Structure and Stability of Ecological Networks : The role of dynamic dimensionality and species variability in resource use

Abstract: The main focus of this thesis is on the response of ecological communities to environmental variability and species loss. My approach is theoretical; I use mathematical models of networks where species population dynamics are described by ordinary differential equations. A common theme of the papers in my thesis is variation – variable link structure (Paper I) and within-species variation in resource use (Paper III and IV). To explore how such variation affect the stability of ecological communities in variable environments, I use numerical methods evaluating for example community persistence (the proportion of species surviving over time; Paper I, II and IV). I also develop a new method for quantifying the dynamical dimensionality of an ecological community and investigate its effect on community persistence in stochastic environments (Paper II). Moreover, if we are to gain trustworthy model output, it is of course of major importance to create study systems that reflect the structures of natural systems. To this end, I also study highly resolved, individual based empirical food web data sets (Paper III, IV).In Paper I, the effects of adaptive rewiring induced by resource loss on the persistence of ecological networks is investigated. Loss of one species in an ecosystem can trigger extinctions of other dependent species. For instance, specialist predators will go extinct following the loss of their only prey unless they can change their diet. It has therefore been suggested that an ability of consumers to rewire to novel prey should mitigate the consequences of species loss by reducing the risk of cascading extinction. Using a new modelling approach on natural and computer-generated food webs I find that, on the contrary, rewiring often aggravates the effects of species loss. This is because rewiring can lead to overexploitation of resources, which eventually causes extinction cascades. Such a scenario is particularly likely if prey species cannot escape predation when rare and if predators are efficient in exploiting novel prey. Indeed, rewiring is a two-edged sword; it might be advantageous for individual predators in the short term, yet harmful for long-term system persistence.The persistence of an ecological community in a variable world depends on the strength of environmental variation pushing the community away from equilibrium compared to the strength of the deterministic feedbacks, caused by interactions among and within species, pulling the community towards the equilibrium. However, it is not clear which characteristics of a community that promote its persistence in a variable world. In Paper II, using a modelling approach on natural and computer-generated food webs, I show that community persistence is strongly and positively related to its dynamic dimensionality (DD), as measured by the inverse participation ratio (IPR) of the real part of the eigenvalues of the community matrix. A high DD means that the real parts of the eigenvalues are of similar magnitude and the system will therefore approach equilibrium from all directions at a similar rate. On the other hand, when DD is low, one of the eigenvalues has a large magnitude of the real part compared to  the others and the deterministic forces pulling the system towards  equilibrium is therefore weak in many directions compared to the stochastic forces pushing the system away from the equilibrium. As a consequence the risk of crossing extinction thresholds and boundaries separating basins of attractions increases, and hence persistence decreases, as DD decreases. Given the forecasted increase in climate variability caused by global warming, Paper II suggests that the dynamic dimensionality of ecological systems is likely to become an increasingly important property for their persistence.In Paper III, I investigate patterns in the size structure of one marine and six running freshwater food webs: that is, how the trophic structure of such ecological networks is governed by the body size of its interacting entities. The data for these food webs are interactions between individuals, including the taxonomic identity and body mass of the prey and the predator. Using these detailed data, I describe how patterns in diet variation and predator variation scales with the body mass of predators or prey, using both a species- and a size-class-based approach. I also compare patterns of size structure derived from analysis of individual-based data with those patterns that result when data are aggregated into species (or size class-based) averages. This comparison shows that analysis based on species averaging can obscure interesting patterns in the size structure of ecological communities. For example, I find that the strength of the relationship between prey body mass and predator body mass is consistently underestimated when species averages are used instead of the individual level data. In some cases, no relationship is found when species averages are used, but when individual-level data are used instead, clear and significant patterns are revealed. These results have potentially important implications for parameterisation of models of ecological communities and hence for predictions concerning their dynamics and response to different kinds of disturbances.Paper IV continues the analysis of the highly resolved individual-based empirical data set used in Paper III and investigates patterns and effects of within- and between species resource specialisation in ecological communities. Within-species size variation can be considerable. For instance, in fishes and reptiles, where growth is continuous, individuals pass through a wide spectrum of sizes, possibly more than four orders of magnitude, during the independent part of their life cycle. Given that the size of an organism is correlated with many of its fundamental ecological properties, it should come as no surprise that an individual’s size affects the type of prey it can consume and what predators will attack it (Paper III). In Paper IV, I quantify within- and between species differences in predator species’ prey preferences in natural food webs and subsequently explore its consequences for dynamical dimensionality (Paper II) and community stability in stage structured food web models. Among the natural food webs there are webs where species overlap widely in their resource use while the resource use of size-classes within species differs. There are also webs where differences in resource use among species is relatively large and the niches of sizeclasses within species are more similar. Model systems with the former structure are found to have low dynamical dimensionality and to be less stable compared to systems with the latter structure. Thus, although differential resource use among individuals within a species is likely to decrease the intensity of intraspecific competition and favor individuals specializing on less exploited resources it can destabilize the community in which the individuals are embedded.