Effects of dynamics on ecological networks

A potential role for rare species in ecosystem dynamics

The ecological importance of common species for many ecosystem processes and functions is unquestionably due to their high abundance. Yet, the importance of rare species is much less understood. Here we take a theoretical approach, exposing dynamical models of ecological networks to small perturbations, to explore the dynamical importance of rare and common species. We find that both species types contribute to the recovery of communities following generic perturbations (i.e. perturbations affecting all species). Yet, when perturbations are selective (i.e. affects only one species), perturbations to rare species have the most pronounced effect on community stability. We show that this is due to the strong indirect effects induced by perturbations to rare species. Because indirect effects typically set in at longer timescales, our results indicate that the importance of rare species may be easily overlooked and thus underrated. Hence, our study provides a potential ecological motive for the management and protection of rare species.

Potential oscillators and keystone modules in food webs

Food web theory suggests that the placement of a weak interaction is critical such that under some conditions even one well-placed weak interaction can stabilise multiple strong interactions. This theory suggests that complex stable webs may be built from pivotal weak interactions such that the removal of even one to a few keystone interactions can have significant cascading impacts on whole system diversity and structure. However, the connection between weak interactions, derived from the theory of modular food web components, and keystone species, derived from empirical results, is not yet well understood. Here, we develop numerical techniques to detect potential oscillators hidden in complex food webs, and show that, both in random and real food webs, keystone consumer-resource interactions often operate to stabilise them. Alarmingly, this result suggests that nature frequently may be dangerously close to precipitous change with even the loss of one or a few weakly interacting species.

How Do Species Interactions Affect Evolutionary Dynamics Across Whole Communities?

Theories of how species evolve in changing environments mostly consider single species in isolation or pairs of interacting species. Yet all organisms live in diverse communities containing many hundreds of species. This review discusses how species interactions influence the evolution of constituent species across whole communities. When species interactions are weak or inconsistent, evolutionary dynamics should be predictable by factors identified by single-species theory. Stronger species interactions, however, can alter evolutionary outcomes and either dampen or promote evolution of constituent species depending on the number of species and the distribution of interaction strengths across the interaction network. Genetic interactions, such as horizontal gene transfer, might also affect evolutionary outcomes. These evolutionary mechanisms in turn affect whole-community properties, such as the level of ecosystem functioning. Successful management of both ecosystems and focal species requires new understanding of evolutionary interactions across whole communities.

Food web framework for size-structured populations

We synthesise traditional unstructured food webs, allometric body size scaling, trait-based modelling, and physiologically structured modelling to provide a novel and ecologically relevant tool for size-structured food webs. The framework allows food web models to include ontogenetic growth and life-history omnivory at the individual level by resolving the population structure of each species as a size-spectrum. Each species is characterised by the trait 'size at maturation', and all model parameters are made species independent through scaling with individual body size and size at maturation. Parameter values are determined from cross-species analysis of fish communities as life-history omnivory is widespread in aquatic systems, but may be reparameterised for other systems. An ensemble of food webs is generated and the resulting communities are analysed at four levels of organisation: community level, species level, trait level, and individual level. The model may be solved analytically by assuming that the community spectrum follows a power law. The analytical solution provides a baseline expectation of the results of complex food web simulations, and agrees well with the predictions of the full model on biomass distribution as a function of individual size, biomass distribution as a function of size at maturation, and relation between predator-prey mass ratio of preferred and eaten food. The full model additionally predicts the diversity distribution as a function of size at maturation.

Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics

Recently we have introduced a simplified model of ecosystem assembly (Capitán et al., 2009) for which we are able to map out all assembly pathways generated by external invasions in an exact manner. In this paper we provide a deeper analysis of the model, obtaining analytical results and introducing some approximations which allow us to reconstruct the results of our previous work. In particular, we show that the population dynamics equations of a very general class of trophic-level structured food-web have an unique interior equilibrium point which is globally stable. We show analytically that communities found as end states of the assembly process are pyramidal and we find that the equilibrium abundance of any species at any trophic level is approximately inversely proportional to the number of species in that level. We also find that the per capita growth rate of a top predator invading a resident community is key to understand the appearance of complex end states reported in our previous work. The sign of these rates allows us to separate regions in the space of parameters where the end state is either a single community or a complex set containing more than one community. We have also built up analytical approximations to the time evolution of species abundances that allow us to determine, with high accuracy, the sequence of extinctions that an invasion may cause. Finally we apply this analysis to obtain the communities in the end states. To test the accuracy of the transition probability matrix generated by this analytical procedure for the end states, we have compared averages over those sets with those obtained from the graph derived by numerical integration of the Lotka-Volterra equations. The agreement is excellent.

Food-web structure in low- and high-dimensional trophic niche spaces

A question central to modelling and, ultimately, managing food webs concerns the dimensionality of trophic niche space, that is, the number of independent traits relevant for determining consumer-resource links. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval on this line. This phenomenon, called intervality, has been known for 30 years and is widely acknowledged to indicate that trophic niche space is close to one-dimensional. We show that the degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces, provided that the processes of evolutionary diversification and adaptation are taken into account. Contrary to expectations, intervality is least pronounced at intermediate dimensions and steadily improves towards lower- and higher-dimensional trophic niche spaces.

Effects of extinction on food web structures on an evolutionary time scale

Extinction affected food web structure in paleoecosystems. Recent theoretical studies that examined the effects of extinction intensity on food web structure on ecological time scales have considered extinction to involve episodic events, with pre-extinction food webs becoming established without dynamics. However, in terms of the paleontological time scale, food web structures are generated from feedback with repeated extinctions, because extinction frequency is affected by food web structure, and food web structure itself is a product of previous extinctions. We constructed a simulation model of changes in tri-trophic-level food webs to examine how continual extinction events affect food webs on an evolutionary time scale. We showed that under high extinction intensity (1) species diversity, especially that of consumer species, decreased; (2) the total population density at each trophic level decreased, while the densities of individual species increased; and (3) the trophic link density of the food web increased. In contrast to previous models, our results were based on an assumption of long-term food web development and are able to explain overall trends posited by empirical investigations based on fossil records.