomly assembled communities. Partial intransitivity became increasingly likely in more diverse communities. The results presented here theoretically explain why more diverse communities are characterized by stronger negative frequency dependent feedbacks, a pattern previously encountered in observational studies. Natural communities are more likely to be maintained by strict negative plant-soil feedback than expected by chance, but our results also show that community stability often depends on partial intransitivity. These results suggest that plant-soil feedbacks can facilitate coexistence in multi-species communities, but that these feedbacks may also initiate cascading effects on community diversity following from single-species loss.

Frequency-dependent feedback constrains plant community coexistence.

Ecological theory suggests that coexistence of many species within communities requires negative frequency-dependent feedbacks to prevent exclusion of the least fit species. For plant communities, empirical evidence of negative frequency dependence driving species coexistence and diversity patterns is rapidly accumulating, but connecting these findings to theory has been difficult as corresponding theoretical frameworks only consider small numbers of species. Here, we show how frequency-dependent feedback constrains community coexistence, regardless of the number of species and inherent fitness inequalities between them. Any interaction network can be characterized by a single community interaction coefficient, IC, which determines whether community-level feedback is positive or negative. Negative feedback is a necessary (but not sufficient) condition for persistence of the entire community. Even in cases where the coexistence equilibrium state cannot recover from perturbations, IC < 0 can enable species persistence via cyclic succession. The number of coexisting species is predicted to increase with the average strength of negative feedback. This prediction is supported by patterns of tree species diversity in more than 200,000 deciduous forest plots in the eastern United States, which can be reproduced in simulations that span the observed range of community feedback. By providing a quantitative metric for the strength of negative feedback needed for coexistence, we can now integrate theory and empirical data to test whether observed feedback-diversity correlations are strong enough to infer causality.

Coexistence and relative abundance in plant communities are determined by feedbacks when the scale of feedback and dispersal is local.

1. Negative plant-soil feedback occurs when the presence of an individual of a particular species at a particular site decreases the relative success of individuals of the same species compared to those other species at that site. This effect favors heterospecifics thereby facilitating coexistence and maintaining diversity. Empirical work has demonstrated that the average strengths of these feedbacks correlate with the relative abundance of species within a community, suggesting that feedbacks are an important driver of plant community composition. Understanding what factors contribute to the generation of this relationship is necessary for diagnosing the dynamic forces that maintain diversity in plant communities. 2. We used a spatially explicit, individual-based computer simulation to test the effects of dispersal distance, the size of feedback neighbourhoods, the strength of pairwise feedbacks and community wide variation of feedbacks, community richness, as well as life-history differences on the dependence of relative abundance on strength of feedback. 3. We found a positive dependence of relative abundance of a species on its average feedback for local scale dispersal and feedback. However, we found that the strength of this dependence decreased as either the spatial scale of dispersal and/or the spatial scale of feedback increased. We also found that for spatially local (i.e. relatively small) scale interaction and dispersal, as the mean strength of feedbacks in the community becomes less negative, the greater the increase in abundance produced by a comparable increase in species-specific average feedback. We found that life-history differences such as mortality rate did not generate a pattern with abundance, nor did they affect the relationship between abundance and average feedback. 4.Synthesis. Our results support the claim that empirical observations of a positive correlation between relative abundance and strength of average feedback serves as evidence that local scale negative feedbacks play a prominent role in structuring plant communities. We also identify that this relationship depends upon local scale plant dispersal and feedback which generates clumping and magnifies the negative feedbacks.

Spatial population expansion promotes the evolution of cooperation in an experimental Prisoner's Dilemma.

Cooperation is ubiquitous in nature, but explaining its existence remains a central interdisciplinary challenge. Cooperation is most difficult to explain in the Prisoner's Dilemma game, where cooperators always lose in direct competition with defectors despite increasing mean fitness. Here we demonstrate how spatial population expansion, a widespread natural phenomenon, promotes the evolution of cooperation. We engineer an experimental Prisoner's Dilemma game in the budding yeast Saccharomyces cerevisiae to show that, despite losing to defectors in nonexpanding conditions, cooperators increase in frequency in spatially expanding populations. Fluorescently labeled colonies show genetic demixing of cooperators and defectors, followed by increase in cooperator frequency as cooperator sectors overtake neighboring defector sectors. Together with lattice-based spatial simulations, our results suggest that spatial population expansion drives the evolution of cooperation by (1) increasing positive genetic assortment at population frontiers and (2) selecting for phenotypes maximizing local deme productivity. Spatial expansion thus creates a selective force whereby cooperator-enriched demes overtake neighboring defector-enriched demes in a "survival of the fastest." We conclude that colony growth alone can promote cooperation and prevent defection in microbes. Our results extend to other species with spatially restricted dispersal undergoing range expansion, including pathogens, invasive species, and humans.