This report develops mathematical models to describe tree growth using Mapscape and Swiss forestry data. We first establish allometric relations between diameter, height, and canopy area, then extend them through time with the von~Bertalanffy--Chapman--Richards equation. To capture spatial effects, we introduce canopy-density PDEs and a mechanistic geometric model. Finally, we present approaches to estimate biomass and CO$_2$ sequestration, with applications to urban planning and forestry management.

Baited traps are routinely used in many ecological and agricultural applications, in particular when information about pest insects is required. However, interpretation of trap counts is challenging, as consistent methods or algorithms relating trap counts to the population abundance in the area around the trap are largely missing. Thus, interpretation of trap counts is usually relative rather than absolute, i.e., a larger average trap count is regarded as an indication of a larger population. In this paper, we challenge this assumption. We show that the key missing point is the animal movement behaviour, which is known to be modified in the presence of attractant (bait), in particular being dependent on the attractant strength. Using an individual-based simulation model of animal movement, we show that an increase in trap counts can happen simply because of changes in the animal movement behaviour even when the population size is constant or even decreasing. Our simulation results are in good qualitative agreement with some available field data. We conclude that, unless reliable biological information about the dependence of animal movement pattern on the type and strength of attractant is available, an increase in trap counts can send a grossly misleading message, resulting in wrong conclusions about the pest population dynamics and hence inadequate conservation or pest management decisions.

There remains considerable doubt, debate, and confusion regarding how biodiversity responds to gradients of important environmental drivers, such as habitat size, resource productivity, and disturbance. Here we develop a simple but comprehensive theoretical framework based on competition-colonization multispecies communities to examine the separate and interactive effects of these drivers. Using both numerical simulations and analytical arguments, we demonstrate that the critical trade-off between competitive and colonization ability can lead to complex nonlinear, zig-zag responses in both species richness and the inverse Simpson index along gradients of these drivers. Furthermore, we find strong interactions between these drivers that can dramatically shift the response of biodiversity to these gradients. The zig-zag patterns in biodiversity along ecological gradients, together with the strong interactions between the drivers, can explain the mixed findings of empirical studies and syntheses, thereby providing a new paradigm that can reconcile debates on the relationships between biodiversity and multiple drivers.

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 should be a critical signature of the underlying competitive dynamics.

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.

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.

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.

Intransitive competition, typically represented by the classic rock-paper-scissors game, provides an endogenous mechanism promoting species coexistence. As well known, species dispersal and interaction in nature might occur on complex patch networks, with species interacting in diverse ways. However, the effects of different interaction modes, combined with spatial heterogeneity in patch connectivities, have not been well integrated into our general understanding of how stable coexistence emerges in cyclic competition. We thus incorporate network heterogeneity into the classic rock-paper-scissors game, in order to compare ecosystem stability under two typical modes of interaction: species compete to fill empty sites, and species seize each other’s colony sites. On lattice-structured regular networks, the two interaction modes produce similar stability patterns through forming conspecific clusters to reduce interspecific competition. However, for heterogeneous networks, the interaction modes have contrasting effects on ecosystem stability. Specifically, if species compete for colony sites, increasing network heterogeneity stabilizes competitive dynamics. When species compete to fill empty sites, an increase in network heterogeneity leads to larger population fluctuations and therefore a higher risk of stochastic extinctions, in stark contrast to current knowledge. Our findings strongly suggest that particular attention should be devoted to testing which mode of interaction is more appropriate for modeling a given system.

Identification of the mechanisms which permit ecological communities to maintain high levels of biodiversity is of both theoretical interest and practical importance. Intransitive competition, in which there is no single superior competitor, is known to play an important role in this problem. In this study, we undertake a systematic comparative analysis of how different competition modes and ranges affect community stability in paper–rock–scissors games. We confirm that short-ranged interactions, in combination with cyclic competition, permits relatively stable coexistence. However, in contrast to previous studies, we show that long-range interactions can also produce stable communities. This stability emerges when competition interactions create asymmetries in the opportunities for population growth depending on the abundance of the species. Our findings demonstrate that small differences in the way species compete can qualitatively change dynamic behaviours of the system, and therefore emphasize the importance of correctly identifying these competition modes when designing conservation actions.

One of the most significant threats to biodiversity is alien species invasion, and consequently understanding and predicting biological invasions has become an important issue in ecology. While numerous studies have explored the effect of community diversity and structure on invasion success, a systematic comparative analysis on system robustness to invasion between antagonistic and mutualistic networks from a metacommunity perspective is still lacking. Here we seek to address this gap using patch-dynamic models, which integrate local communities into the landscape metacommunity. We find that both mutualistic and antagonistic metacommunities displayed qualitatively similar responses to species invasion, except for animal invasion in antagonistic networks. Specifically, increasing network size and connectance generally promoted metacommunity persistence, while nestedness (negative) and modularity (positive) had contrasting effects on metacommunity robustness to invasion. However, these structural effects were strongly dependent on the generalization levels of both invader and the resident species it displaces. Overall, this study provides new and more general insights into how alien species are well integrated into native networks and how they affect metacommunity persistence.

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.

Global declines in elasmobranchs have been observed. Conservation measures such as area closures and fisheries prohibitions have been put in place to support the recovery of vulnerable species. However, the effectiveness of such measures is rarely evaluated in the context of other factors that may affect population abundance. This study investigates the effectiveness of management measures using 1) General additive mixed model derivative changes, taking into account environmental factors that may affect population stochasticity and 2) an age-structured density dependent population dynamic model. The Raja undulata (undulate ray) 2009 targeted fisheries prohibition was used as a case study. Potential beneficial responses on sympatric species Raja clavata (thornback ray) were modelled. A significant increase in abundance was observed in both IUCN red list species during the ban. Surface seawater temperature had a marginal effect on the abundance of both species. The prohibition was in place for an insufficient length of time for long lasting effects to be detected on skate length. The population dynamic model indicated that the increase in abundance was only possible when combining the fisheries ban with increased juvenile discard survival. Our results indicate that species conservation measures may not only have positive effects on the species in question, but also on species with a niche overlap. Nonetheless, due to ongoing fishing for other species, the full potential of fisheries prohibitions may not be realised. For real benefits to be assessed, evaluation of bans should take place once a steady state is observed.

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.

We investigate the combinatorial data arising from the classification of equivariant homotopy commutativity for cyclic groups of order \(G = C_{p1···pn}\) for \(p_i\) distinct primes. In particular, we will prove a structural result which allows us to enumerate the number of \(N_∞\)-operads for \(C_{pqr}\), verifying a computational result.

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.

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.

Despite years of attention, the dynamics of species constrained to disperse within riverine networks are not well captured by existing metapopulation models, which often ignore local dynamics within branches. We develop a modelling framework, based on traditional metapopulation theory, for patch occupancy dynamics subject to local colonisation-extinction dynamics within branches and regional dispersal between branches in size-structured, bifurcating riverine networks. Using this framework, we investigate whether and how spatial variation in branch size affects species persistence for dendritic systems with directional dispersal, including one-way (up- or downstream only) and two-way (both up- and downstream) dispersal. Variation in branch size generally promotes species persistence more obviously at higher relative extinction rate, suggesting that previous studies ignoring differences in branch size in real riverine systems might overestimate species extinction risk. Two-way dispersal is not always superior to one-way dispersal as a strategy for metapopulation persistence especially at high relative extinction rate. The type of dispersal that maximises species persistence is determined by the hierarchical level of the largest, and hence most influential, branch within the network. When considering the interactive effects of up- and downstream dispersal, we find that moderate upstream-biased dispersal maximises metapopulation viability, mediated by spatial branch arrangement. Overall, these results suggest that both branch-size variation and species traits interact to determine species persistence, theoretically demonstrating the ecological significance of their interplay.

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.