Self-organised pattern formation increases local diversity in metacommunities.

Self-organised formation of spatial patterns is known from a variety of different ecosystems, yet little is known about how these patterns affect the diversity of communities. Here, we use a food chain model in which autotroph diversity is described by a continuous distribution of a trait that affects both growth and defence against heterotrophs. On isolated patches, diversity is always lost over time due to stabilising selection, and the local communities settle on one of two alternative stable community states that are characterised by a dominance of either defended or undefended species. In a metacommunity context, dispersal can destabilise these states and complex spatio-temporal patterns in the species' abundances emerge. The resulting biomass-trait feedback increases local diversity by an order of magnitude compared to scenarios without self-organised pattern formation, thereby maintaining the ability of communities to adapt to potential future changes in biotic or abiotic environmental conditions.

Top predators govern multitrophic diversity effects in tritrophic food webs.

It is well known that functional diversity strongly affects ecosystem functioning. However, even in rather simple model communities consisting of only two or, at best, three trophic levels, the relationship between multitrophic functional diversity and ecosystem functioning appears difficult to generalize, because of its high contextuality. In this study, we considered several differently structured tritrophic food webs, in which the amount of functional diversity was varied independently on each trophic level. To achieve generalizable results, largely independent of parametrization, we examined the outcomes of 128,000 parameter combinations sampled from ecologically plausible intervals, with each tested for 200 randomly sampled initial conditions. Analysis of our data was done by training a random forest model. This method enables the identification of complex patterns in the data through partial dependence graphs, and the comparison of the relative influence of model parameters, including the degree of diversity, on food-web properties. We found that bottom-up and top-down effects cascade simultaneously throughout the food web, intimately linking the effects of functional diversity of any trophic level to the amount of diversity of other trophic levels, which may explain the difficulty in unifying results from previous studies. Strikingly, only with high diversity throughout the whole food web, different interactions synergize to ensure efficient exploitation of the available nutrients and efficient biomass transfer to higher trophic levels, ultimately leading to a high biomass and production on the top level. The temporal variation of biomass showed a more complex pattern with increasing multitrophic diversity: while the system initially became less variable, eventually the temporal variation rose again because of the increasingly complex dynamical patterns. Importantly, top predator diversity and food-web parameters affecting the top trophic level were of highest importance to determine the biomass and temporal variability of any trophic level. Overall, our study reveals that the mechanisms by which diversity influences ecosystem functioning are affected by every part of the food web, hampering the extrapolation of insights from simple monotrophic or bitrophic systems to complex natural food webs.

Modern models of trophic meta-communities.

Dispersal and foodweb dynamics have long been studied in separate models. However, over the past decades, it has become abundantly clear that there are intricate interactions between local dynamics and spatial patterns. Trophic meta-communities, i.e. meta-foodwebs, are very complex systems that exhibit complex and often counterintuitive dynamics. Over the past decade, a broad range of modelling approaches have been used to study these systems. In this paper, we review these approaches and the insights that they have revealed. We focus particularly on recent papers that study trophic interactions in spatially extensive settings and highlight the common themes that emerged in different models. There is overwhelming evidence that dispersal (and particularly intermediate levels of dispersal) benefits the maintenance of biodiversity in several different ways. Moreover, some insights have been gained into the effect of different habitat topologies, but these results also show that the exact relationships are much more complex than previously thought, highlighting the need for further research in this area. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

Non-trophic interactions strengthen the diversity-functioning relationship in an ecological bioenergetic network model.

Ecological communities are undeniably diverse, both in terms of the species that compose them as well as the type of interactions that link species to each other. Despite this long recognition of the coexistence of multiple interaction types in nature, little is known about the consequences of this diversity for community functioning. In the ongoing context of global change and increasing species extinction rates, it seems crucial to improve our understanding of the drivers of the relationship between species diversity and ecosystem functioning. Here, using a multispecies dynamical model of ecological communities including various interaction types (e.g. competition for space, predator interference, recruitment facilitation in addition to feeding), we studied the role of the presence and the intensity of these interactions for species diversity, community functioning (biomass and production) and the relationship between diversity and functioning.Taken jointly, the diverse interactions have significant effects on species diversity, whose amplitude and sign depend on the type of interactions involved and their relative abundance. They however consistently increase the slope of the relationship between diversity and functioning, suggesting that species losses might have stronger effects on community functioning than expected when ignoring the diversity of interaction types and focusing on feeding interactions only.

The biggest losers: habitat isolation deconstructs complex food webs from top to bottom.

Habitat fragmentation threatens global biodiversity. To date, there is only limited understanding of how the different aspects of habitat fragmentation (habitat loss, number of fragments and isolation) affect species diversity within complex ecological networks such as food webs. Here, we present a dynamic and spatially explicit food web model which integrates complex food web dynamics at the local scale and species-specific dispersal dynamics at the landscape scale, allowing us to study the interplay of local and spatial processes in metacommunities. We here explore how the number of habitat patches, i.e. the number of fragments, and an increase of habitat isolation affect the species diversity patterns of complex food webs (α-, ß-, γ-diversities). We specifically test whether there is a trophic dependency in the effect of these two factors on species diversity. In our model, habitat isolation is the main driver causing species loss and diversity decline. Our results emphasize that large-bodied consumer species at high trophic positions go extinct faster than smaller species at lower trophic levels, despite being superior dispersers that connect fragmented landscapes better. We attribute the loss of top species to a combined effect of higher biomass loss during dispersal with increasing habitat isolation in general, and the associated energy limitation in highly fragmented landscapes, preventing higher trophic levels to persist. To maintain trophic-complex and species-rich communities calls for effective conservation planning which considers the interdependence of trophic and spatial dynamics as well as the spatial context of a landscape and its energy availability.

The effects of functional diversity on biomass production, variability, and resilience of ecosystem functions in a tritrophic system.

Diverse communities can adjust their trait composition to altered environmental conditions, which may strongly influence their dynamics. Previous studies of trait-based models mainly considered only one or two trophic levels, whereas most natural system are at least tritrophic. Therefore, we investigated how the addition of trait variation to each trophic level influences population and community dynamics in a tritrophic model. Examining the phase relationships between species of adjacent trophic levels informs about the strength of top-down or bottom-up control in non-steady-state situations. Phase relationships within a trophic level highlight compensatory dynamical patterns between functionally different species, which are responsible for dampening the community temporal variability. Furthermore, even without trait variation, our tritrophic model always exhibits regions with two alternative states with either weak or strong nutrient exploitation, and correspondingly low or high biomass production at the top level. However, adding trait variation increased the basin of attraction of the high-production state, and decreased the likelihood of a critical transition from the high- to the low-production state with no apparent early warning signals. Hence, our study shows that trait variation enhances resource use efficiency, production, stability, and resilience of entire food webs.

Animal diversity and ecosystem functioning in dynamic food webs.

Species diversity is changing globally and locally, but the complexity of ecological communities hampers a general understanding of the consequences of animal species loss on ecosystem functioning. High animal diversity increases complementarity of herbivores but also increases feeding rates within the consumer guild. Depending on the balance of these counteracting mechanisms, species-rich animal communities may put plants under top-down control or may release them from grazing pressure. Using a dynamic food-web model with body-mass constraints, we simulate ecosystem functions of 20,000 communities of varying animal diversity. We show that diverse animal communities accumulate more biomass and are more exploitative on plants, despite their higher rates of intra-guild predation. However, they do not reduce plant biomass because the communities are composed of larger, and thus energetically more efficient, plant and animal species. This plasticity of community body-size structure reconciles the debate on the consequences of animal species loss for primary productivity.

Interactive effects of warming, eutrophication and size structure: impacts on biodiversity and food-web structure.

Warming and eutrophication are two of the most important global change stressors for natural ecosystems, but their interaction is poorly understood. We used a dynamic model of complex, size-structured food webs to assess interactive effects on diversity and network structure. We found antagonistic impacts: Warming increases diversity in eutrophic systems and decreases it in oligotrophic systems. These effects interact with the community size structure: Communities of similarly sized species such as parasitoid-host systems are stabilized by warming and destabilized by eutrophication, whereas the diversity of size-structured predator-prey networks decreases strongly with warming, but decreases only weakly with eutrophication. Nonrandom extinction risks for generalists and specialists lead to higher connectance in networks without size structure and lower connectance in size-structured communities. Overall, our results unravel interactive impacts of warming and eutrophication and suggest that size structure may serve as an important proxy for predicting the community sensitivity to these global change stressors.

Effect of introducing a competitor on cyclic dominance of sockeye salmon.

We study the effects of introducing a competing species into a 3-species model for the population dynamics of sockeye salmon, thereby converting a food chain into a diamond module. We find that this often leads to the disappearance of the 4-year oscillation of sockeye salmon known as cyclic dominance when parameters are chosen such that all four species can coexist. Only when the population size of the competitor is small the phenomenon of cyclic dominance can persist. There is also a large region of parameter space where either the sockeye salmon or the competitor goes extinct. We discuss how these findings can be reconciled with the prevalence of cyclic dominance in many sockeye brood lakes.

Body masses, functional responses and predator-prey stability.

The stability of ecological communities depends strongly on quantitative characteristics of population interactions (type-II vs. type-III functional responses) and the distribution of body masses across species. Until now, these two aspects have almost exclusively been treated separately leaving a substantial gap in our general understanding of food webs. We analysed a large data set of arthropod feeding rates and found that all functional-response parameters depend on the body masses of predator and prey. Thus, we propose generalised functional responses which predict gradual shifts from type-II predation of small predators on equally sized prey to type-III functional-responses of large predators on small prey. Models including these generalised functional responses predict population dynamics and persistence only depending on predator and prey body masses, and we show that these predictions are strongly supported by empirical data on forest soil food webs. These results help unravelling systematic relationships between quantitative population interactions and large-scale community patterns.

The dynamics of food chains under climate change and nutrient enrichment.

Warming has profound effects on biological rates such as metabolism, growth, feeding and death of organisms, eventually affecting their ability to survive. Using a nonlinear bioenergetic population-dynamic model that accounts for temperature and body-mass dependencies of biological rates, we analysed the individual and interactive effects of increasing temperature and nutrient enrichment on the dynamics of a three-species food chain. At low temperatures, warming counteracts the destabilizing effects of enrichment by both bottom-up (via the carrying capacity) and top-down (via biological rates) mechanisms. Together with increasing consumer body masses, warming increases the system tolerance to fertilization. Simultaneously, warming increases the risk of starvation for large species in low-fertility systems. This effect can be counteracted by increased fertilization. In combination, therefore, two main drivers of global change and biodiversity loss can have positive and negative effects on food chain stability. Our model incorporates the most recent empirical data and may thus be used as the basis for more complex forecasting models incorporating food-web structure.

The robustness of cyclic dominance under random fluctuations.

We investigate the influence of random perturbations on a recently introduced three-species model that reproduces the empirically observed pattern of cyclic dominance in Fraser River sockeye salmon. Since the sockeye populations are subject to various types of fluctuations affecting their growth and survival, we investigate the robustness of the model under several types of noise. In particular, we evaluate the variation of population sizes around their values in the deterministic model, the frequency of phase shifts in the 4-year oscillation, the extent of synchronization between different sockeye populations, and the response to strong one-time perturbations. Our main conclusion is that cyclic dominance is very stable even under strong noise in this model.

Complexity-stability relations in generalized food-web models with realistic parameters.

We investigate the relation between complexity and stability in model food webs by evaluating the local stability of fixed points of the population dynamics using the recently developed method of generalized modeling. We first determine general conditions that lead to positive complexity-stability relations. These include (1) high resource abundance and (2) strong density-dependent mortality effects that limit consumer populations. The parameters that constitute a generalized model have clear biological meanings. In this work, emphasis is placed on using realistic values for these generalized parameters. They are derived from conventional ordinary differential equations which are commonly used to describe population dynamics and for which empirical parameter estimates exist. We find that the empirically supported generalized parameters fall in regions of the parameter space that allow for a positive relation between food-web complexity and stability.

Interactive effects of body-size structure and adaptive foraging on food-web stability.

Body-size structure of food webs and adaptive foraging of consumers are two of the dominant concepts of our understanding how natural ecosystems maintain their stability and diversity. The interplay of these two processes, however, is a critically important yet unresolved issue. To fill this gap in our knowledge of ecosystem stability, we investigate dynamic random and niche model food webs to evaluate the proportion of persistent species. We show that stronger body-size structures and faster adaptation stabilise these food webs. Body-size structures yield stabilising configurations of interaction strength distributions across food webs, and adaptive foraging emphasises links to resources closer to the base. Moreover, both mechanisms combined have a cumulative effect. Most importantly, unstructured random webs evolve via adaptive foraging into stable size-structured food webs. This offers a mechanistic explanation of how size structure adaptively emerges in complex food webs, thus building a novel bridge between these two important stabilising mechanisms.

Coexisting patterns of population oscillations: the degenerate Neimark-Sacker bifurcation as a generic mechanism.

We investigate a population dynamics model that exhibits a Neimark-Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period soon becomes locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.

A three-species model explaining cyclic dominance of Pacific salmon.

The four-year oscillations of the number of spawning sockeye salmon (Oncorhynchus nerka) that return to their native stream within the Fraser River basin in Canada are a striking example of population oscillations. The period of the oscillation corresponds to the dominant generation time of these fish. Various-not fully convincing-explanations for these oscillations have been proposed, including stochastic influences, depensatory fishing, or genetic effects. Here, we show that the oscillations can be explained as an attractor of the population dynamics, resulting from a strong resonance near a Neimark Sacker bifurcation. This explains not only the long-term persistence of these oscillations, but also reproduces correctly the empirical sequence of salmon abundance within one period of the oscillations. Furthermore, it explains the observation that these oscillations occur only in sockeye stocks originating from large oligotrophic lakes, and that they are usually not observed in salmon species that have a longer generation time.

Alternative dynamical states in stage-structured consumer populations.

The population dynamics of a consumer population with an internal structure is investigated. The population is divided into juvenile and adult individuals that consume different resources and do not interfere with each other. Over a broad range of external conditions (varying mortality and different resource levels), alternative stable states exist. These population states correspond to domination of juveniles and domination of adults, respectively. When mortality is varied, hysteresis between the alternative states only occurs if juveniles have more resources than adults. In the opposite case the juvenile-dominated state is stable for all values of mortality, but the adult-dominated state is not. When the population is modelled with more than one juvenile stage, the adult-dominated state becomes a periodic orbit due to a delay in the regulatory mechanism of the population dynamics. It is shown numerically that the stage-structured model converges to a model with continuous size structure for very large numbers of successive juvenile stages.

Positive complexity-stability relations in food web models without foraging adaptation.

May's [1972. Will a large complex system be stable? Nature 238, 413-414] local stability analysis of random food web models showed that increasing network complexity leads to decreasing stability, a result that is contradictory to earlier empirical findings. Since this seminal work, research of complexity-stability relations became one of the most challenging issues in theoretical ecology. We investigate conditions for positive complexity-stability relations in the niche, cascade, nested hierarchy, and random models by evaluating the network robustness, i.e., the fraction of surviving species after population dynamics. We find that positive relations between robustness and complexity can be obtained when resources are large, Holling II functional response is used and interaction strengths are weighted with the number of prey species, in order to take foraging efforts into account. In order to obtain these results, no foraging dynamics needs to be included. However, the niche model does not show positive complexity-stability relations under these conditions. By comparing to empirical food web data, we show that the niche model has unrealistic distributions of predator numbers. When this distribution is randomized, positive complexity-stability relations can be found also in the niche model.

Emergence of complexity in evolving niche-model food webs.

We have analysed mechanisms that promote the emergence of complex structures in evolving model food webs. The niche model is used to determine predator-prey relationships. Complexity is measured by species richness as well as trophic level structure and link density. Adaptive dynamics that allow predators to concentrate on the prey species they are best adapted to lead to a strong increase in species number but have only a small effect on the number and relative occupancy of trophic levels. The density of active links also remains small but a high number of potential links allows the network to adjust to changes in the species composition (emergence and extinction of species). Incorporating effects of body size on individual metabolism leads to a more complex trophic level structure: both the maximum and the average trophic level increase. So does the density of active links. Taking body size effects into consideration does not have a measurable influence on species richness. If species are allowed to adjust their foraging behaviour, the complexity of the evolving networks can also be influenced by the size of the external resources. The larger the resources, the larger and more complex is the food web it can sustain. Body size effects and increasing resources do not change size and the simple structure of the evolving networks if adaptive foraging is prohibited. This leads to the conclusion that in the framework of the niche model adaptive foraging is a necessary but not sufficient condition for the emergence of complex networks. It is found that despite the stabilising effect of foraging adaptation the system displays elements of self-organised critical behaviour.