Network spandrels reflect ecological assembly

Random evolutionary dynamics in predator-prey systems yields large, clustered ecosystems

We study the effect of introducing new species through evolution into communities. We use the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra (LV) equations, also when multiple predator and prey species co-exist. We use a stochastic method to introduce new species in a two-trophic LV system. We find that introducing random evolving species leads to robust ecosystems in which large numbers of species coexist. Crucially, in these large ecosystems an emergent clustering of species is observed, tying functional differences to phylogenetic history.

Effects of Phylogeny on Coexistence in Model Communities

AbstractSpecies' interactions are shaped by their traits. Thus, we expect traits-in particular, trait (dis)similarity-to play a central role in determining whether a particular set of species coexists. Traits are, in turn, the outcome of an eco-evolutionary process summarized by a phylogenetic tree. Therefore, the phylogenetic tree associated with a set of species should carry information about the dynamics and assembly properties of the community. Many studies have highlighted the potentially complex ways in which this phylogenetic information is translated into species' ecological properties. However, much less emphasis has been placed on developing clear, quantitative expectations for community properties under a particular hypothesis. To address this gap, we couple a simple model of trait evolution on a phylogenetic tree with Lotka-Volterra community dynamics. This allows us to derive properties of a community of coexisting species as a function of the number of traits, tree topology, and the size of the species pool. Our analysis highlights how phylogenies, through traits, affect the coexistence of a set of species. Together, these results provide much-needed baseline expectations for the ways in which evolutionary history, summarized by phylogeny, is reflected in the size and structure of ecological communities.

Mechanistic interactions as the origin of modularity in biological networks

Biological networks are often modular. Explanations for this peculiarity either assume an adaptive advantage of a modular design such as higher robustness, or attribute it to neutral factors such as constraints underlying network assembly. Interestingly, most insights on the origin of modularity stem from models in which interactions are either determined by highly simplistic mechanisms, or have no mechanistic basis at all. Yet, empirical knowledge suggests that biological interactions are often mediated by complex structural or behavioural traits. Here, we investigate the origins of modularity using a model in which interactions are determined by potentially complex traits. Specifically, we model system elements-such as the species in an ecosystem-as finite-state machines (FSMs), and determine their interactions by means of communication between the corresponding FSMs. Using this model, we show that modularity probably emerges for free. We further find that the more modular an interaction network is, the less complex are the traits that mediate the interactions. Altogether, our results suggest that the conditions for modularity to evolve may be much broader than previously thought.

Plant interaction networks reveal the limits of our understanding of diversity maintenance

Species interactions are key drivers of biodiversity and ecosystem stability. Current theoretical frameworks for understanding the role of interactions make many assumptions which unfortunately, do not always hold in natural, diverse communities. This mismatch extends to annual plants, a common model system for studying coexistence, where interactions are typically averaged across environmental conditions and transitive competitive hierarchies are assumed to dominate. We quantify interaction networks for a community of annual wildflowers in Western Australia across a natural shade gradient at local scales. Whilst competition dominated, intraspecific and interspecific facilitation were widespread in all shade categories. Interaction strengths and directions varied substantially despite close spatial proximity and similar levels of local species richness, with most species interacting in different ways under different environmental conditions. Contrary to expectations, all networks were predominantly intransitive. These findings encourage us to rethink how we conceive of and categorize the mechanisms driving biodiversity in plant systems.

Maximal ecological diversity exceeds evolutionary diversity in model ecosystems

Understanding community saturation is fundamental to ecological theory. While investigations of the diversity of evolutionary stable states (ESSs) are widespread, the diversity of communities that have yet to reach an evolutionary endpoint is poorly understood. We use Lotka-Volterra dynamics and trait-based competition to compare the diversity of randomly assembled communities to the diversity of the ESS. We show that, with a large enough founding diversity (whether assembled at once or through sequential invasions), the number of long-time surviving species exceeds that of the ESS. However, the excessive founding diversity required to assemble a saturated community increases rapidly with the dimension of phenotype space. Additionally, traits present in communities resulting from random assembly are more clustered in phenotype space compared to random, although still markedly less ordered than the ESS. By combining theories of random assembly and ESSs we bring a new viewpoint to both the saturation and random assembly literature.

From kill the winner to eliminate the winner in open phage-bacteria systems

Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, despite limited resources and heavy predation. This diversity can be explained by the “kill the winner” model where virulent phages predominantly prey on fast-growing bacteria and thereby suppress the competitive exclusion of slower-growing bacteria. Here we computationally investigate the robustness of these systems against invasions, where new phages or bacteria may interact with more than one of the resident strains. The resulting interaction networks were found to self-organize into a network with strongly interacting specialized predator-prey pairs, resembling that of the “kill the winner” model. Furthermore, the “kill the winner” dynamics is enforced with the occasional elimination of even the fastest-growing bacteria strains due to a phage infecting the fast and slow growers. The frequency of slower-growing strains was increased with the introduction of even a few non-diagonal interactions. Hence, phages capable of infecting multiple hosts play significant roles both in the evolution of the ecosystem by eliminating the winner and in supporting diversity by allowing slow growers to coexist with faster growers.

We demonstrate that in an open system of phages and bacteria with very limited resources, a bacterial strain that has a high growth rate can still be outcompeted by a slower-growing strain if they have a common phage. The impact of this on ecosystem structure is significant as soon as there is a small probability to have a common phage among bacterial strains. Furthermore, by analysing the structure of the interaction network we show that it self-organizes into a network with strongly interacting specialized predator-prey pairs, in order to reduce phages competition. Nevertheless, the presence of the remaining links is very important for the network dynamics since even a few of them significantly enhance the frequency of slower-growing strains.

Explosive networking: The role of adaptive host radiations and ecological opportunity in a species-rich host-parasite assembly

Many species-rich ecological communities emerge from adaptive radiation events. Yet the effects of adaptive radiation on community assembly remain poorly understood. Here, we explore the well-documented radiations of African cichlid fishes and their interactions with the flatworm gill parasites Cichlidogyrus spp., including 10,529 reported infections and 477 different host-parasite combinations collected through a survey of peer-reviewed literature. We assess how evolutionary, ecological, and morphological parameters determine host-parasite meta-communities affected by adaptive radiation events through network metrics, host repertoire measures, and network link prediction. The hosts' evolutionary history mostly determined host repertoires of the parasites. Ecological and evolutionary parameters predicted host-parasite interactions. Generally, ecological opportunity and fitting have shaped cichlid-Cichlidogyrus meta-communities suggesting an invasive potential for hosts used in aquaculture. Meta-communities affected by adaptive radiations are increasingly specialised with higher environmental stability. These trends should be verified across other systems to infer generalities in the evolution of species-rich host-parasite networks.

How Multiple Interaction Types Affect Disease Spread and Dilution in Ecological Networks

Ecological communities are composed of different functional guilds that are engaging in multiple types of biotic interactions. We explore how ecological networks fare when confronting infectious diseases according to density-dependent (DD) and frequency-dependent (FD) transmission modes. Our model shows that network compositions can dictate both disease spreading and the relationship between disease and community diversity (including species richness and Shannon’s diversity) as depicted in the dilution effect. The disease becomes more prevalent within communities harboring more mutualistic interactions, generating a positive relationship between disease prevalence and community diversity (i.e., an amplification effect). By contrast, in communities with a fixed proportion of mutualistic interactions, higher diversity from the balance of competition and predation can impede disease prevalence (i.e., the dilution effect). Within-species disease prevalence increases linearly with a species’ degree centrality. These patterns of disease transmission and the diversity-disease relationship hold for both transmission modes. Our analyses highlight the complex effects of interaction compositions in ecological networks on infectious disease dynamics and further advance the debate on the dilution effect of host diversity on disease prevalence.

Interaction capacity as a potential driver of community diversity

How patterns in community diversity emerge is a long-standing question in ecology. Studies suggested that community diversity and interspecific interactions are interdependent. However, evidence from high-diversity ecological communities is lacking because of practical challenges in characterizing speciose communities and their interactions. Here, I analysed time-varying interaction networks that were reconstructed using 1197 species, DNA-based ecological time series taken from experimental rice plots and empirical dynamic modelling, and introduced 'interaction capacity', namely, the sum of interaction strength that a single species gives and receives, as a potential driver of community diversity. As community diversity increases, the number of interactions increases exponentially but the mean interaction capacity of a community becomes saturated, weakening interspecific interactions. These patterns are modelled with simple mathematical equations, based on which I propose the 'interaction capacity hypothesis': that interaction capacity and network connectance can be two fundamental properties that influence community diversity. Furthermore, I show that total DNA abundance and temperature influence interaction capacity and connectance nonlinearly, explaining a large proportion of diversity patterns observed in various systems. The interaction capacity hypothesis enables mechanistic explanations of community diversity. Therefore, analysing ecological community data from the viewpoint of interaction capacity would provide new insight into community diversity.

The structure of tropical bat-plant interaction networks during an extreme El Niño-Southern Oscillation event

Interaction network structure reflects the ecological mechanisms acting within biological communities, which are affected by environmental conditions. In tropical forests, higher precipitation usually increases fruit production, which may lead frugivores to increase specialization, resulting in more modular and less nested animal–plant networks. In these ecosystems, El Niño is a major driver of precipitation, but we still lack knowledge of how species interactions change under this influence. To understand bat–plant network structure during an extreme El Niño‐Southern Oscillation event, we determined the links between plantivorous bat species and the plants they consume by DNA barcoding seeds and pulp in bat faeces. These interactions were recorded in the dry forest and rainforest of Costa Rica, during the dry and the wet seasons of an extreme El Niño year. From these we constructed seasonal and whole‐year bat–plant networks and analysed their structures and dissimilarities. In general, networks had low nestedness, had high modularity, and were dominated by one large compartment which included most species and interactions. Contrary to our expectations, networks were less nested and more modular in drier conditions, both in the comparison between forest types and between seasons. We suggest that increased competition, when resources are scarce during drier seasons and habitats, lead to higher resource partitioning among bats and thus higher modularity. Moreover, we have found similar network structures between dry and rainforests during El Niño and non‐El Niño years. Finally, most interaction dissimilarity among networks occurred due to interaction rewiring among species, potentially driven by seasonal changes in resource availability.

Ecological network assembly: how the regional metaweb influences local food webs

1. Local food webs result from a sequence of colonisations and extinctions by species from the regional pool or metaweb, i.e., the assembly process. Assembly is theorised to be a selective process: whether or not certain species or network structures can persist is partly determined by local processes including habitat filtering and dynamical constraints. Consequently, local food web structure should reflect these processes. 2. The goal of this study was to test evidence for these selective processes by comparing the structural properties of real food webs to the expected distribution given the metaweb. We were particularly interested in ecological dynamics; if the network properties commonly associated with dynamical stability are indeed the result of stability constraints, then they should deviate from expectation in the direction predicted by theory. 3. To create a null expectation, we used the novel approach of randomly assembling model webs by drawing species and interactions from the empirical metaweb. The assembly model permitted colonisation and extinction, and required a consumer species to have at least one prey, but had no habitat type nor population dynamical constraints. Three data sets were used: (1) the marine Antarctic metaweb, with 2 local food-webs; (2) the 50 lakes of the Adirondacks; and (3) the arthropod community from Florida Keys' classic defaunation experiment. 4. Contrary to our expectations, we found that there were almost no differences between empirical webs and those resulting from the null assembly model. Few empirical food webs showed significant differences with network properties, motif representations and topological roles. Network properties associated with stability did not deviate from expectation in the direction predicted by theory. 5. Our results suggest that - for the commonly used metrics we considered - local food web structure is not strongly influenced by dynamical nor habitat restrictions. Instead, the structure is inherited from the metaweb. This suggests that the network properties typically attributed as causes or consequences of ecological stability are instead a by-product of the assembly process (i.e., spandrels), and may potentially be too coarse to detect the true signal of dynamical constraint.

SVD Entropy Reveals the High Complexity of Ecological Networks

Quantifying the complexity of ecological networks has remained elusive. Primarily, complexity has been defined on the basis of the structural (or behavioural) complexity of the system. These definitions ignore the notion of “physical complexity,” which can measure the amount of information contained in an ecological network, and how difficult it would be to compress. We present relative rank deficiency and SVD entropy as measures of “external” and “internal” complexity, respectively. Using bipartite ecological networks, we find that they all show a very high, almost maximal, physical complexity. Pollination networks, in particular, are more complex when compared to other types of interactions. In addition, we find that SVD entropy relates to other structural measures of complexity (nestedness, connectance, and spectral radius), but does not inform about the resilience of a network when using simulated extinction cascades, which has previously been reported for structural measures of complexity. We argue that SVD entropy provides a fundamentally more “correct” measure of network complexity and should be added to the toolkit of descriptors of ecological networks moving forward.

Tractable models of ecological assembly

Ecological assembly is a fundamental and yet poorly understood process. Three main obstacles hinder the development of a theory of assembly, and when these issues are sidestepped by making strong assumptions, one can build an assembly graph in which nodes are ecological communities and edges are invasions shifting their composition. The graph can then be analysed directly, without the need to consider dynamics. To showcase this framework, we build and analyse assembly graphs for the competitive Lotka-Volterra model, showing that in these cases sequential assembly (in which species invade a community one at a time) can reach the same configurations found when starting the system with all species present at different initial conditions. We discuss how our results can advance our understanding of assembly both from an empirical and a theoretical point of view, informing the study of ecological restoration and the design of ecological communities.

Stability of ecosystems enhanced by species-interaction constraints

Ecosystem stability is a central question both in theoretical and applied biology. Dynamical systems theory can be used to analyze how growth rates, carrying capacities, and patterns of species interactions affect the stability of an ecosystem. The response to increasing complexity has been extensively studied and the general conclusion is that there is a limit. While there is a complexity limit to stability at which global destabilisation occurs, the collapse rarely happens suddenly if a system is fully viable (no species is extinct). In fact, when complexity is successively increased, we find that the generic response is to go through multiple single-species extinctions before a global collapse. In this paper we demonstrate this finding via both numerical simulations and elaborations of theoretical predictions. We explore more biological interaction patterns, and, perhaps most importantly, we show that constrained interaction structures-a constant row sum in the interaction matrix-prevent extinctions from occurring. This makes an ecosystem more robust in terms of allowed complexity, but it also means singles-species extinctions do not precede or signal collapse-a drastically different behavior compared to the generic and commonly assumed case. We further argue that this constrained interaction structure-limiting the total interactions for each species-is biologically plausible.

Measuring nestedness: A comparative study of the performance of different metrics

Nestedness is a property of interaction networks widely observed in natural mutualistic communities, among other systems. A perfectly nested network is characterized by the peculiarity that the interactions of any node form a subset of the interactions of all nodes with higher degree. Despite a widespread interest on this pattern, no general consensus exists on how to measure it. Instead, several nestedness metrics, based on different but not necessarily independent properties of the networks, coexist in the literature, blurring the comparison between ecosystems. In this work, we present a detailed critical study of the behavior of six nestedness metrics and the variants of two of them. In order to evaluate their performance, we compare the obtained values of the nestedness of a large set of real networks among them and against a maximum-entropy and maximum-likelihood null model. We also analyze the dependencies of each metrics on different network parameters, as size, fill, and eccentricity. Our results point out, first, that the metrics do not rank networks universally in terms of their degree of nestedness. Furthermore, several metrics show significant dependencies on the network properties considered. The study of these dependencies allows us to understand some of the observed systematic shifts against the null model. Altogether, this paper intends to provide readers with a critical guide on how to measure nestedness patterns, by explaining the functioning of several metrics and disclosing their qualities and flaws. Besides, we also aim to extend the application of null models based on maximum entropy to the scarcely explored area of ecological networks. Finally, we provide a fully documented repository that allows constructing the null model and calculating the studied nestedness indexes. In addition, it provides the probability matrices to build the null model for a large dataset of more than 200 bipartite networks.

The multiple meanings of omnivory influence empirical, modular theory and whole food web stability relationships

The persistence of whole communities hinges on the presence of select interactions which act to stabilize communities making the identification of these keystone interactions critical. One potential candidate is omnivory, yet theoretical research on omnivory thus far has been dominated by a modular theory approach whereby an omnivore and consumer compete for a shared resource. Empirical research, however, has highlighted the presence of a broader suite of omnivory modules. Here, we integrate empirical data analysis and mathematical models to explore the influence of both omnivory module (including classic, multi-resource, higher level, mutual predation and cannibalism) and omnivore-resource interaction type on food web stability. We use six classic empirical food webs to examine the prevalence of the different types of omnivory, a multi-species consumer-resource model to determine the stability of these different kinds of omnivory within a module context, and finally extend these models to a 50 species, whole food web model to examine the influence of omnivory on whole food web persistence. Our results challenge the concept that omnivory is broadly stabilizing. In particular, we demonstrate that the impact of omnivory depends on the type of omnivory being examined with multi-resource omnivory having the largest correlation with whole food web persistence. Moreover, our results highlight that we need to exercise caution when scaling modular theory to whole food web theory. Cannibalism, for example, was the most persistent and stable omnivory module in the modular theory analysis, but only demonstrated a weak correlation with whole food web persistence. Lastly, our results demonstrate that the frequency of omnivory modules are more important for whole food web persistence than the frequency of omnivore-resource interactions. Together, these results demonstrate that the role of omnivory often depends both on the type of omnivory being examined and the food web within which it is nested. In whole food web models, omnivory acts less as a keystone interaction, rather, specific types of omnivory, particularly multi-resource omnivory, act as keystone modules. Future work integrating module and whole food web theory is critical for resolving the role of key interactions in food webs.

An individual-based model for the eco-evolutionary emergence of bipartite interaction networks

How ecological interaction networks emerge on evolutionary time scales remains unclear. Here we build an individual-based eco-evolutionary model for the emergence of mutualistic, antagonistic and neutral bipartite interaction networks. Exploring networks evolved under these scenarios, we find three main results. First, antagonistic interactions tend to foster species and trait diversity, while mutualistic interactions reduce diversity. Second, antagonistic interactors evolve higher specialisation, which results in networks that are often more modular than neutral ones; resource species in these networks often display phylogenetic conservatism in interaction partners. Third, mutualistic interactions lead to networks that are more nested than neutral ones, with low phylogenetic conservatism in interaction partners. These results tend to match overall empirical trends, demonstrating that structures of empirical networks that have most often been explained by ecological processes can result from an evolutionary emergence. Our model contributes to the ongoing effort of better integrating ecological interactions and macroevolution.

Strength of niche processes for species interactions is lower for generalists and exotic species

Niche and neutral processes jointly influence species interactions. Predictions of interactions based on these processes assume that they operate similarly across all species. However, species characteristics could systematically create differences in the strength of niche or neutral processes for each interspecific interaction. We used national-level records of plant-frugivore interactions, species traits, biogeographic status (native vs. exotic), phylogenies and species range sizes to test the hypothesis that the strength of niche processes in species interactions changes in predictable ways depending on trophic generalism and biogeographic status of the interacting species. The strength of niche processes (measured as trait matching) decreased when the generalism of the interacting partners increased. Furthermore, the slope of this negative relationship between trait matching and generalism of the interacting partners was steeper (more negative) for interactions between exotic species than those between native species. These results remained significant after accounting for the potential effects of neutral processes (estimated by species range size). These observed changes in the strength of niche processes in generating species interactions, after accounting for effects of neutral processes, could improve predictions of ecological networks from species trait data. Specifically, due to their shorter co-evolutionary history, exotic species tend to interact with native species even when lower trait matching occurs than in interactions among native species. Likewise, interactions between generalist bird species and generalist plant species should be expected to occur despite low trait matching between species, whereas interactions between specialist species involve higher trait matching.

Telling ecological networks apart by their structure: An environment-dependent approach

The network architecture of an ecological community describes the structure of species interactions established in a given place and time. It has been suggested that this architecture presents unique features for each type of ecological interaction: e.g., nested and modular architectures would correspond to mutualistic and antagonistic interactions, respectively. Recently, Michalska-Smith and Allesina (2019) proposed a computational challenge to test whether it is indeed possible to differentiate ecological interactions based on network architecture. Contrary to the expectation, they found that this differentiation is practically impossible, moving the question to why it is not possible to differentiate ecological interactions based on their network architecture alone. Here, we show that this differentiation becomes possible by adding the local environmental information where the networks were sampled. We show that this can be explained by the fact that environmental conditions are a confounder of ecological interactions and network architecture. That is, the lack of association between network architecture and type of ecological interactions changes by conditioning on the local environmental conditions. Additionally, we find that environmental conditions are linked to the stability of ecological networks, but the direction of this effect depends on the type of interaction network. This suggests that the association between ecological interactions and network architectures exists, but cannot be fully understood without attention to the environmental conditions acting upon them.

It has been suggested that different types of species interactions lead to ecological networks with different architectures. For example, mutualistic and antagonistic interaction networks have been shown to have nested and modular architectures, respectively. Importantly, this differentiation can provide clues about the link between the dynamics and structures shaping ecological communities. Recently, Michalska-Smith and Allesina (2019) turned this assumption into a serious computational challenge for the scientific community. Here, we embrace this challenge. We confirm that network architecture alone is not enough to differentiate interaction networks. However, we show that network architectures can differentiate between mutualistic and antagonistic interaction networks by using information about their local environmental conditions. In other words, ignoring environmental information throws out the predictable patterns of network architectures along environmental gradients. Thus, this response is also a reminder that ecological networks may only make sense in the light of environmental information.

Evolving complexity: how tinkering shapes cells, software and ecological networks

A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organization (more than the parts) that largely conditions most higher-level properties, which are not reducible to the properties of the individual parts. Can the topological organization of these webs provide some insight into their evolutionary origins? Both biological and artificial networks share some common architectural traits. They are often heterogeneous and sparse, and most exhibit different types of correlations, such as nestedness, modularity or hierarchical patterns. These properties have often been attributed to the selection of functionally meaningful traits. However, a proper formulation of generative network models suggests a rather different picture. Against the standard selection-optimization argument, some networks reveal the inevitable generation of complex patterns resulting from reuse and can be modelled using duplication-rewiring rules lacking functionality. These give rise to the observed heterogeneous, scale-free and modular architectures. Here, we examine the evidence for tinkering in cellular, technological and ecological webs and its impact in shaping their architecture. Our analysis suggests a serious consideration of the role played by selection as the origin of network topology. Instead, we suggest that the amplification processes associated with reuse might shape these graphs at the topological level. In biological systems, selection forces would take advantage of emergent patterns. This article is part of the theme issue 'Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Coexistence of nestedness and modularity in host-pathogen infection networks

The long-term coevolution of hosts and pathogens in their environment forms a complex web of multi-scale interactions. Understanding how environmental heterogeneity affects the structure of host-pathogen networks is a prerequisite for predicting disease dynamics and emergence. Although nestedness is common in ecological networks, and theory suggests that nested ecosystems are less prone to dynamic instability, why nestedness varies in time and space is not fully understood. Many studies have been limited by a focus on single habitats and the absence of a link between spatial variation and structural heterogeneity such as nestedness and modularity. Here we propose a neutral model for the evolution of host-pathogen networks in multiple habitats. In contrast to previous studies, our study proposes that local modularity can coexist with global nestedness, and shows that real ecosystems are found in a continuum between nested-modular and nested networks driven by intraspecific competition. Nestedness depends on neutral mechanisms of community assembly, whereas modularity is contingent on local adaptation and competition. The structural pattern may change spatially and temporally but remains stable over evolutionary timescales. We validate our theoretical predictions with a longitudinal study of plant-virus interactions in a heterogeneous agricultural landscape.

The balance of interaction types determines the assembly and stability of ecological communities

What determines the assembly and stability of complex communities is a central question in ecology. Past work has suggested that mutualistic interactions are inherently destabilizing. However, this conclusion relies on the assumption that benefits from mutualisms never stop increasing. Furthermore, almost all theoretical work focuses on the internal (asymptotic) stability of communities assembled all at once. Here, we present a model with saturating benefits from mutualisms and sequentially assembled communities. We show that such communities are internally stable for any level of diversity and any combination of species interaction types. External stability, or resistance to invasion, is thus an important but overlooked measure of stability. We demonstrate that the balance of different interaction types governs community dynamics. A higher fraction of mutualistic interactions can increase the external stability and diversity of communities as well as species persistence, if mutualistic interactions tend to provide unique benefits. Ecological selection increases the prevalence of mutualisms, and limits on biodiversity emerge from species interactions. Our results help resolve long-standing debates on the stability, saturation and diversity of communities.

An Approach to Study Species Persistence in Unconstrained Random Networks

The connection between structure and stability of ecological networks has been widely studied in the last fifty years. A challenge that scientists continue to face is that in-depth mathematical model analysis is often difficult, unless the considered systems are specifically constrained. This makes it challenging to generalize results. Therefore, methods are needed that relax the required restrictions. Here, we introduce a novel heuristic approach that provides persistence estimates for random systems without limiting the admissible parameter range and system behaviour. We apply our approach to study persistence of species in random generalized Lotka-Volterra systems and present simulation results, which confirm the accuracy of our predictions. Our results suggest that persistence is mainly driven by the linkage density, whereby additional links can both favour and hinder persistence. In particular, we observed "persistence bistability", a rarely studied feature of random networks, leading to a dependency of persistence on initial species densities. Networks with this property exhibit tipping points, in which species loss can lead to a cascade of extinctions. The methods developed in this paper may facilitate the study of more general models and thereby provide a step forward towards a unifying framework of network architecture and stability.

A new model explaining the origin of different topologies in interaction networks

Nestedness and modularity have been recurrently observed in species interaction networks. Some studies argue that those topologies result from selection against unstable networks, and others propose that they likely emerge from processes driving the interactions between pairs of species. Here we present a model that simulates the evolution of consumer species using resource species following simple rules derived from the integrative hypothesis of specialization (IHS). Without any selection on stability, our model reproduced all commonly observed network topologies. Our simulations demonstrate that resource heterogeneity drives network topology. On the one hand, systems containing only homogeneous resources form generalized nested networks, in which generalist consumers have higher performance on each resource than specialists. On the other hand, heterogeneous systems tend to have a compound topology: modular with internally nested modules, in which generalists that divide their interactions between modules have low performance. Our results demonstrate that all real-world topologies likely emerge through processes driving interactions between pairs of species. Additionally, our simulations suggest that networks containing similar species differ from heterogeneous networks and that modules may not present the topology of entire networks.

Trait-Based Modeling of Multihost Pathogen Transmission: Plant-Pollinator Networks

Epidemiological models for multihost pathogen systems often classify individuals taxonomically and use species-specific parameter values, but in species-rich communities that approach may require intractably many parameters. Trait-based epidemiological models offer a potential solution but have not accounted for within-species trait variation or between-species trait overlap. Here we propose and study trait-based models with host and vector communities represented as trait distributions without regard to species identity. To illustrate this approach, we develop susceptible-infectious-susceptible models for disease spread in plant-pollinator networks with continuous trait distributions. We model trait-dependent contact rates in two common scenarios: nested networks and specialized plant-pollinator interactions based on trait matching. We find that disease spread in plant-pollinator networks is impacted the most by selective pollinators, universally attractive flowers, and cospecialized plant-pollinator pairs. When extreme pollinator traits are rare, pollinators with common traits are most important for disease spread, whereas when extreme flower traits are rare, flowers with uncommon traits impact disease spread the most. Greater nestedness and specialization both typically promote disease persistence. Given recent pollinator declines caused in part by pathogens, we discuss how trait-based models could inform conservation strategies for wild and managed pollinators. Furthermore, while we have applied our model to pollinators and pathogens, its framework is general and can be transferred to any kind of species interactions in any community.

Horizontal and vertical diversity jointly shape food web stability against small and large perturbations

The biodiversity of food webs is composed of horizontal (i.e. within trophic levels) and vertical diversity (i.e. the number of trophic levels). Understanding their joint effect on stability is a key challenge. Theory mostly considers their individual effects and focuses on small perturbations near equilibrium in hypothetical food webs. Here, we study the joint effects of horizontal and vertical diversity on the stability of hypothetical (modelled) and empirical food webs. In modelled food webs, horizontal and vertical diversity increased and decreased stability, respectively, with a stronger positive effect of producer diversity on stability at higher consumer diversity. Experiments with an empirical plankton food web, where we manipulated horizontal and vertical diversity and measured stability from species interactions and from resilience against large perturbations, confirmed these predictions. Taken together, our findings highlight the need to conserve horizontal biodiversity at different trophic levels to ensure stability.

How to Invade an Ecological Network

Invasion science is in a state of paradox, having low predictability despite strong, identifiable covariates of invasion performance. We propose shifting the foundation metaphor of biological invasions from a linear filtering scheme to one that invokes complex adaptive networks. We link invasion performance and invasibility directly to the loss of network stability and indirectly to network topology through constraints from the emergence of the stability criterion in complex systems. We propose the wind vane of an invaded network - the major axis of its adjacency matrix - which reveals how species respond dynamically to invasions. We suggest that invasion ecology should steer away from comparative macroecological studies, to rather explore the ecological network centred on the focal species.

Nestedness Maximization in Complex Networks through the Fitness-Complexity Algorithm

Nestedness refers to the structural property of complex networks that the neighborhood of a given node is a subset of the neighborhoods of better-connected nodes. Following the seminal work by Patterson and Atmar (1986), ecologists have been long interested in revealing the configuration of maximal nestedness of spatial and interaction matrices of ecological communities. In ecology, the BINMATNEST genetic algorithm can be considered as the state-of-the-art approach for this task. On the other hand, the fitness-complexity ranking algorithm has been recently introduced in the economic complexity literature with the original goal to rank countries and products in World Trade export networks. Here, by bringing together quantitative methods from ecology and economic complexity, we show that the fitness-complexity algorithm is highly effective in the nestedness maximization task. More specifically, it generates matrices that are more nested than the optimal ones by BINMATNEST for 61.27% of the analyzed mutualistic networks. Our findings on ecological and World Trade data suggest that beyond its applications in economic complexity, the fitness-complexity algorithm has the potential to become a standard tool in nestedness analysis.

Coexistence of many species in random ecosystems

Rich ecosystems harbour thousands of species interacting in tangled networks encompassing predation, mutualism and competition. Such widespread biodiversity is puzzling, because in ecological models it is exceedingly improbable for large communities to stably coexist. One aspect rarely considered in these models, however, is that coexisting species in natural communities are a selected portion of a much larger pool, which has been pruned by population dynamics. Here we compute the distribution of the number of species that can coexist when we start from a pool of species interacting randomly, and show that even in this case we can observe rich, stable communities. Interestingly, our results show that, once stability conditions are met, network structure has very little influence on the level of biodiversity attained. Our results identify the main drivers responsible for widespread coexistence in natural communities, providing a baseline for determining which structural aspects of empirical communities promote or hinder coexistence.

Symmetric assembly and disassembly processes in an ecological network

The processes whereby ecological networks emerge, persist and decay throughout ecosystem development are largely unknown. Here we study networks of plant and arbuscular mycorrhizal fungal (AMF) communities along a 120 000 year soil chronosequence, as they undergo assembly (progression) and then disassembly (retrogression). We found that network assembly and disassembly were symmetrical, self-reinforcing processes that together were capable of generating key attributes of network architecture. Plant and AMF species that had short indirect paths to others in the community (i.e. high centrality), rather than many direct interaction partners (i.e. high degree), were best able to attract new interaction partners and, in the case of AMF species, also to retain existing interactions with plants during retrogression. We then show using simulations that these non-random patterns of attachment and detachment promote nestedness of the network. These results have implications for predicting extinction sequences, identifying focal points for invasions and suggesting trajectories for restoration.