Tractable models of ecological assembly.

Ecological assembly is a fundamental and yet poorly understood process. Three main obstacles hinder the development of a theory of assembly, and when these issues are sidestepped by making strong assumptions, one can build an assembly graph in which nodes are ecological communities and edges are invasions shifting their composition. The graph can then be analysed directly, without the need to consider dynamics. To showcase this framework, we build and analyse assembly graphs for the competitive Lotka-Volterra model, showing that in these cases sequential assembly (in which species invade a community one at a time) can reach the same configurations found when starting the system with all species present at different initial conditions. We discuss how our results can advance our understanding of assembly both from an empirical and a theoretical point of view, informing the study of ecological restoration and the design of ecological communities.

Thresholding normally distributed data creates complex networks.

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components, and short average shortest path lengths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple model for correlated relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding the correlated data, even though the underlying data are not "complex." In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe nonvanishing clustering or community structure.

Phenotypic variability promotes diversity and stability in competitive communities.

Intraspecific variation is at the core of evolutionary theory, and yet, from an ecological perspective, we have few robust expectations for how this variation should affect the dynamics of large communities. Here, by adapting an approach from evolutionary game theory, we show that the incorporation of phenotypic variability into competitive networks dramatically alters the dynamics across ecological timescales, stabilising the systems and buffering the communities against demographic perturbations. The beneficial effects of phenotypic variability are strongest when there are substantial differences among phenotypes and when phenotypes are inherited with moderately high fidelity; yet even low levels of variation lead to significant increases in diversity, stability, and robustness. By identifying a simple and ubiquitous stabilising force in competitive communities, this work contributes to our core understanding of how biological diversity is maintained in natural systems.

Reconciling empirical interactions and species coexistence.

Coexistence in ecological communities is governed largely by the nature and intensity of species interactions. Countless studies have proposed methods to infer these interactions from empirical data, yet models parameterised using such data often fail to recover observed coexistence patterns. Here, we propose a method to reconcile empirical parameterisations of community dynamics with species-abundance data, ensuring that the predicted equilibrium is consistent with the observed abundance distribution. To illustrate the approach, we explore two case studies: an experimental freshwater algal community and a long-term time series of displacement in an intertidal community. We demonstrate how our method helps recover observed coexistence patterns, capture the core dynamics of the system, and, in the latter case, predict the impacts of experimental extinctions. Collectively, these results demonstrate an intuitive approach for reconciling observed and empirical data, improving our ability to explore the links between species interactions and coexistence in natural systems.

Coexistence of many species in random ecosystems.

Rich ecosystems harbour thousands of species interacting in tangled networks encompassing predation, mutualism and competition. Such widespread biodiversity is puzzling, because in ecological models it is exceedingly improbable for large communities to stably coexist. One aspect rarely considered in these models, however, is that coexisting species in natural communities are a selected portion of a much larger pool, which has been pruned by population dynamics. Here we compute the distribution of the number of species that can coexist when we start from a pool of species interacting randomly, and show that even in this case we can observe rich, stable communities. Interestingly, our results show that, once stability conditions are met, network structure has very little influence on the level of biodiversity attained. Our results identify the main drivers responsible for widespread coexistence in natural communities, providing a baseline for determining which structural aspects of empirical communities promote or hinder coexistence.

Network spandrels reflect ecological assembly.

Ecological networks that exhibit stable dynamics should theoretically persist longer than those that fluctuate wildly. Thus, network structures which are over-represented in natural systems are often hypothesised to be either a cause or consequence of ecological stability. Rarely considered, however, is that these network structures can also be by-products of the processes that determine how new species attempt to join the community. Using a simulation approach in tandem with key results from random matrix theory, we illustrate how historical assembly mechanisms alter the structure of ecological networks. We demonstrate that different community assembly scenarios can lead to the emergence of structures that are often interpreted as evidence of 'selection for stability'. However, by controlling for the underlying selection pressures, we show that these assembly artefacts-or spandrels-are completely unrelated to stability or selection, and are instead by-products of how new species are introduced into the system. We propose that these network-assembly spandrels are critically overlooked aspects of network theory and stability analysis, and we illustrate how a failure to adequately account for historical assembly can lead to incorrect inference about the causes and consequences of ecological stability.