Why allometric scaling enhances stability in food web models

Colonization-competition dynamics of basal species shape food web complexity in island metacommunities

Exploring how food web complexity emerges and evolves in island ecosystems remains a major challenge in ecology. Food webs assembled from multiple islands are commonly recognized as highly complex trophic networks that are dynamic in both space and time. In the context of global climate change, it remains unclear whether food web complexity will decrease in a monotonic fashion when undergoing habitat destruction (e.g., the inundation of islands due to sea-level rise). Here, we develop a simple yet comprehensive patch-dynamic framework for complex food web metacommunities subject to the competition-colonization tradeoff between basal species. We found that oscillations in food web topological complexity (characterized by species diversity, mean food chain length and the degree of omnivory) emerge along the habitat destruction gradient. This outcome is robust to changing parameters or relaxing the assumption of a strict competitive hierarchy. Having oscillations in food web complexity indicates that small habitat changes could have disproportionate negative effects on species diversity, thus the success of conservation actions should be evaluated not only on changes in biodiversity, but also on system robustness to habitat alteration. Overall, this study provides a parsimonious mechanistic explanation for the emergence of food web complexity in island ecosystems, further enriching our understanding of metacommunity assembly.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42995-023-00167-0.

Body size dependent dispersal influences stability in heterogeneous metacommunities

Body size affects key biological processes across the tree of life, with particular importance for food web dynamics and stability. Traits influencing movement capabilities depend strongly on body size, yet the effects of allometrically-structured dispersal on food web stability are less well understood than other demographic processes. Here we study the stability properties of spatially-arranged model food webs in which larger bodied species occupy higher trophic positions, while species’ body sizes also determine the rates at which they traverse spatial networks of heterogeneous habitat patches. Our analysis shows an apparent stabilizing effect of positive dispersal rate scaling with body size compared to negative scaling relationships or uniform dispersal. However, as the global coupling strength among patches increases, the benefits of positive body size-dispersal scaling disappear. A permutational analysis shows that breaking allometric dispersal hierarchies while preserving dispersal rate distributions rarely alters qualitative aspects of metacommunity stability. Taken together, these results suggest that the oft-predicted stabilizing effects of large mobile predators may, for some dimensions of ecological stability, be attributed to increased patch coupling per se, and not necessarily coupling by top trophic levels in particular.

From winter to summer and back: Lessons from the parameterization of a seasonal food web model for the Białowieża forest

Dynamic food web models describe how species abundances change over time as a function of trophic and life-history parameters. They are essential to predicting the response of ecosystems to perturbations. However, they are notoriously difficult to parameterize, so that most models rely heavily either on allometric scaling of parameters or inverse estimation of biomass flows. The allometric approach makes species of comparable body mass have near-identical parameters which can generate extinctions within a trophic level. The biomass flow approach is more precise, but is restricted to steady-states, which is not appropriate for time-varying environments. Adequately parameterizing large food webs of temperate and arctic environments requires dealing both with many species of similar sizes and a strongly seasonal environment. Inspired by the rich empirical knowledge on the vertebrate food web of the Białowieża forest, we parameterize a bipartite food web model comprising 21 predators and 124 prey species. Our model is a non-autonomous coupled ordinary differential equations system that allows for seasonality in life-history and predation parameters. Birth and death rates, seasonal descriptions of diet for each species, food requirements and biomass information are combined into a seasonal parameterization of a dynamic food web model. Food web seasonality is implemented with time-varying intrinsic growth rate and interaction parameters, while predation is modelled with both type I and type II functional responses. All our model variants allow for >80% persistence in spite of massive apparent competition, and a quantitative match to observed (seasonal) biomasses. We also identify trade-offs between maximizing persistence, reproducing observed biomasses, and ensuring model robustness to sampling errors. Although multi-annual cycles are expected with type II functional responses, they are here prevented by a strong predator self-regulation. We discuss these results and possible improvements on the model. We provide a general workflow to parameterize dynamic food web models in seasonal environments, based on a real case study. This may help to better predict how biodiverse food webs respond to changing environments.

Far-ranging generalist top predators enhance the stability of meta-foodwebs

Identifying stabilizing factors in foodwebs is a long standing challenge with wide implications for community ecology and conservation. Here, we investigate the stability of spatially resolved meta-foodwebs with far-ranging super-predators for whom the whole meta-foodwebs appears to be a single habitat. By using a combination of generalized modeling with a master stability function approach, we are able to efficiently explore the asymptotic stability of large classes of realistic many-patch meta-foodwebs. We show that meta-foodwebs with far-ranging top predators are more stable than those with localized top predators. Moreover, adding far-ranging generalist top predators to a system can have a net stabilizing effect. These results highlight the importance of top predator conservation.

Impact of stochastic migration on species diversity in meta-food webs consisting of several patches

The structure of space has an appreciable influence on the diversity and stability of ecosystems. So far, there are only few theoretical studies investigating the population dynamics of food webs consisting of many species that can migrate between several patches, and in most of these models migration is a continuous, deterministic process. However, when migration events are rare (for instance because the patches are far apart), migration is a stochastic process and should be modeled accordingly. We present computer simulations of a food web model of many species on a spatial network of several patches, combining deterministic local population dynamics with stochastic migration. We evaluate the influence of the migration rate and other model parameters on local and regional species diversity and on stability. We find that migration increases the number of surviving and coexisting populations by two effects. These are the rescue effect, which restores local populations that have gone extinct, and dynamical coexistence, which sustains local populations that could not persist in the absence of immigration. Both effects occur even when migration events are rare. Species diversity increases on local and regional scales with the frequency of migration events. Furthermore, we investigate the adiabatic limit in which population dynamics always reaches an equilibrium before the next migration event, and we investigate the possible long-term scenarios. While the final state often contains the same food web on all patches, we also find instances where two slightly different food webs coexist on different patches, even when initially each patch contained the same food web.

Master stability functions reveal diffusion-driven pattern formation in networks

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

Synergistic impacts of habitat loss and fragmentation on model ecosystems

Habitat loss and fragmentation are major threats to biodiversity, yet separating their effects is challenging. We use a multi-trophic, trait-based, and spatially explicit general ecosystem model to examine the independent and synergistic effects of these processes on ecosystem structure. We manipulated habitat by removing plant biomass in varying spatial extents, intensities, and configurations. We found that emergent synergistic interactions of loss and fragmentation are major determinants of ecosystem response, including population declines and trophic pyramid shifts. Furthermore, trait-mediated interactions, such as a disproportionate sensitivity of large-sized organisms to fragmentation, produce significant effects in shaping responses. We also show that top-down regulation mitigates the effects of land use on plant biomass loss, suggesting that models lacking these interactions—including most carbon stock models—may not adequately capture land-use change impacts. Our results have important implications for understanding ecosystem responses to environmental change, and assessing the impacts of habitat fragmentation.

Examining predator-prey body size, trophic level and body mass across marine and terrestrial mammals

Predator-prey relationships and trophic levels are indicators of community structure, and are important for monitoring ecosystem changes. Mammals colonized the marine environment on seven separate occasions, which resulted in differences in species' physiology, morphology and behaviour. It is likely that these changes have had a major effect upon predator-prey relationships and trophic position; however, the effect of environment is yet to be clarified. We compiled a dataset, based on the literature, to explore the relationship between body mass, trophic level and predator-prey ratio across terrestrial (n = 51) and marine (n = 56) mammals. We did not find the expected positive relationship between trophic level and body mass, but we did find that marine carnivores sit 1.3 trophic levels higher than terrestrial carnivores. Also, marine mammals are largely carnivorous and have significantly larger predator-prey ratios compared with their terrestrial counterparts. We propose that primary productivity, and its availability, is important for mammalian trophic structure and body size. Also, energy flow and community structure in the marine environment are influenced by differences in energy efficiency and increased food web stability. Enhancing our knowledge of feeding ecology in mammals has the potential to provide insights into the structure and functioning of marine and terrestrial communities.

Prohibition rules for three-node substructures in ordered food webs with cannibalistic species

We evaluate the spectrum of ordered three-node substructures in food webs taking self-links (cannibalism) into account. If the order of nodes in the network cannot be neglected, 512 substructures can be distinguished. Simple statistical models of networks impose constraints on the structure that prohibit a large number of substructures completely. We analyse two variants of the widely used niche model, the original niche model and the generalised niche model, and show analytically and numerically that they exclude 344 and 320 substructures, respectively. The prohibition rules for three-node substructures in the two niche-model variants are further contrasted with a large set of empirical food webs, which reveals that up to about 30% of the three-node substructures that occur in empirical food webs are prohibited by the model algorithms.

Complex response of a food-web module to symmetric and asymmetric migration between several patches

We investigate the stability of a diamond food-web module on two patches coupled by migration in terms of robustness, which is the proportion of surviving species in the system. The parameters are chosen such that the dynamics on an isolated patch have a periodic attractor with all four species present as well as an attractor where the prey that is preferred by the top predator dies out. The migration rate and the migration bias between the two patches are varied, resulting in a surprisingly complex relation between migration rate and robustness. In particular, while the degree of synchronization usually increases with increasing migration rate, robustness can increase as well as decrease. We find that the main results also hold when the number of patches is larger. Different types of connectivity patterns between patches can lead to different extent of migration bias if the migration rate out of each patch is the same.

Climate change in size-structured ecosystems

One important aspect of climate change is the increase in average temperature, which will not only have direct physiological effects on all species but also indirectly modifies abundances, interaction strengths, food-web topologies, community stability and functioning. In this theme issue, we highlight a novel pathway through which warming indirectly affects ecological communities: by changing their size structure (i.e. the body-size distributions). Warming can shift these distributions towards dominance of small- over large-bodied species. The conceptual, theoretical and empirical research described in this issue, in sum, suggests that effects of temperature may be dominated by changes in size structure, with relatively weak direct effects. For example, temperature effects via size structure have implications for top-down and bottom-up control in ecosystems and may ultimately yield novel communities. Moreover, scaling up effects of temperature and body size from physiology to the levels of populations, communities and ecosystems may provide a crucially important mechanistic approach for forecasting future consequences of global warming.

Life histories and Cope's rule from an explicit resource-consumer model based on metabolic theory

We explore the consequences of metabolic theory for life histories and life history evolution. We use a mathematical model for an iteroparous species and its resources, taking into account the allometric scaling of consumption, metabolism, and mortality with consumer body mass. Mortality is assumed to be density-dependent, and the dynamics of resources are modeled explicitly. By evaluating life history features in equilibrium populations, we find that in populations that use more or faster growing resources the individuals have a shorter lifespan and a higher mortality, and that individuals in populations with a larger adult body mass have a longer lifespan, a larger number of offspring per female, and a higher biomass density. When we allow the adult body mass to evolve, it increases in time without limits. When we allow the offspring body mass to evolve independently from adult body mass, it becomes smaller. However, when we take into account that larger individuals have larger offspring, both body masses evolve to larger values. These trends result from the allometric scaling of mortality and can be kept in limits by trade-offs other than those included in our 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.