What constrains food webs? A maximum entropy framework for predicting their structure with minimal biases.

Food webs are complex ecological networks whose structure is both ecologically and statistically constrained, with many network properties being correlated with each other. Despite the recognition of these invariable relationships in food webs, the use of the principle of maximum entropy (MaxEnt) in network ecology is still rare. This is surprising considering that MaxEnt is a statistical tool precisely designed for understanding and predicting many types of constrained systems. This principle asserts that the least-biased probability distribution of a system's property, constrained by prior knowledge about that system, is the one with maximum information entropy. MaxEnt has been proven useful in many ecological modeling problems, but its application in food webs and other ecological networks is limited. Here we show how MaxEnt can be used to derive many food-web properties both analytically and heuristically. First, we show how the joint degree distribution (the joint probability distribution of the numbers of prey and predators for each species in the network) can be derived analytically using the number of species and the number of interactions in food webs. Second, we present a heuristic and flexible approach of finding a network's adjacency matrix (the network's representation in matrix format) based on simulated annealing and SVD entropy. We built two heuristic models using the connectance and the joint degree sequence as statistical constraints, respectively. We compared both models' predictions against corresponding null and neutral models commonly used in network ecology using open access data of terrestrial and aquatic food webs sampled globally (N = 257). We found that the heuristic model constrained by the joint degree sequence was a good predictor of many measures of food-web structure, especially the nestedness and motifs distribution. Specifically, our results suggest that the structure of terrestrial and aquatic food webs is mainly driven by their joint degree distribution.

Predator-mediated interactions through changes in predator home range size can lead to local prey exclusion.

The strength of indirect biotic interactions is difficult to quantify in the wild and can alter community composition. To investigate whether the presence of a prey species affects the population growth rate of another prey species, we quantified predator-mediated interaction strength using a multi-prey mechanistic model of predation and a population matrix model. Models were parametrized using behavioural, demographic and experimental data from a vertebrate community that includes the arctic fox (Vulpes lagopus), a predator feeding on lemmings and eggs of various species such as sandpipers and geese. We show that the positive effects of the goose colony on sandpiper nesting success (due to reduction of search time for sandpiper nests) were outweighed by the negative effect of an increase in fox density. The fox numerical response was driven by changes in home range size. As a result, the net interaction from the presence of geese was negative and could lead to local exclusion of sandpipers. Our study provides a rare empirically based model that integrates mechanistic multi-species functional responses and behavioural processes underlying the predator numerical response. This is an important step forward in our ability to quantify the consequences of predation for community structure and dynamics.

Exotic tree species have consistently lower herbivore load in a cross-Atlantic tree biodiversity experiment.

It is commonly expected that exotic plants experience reduced herbivory, but experimental evidence for such enemy release is still controversial. One reason for conflicting results might be that community context has rarely been accounted for, although the surrounding plant diversity may moderate enemy release. Here, we tested the effects of focal tree origin and surrounding tree diversity on herbivore abundance and leaf damage in a cross-Atlantic tree-diversity experiment in Canada and Germany. We evaluated six European tree species paired with six North American congeners in both their native and exotic range, expecting lower herbivory for the exotic tree species in each pair at each site. Such reciprocal experiments have long been called for, but have not been realized thus far. In addition to a thorough evaluation of overall enemy release effects, we tested whether enemy release effects changed with the surrounding tree diversity. Herbivore abundance was indeed consistently lower on exotics across all six tree genera (12 comparisons). This effect of exotic status was independent of the continent, phylogenetic relatedness, and surrounding tree diversity. In contrast, leaf damage associated with generalist leaf chewers was consistently higher on North American tree species. Interestingly, several species of European weevils were the most abundant leaf chewers on both continents and the dominant herbivores at the Canadian site. Thus, most observed leaf damage is likely to reflect the effect of generalist herbivores that feed heavily on plant species with which they have not evolved. At the German site, sap suckers were the dominant herbivores and showed a pattern consistent with enemy release. Taken together, the consistently lower herbivory on exotics on both continents is not purely a pattern of enemy release in the strictest sense, but to some degree additionally reflects the susceptibility of native plants to invasive herbivores. In conclusion, our cross-Atlantic study is consistent with the idea that nonnative trees have generally reduced herbivory, regardless of tree community diversity and species identity, but for different reasons depending on the dominant herbivore guild.

Will a large complex system be productive?

While the relationship between food web complexity and stability has been well documented, how complexity affects productivity remains elusive. In this study, we combine food web theory and a data set of 149 aquatic food webs to investigate the effect of complexity (i.e. species richness, connectance, and average interaction strength) on ecosystem productivity. We find that more complex ecosystems tend to be more productive, although different facets of complexity have contrasting effects. A higher species richness and/or average interaction strength increases productivity, whereas a higher connectance often decreases it. These patterns hold not only between realized complexity and productivity, but also characterize responses of productivity to simulated declines of complexity. Our model also predicts a negative association between productivity and stability along gradients of complexity. Empirical analyses support our predictions on positive complexity-productivity relationships and negative productivity-stability relationships. Our study provides a step forward towards reconciling ecosystem complexity, productivity and stability.

The Living Planet Index's ability to capture biodiversity change from uncertain data.

The Living Planet Index (LPI) is a crucial tool to track global biodiversity change, but necessarily sacrifices information to summarize thousands of population trends into a single communicable index. Evaluating when and how this information loss affects the LPI's performance is essential to ensure interpretations of the index reflect the truth as reliably as possible. Here, we evaluated the ability of the LPI to accurately and precisely capture trends of population change from uncertain data. We derived a mathematical analysis of uncertainty propagation in the LPI to track how measurement and process uncertainty may bias estimates of population growth rate trends, and to measure the overall uncertainty of the LPI. We demonstrated the propagation of uncertainty using simulated scenarios of declining, stable, or growing populations fluctuating independently, synchronously, or asynchronously, to assess the bias and uncertainty of the LPI in each scenario. We found that measurement and process uncertainty consistently pull the index below the expected true trend. Importantly, variability in the raw data scales up to draw the index further below the expected trend and to amplify its uncertainty, particularly when populations are small. These findings echo suggestions that a more complete assessment of the variability in population change trends, with particular attention to covarying populations, would enrich the LPI's already critical influence on conservation communication and decisions.

Disentangling drivers of litter decomposition in a multi-continent network of tree diversity experiments.

Litter decomposition is a key ecosystem function in forests and varies in response to a range of climatic, edaphic, and local stand characteristics. Disentangling the relative contribution of these factors is challenging, especially along large environmental gradients. In particular, knowledge of the effect of management options, such as tree planting density and species composition, on litter decomposition would be highly valuable in forestry. In this study, we made use of 15 tree diversity experiments spread over eight countries and three continents within the global TreeDivNet network. We evaluated the effects of overstory composition (tree identity, species/mixture composition and species richness), plantation conditions (density and age), and climate (temperature and precipitation) on mass loss (after 3 months and 1 year) of two standardized litters: high-quality green tea and low-quality rooibos tea. Across continents, we found that early-stage decomposition of the low-quality rooibos tea was influenced locally by overstory tree identity. Mass loss of rooibos litter was higher under young gymnosperm overstories compared to angiosperm overstories, but this trend reversed with age of the experiment. Tree species richness did not influence decomposition and explained almost no variation in our multi-continent dataset. Hence, in the young plantations of our study, overstory composition effects on decomposition were mainly driven by tree species identity on decomposer communities and forest microclimates. After 12 months of incubation, mass loss of the high-quality green tea litter was mainly influenced by temperature whereas the low-quality rooibos tea litter decomposition showed stronger relationships with overstory composition and stand age. Our findings highlight that decomposition dynamics are not only affected by climate but also by management options, via litter quality of the identity of planted trees but also by overstory composition and structure.

Synchrony of biomarker variability indicates a critical transition: Application to mortality prediction in hemodialysis.

Critical transition theory suggests that complex systems should experience increased temporal variability just before abrupt state changes. We tested this hypothesis in 763 patients on long-term hemodialysis, using 11 biomarkers collected every two weeks and all-cause mortality as a proxy for critical transitions. We find that variability-measured by coefficients of variation (CVs)-increases before death for all 11 clinical biomarkers, and is strikingly synchronized across all biomarkers: the first axis of a principal component analysis on all CVs explains 49% of the variance. This axis then generates powerful predictions of mortality (HR95 = 9.7, p < 0.0001, where HR95 is a scale-invariant metric of hazard ratio; AUC up to 0.82) and starts to increase markedly ∼3 months prior to death. Our results provide an early warning sign of physiological collapse and, more broadly, a quantification of joint system dynamics that opens questions of how system modularity may break down before critical transitions.

A mechanistic model of functional response provides new insights into indirect interactions among arctic tundra prey.

Prey handling processes are considered a dominant mechanism leading to short-term positive indirect effects between prey that share a predator. However, a growing body of research indicates that predators are not necessarily limited by such processes in the wild. Density-dependent changes in predator foraging behavior can also generate positive indirect effects but they are rarely included as explicit functions of prey densities in functional response models. With the aim of untangling proximate mechanisms of species interactions in natural communities and improving our ability to quantify interaction strength, we extended the multi-prey version of the Holling disk equation by including density-dependent changes in predator foraging behavior. Our model, based on species traits and behavior, was inspired by the vertebrate community of the arctic tundra, where the main predator (the arctic fox) is an active forager feeding primarily on cyclic small rodent (lemming) and eggs of various tundra-nesting bird species. Short-term positive indirect effects of lemmings on birds have been documented over the circumpolar Arctic but the underlying mechanisms remain poorly understood. We used a unique data set, containing high-frequency GPS tracking, accelerometer, behavioral, and experimental data to parameterize the multi-prey model, and a 15-year time series of prey densities and bird nesting success to evaluate interaction strength between species. We found that (1) prey handling processes play a minor role in our system and (2) changes in arctic fox daily activity budget and distance traveled can partly explain the predation release on birds observed during lemming peaks. These adjustments in predator foraging behavior with respect to the main prey density thus appear as the dominant mechanism leading to positive indirect effects commonly reported among arctic tundra prey. Density-dependent changes in functional response components have been little studied in natural vertebrate communities and deserve more attention to improve our ability to quantify the strength of species interactions.

Regional variation drives differences in microbial communities associated with sugar maple across a latitudinal range.

Climate change is prompting plants to migrate and establish novel interactions in new habitats. Because of the pivotal roles that microbes have on plant health and function, it is important to understand the ecological consequences of these shifts in host-microbe interactions with range expansion. Here we examine how the diversity of plant-associated microbes varies along the host's current range and extended range according with climate change predictions, and assess the relative influence of host genotype (seed provenance) and environment in structuring the host microbiome. We collected sugar maple seeds from across the species current range, then planted them in temperate and mixedwood/transitional forests (current range) and in the boreal region (beyond range but predicted future range in response to climate change). We used amplicon sequencing to quantify bacterial, fungal, and mycorrhizal communities from seedling leaves and roots. Variation among sites and regions were the main drivers of the differences in host microbial communities, whereas seed provenance did not play a large role. No unifying pattern was observed for microbial community richness, diversity, or specialization, demonstrating the complexity of responses of different taxa on above- and belowground plant compartments. Along the latitudinal gradient, we (1) observed reductions in mycorrhizal diversity that can negatively impact maple establishment; (2) and revealed reductions in fungal leaf pathogens that can have opposite effects. Our results highlight the need for an integrated approach including the examination of various microbial taxa on different plant compartments to improve our understanding of plant range shifts and plant-microbe interactions.

Effects of land use and weather on the presence and abundance of mosquito-borne disease vectors in a urban and agricultural landscape in Eastern Ontario, Canada.

Weather and land use can significantly impact mosquito abundance and presence, and by consequence, mosquito-borne disease (MBD) dynamics. Knowledge of vector ecology and mosquito species response to these drivers will help us better predict risk from MBD. In this study, we evaluated and compared the independent and combined effects of weather and land use on mosquito species occurrence and abundance in Eastern Ontario, Canada. Data on occurrence and abundance (245,591 individuals) of 30 mosquito species were obtained from mosquito capture at 85 field sites in 2017 and 2018. Environmental variables were extracted from weather and land use datasets in a 1-km buffer around trapping sites. The relative importance of weather and land use on mosquito abundance (for common species) or occurrence (for all species) was evaluated using multivariate hierarchical statistical models. Models incorporating both weather and land use performed better than models that include weather only for approximately half of species (59% for occurrence model and 50% for abundance model). Mosquito occurrence was mainly associated with temperature whereas abundance was associated with precipitation and temperature combined. Land use was more often associated with abundance than occurrence. For most species, occurrence and abundance were positively associated with forest cover but for some there was a negative association. Occurrence and abundance of some species (47% for occurrence model and 88% for abundance model) were positively associated with wetlands, but negatively associated with urban (Culiseta melanura and Anopheles walkeri) and agriculture (An. quadrimaculatus, Cs. minnesotae and An. walkeri) environments. This study provides predictive relationships between weather, land use and mosquito occurrence and abundance for a wide range of species including those that are currently uncommon, yet known as arboviruses vectors. Elucidation of these relationships has the potential to contribute to better prediction of MBD risk, and thus more efficiently targeted prevention and control measures.

No complementarity no gain-Net diversity effects on tree productivity occur once complementarity emerges during early stand development.

Although there is compelling evidence that tree diversity has an overall positive effect on forest productivity, there are important divergences among studies on the nature and strength of these diversity effects and their timing during forest stand development. To clarify conflicting results related to stand developmental stage, we explored how diversity effects on productivity change through time in a diversity experiment spanning 11 years. We show that the strength of diversity effects on productivity progressively increases through time, becoming significantly positive after 9 years. Moreover, we demonstrate that the strengthening of diversity effects is driven primarily by gradual increases in complementarity. We also show that mixing species with contrasting resource-acquisition strategies, and the dominance of deciduous, fast-developing species, promote positive diversity effects on productivity. Our results suggest that the canopy closure and subsequent stem exclusion phase are key for promoting niche complementarity in diverse tree communities.

Ecological network complexity scales with area.

Larger geographical areas contain more species-an observation raised to a law in ecology. Less explored is whether biodiversity changes are accompanied by a modification of interaction networks. We use data from 32 spatial interaction networks from different ecosystems to analyse how network structure changes with area. We find that basic community structure descriptors (number of species, links and links per species) increase with area following a power law. Yet, the distribution of links per species varies little with area, indicating that the fundamental organization of interactions within networks is conserved. Our null model analyses suggest that the spatial scaling of network structure is determined by factors beyond species richness and the number of links. We demonstrate that biodiversity-area relationships can be extended from species counts to higher levels of network complexity. Therefore, the consequences of anthropogenic habitat destruction may extend from species loss to wider simplification of natural communities.

A complex systems approach to aging biology.

Having made substantial progress understanding molecules, cells, genes and pathways, aging biology research is now moving toward integration of these parts, attempting to understand how their joint dynamics may contribute to aging. Such a shift of perspective requires the adoption of a formal complex systems framework, a transition being facilitated by large-scale data collection and new analytical tools. Here, we provide a theoretical framework to orient researchers around key concepts for this transition, notably emergence, interaction networks and resilience. Drawing on evolutionary theory, network theory and principles of homeostasis, we propose that organismal function is accomplished by the integration of regulatory mechanisms at multiple hierarchical scales, and that the disruption of this ensemble causes the phenotypic and functional manifestations of aging. We present key examples at scales ranging from sub-organismal biology to clinical geriatrics, outlining how this approach can potentially enrich our understanding of aging.

A roadmap towards predicting species interaction networks (across space and time).

Networks of species interactions underpin numerous ecosystem processes, but comprehensively sampling these interactions is difficult. Interactions intrinsically vary across space and time, and given the number of species that compose ecological communities, it can be tough to distinguish between a true negative (where two species never interact) from a false negative (where two species have not been observed interacting even though they actually do). Assessing the likelihood of interactions between species is an imperative for several fields of ecology. This means that to predict interactions between species-and to describe the structure, variation, and change of the ecological networks they form-we need to rely on modelling tools. Here, we provide a proof-of-concept, where we show how a simple neural network model makes accurate predictions about species interactions given limited data. We then assess the challenges and opportunities associated with improving interaction predictions, and provide a conceptual roadmap forward towards predictive models of ecological networks that is explicitly spatial and temporal. We conclude with a brief primer on the relevant methods and tools needed to start building these models, which we hope will guide this research programme forward. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Forecasting parasite sharing under climate change.

Species are shifting their distributions in response to climate change. This geographic reshuffling may result in novel co-occurrences among species, which could lead to unseen biotic interactions, including the exchange of parasites between previously isolated hosts. Identifying potential new host-parasite interactions would improve forecasting of disease emergence and inform proactive disease surveillance. However, accurate predictions of future cross-species disease transmission have been hampered by the lack of a generalized approach and data availability. Here, we propose a framework to predict novel host-parasite interactions based on a combination of niche modelling of future host distributions and parasite sharing models. Using the North American ungulates as a proof of concept, we show this approach has high cross-validation accuracy in over 85% of modelled parasites and find that more than 34% of the host-parasite associations forecasted by our models have already been recorded in the literature. We discuss potential sources of uncertainty and bias that may affect our results and similar forecasting approaches, and propose pathways to generate increasingly accurate predictions. Our results indicate that forecasting parasite sharing in response to shifts in host geographic distributions allow for the identification of regions and taxa most susceptible to emergent pathogens under climate change. This article is part of the theme issue 'Infectious disease macroecology: parasite diversity and dynamics across the globe'.

Landscape heterogeneity buffers biodiversity of simulated meta-food-webs under global change through rescue and drainage effects.

Habitat fragmentation and eutrophication have strong impacts on biodiversity. Metacommunity research demonstrated that reduction in landscape connectivity may cause biodiversity loss in fragmented landscapes. Food-web research addressed how eutrophication can cause local biodiversity declines. However, there is very limited understanding of their cumulative impacts as they could amplify or cancel each other. Our simulations of meta-food-webs show that dispersal and trophic processes interact through two complementary mechanisms. First, the 'rescue effect' maintains local biodiversity by rapid recolonization after a local crash in population densities. Second, the 'drainage effect' stabilizes biodiversity by preventing overshooting of population densities on eutrophic patches. In complex food webs on large spatial networks of habitat patches, these effects yield systematically higher biodiversity in heterogeneous than in homogeneous landscapes. Our meta-food-web approach reveals a strong interaction between habitat fragmentation and eutrophication and provides a mechanistic explanation of how landscape heterogeneity promotes biodiversity.

On the sensitivity of food webs to multiple stressors.

Evaluating the effects of multiple stressors on ecosystems is becoming increasingly vital with global changes. The role of species interactions in propagating the effects of stressors, although widely acknowledged, has yet to be formally explored. Here, we conceptualise how stressors propagate through food webs and explore how they affect simulated three-species motifs and food webs of the Canadian St. Lawrence System. We find that overlooking species interactions invariably underestimate the effects of stressors, and that synergistic and antagonistic effects through food webs are prevalent. We also find that interaction type influences a species' susceptibility to stressors; species in omnivory and tri-trophic food chain interactions in particular are sensitive and prone to synergistic and antagonistic effects. Finally, we find that apex predators were negatively affected and mesopredators benefited from the effects of stressors due to their trophic position in the St. Lawrence System, but that species sensitivity is dependent on food web structure. In conceptualising the effects of multiple stressors on food webs, we bring theory closer to practice and show that considering the intricacies of ecological communities is key to assess the net effects of stressors on species.

Biodiversity as insurance: from concept to measurement and application.

Biological insurance theory predicts that, in a variable environment, aggregate ecosystem properties will vary less in more diverse communities because declines in the performance or abundance of some species or phenotypes will be offset, at least partly, by smoother declines or increases in others. During the past two decades, ecology has accumulated strong evidence for the stabilising effect of biodiversity on ecosystem functioning. As biological insurance is reaching the stage of a mature theory, it is critical to revisit and clarify its conceptual foundations to guide future developments, applications and measurements. In this review, we first clarify the connections between the insurance and portfolio concepts that have been used in ecology and the economic concepts that inspired them. Doing so points to gaps and mismatches between ecology and economics that could be filled profitably by new theoretical developments and new management applications. Second, we discuss some fundamental issues in biological insurance theory that have remained unnoticed so far and that emerge from some of its recent applications. In particular, we draw a clear distinction between the two effects embedded in biological insurance theory, i.e. the effects of biodiversity on the mean and variability of ecosystem properties. This distinction allows explicit consideration of trade-offs between the mean and stability of ecosystem processes and services. We also review applications of biological insurance theory in ecosystem management. Finally, we provide a synthetic conceptual framework that unifies the various approaches across disciplines, and we suggest new ways in which biological insurance theory could be extended to address new issues in ecology and ecosystem management. Exciting future challenges include linking the effects of biodiversity on ecosystem functioning and stability, incorporating multiple functions and feedbacks, developing new approaches to partition biodiversity effects across scales, extending biological insurance theory to complex interaction networks, and developing new applications to biodiversity and ecosystem management.