Diversity indices for ecological networks: a unifying framework using Hill numbers

The reorganization of predator-prey networks over 20 million years explains extinction patterns of mammalian carnivores

Linking the species interactions occurring at the scale of local communities to their potential impact at evolutionary timescales is challenging. Here, we used the high-resolution fossil record of mammals from the Iberian Peninsula to reconstruct a timeseries of trophic networks spanning more than 20 million years and asked whether predator-prey interactions affected regional extinction patterns. We found that, despite small changes in species richness, trophic networks showed long-term trends, gradually losing interactions and becoming sparser towards the present. This restructuring of the ecological networks was driven by the loss of medium-sized herbivores, which reduced prey availability for predators. The decrease in prey availability was associated with predator longevity, such that predators with less available prey had greater extinction risk. These results not only reveal long-term trends in network structure but suggest that prey species richness in ecological communities may shape large scale patterns of extinction and persistence among predators.

Assessing mutualistic metacommunity capacity by integrating spatial and interaction networks

We develop a spatially realistic model of mutualistic metacommunities that exploits the joint structure of spatial and interaction networks. Assuming that all species have the same colonisation and extinction parameters, this model exhibits a sharp transition between stable non-null equilibrium states and a global extinction state. This behaviour allows defining a threshold on colonisation/extinction parameters for the long-term metacommunity persistence. This threshold, the 'metacommunity capacity', extends the metapopulation capacity concept and can be calculated from the spatial and interaction networks without needing to simulate the whole dynamics. In several applications we illustrate how the joint structure of the spatial and the interaction networks affects metacommunity capacity. It results that a weakly modular spatial network and a power-law degree distribution of the interaction network provide the most favourable configuration for the long-term persistence of a mutualistic metacommunity. Our model that encodes several explicit ecological assumptions should pave the way for a larger exploration of spatially realistic metacommunity models involving multiple interaction types.

Mathematical constraints on a family of biodiversity measures via connections with Rényi entropy

The Hill numbers are statistics for biodiversity measurement in ecological studies, closely related to the Rényi and Shannon entropies from information theory. Recent developments in the mathematics of diversity in the setting of population genetics have produced mathematical constraints that characterize how standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we apply these constraints to diversity statistics in ecology, focusing on the Hill numbers and the Rényi and Shannon entropies. The mathematical bounds can shift perspectives on the diversities of communities, in that when upper and lower bounds on Hill numbers are evaluated in a classic butterfly example, Hill numbers that are initially larger in one community switch positions-so that associated normalized Hill numbers are instead smaller than those of the other community. The new bounds hence add to the tools available for interpreting a commonly used family of statistics for ecological data.

Dissimilarity of vertebrate trophic interactions reveals spatial uniqueness but functional redundancy across Europe

Identifying areas that contain species assemblages not found elsewhere in a region is central to conservation planning.1,2 Species assemblages contain networks of species interactions that underpin species dynamics,3,4 ecosystem processes, and contributions to people.5,6,7 Yet the uniqueness of interaction networks in a regional context has rarely been assessed. Here, we estimated the spatial uniqueness of 10,000 terrestrial vertebrate trophic networks across Europe (1,164 species, 50,408 potential interactions8) based on the amount of similarity between all local networks mapped at a 10 km resolution. Our results revealed more unique networks in the Arctic bioregion, but also in southern Europe and isolated islands. We then contrasted the uniqueness of trophic networks with their vulnerability to human footprint and future climate change and measured their coverage within protected areas. This analysis revealed that unique networks situated in southern Europe were particularly exposed to human footprint and that unique networks in the Arctic might be at risk from future climate change. However, considering interaction networks at the level of trophic groups, rather than species, revealed that the general structure of trophic networks was redundant across the continent, in contrast to species' interactions. We argue that proactive European conservation strategies might gain relevance by turning their eyes toward interaction networks that are both unique and vulnerable.

Mammals show distinct functional gut microbiome dynamics to identical series of environmental stressors

IMPORTANCE

In our manuscript, we report the first interspecific comparative study about the plasticity of the gut microbiota. We conducted a captivity experiment that exposed wild-captured mammals to a series of environmental challenges over 45 days. We characterized their gut microbial communities using genome-resolved metagenomics and modeled how the taxonomic, phylogenetic, and functional microbial dynamics varied across a series of disturbances in both species. Our results indicate that the intrinsic properties (e.g., diversity and functional redundancy) of microbial communities coupled with physiological attributes (e.g., thermal plasticity) of hosts shape the taxonomic, phylogenetic, and functional response of gut microbiomes to environmental stressors, which might influence their contribution to the acclimation and adaptation capacity of animal hosts.

metanetwork: A R package dedicated to handling and representing trophic metanetworks

Trophic networks describe interactions between species at a given location and time. Due to environmental changes, anthropogenic perturbations or sampling effects, trophic networks may vary in space and time. The collection of network time series or networks in different sites thus constitutes a metanetwork. We present here the R package metanetwork, which will ease the representation, the exploration and analysis of trophic metanetwork data sets that are increasingly available. Our main methodological advance consists in suitable layout algorithm for trophic networks, which is based on trophic levels and dimension reduction in a graph diffusion kernel. In particular, it highlights relevant features of trophic networks (trophic levels, energetic channels). In addition, we developed tools to handle, compare visually and quantitatively and aggregate those networks. Static and dynamic visualisation functions have been developed to represent large networks. We apply our package workflow to several trophic network data sets.

Quantifying and estimating ecological network diversity based on incomplete sampling data

An ecological network refers to the ecological interactions among sets of species. Quantification of ecological network diversity and related sampling/estimation challenges have explicit analogues in species diversity research. A unified framework based on Hill numbers and their generalizations was developed to quantify taxonomic, phylogenetic and functional diversity. Drawing on this unified framework, we propose three dimensions of network diversity that incorporate the frequency (or strength) of interactions, species phylogenies and traits. As with surveys in species inventories, nearly all network studies are based on sampling data and thus also suffer from under-sampling effects. Adapting the sampling/estimation theory and the iNEXT (interpolation/extrapolation) standardization developed for species diversity research, we propose the iNEXT.link method to analyse network sampling data. The proposed method integrates the following four inference procedures: (i) assessment of sample completeness of networks; (ii) asymptotic analysis via estimating the true network diversity; (iii) non-asymptotic analysis based on standardizing sample completeness via rarefaction and extrapolation with network diversity; and (iv) estimation of the degree of unevenness or specialization in networks based on standardized diversity. Interaction data between European trees and saproxylic beetles are used to illustrate the proposed procedures. The software iNEXT.link has been developed to facilitate all computations and graphics. This article is part of the theme issue 'Detecting and attributing the causes of biodiversity change: needs, gaps and solutions'.

Construction and Optimization of an Ecological Network in the Yellow River Source Region Based on MSPA and MCR Modelling

The source region of the Yellow River (SRYR) is an important water conservation and farming area in China. Under the dual influence of the natural environment and external pressure, ecological patches in the region are becoming increasingly fragmented, and landscape connectivity is continuously declining, which directly affect the landscape patch pattern and SRYR sustainable development. In the SRYR, morphological spatial pattern analysis (MSPA) and landscape index methods were used to extract ecologically important sources. Based on the minimum cumulative resistance model (MCR), Linkage Mapper was used to generate a potential corridor, and then potential stepped stone patches were identified and extracted by the gravity model and betweenness centrality to build an optimal SRYR ecological network. The distribution of patches in the core area of the SRYR was fragmented, accounting for 80.53% of the total grassland area. The 10 ecological sources based on the landscape connectivity index and 15 important corridors identified based on the MCR model were mainly distributed in the central and eastern regions of the SRYR. Through betweenness centrality, 10 stepped stone patches were added, and 45 planned ecological corridors were obtained to optimize the SRYR ecological network and enhance east and west connectivity. Our research results can provide an important reference for the protection of the SRYR ecosystem, and have important guiding significance and practical value for ecological network construction in ecologically fragmented areas.

Advancing biological invasion hypothesis testing using functional diversity indices

Pioneering investigations on the effects of introduced populations on community structure, ecosystem functioning and services have focused on the effects of invaders on taxonomic diversity. However, taxonomic-based diversity metrics overlook the heterogeneity of species roles within and among communities. As the homogenizing effects of biological invasions on community and ecosystem processes can be subtle, they may require the use of functional diversity indices to be properly evidenced. Starting from the listing of major functional diversity indices, alongside the presentation of their strengths and limitations, we focus on studies pertaining to the effects of invasive species on native communities and recipient ecosystems using functional diversity indices. By doing so, we reveal that functional diversity of the recipient community may strongly vary at the onset of the invasion process, while it stabilizes at intermediate and high levels of invasion. As functional changes occurring during the lag phase of an invasion have been poorly investigated, we show that it is still unknown whether there are consistent changes in functional diversity metrics that could indicate the end of the lag phase. Thus, we recommend providing information on the invasion stage under consideration when computing functional diversity metrics. For the existing literature, it is also surprising that very few studies explored the functional difference between organisms from the recipient communities and invaders of the same trophic levels, or assessed the effects of non-native organism establishment into a non-analogue versus an analogue community. By providing valuable tools for obtaining in-depth diagnostics of community structure and functioning, functional diversity indices can be applied for timely implementation of restoration plans and improved conservation strategies. To conclude, our work provides a first synthetic guide for their use in hypothesis testing in invasion biology.

Anthropogenic Induced Beta Diversity in Plant–Pollinator Networks: Dissimilarity, Turnover, and Predictive Power

Biogeography has traditionally focused on the distribution of species, while community ecology has sought to explain the patterns of community composition. Species interactions networks have rarely been subjected to such analyses, as modeling tools have only recently been developed for interaction networks. Here, we examine beta diversity of ecological networks using pollination networks sampled along an urbanization and agricultural intensification gradient in east Leinster, Ireland. We show, for the first time, that anthropogenic gradients structure interaction networks, and exert greater structuring force than geographical proximity. We further showed that species turnover, especially of plants, is the major driver of interaction turnover, and that this contribution increased with anthropogenic induced environmental dissimilarity, but not spatial distance. Finally, to explore the extent to which it is possible to predict each of the components of interaction turnover, we compared the predictive performance of models that included site characteristics and interaction properties to models that contained species level effects. We show that if we are to accurately predict interaction turnover, data are required on the species-specific responses to environmental gradients. This study highlights the importance of anthropogenic disturbances when considering the biogeography of interaction networks, especially in human dominated landscapes where geographical effects can be secondary sources of variation. Yet, to build a predictive science of the biogeography of interaction networks, further species-specific responses need to be incorporated into interaction distribution modeling approaches.

The diversity of biotic interactions complements functional and phylogenetic facets of biodiversity

Taxonomic, functional, and phylogenetic diversities are important facets of biodiversity. Studying them together has improved our understanding of community dynamics, ecosystem functioning, and conservation values.^1-3 In contrast to species, traits, and phylogenies, the diversity of biotic interactions has so far been largely ignored as a biodiversity facet in large-scale studies. This neglect represents a crucial shortfall because biotic interactions shape community dynamics, drive important aspects of ecosystem functioning,^4-7 provide services to humans, and have intrinsic conservation value.^8,9 Hence, the diversity of interactions can provide crucial and unique information with respect to other diversity facets. Here, we leveraged large datasets of trophic interactions, functional traits, phylogenies, and spatial distributions of >1,000 terrestrial vertebrate species across Europe at a 10-km resolution. We computed the diversity of interactions (interaction diversity [ID]) in addition to functional diversity (FD) and phylogenetic diversity (PD). After controlling for species richness, surplus and deficits of ID were neither correlated with FD nor with PD, thus representing unique and complementary information to the commonly studied facets of diversity. A three-dimensional mapping allowed for visualizing different combinations of ID-FD-PD simultaneously. Interestingly, the spatial distribution of these diversity combinations closely matched the boundaries between 10 European biogeographic regions and revealed new interaction-rich areas in the European Boreal region and interaction-poor areas in Central Europe. Our study demonstrates that the diversity of interactions adds new and ecologically relevant information to multifacetted, large-scale diversity studies with implications for understanding eco-evolutionary processes and informing conservation planning.

A multi-site method to capture turnover in rare to common interactions in bipartite species networks

Ecological network structure is maintained by a generalist core of common species. However, rare species contribute substantially to both the species and functional diversity of networks. Capturing changes in species composition and interactions, measured as turnover, is central to understanding the contribution of rare and common species and their interactions. Due to a large contribution of rare interactions, the pairwise metrics used to quantify interaction turnover are, however, sensitive to compositional change in the interactions of, often rare, peripheral specialists rather than common generalists in the network. Here we expand on pairwise interaction turnover using a multi-site metric that enables quantifying turnover in rare to common interactions (in terms of occurrence of interactions). The metric further separates this turnover into interaction turnover due to species turnover and interaction rewiring. We demonstrate the application and value of this method using a host-parasitoid system sampled along gradients of environmental modification. In the study system, both the type and amount of habitat needed to maintain interaction composition depended on the properties of the interactions considered, that is, from rare to common. The analyses further revealed the potential of host switching to prevent or delay species loss, and thereby buffer the system from perturbation. Multi-site interaction turnover provides a comprehensive measure of network change that can, for example, detect ecological thresholds to habitat loss for rare to common interactions. Accurate description of turnover in common, in addition to rare, species and their interactions is particularly relevant for understanding how network structure and function can be maintained.

Dynamics of Ecological Communities Following Current Retreat of Glaciers

Glaciers are retreating globally, and the resulting ice-free areas provide an experimental system for understanding species colonization patterns, community formation, and dynamics. The last several years have seen crucial advances in our understanding of biotic colonization after glacier retreats, resulting from the integration of methodological innovations and ecological theories. Recent empirical studies have demonstrated how multiple factors can speed up or slow down the velocity of colonization and have helped scientists develop theoretical models that describe spatiotemporalchanges in community structure. There is a growing awareness of how different processes (e.g., time since glacier retreat, onset or interruption of surface processes, abiotic factors, dispersal, biotic interactions) interact to shape community formation and, ultimately, their functional structure through succession. Here, we examine how these studies address key theoretical questions about community dynamics and show how classical approaches are increasingly being combined with environmental DNA metabarcoding and functional trait analysis to document the formation of multitrophic communities, revolutionizing our understanding of the biotic processes that occur following glacier retreat.

Refocusing multiple stressor research around the targets and scales of ecological impacts

Ecological communities face a variety of environmental and anthropogenic stressors acting simultaneously. Stressor impacts can combine additively or can interact, causing synergistic or antagonistic effects. Our knowledge of when and how interactions arise is limited, as most models and experiments only consider the effect of a small number of non-interacting stressors at one or few scales of ecological organization. This is concerning because it could lead to significant underestimations or overestimations of threats to biodiversity. Furthermore, stressors have been largely classified by their source rather than by the mechanisms and ecological scales at which they act (the target). Here, we argue, first, that a more nuanced classification of stressors by target and ecological scale can generate valuable new insights and hypotheses about stressor interactions. Second, that the predictability of multiple stressor effects, and consistent patterns in their impacts, can be evaluated by examining the distribution of stressor effects across targets and ecological scales. Third, that a variety of existing mechanistic and statistical modelling tools can play an important role in our framework and advance multiple stressor research.

Interaction networks between solitary hymenopterans and their natural enemies in different restoration areas

The diversity of species and their interactions have been positively related with environmental complexity. Therefore, highly anthropized environments have their integrity under serious threat. These effects may last for years compromising the dynamics of natural communities, such as antagonistic and mutualistic interactions, including host-natural enemy interactions. To investigate these effects, trap nest methodology was used to assess the diversity of solitary bees, wasps and their natural enemies in three fragmented environments with different degree of anthropic perturbation, composed of a Eucalyptus plantation (considered here as higher perturbation), a Cerrado area (medium perturbation) and a Riparian forest (lesser perturbation). Then, host-natural enemies associations were analysed to verify the size, specialization degree and modularity of interaction network. The gradient from highest to lowest degree of anthropic perturbation was evidenced in the species diversity index, the size of the interaction network and the specialization indexes of the host-natural enemy network. The environment with Eucalyptus plantation showed higher values of diversity of natural enemies, greater number of species in the interaction network, lesser degree of specialization in the interaction and lesser modularity, than Cerrado and Riparian forest environments, respectively. The low degree of nestedness and lack of significance of this index to all sampled areas are indicative of a specialized pattern of networks. The results corroborate the notion that human impact may affect interaction networks, this being an important tool for checking the degree of anthropic alteration.

Analysis of complex trophic networks reveals the signature of land-use intensification on soil communities in agroecosystems

Increasing evidence suggests that agricultural intensification is a threat to many groups of soil biota, but how the impacts of land-use intensity on soil organisms translate into changes in comprehensive soil interaction networks remains unclear. Here for the first time, we use environmental DNA to examine total soil multi-trophic diversity and food web structure for temperate agroecosystems along a gradient of land-use intensity. We tested for response patterns in key properties of the soil food webs in sixteen fields ranging from arable crops to grazed permanent grasslands as part of a long-term management experiment. We found that agricultural intensification drives reductions in trophic group diversity, although taxa richness remained unchanged. Intensification generally reduced the complexity and connectance of soil interaction networks and induced consistent changes in energy pathways, but the magnitude of management-induced changes depended on the variable considered. Average path length (an indicator of food web redundancy and resilience) did not respond to our management intensity gradient. Moreover, turnover of network structure showed little response to increasing management intensity. Our data demonstrates the importance of considering different facets of trophic networks for a clearer understanding of agriculture-biodiversity relationships, with implications for nature-based solutions and sustainable agriculture.

Cascading effects of moth outbreaks on subarctic soil food webs

The increasing severity and frequency of natural disturbances requires a better understanding of their effects on all compartments of biodiversity. In Northern Fennoscandia, recent large-scale moth outbreaks have led to an abrupt change in plant communities from birch forests dominated by dwarf shrubs to grass-dominated systems. However, the indirect effects on the belowground compartment remained unclear. Here, we combined eDNA surveys of multiple trophic groups with network analyses to demonstrate that moth defoliation has far-reaching consequences on soil food webs. Following this disturbance, diversity and relative abundance of certain trophic groups declined (e.g., ectomycorrhizal fungi), while many others expanded (e.g., bacterivores and omnivores) making soil food webs more diverse and structurally different. Overall, the direct and indirect consequences of moth outbreaks increased belowground diversity at different trophic levels. Our results highlight that a holistic view of ecosystems improves our understanding of cascading effects of major disturbances on soil food webs.

Forest structure, not climate, is the primary driver of functional diversity in northeastern North America

Functional diversity (FD), represented by plant traits, is fundamentally linked to an ecosystem's capacity to respond to environmental change. Yet, little is known about the spatial distribution of FD and its drivers. These knowledge gaps prevent the development of FD-based forest management approaches to increase the trait diversity insurance (i.e., the response diversity) against future environmental fluctuations and disturbances. Our study helps fill these knowledge gaps by (i) mapping the current FD distribution, (ii) and analyzing FD drivers across northeastern North America. Following the stress-dominance hypothesis, we expected a strong environmental filtering effect on FD. Moreover, we expected abundant species to determine the bulk of FD distributions as suggested by the mass-ratio hypothesis. We combined a literature and database review of 44 traits for 43 tree species with terrestrial inventory data of 48,426 plots spanning an environmental gradient from northern boreal to temperate biomes. We evaluated the statistical influence of 25 covariates related to forest structure, climate, topography, soils, and stewardship on FD by employing an ensemble approach consisting of 90 non-parametric models. Temperate forests and the boreal-temperate ecotone east and northeast of the Great Lakes were identified as FD hotspots. Environmental filtering by climate was of secondary importance, with forest structure explaining most of the FD distribution of tree species in northeastern North America. Thus, our study provides only partial support for the stress-dominance hypothesis. Species abundance weightings altered trait diversity distributions and drivers only marginally, supporting the mass-ratio hypothesis. Our results suggest that forest management could increase FD without requiring knowledge of functional ecology by fostering stand structural complexity instead. Further, mixing species from different functional groups identified in this study can enhance the trait diversity insurance of forests to an uncertain future.

Clustering Species With Residual Covariance Matrix in Joint Species Distribution Models

Modeling species distributions over space and time is one of the major research topics in both ecology and conservation biology. Joint Species Distribution models (JSDMs) have recently been introduced as a tool to better model community data, by inferring a residual covariance matrix between species, after accounting for species' response to the environment. However, these models are computationally demanding, even when latent factors, a common tool for dimension reduction, are used. To address this issue, Taylor-Rodriguez et al. (2017) proposed to use a Dirichlet process, a Bayesian nonparametric prior, to further reduce model dimension by clustering species in the residual covariance matrix. Here, we built on this approach to include a prior knowledge on the potential number of clusters, and instead used a Pitman–Yor process to address some critical limitations of the Dirichlet process. We therefore propose a framework that includes prior knowledge in the residual covariance matrix, providing a tool to analyze clusters of species that share the same residual associations with respect to other species. We applied our methodology to a case study of plant communities in a protected area of the French Alps (the Bauges Regional Park), and demonstrated that our extensions improve dimension reduction and reveal additional information from the residual covariance matrix, notably showing how the estimated clusters are compatible with plant traits, endorsing their importance in shaping communities.

Assessment of congruence between co-occurrence and functional networks: A new framework for revealing community assembly rules

Describing how communities change over space and time is crucial to better understand and predict the functioning of ecosystems. We propose a new methodological framework, based on network theory and modularity concept, to determine which type of mechanisms (i.e. deterministic versus stochastic processes) has the strongest influence on structuring communities. This framework is based on the computation and comparison of two networks: the co-occurrence (based on species abundances) and the functional networks (based on the species traits values). In this way we can assess whether the species belonging to a given functional group also belong to the same co-occurrence group. We adapted the Dg index of Gauzens et al. (2015) to analyze congruence between both networks. This offers the opportunity to identify which assembly rule(s) play(s) the major role in structuring the community. We illustrate our framework with two datasets corresponding to different faunal groups and ecosystems, and characterized by different scales (spatial and temporal scales). By considering both species abundance and multiple functional traits, our framework improves significantly the ability to discriminate the main assembly rules structuring the communities. This point is critical not only to understand community structuring but also its response to global changes and other disturbances.