Complex nonmonotonic responses of biodiversity to habitat destruction.

It has typically been assumed that habitat destruction, characterized by habitat loss and fragmentation, has consistently negative effects on biodiversity. While numerous empirical studies have shown the detrimental effects of habitat loss, debate continues as to whether habitat fragmentation has universally negative effects. To explore the effects of habitat fragmentation, we developed a simple model for site-occupancy dynamics in fragmented landscapes. With the model, we demonstrate that a competition-colonization trade-off can result in nonlinear oscillatory responses in biodiversity to both habitat loss and fragmentation. However, the overall pattern of habitat loss reducing species richness is still established, in line with empirical observations. Interestingly, the existence of localized oscillations in biodiversity can explain the mixed responses of species richness to habitat fragmentation per se observed in nature, thereby reconciling the debate on the fragmentation-diversity relationship. Therefore, this study offers a parsimonious mechanistic explanation for empirically observed biodiversity patterns in response to habitat destruction.

Towards a mechanistic understanding of variation in aquatic food chain length.

Ecologists have long sought to understand variation in food chain length (FCL) among natural ecosystems. Various drivers of FCL, including ecosystem size, resource productivity and disturbance, have been hypothesised. However, when results are aggregated across existing empirical studies from aquatic ecosystems, we observe mixed FCL responses to these drivers. To understand this variability, we develop a unified competition-colonisation framework for complex food webs incorporating all of these drivers. With competition-colonisation tradeoffs among basal species, our model predicts that increasing ecosystem size generally results in a monotonic increase in FCL, while FCL displays non-linear, oscillatory responses to resource productivity or disturbance in large ecosystems featuring little disturbance or high productivity. Interestingly, such complex responses mirror patterns in empirical data. Therefore, this study offers a novel mechanistic explanation for observed variations in aquatic FCL driven by multiple environmental factors.

A patch-dynamic metacommunity perspective on the persistence of mutualistic and antagonistic bipartite networks.

The structure of interactions between species within a community plays a key role in maintaining biodiversity. Previous studies found that the effects of these structures might vary substantially depending on interaction type, for example, a highly connected and nested architecture stabilizes mutualistic communities, while the stability of antagonistic communities is enhanced in modular and weakly connected structures. Here we show that, when network dynamics are modeled using a patch-dynamic metacommunity framework, the qualitative differences between antagonistic and mutualistic systems disappear, with nestedness and modularity interacting to promote metacommunity persistence. However, the interactive effects are significantly weaker in antagonistic metacommunities. Our model also predicts an increase in connectance, nestedness, and modularity over time in both types of interaction, except in antagonistic networks, where nestedness declines. At steady state, we find a strong negative correlation between nestedness and modularity in both mutualistic and antagonistic metacommunities. These predictions are consistent with the structural trends found in a large data set of real-world antagonistic and mutualistic communities.

Competition-colonization dynamics and multimodality in diversity-disturbance relationships.

Disturbance has long been recognized as a critical driver of species diversity in community ecology. Recently, it has been found that the well-known intermediate disturbance hypothesis, which predicts a unimodal diversity-disturbance relationship (DDR), fails to describe numerous experimental observations, as empirical DDRs are diverse. Consequently, the precise form of the DDR remains a topic of debate. Here we develop a simple yet comprehensive metacommunity framework that can account for complex competition patterns. Using both numerical simulations and analytical arguments, we show that strongly multimodal DDRs arise naturally, and this multimodality is quite robust to changing parameters or relaxing the assumption of a strict competitive hierarchy. Having multimodality as a robust property of DDRs in competition models suggests that much of the noise observed in empirical DDRs could be a critical signature of the underlying competitive dynamics.

Dispersal network heterogeneity promotes species coexistence in hierarchical competitive communities.

Understanding the mechanisms of biodiversity maintenance is a fundamental issue in ecology. The possibility that species disperse within the landscape along differing paths presents a relatively unexplored mechanism by which diversity could emerge. By embedding a classical metapopulation model within a network framework, we explore how access to different dispersal networks can promote species coexistence. While it is clear that species with the same demography cannot coexist stably on shared dispersal networks, we find that coexistence is possible on unshared networks, as species can surprisingly form self-organised clusters of occupied patches with the most connected patches at the core. Furthermore, a unimodal biodiversity response to an increase in species colonisation rates or average patch connectivity emerges in unshared networks. Increasing network size also increases species richness monotonically, producing characteristic species-area curves. This suggests that, in contrast to previous predictions, many more species can co-occur than the number of limiting resources.

Habitat loss alters effects of intransitive higher-order competition on biodiversity: a new metapopulation framework.

Recent studies have suggested that intransitive competition, as opposed to hierarchical competition, allows more species to coexist. Furthermore, it is recognized that the prevalent paradigm, which assumes that species interactions are exclusively pairwise, may be insufficient. More importantly, whether and how habitat loss, a key driver of biodiversity loss, can alter these complex competition structures (and therefore species coexistence) remain unclear. We thus present a new, simple yet comprehensive metapopulation framework that can account for any competition pattern and more complex higher-order interactions (HOIs) among species. We find that competitive intransitivity increases community diversity and that HOIs generally enhance this effect. Essentially, intransitivity promotes species richness by preventing the dominance of a few species, unlike the hierarchical competition, while HOIs facilitate species coexistence through stabilizing community fluctuations. However, variation in species' vital rates and habitat loss can weaken or even reverse such higher-order effects, as their interaction can lead to a more rapid decline in competitive intransitivity under HOIs. Thus, it is essential to correctly identify the most appropriate interaction model for a given system before models are used to inform conservation efforts. Overall, our simple model framework provides a more parsimonious explanation for biodiversity maintenance than the existing theory.

Metacommunity robustness of plant-fly-wasp tripartite networks with specialization to habitat loss.

Recent observations have found plant-species-specific fly-host selection (i.e., specialization) of wasp parasitoids (wasps) in plant-fly-wasp (P-F-W) tripartite networks, yet no study has explored the dynamical implications of such high-order specialization for the persistence of this network. Here we develop a patch-dynamic framework for a unique P-F-W tripartite network with specialization observed in eastern Tibetan Plateau and explore its metacommunity robustness to habitat loss. We show that specialization in parasitoidism promotes fly species diversity, while the richness of both plant and wasp decreases. Compared to other two null models, real network structure favors plant species coexistence but increases the extinction risk for both flies and wasps. However, these effects of specialization and network structure would be weakened and ultimately disappear with increasing habitat loss. Interestingly, intermediate levels of habitat loss can maximize the diversity of flies and wasps, while increasing or decreasing habitat loss results in more species losses, supporting intermediate disturbance hypothesis. Finally, we observe that high levels of habitat loss initiate a bottom-up cascade of species extinction from plants to both flies and wasps, resulting in a rapid collapse of the whole tripartite networks. Overall, this theoretical framework is the first attempt to characterize the dynamics of whole tripartite metacommunities interacting in realistic high-order ways, offering new insights into complex multipartite networks.

The role of omnivory in mediating metacommunity robustness to habitat destruction.

Omnivores have long been known to play an important role in determining the stability of ecological communities. Recent theoretical studies have suggested that they may also increase the resilience of their communities to habitat destruction, one of the major drivers of species extinctions globally. However, these outcomes were obtained for minimal food webs consisting of only a single omnivore and its prey species, while much more complex communities can be anticipated in nature. In this study, we undertake a systematic comparative analysis of the robustness of metacommunities containing various omnivory structures to habitat loss and fragmentation using a mathematical model. We observe that, in general, omnivores are better able to survive facing habitat destruction than specialist predators of similar trophic level. However, the community as a whole does not always benefit from the presence of omnivores, as they may drive their intraguild prey to extinction. We also analyze the frequency with which these modules occur in a set of empirical food webs, and demonstrate that variation in their rate of occurrence is consistent with our model predictions. Our findings demonstrate the importance of considering the complete food web in which an omnivore is embedded, suggesting that future study should focus on more holistic community analysis.

Habitat heterogeneity mediates effects of individual variation on spatial species coexistence.

Numerous studies have documented the importance of individual variation (IV) in determining the outcome of competition between species. However, little is known about how the interplay between IV and habitat heterogeneity (i.e. variation and spatial autocorrelation in habitat quality) affects species coexistence at the landscape scale. Here, we incorporate habitat heterogeneity into a competition model with IV, in order to explore the mechanism of spatial species coexistence. We find that individual-level variation and habitat heterogeneity interact to promote species coexistence, more obviously at lower dispersal rates. This is in stark contrast to early non-spatial models, which predicted that IV reinforces competitive hierarchies and therefore speeds up species exclusion. In essence, increasing variation in patch quality and/or spatial habitat autocorrelation moderates differences in the competitive ability of species, thereby allowing species to coexist both locally and globally. Overall, our theoretical study offers a mechanistic explanation for emerging empirical evidence that both habitat heterogeneity and IV promote species coexistence and therefore biodiversity maintenance.

Funder Restrictions on Application Numbers Lead to Chaos.

Restricting application rates is an attractive way for funders to reduce time and money wasted evaluating uncompetitive applications. However, mathematical models show that this could induce chaotic cycles in total application numbers, increasing uncertainty in the funding process. One emergent property is that smaller institutions spend disproportionally more time unfunded.

Food web persistence in fragmented landscapes.

Habitat destruction, characterized by patch loss and fragmentation, is a key driver of biodiversity loss. There has been some progress in the theory of spatial food webs; however, to date, practically nothing is known about how patch configurational fragmentation influences multi-trophic food web dynamics. We develop a spatially extended patch-dynamic model for different food webs by linking patch connectivity with trophic-dependent dispersal (i.e. higher trophic levels displaying longer-range dispersal). Using this model, we find that species display different sensitivities to patch loss and fragmentation, depending on their trophic position and the overall food web structure. Relative to other food webs, omnivory structure significantly increases system robustness to habitat destruction, as feeding on different trophic levels increases the omnivore's persistence. Additionally, in food webs with a dispersal-competition trade-off between species, intermediate levels of habitat destruction can enhance biodiversity by creating refuges for the weaker competitor. This demonstrates that maximizing patch connectivity is not always effective for biodiversity maintenance, as in food webs containing indirect competition, doing so may lead to further species loss.

Diverse responses of species to landscape fragmentation in a simple food chain.

Habitat destruction, characterized by habitat loss and fragmentation, is a key driver of species extinction in spatial extended communities. Recently, there has been some progress in the theory of spatial food webs, however to date practically little is known about how habitat configurational fragmentation influences multi-trophic food web dynamics. To explore how habitat fragmentation affects species persistence in food webs, we introduce a modelling framework that describes the site occupancy of species in a tri-trophic system. We assume that species dispersal range increases with trophic level, exploiting pair-approximation techniques to describe the effect of habitat clustering. In accordance with the trophic rank hypothesis, both habitat loss and fragmentation generally cause species extinction, with stronger effects occurring at higher trophic levels. However, species display diverse responses (negative, neutral or positive) to habitat loss and fragmentation separately, depending on their dispersal range and trophic position. Counter-intuitively, prey species may benefit from habitat loss due to a release in top-down control. Similarly, habitat fragmentation has almost no influence on the site occupancy of the intermediate consumer in the tri-trophic system, though it decreases those of both basal species and top predator. Consequently, species' responses to habitat destruction vary as other species become extinct. Our results reiterate the importance of the interplay between bottom-up and top-down control in trophically linked communities, and highlight the complex responses occurring in even a simple food chain.

Robustness of metacommunities with omnivory to habitat destruction: disentangling patch fragmentation from patch loss.

Habitat destruction, characterized by patch loss and fragmentation, is a major driving force of species extinction, and understanding its mechanisms has become a central issue in biodiversity conservation. Numerous studies have explored the effect of patch loss on food web dynamics, but ignored the critical role of patch fragmentation. Here we develop an extended patch-dynamic model for a tri-trophic omnivory system with trophic-dependent dispersal in fragmented landscapes. We found that species display different vulnerabilities to both patch loss and fragmentation, depending on their dispersal range and trophic position. The resulting trophic structure varies depending on the degree of habitat loss and fragmentation, due to a tradeoff between bottom-up control on omnivores (dominated by patch loss) and dispersal limitation on intermediate consumers (dominated by patch fragmentation). Overall, we find that omnivory increases system robustness to habitat destruction relative to a simple food chain.

Emergence of evolutionary cycles in size-structured food webs.

The interplay of population dynamics and evolution within ecological communities has been of long-standing interest for ecologists and can give rise to evolutionary cycles, e.g. taxon cycles. Evolutionary cycling was intensely studied in small communities with asymmetric competition; the latter drives the evolutionary processes. Here we demonstrate that evolutionary cycling arises naturally in larger communities if trophic interactions are present, since these are intrinsically asymmetric. To investigate the evolutionary dynamics of a trophic community, we use an allometric food web model. We find that evolutionary cycles emerge naturally for a large parameter ranges. The origin of the evolutionary dynamics is an intrinsic asymmetry in the feeding kernel which creates an evolutionary ratchet, driving species towards larger bodysize. We reveal different kinds of cycles: single morph cycles, and coevolutionary and mixed cycling of complete food webs. The latter refers to the case where each trophic level can have different evolutionary dynamics. We discuss the generality of our findings and conclude that ongoing evolution in food webs may be more frequent than commonly believed.

A new dimension: Evolutionary food web dynamics in two dimensional trait space.

Species within a habitat are not uniformly distributed. However this aspect of community structure, which is fundamental to many conservation activities, is neglected in the majority of models of food web assembly. To address this issue, we introduce a model which incorporates a second dimension, which can be interpreted as space, into the trait space used in evolutionary food web models. Our results show that the additional trait axis allows the emergence of communities with a much greater range of network structures, similar to the diversity observed in real ecological communities. Moreover, the network properties of the food webs obtained are in good agreement with those of empirical food webs. Community emergence follows a consistent pattern with spread along the second trait axis occurring before the assembly of higher trophic levels. Communities can reach either a static final structure, or constantly evolve. We observe that the relative importance of competition and predation is a key determinant of the network structure and the evolutionary dynamics. The latter are driven by the interaction-competition and predation-between small groups of species. The model remains sufficiently simple that we are able to identify the factors, and mechanisms, which determine the final community state.

Some analytical and numerical approaches to understanding trap counts resulting from pest insect immigration.

Monitoring of pest insects is an important part of the integrated pest management. It aims to provide information about pest insect abundance at a given location. This includes data collection, usually using traps, and their subsequent analysis and/or interpretation. However, interpretation of trap count (number of insects caught over a fixed time) remains a challenging problem. First, an increase in either the population density or insects activity can result in a similar increase in the number of insects trapped (the so called "activity-density" problem). Second, a genuine increase of the local population density can be attributed to qualitatively different ecological mechanisms such as multiplication or immigration. Identification of the true factor causing an increase in trap count is important as different mechanisms require different control strategies. In this paper, we consider a mean-field mathematical model of insect trapping based on the diffusion equation. Although the diffusion equation is a well-studied model, its analytical solution in closed form is actually available only for a few special cases, whilst in a more general case the problem has to be solved numerically. We choose finite differences as the baseline numerical method and show that numerical solution of the problem, especially in the realistic 2D case, is not at all straightforward as it requires a sufficiently accurate approximation of the diffusion fluxes. Once the numerical method is justified and tested, we apply it to the corresponding boundary problem where different types of boundary forcing describe different scenarios of pest insect immigration and reveal the corresponding patterns in the trap count growth.

On time scale invariance of random walks in confined space.

Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is non-conservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour.

Multiscale approach to pest insect monitoring: random walks, pattern formation, synchronization, and networks.

Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.

Synchronized dynamics of Tipula paludosa metapopulation in a southwestern Scotland agroecosystem: linking pattern to process.

Synchronization of population fluctuations at disjoint habitats has been observed in many studies, but its mechanisms often remain obscure. Synchronization may appear as a result of either interhabitat dispersal or regionally correlated environmental stochastic factors, the latter being known as the Moran effect. In this article, we consider the population dynamics of a common agricultural pest insect, Tipula paludosa, on a fragmented habitat by analyzing data derived from a multiannual survey of its abundance in 38 agricultural fields in southwestern Scotland. We use cross-correlation coefficients and show that there is a considerable synchronization between different populations across the whole area. The correlation strength exhibits an intermittent behavior, such that close populations can be virtually uncorrelated, but populations separated by distances up to approximately 150 km can have a cross-correlation coefficient close to one. To distinguish between the effects of stochasticity and dispersal, we then calculate a time-lagged cross-correlation coefficient and show that it possesses considerably different properties to the nonlagged one. In particular, the time-lagged correlation coefficient shows a clear directional dependence. The distribution of the time-lagged correlations with respect to the bearing between the populations has a striking similarity to the distribution of wind velocities, which we regard as evidence of long-distance wind-assisted dispersal.