Scaling up our understanding of tipping points.

Anthropogenic activities are increasingly affecting ecosystems across the globe. Meanwhile, empirical and theoretical evidence suggest that natural systems can exhibit abrupt collapses in response to incremental increases in the stressors, sometimes with dramatic ecological and economic consequences. These catastrophic shifts are faster and larger than expected from the changes in the stressors and happen once a tipping point is crossed. The primary mechanisms that drive ecosystem responses to perturbations lie in their architecture of relationships, i.e. how species interact with each other and with the physical environment and the spatial structure of the environment. Nonetheless, existing theoretical work on catastrophic shifts has so far largely focused on relatively simple systems that have either few species and/or no spatial structure. This work has laid a critical foundation for understanding how abrupt responses to incremental stressors are possible, but it remains difficult to predict (let alone manage) where or when they are most likely to occur in more complex real-world settings. Here, we discuss how scaling up our investigations of catastrophic shifts from simple to more complex-species rich and spatially structured-systems could contribute to expanding our understanding of how nature works and improve our ability to anticipate the effects of global change on ecological systems. This article is part of the theme issue 'Ecological complexity and the biosphere: the next 30 years'.

Species traits and network structure predict the success and impacts of pollinator invasions.

Species invasions constitute a major and poorly understood threat to plant-pollinator systems. General theory predicting which factors drive species invasion success and subsequent effects on native ecosystems is particularly lacking. We address this problem using a consumer-resource model of adaptive behavior and population dynamics to evaluate the invasion success of alien pollinators into plant-pollinator networks and their impact on native species. We introduce pollinator species with different foraging traits into network models with different levels of species richness, connectance, and nestedness. Among 31 factors tested, including network and alien properties, we find that aliens with high foraging efficiency are the most successful invaders. Networks exhibiting high alien-native diet overlap, fraction of alien-visited plant species, most-generalist plant connectivity, and number of specialist pollinator species are the most impacted by invaders. Our results mimic several disparate observations conducted in the field and potentially elucidate the mechanisms responsible for their variability.

A multi-scale evaluation of pack stock effects on subalpine meadow plant communities in the Sierra Nevada.

We evaluated the influence of pack stock (i.e., horse and mule) use on meadow plant communities in Sequoia and Yosemite National Parks in the Sierra Nevada of California. Meadows were sampled to account for inherent variability across multiple scales by: 1) controlling for among-meadow variability by using remotely sensed hydro-climatic and geospatial data to pair stock use meadows with similar non-stock (reference) sites, 2) accounting for within-meadow variation in the local hydrology using in-situ soil moisture readings, and 3) incorporating variation in stock use intensity by sampling across the entire available gradient of pack stock use. Increased cover of bare ground was detected only within "dry" meadow areas at the two most heavily used pack stock meadows (maximum animals per night per hectare). There was no difference in plant community composition for any level of soil moisture or pack stock use. Increased local-scale spatial variability in plant community composition (species dispersion) was detected in "wet" meadow areas at the two most heavily used meadows. These results suggest that at the meadow scale, plant communities are generally resistant to the contemporary levels of recreational pack stock use. However, finer-scale within-meadow responses such as increased bare ground or spatial variability in the plant community can be a function of local-scale hydrological conditions. Wilderness managers can improve monitoring of disturbance in Sierra Nevada meadows by adopting multiple plant community indices while simultaneously considering local moisture regimes.

How Structured Is the Entangled Bank? The Surprisingly Simple Organization of Multiplex Ecological Networks Leads to Increased Persistence and Resilience.

Species are linked to each other by a myriad of positive and negative interactions. This complex spectrum of interactions constitutes a network of links that mediates ecological communities' response to perturbations, such as exploitation and climate change. In the last decades, there have been great advances in the study of intricate ecological networks. We have, nonetheless, lacked both the data and the tools to more rigorously understand the patterning of multiple interaction types between species (i.e., "multiplex networks"), as well as their consequences for community dynamics. Using network statistical modeling applied to a comprehensive ecological network, which includes trophic and diverse non-trophic links, we provide a first glimpse at what the full "entangled bank" of species looks like. The community exhibits clear multidimensional structure, which is taxonomically coherent and broadly predictable from species traits. Moreover, dynamic simulations suggest that this non-random patterning of how diverse non-trophic interactions map onto the food web could allow for higher species persistence and higher total biomass than expected by chance and tends to promote a higher robustness to extinctions.

Social Network Analysis and Qualitative Interviews for Assessing Geographic Characteristics of Tourism Business Networks.

This study integrates quantitative social network analysis (SNA) and qualitative interviews for understanding tourism business links in isolated communities through analysing spatial characteristics. Two case studies are used, the Surselva-Gotthard region in the Swiss Alps and Longyearbyen in the Arctic archipelago of Svalbard, to test the spatial characteristics of physical proximity, isolation, and smallness for understanding tourism business links. In the larger Surselva-Gotthard region, we found a strong relationship between geographic separation of the three communities on compartmentalization of the collaboration network. A small set of businesses played a central role in steering collaborative decisions for this community, while a group of structurally 'peripheral' actors were less influential. By contrast, the business community in Svalbard showed compartmentalization that was independent of geographic distance between actors. Within towns of similar size and governance scale, Svalbard is more compartmentalized, and those compartments are not driven by geographic separation of the collaboration clusters. This compartmentalization in Svalbard was reflected in a lower density of formal business collaboration ties compared to the communities of the Alps. We infer that the difference is due to Svalbard having higher cultural diversity and population turnover than the Alps communities. We propose that integrating quantitative network analysis from simple surveys with qualitative interviews targeted from the network results is an efficient general approach to identify regionally specific constraints and opportunities for effective governance.

Network structure beyond food webs: mapping non-trophic and trophic interactions on Chilean rocky shores.

How multiple types of non-trophic interactions map onto trophic networks in real communities remains largely unknown. We present the first effort, to our knowledge, describing a comprehensive ecological network that includes all known trophic and diverse non-trophic links among >100 coexisting species for the marine rocky intertidal community of the central Chilean coast. Our results suggest that non-trophic interactions exhibit highly nonrandom structures both alone and with respect to food web structure. The occurrence of different types of interactions, relative to all possible links, was well predicted by trophic structure and simple traits of the source and target species. In this community, competition for space and positive interactions related to habitat/refuge provisioning by sessile and/or basal species were by far the most abundant non-trophic interactions. If these patterns are orroborated in other ecosystems, they may suggest potentially important dynamic constraints on the combined architecture of trophic and non-trophic interactions. The nonrandom patterning of non-trophic interactions suggests a path forward for developing a more comprehensive ecological network theory to predict the functioning and resilience of ecological communities.

Detecting the influence of rare stressors on rare species in Yosemite National Park using a novel stratified permutation test.

Statistical models often use observational data to predict phenomena; however, interpreting model terms to understand their influence can be problematic. This issue poses a challenge in species conservation where setting priorities requires estimating influences of potential stressors using observational data. We present a novel approach for inferring influence of a rare stressor on a rare species by blending predictive models with nonparametric permutation tests. We illustrate the approach with two case studies involving rare amphibians in Yosemite National Park, USA. The endangered frog, Rana sierrae, is known to be negatively impacted by non-native fish, while the threatened toad, Anaxyrus canorus, is potentially affected by packstock. Both stressors and amphibians are rare, occurring in ~10% of potential habitat patches. We first predict amphibian occupancy with a statistical model that includes all predictors but the stressor to stratify potential habitat by predicted suitability. A stratified permutation test then evaluates the association between stressor and amphibian, all else equal. Our approach confirms the known negative relationship between fish and R. sierrae, but finds no evidence of a negative relationship between current packstock use and A. canorus breeding. Our statistical approach has potential broad application for deriving understanding (not just prediction) from observational data.

A network extension of species occupancy models in a patchy environment applied to the Yosemite Toad (Anaxyrus canorus).

A central challenge of conservation biology is using limited data to predict rare species occurrence and identify conservation areas that play a disproportionate role in regional persistence. Where species occupy discrete patches in a landscape, such predictions require data about environmental quality of individual patches and the connectivity among high quality patches. We present a novel extension to species occupancy modeling that blends traditional predictions of individual patch environmental quality with network analysis to estimate connectivity characteristics using limited survey data. We demonstrate this approach using environmental and geospatial attributes to predict observed occupancy patterns of the Yosemite toad (Anaxyrus (= Bufo) canorus) across >2,500 meadows in Yosemite National Park (USA). A. canorus, a Federal Proposed Species, breeds in shallow water associated with meadows. Our generalized linear model (GLM) accurately predicted ~84% of true presence-absence data on a subset of data withheld for testing. The predicted environmental quality of each meadow was iteratively 'boosted' by the quality of neighbors within dispersal distance. We used this park-wide meadow connectivity network to estimate the relative influence of an individual Meadow's 'environmental quality' versus its 'network quality' to predict: a) clusters of high quality breeding meadows potentially linked by dispersal, b) breeding meadows with high environmental quality that are isolated from other such meadows, c) breeding meadows with lower environmental quality where long-term persistence may critically depend on the network neighborhood, and d) breeding meadows with the biggest impact on park-wide breeding patterns. Combined with targeted data on dispersal, genetics, disease, and other potential stressors, these results can guide designation of core conservation areas for A. canorus in Yosemite National Park.

Approaching a state shift in Earth's biosphere.

Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale 'tipping point' highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes.

More than a meal integrating non-feeding interactions into food webs.

Organisms eating each other are only one of many types of well documented and important interactions among species. Other such types include habitat modification, predator interference and facilitation. However, ecological network research has been typically limited to either pure food webs or to networks of only a few (<3) interaction types. The great diversity of non-trophic interactions observed in nature has been poorly addressed by ecologists and largely excluded from network theory. Herein, we propose a conceptual framework that organises this diversity into three main functional classes defined by how they modify specific parameters in a dynamic food web model. This approach provides a path forward for incorporating non-trophic interactions in traditional food web models and offers a new perspective on tackling ecological complexity that should stimulate both theoretical and empirical approaches to understanding the patterns and dynamics of diverse species interactions in nature.

Predicting invasion success in complex ecological networks.

A central and perhaps insurmountable challenge of invasion ecology is to predict which combinations of species and habitats most effectively promote and prevent biological invasions. Here, we integrate models of network structure and nonlinear population dynamics to search for potential generalities among trophic factors that may drive invasion success and failure. We simulate invasions where 100 different species attempt to invade 150 different food webs with 15-26 species and a wide range (0.06-0.32) of connectance. These simulations yield 11 438 invasion attempts by non-basal species, 47 per cent of which are successful. At the time of introduction, whether or not the invader is a generalist best predicts final invasion success; however, once the invader establishes itself, it is best distinguished from unsuccessful invaders by occupying a lower trophic position and being relatively invulnerable to predation. In general, variables that reflect the interaction between an invading species and its new community, such as generality and trophic position, best predict invasion success; however, for some trophic categories of invaders, fundamental species traits, such as having the centre of the feeding range low on the theoretical niche axis (for non-omnivorous and omnivorous herbivores), or the topology of the food web (for tertiary carnivores), best predict invasion success. Across all invasion scenarios, a discriminant analysis model predicted successful and failed invasions with 76.5 per cent accuracy for properties at the time of introduction or 100 per cent accuracy for properties at the time of establishment. More generally, our results suggest that tackling the challenge of predicting the properties of species and habitats that promote or inhibit invasions from food web perspective may aid ecologists in identifying rules that govern invasions in natural ecosystems.

Simple prediction of interaction strengths in complex food webs.

Darwin's classic image of an "entangled bank" of interdependencies among species has long suggested that it is difficult to predict how the loss of one species affects the abundance of others. We show that for dynamical models of realistically structured ecological networks in which pair-wise consumer-resource interactions allometrically scale to the (3/4) power--as suggested by metabolic theory--the effect of losing one species on another can be predicted well by simple functions of variables easily observed in nature. By systematically removing individual species from 600 networks ranging from 10-30 species, we analyzed how the strength of 254,032 possible pair-wise species interactions depended on 90 stochastically varied species, link, and network attributes. We found that the interaction strength between a pair of species is predicted well by simple functions of the two species' biomasses and the body mass of the species removed. On average, prediction accuracy increases with network size, suggesting that greater web complexity simplifies predicting interaction strengths. Applied to field data, our model successfully predicts interactions dominated by trophic effects and illuminates the sign and magnitude of important nontrophic interactions.

Predator diversity and identity drive interaction strength and trophic cascades in a food web.

Declining predator diversity may drastically affect the biomass and productivity of herbivores and plants. Understanding how changes in predator diversity can propagate through food webs to alter ecosystem function is one of the most challenging ecological research topics today. We studied the effects of predator removal in a simple natural food web in the Sierra Nevada mountains of California (USA). By excluding the predators of the third trophic level of a food web in a full-factorial design, we monitored cascading effects of varying predator diversity and composition on the herbivorous beetle Chrysomela aeneicollis and the willow Salix orestera, which compose the first and second trophic levels of the food web. Decreasing predator diversity increased herbivore biomass and survivorship, and consequently increased the amount of plant biomass consumed via a trophic cascade. Despite this simple linear mean effect of diversity on the strength of the trophic cascade, we found additivity, compensation, and interference in the effects of multiple predators on herbivores and plants. Herbivore survivorship and predator-prey interaction strengths varied with predator diversity, predator identity, and the identity of coexisting predators. Additive effects of predators on herbivores and plants may have been driven by temporal niche separation, whereas compensatory effects and interference occurred among predators with a similar phenology. Together, these results suggest that while the general trends of diversity effects may appear linear and additive, other information about species identity was required to predict the effects of removing individual predators. In a community that is not temporally well-mixed, predator traits such as phenology may help predict impacts of species loss on other species. Information about predator natural history and food web structure may help explain variation in predator diversity effects on trophic cascades and ecosystem function.

Consumer-resource body-size relationships in natural food webs.

It has been suggested that differences in body size between consumer and resource species may have important implications for interaction strengths, population dynamics, and eventually food web structure, function, and evolution. Still, the general distribution of consumer-'resource body-size ratios in real ecosystems, and whether they vary systematically among habitats or broad taxonomic groups, is poorly understood. Using a unique global database on consumer and resource body sizes, we show that the mean body-size ratios of aquatic herbivorous and detritivorous consumers are several orders of magnitude larger than those of carnivorous predators. Carnivorous predator-prey body-size ratios vary across different habitats and predator and prey types (invertebrates, ectotherm, and endotherm vertebrates). Predator-prey body-size ratios are on average significantly higher (1) in freshwater habitats than in marine or terrestrial habitats, (2) for vertebrate than for invertebrate predators, and (3) for invertebrate than for ectotherm vertebrate prey. If recent studies that relate body-size ratios to interaction strengths are general, our results suggest that mean consumer-resource interaction strengths may vary systematically across different habitat categories and consumer types.

Variable interaction strengths stabilize marine community pattern.

High variability in the strength of species interactions is usually considered a source of unstable or unpredictable community patterns. However, recent theoretical work suggests that some types of variance in interaction strength may actually promote stability. Here we provide the first empirical evidence that highly variable, context-dependent species interaction strengths and resilient community patterns can be two sides of the same coin. Field experiments show that a persistent rocky intertidal seascape is remarkably resilient to multiple sources of environmental stochasticity largely because of scale dependent and variable species interaction strengths. Biological interactions exert a stabilizing effect because their intensity varies systematically with changes in both physical sources of mortality of established species, as well as recruitment of new individuals. Strong variation in species interaction strengths with disturbance size and environmental conditions is ubiquitous in nature. Elucidating when this context dependency will be stabilizing is critical to predict community-level responses to anthropogenic disturbances.

Two degrees of separation in complex food webs.

Feeding relationships can cause invasions, extirpations, and population fluctuations of a species to dramatically affect other species within a variety of natural habitats. Empirical evidence suggests that such strong effects rarely propagate through food webs more than three links away from the initial perturbation. However, the size of these spheres of potential influence within complex communities is generally unknown. Here, we show for that species within large communities from a variety of aquatic and terrestrial ecosystems are on average two links apart, with >95% of species typically within three links of each other. Species are drawn even closer as network complexity and, more unexpectedly, species richness increase. Our findings are based on seven of the largest and most complex food webs available as well as a food-web model that extends the generality of the empirical results. These results indicate that the dynamics of species within ecosystems may be more highly interconnected and that biodiversity loss and species invasions may affect more species than previously thought.