Parameter Sensitivity of Transient Community Dynamics.

AbstractTransient dynamics have always intrigued ecologists, but current rapid environmental change (inducing transients even in previously undisturbed systems) has highlighted their importance more than ever. Here, I introduce a method for analyzing the sensitivity of transient ecological dynamics to parameter perturbations. The question the method answers is: how would the community dynamics have unfolded for some time horizon had the parameters been slightly different? I apply the method to three empirically parameterized models: competition between native forbs and exotic grasses in California, a host-parasitoid system, and an experimental chemostat predator-prey model. These applications showcase the ecological insights one can gain from models using transient sensitivity analysis. First, one can find parameters and their combinations whose perturbations disproportionately affect a system. Second, one can identify particular windows of time during which the predicted deviation from the unperturbed trajectories is especially large and utilize this information for management purposes. Third, there is an inverse relationship between transient and long-term sensitivities whenever the interacting populations are ecologically similar; paradoxically, the smaller the immediate response of the system, the more extreme its long-term response will be.

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.

Mean species responses predict effects of environmental change on coexistence.

Environmental change research is plagued by the curse of dimensionality: the number of communities at risk and the number of environmental drivers are both large. This raises the pressing question if a general understanding of ecological effects is achievable. Here, we show evidence that this is indeed possible. Using theoretical and simulation-based evidence for bi- and tritrophic communities, we show that environmental change effects on coexistence are proportional to mean species responses and depend on how trophic levels on average interact prior to environmental change. We then benchmark our findings using relevant cases of environmental change, showing that means of temperature optima and of species sensitivities to pollution predict concomitant effects on coexistence. Finally, we demonstrate how to apply our theory to the analysis of field data, finding support for effects of land use change on coexistence in natural invertebrate communities.

Higher-order interactions stabilize dynamics in competitive network models.

Ecologists have long sought a way to explain how the remarkable biodiversity observed in nature is maintained. On the one hand, simple models of interacting competitors cannot produce the stable persistence of very large ecological communities. On the other hand, neutral models, in which species do not interact and diversity is maintained by immigration and speciation, yield unrealistically small fluctuations in population abundance, and a strong positive correlation between a species' abundance and its age, contrary to empirical evidence. Models allowing for the robust persistence of large communities of interacting competitors are lacking. Here we show that very diverse communities could persist thanks to the stabilizing role of higher-order interactions, in which the presence of a species influences the interaction between other species. Although higher-order interactions have been studied for decades, their role in shaping ecological communities is still unclear. The inclusion of higher-order interactions in competitive network models stabilizes dynamics, making species coexistence robust to the perturbation of both population abundance and parameter values. We show that higher-order interactions have strong effects in models of closed ecological communities, as well as of open communities in which new species are constantly introduced. In our framework, higher-order interactions are completely defined by pairwise interactions, facilitating empirical parameterization and validation of our models.

Disentangling key species interactions in diverse and heterogeneous communities: A Bayesian sparse modelling approach.

Modelling species interactions in diverse communities traditionally requires a prohibitively large number of species-interaction coefficients, especially when considering environmental dependence of parameters. We implemented Bayesian variable selection via sparsity-inducing priors on non-linear species abundance models to determine which species interactions should be retained and which can be represented as an average heterospecific interaction term, reducing the number of model parameters. We evaluated model performance using simulated communities, computing out-of-sample predictive accuracy and parameter recovery across different input sample sizes. We applied our method to a diverse empirical community, allowing us to disentangle the direct role of environmental gradients on species' intrinsic growth rates from indirect effects via competitive interactions. We also identified a few neighbouring species from the diverse community that had non-generic interactions with our focal species. This sparse modelling approach facilitates exploration of species interactions in diverse communities while maintaining a manageable number of parameters.

Application of modern coexistence theory to rare plant restoration provides early indication of restoration trajectories.

Restoration ecology commonly seeks to re-establish species of interest in degraded habitats. Despite a rich understanding of how succession influences re-establishment, there are several outstanding questions that remain unaddressed: are short-term abundances sufficient to determine long-term re-establishment success, and what factors contribute to unpredictable restorations outcomes? In other words, when restoration fails, is it because the restored habitat is substandard, because of strong competition with invasive species, or alternatively due to changing environmental conditions that would equally impact established populations? Here, we re-purpose tools developed from modern coexistence theory to address these questions, and apply them to an effort to restore the endangered Contra Costa goldfields (Lasthenia conjugens) in constructed ("restored") California vernal pools. Using 16 years of data, we construct a population model of L. conjugens, a species of conservation concern due primarily to habitat loss and invasion of exotic grasses. We show that initial, short-term appearances of restoration success from population abundances is misleading, as year-to-year fluctuations cause long-term population growth rates to fall below zero. The failure of constructed pools is driven by lower maximum growth rates compared with reference ("natural") pools, coupled with a stronger negative sensitivity to annual fluctuations in abiotic conditions that yield decreased maximum growth rates. Nonetheless, our modeling shows that fluctuations in competition (mainly with exotic grasses) benefit L. conjugens through periods of competitive release, especially in constructed pools of intermediate pool depth. We therefore show how reductions in invasives and seed addition in pools of particular depths could change the outcome of restoration for L. conjugens. By applying a largely theoretical framework to the urgent goal of ecological restoration, our study provides a blueprint for predicting restoration success, and identifies future actions to reverse species loss.

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.

General statistical scaling laws for stability in ecological systems.

Ecological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross-study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity.

A Bayesian network approach to trophic metacommunities shows that habitat loss accelerates top species extinctions.

We develop a novel approach to analyse trophic metacommunities, which allows us to explore how progressive habitat loss affects food webs. Our method combines classic metapopulation models on fragmented landscapes with a Bayesian network representation of trophic interactions for calculating local extinction rates. This means that we can repurpose known results from classic metapopulation theory for trophic metacommunities, such as ranking the habitat patches of the landscape with respect to their importance to the persistence of the metacommunity as a whole. We use this to study the effects of habitat loss, both on model communities and the plant-mammal Serengeti food web dataset as a case study. Combining straightforward parameterisability with computational efficiency, our method permits the analysis of species-rich food webs over large landscapes, with hundreds or even thousands of species and habitat patches, while still retaining much of the flexibility of explicit dynamical models.

Competitive Exclusion and Evolution: Convergence Almost Never Produces Ecologically Equivalent Species: (A Comment on McPeek, "Limiting Similarity? The Ecological Dynamics of Natural Selection among Resources and Consumers Caused by Both Apparent and Resource Competition").

In a recent modeling study ("Limiting Similarity? The Ecological Dynamics of Natural Selection among Resources and Consumers Caused by Both Apparent and Resource Competition") that appeared in the April 2019 issue of The American Naturalist, Mark A. McPeek argued that ecologically equivalent species may emerge via competition-induced trait convergence, in conflict with naive expectations based on the limiting similarity principle. Although the emphasis on the possibility of the convergence of competitors is very timely, here we show that the proposed mechanism will only lead to actual coexistence in the converged state for specially chosen fine-tuned parameter settings. It is therefore not a robust mechanism for the evolution of ecologically equivalent species. We conclude that invoking trait convergence as an explanation for the co-occurrence of seemingly fully equivalent species in nature would be premature.

On the Consequences of the Interdependence of Stabilizing and Equalizing Mechanisms.

We present an overlooked but important property of modern coexistence theory (MCT), along with two key new results and their consequences. The overlooked property is that stabilizing mechanisms (increasing species' niche differences) and equalizing mechanisms (reducing species' fitness differences) have two distinct sets of meanings within MCT: one in a two-species context and another in a general multispecies context. We demonstrate that the two-species framework is not a special case of the multispecies one, and therefore these two parallel frameworks must be studied independently. Our first result is that, using the two-species framework and mechanistic consumer-resource models, stabilizing and equalizing mechanisms exhibit complex interdependence, such that changing one will simultaneously change the other. Furthermore, the nature and direction of this simultaneous change sensitively depend on model parameters. The second result states that while MCT is often seen as bridging niche and neutral modes of coexistence by building a niche-neutrality continuum, the interdependence between stabilizing and equalizing mechanisms acts to break this continuum under almost any biologically relevant circumstance. We conclude that the complex entanglement of stabilizing and equalizing terms makes their impact on coexistence difficult to understand, but by seeing them as aggregated effects (rather than underlying causes) of coexistence, we may increase our understanding of ecological dynamics.

Emergent niche structuring leads to increased differences from neutrality in species abundance distributions.

Species abundance distributions must reflect the dynamic processes involved in community assembly, but whether and when specific processes lead to distinguishable signals is not well understood. Biodiversity and species abundances may be shaped by a variety of influences, but particular attention has been paid to competition, which can involve neutral dynamics, where competitor abundances are governed only by demographic stochasticity and immigration, and dynamics driven by trait differences that enable stable coexistence through the formation of niches. Key recent studies of the species abundance patterns of communities with niches employ simple models with pre-imposed niche structure. These studies suggest that species abundance distributions are insensitive to the relative contributions of niche and neutral processes, especially when diversity is much higher than the number of niches. Here we analyze results from a stochastic population model with competition driven by trait differences. With this model, niche structure emerges as clumps of species that persist along the trait axis, and leads to more substantial differences from neutral species abundance distributions than have been previously shown. We show that heterogeneity in "between-niche" interaction strength (i.e., in the strength of competition between species in different niches) plays the dominant role in shaping the species abundances along the trait axis, acting as a biotic filter favoring species at the centers of niches. Furthermore, we show that heterogeneity in "within-niche" interactions (i.e., in the competition between species in the same niche) counteracts the influence of heterogeneity in "between-niche" interactions on the SAD to some degree. Our results suggest that competitive interactions that produce niches can also influence the shapes of SADs.

The effect of intraspecific variation and heritability on community pattern and robustness.

Intraspecific trait variation is widespread in nature, yet its effects on community dynamics are not well understood. Here we explore the consequences of intraspecific trait variation for coexistence in two- and multispecies competitive communities. For two species, the likelihood of coexistence is in general reduced by intraspecific variation, except when the species have almost equal trait means but different trait variances, such that one is a generalist and the other a specialist consumer. In multispecies communities, the only strong effect of non-heritable intraspecific variation is to reduce expected species richness. However, when intraspecific variation is heritable, allowing for the possibility of trait evolution, communities are much more resilient against environmental disturbance and exhibit far more predictable trait patterns. Our results are robust to varying model parameters and relaxing model assumptions.

The Effect of Intra- and Interspecific Competition on Coexistence in Multispecies Communities.

For two competing species, intraspecific competition must exceed interspecific competition for coexistence. To generalize this well-known criterion to multiple competing species, one must take into account both the distribution of interaction strengths and community structure. Here we derive a multispecies generalization of the two-species rule in the context of symmetric Lotka-Volterra competition and obtain explicit stability conditions for random competitive communities. We then explore the influence of community structure on coexistence. Results show that both the most and least stabilized cases have striking global structures, with a nested pattern emerging in both cases. The distribution of intraspecific coefficients leading to the most and least stabilized communities also follows a predictable pattern that can be justified analytically. In addition, we show that the size of the parameter space allowing for feasible communities always increases with the strength of intraspecific effects in a characteristic way that is independent of the interspecific interaction structure. We conclude by discussing possible extensions of our results to nonsymmetric competition.

Metapopulation persistence in random fragmented landscapes.

Habitat destruction and land use change are making the world in which natural populations live increasingly fragmented, often leading to local extinctions. Although local populations might undergo extinction, a metapopulation may still be viable as long as patches of suitable habitat are connected by dispersal, so that empty patches can be recolonized. Thus far, metapopulations models have either taken a mean-field approach, or have modeled empirically-based, realistic landscapes. Here we show that an intermediate level of complexity between these two extremes is to consider random landscapes, in which the patches of suitable habitat are randomly arranged in an area (or volume). Using methods borrowed from the mathematics of Random Geometric Graphs and Euclidean Random Matrices, we derive a simple, analytic criterion for the persistence of the metapopulation in random fragmented landscapes. Our results show how the density of patches, the variability in their value, the shape of the dispersal kernel, and the dimensionality of the landscape all contribute to determining the fate of the metapopulation. Using this framework, we derive sufficient conditions for the population to be spatially localized, such that spatially confined clusters of patches act as a source of dispersal for the whole landscape. Finally, we show that a regular arrangement of the patches is always detrimental for persistence, compared to the random arrangement of the patches. Given the strong parallel between metapopulation models and contact processes, our results are also applicable to models of disease spread on spatial networks.

Stability and feedback levels in food web models.

Neutel & Thorne (Ecology Letters, 17:651-661, June 2014) provide an approximation for the leading eigenvalue of a food web community matrix involving coefficients of its characteristic polynomial. Though valuably incorporating three-way species interactions, two critical problems emerge when one considers the dimensions of the system, calling the approach's accuracy and precision into question.

Sensitivity analysis of coexistence in ecological communities: theory and application.

Sensitivity analysis, the study of how ecological variables of interest respond to changes in external conditions, is a theoretically well-developed and widely applied approach in population ecology. Though the application of sensitivity analysis to predicting the response of species-rich communities to disturbances also has a long history, derivation of a mathematical framework for understanding the factors leading to robust coexistence has only been a recent undertaking. Here we suggest that this development opens up a new perspective, providing advances ranging from the applied to the theoretical. First, it yields a framework to be applied in specific cases for assessing the extinction risk of community modules in the face of environmental change. Second, it can be used to determine trait combinations allowing for coexistence that is robust to environmental variation, and limits to diversity in the presence of environmental variation, for specific community types. Third, it offers general insights into the nature of communities that are robust to environmental variation. We apply recent community-level extensions of mathematical sensitivity analysis to example models for illustration. We discuss the advantages and limitations of the method, and some of the empirical questions the theoretical framework could help answer.

Fixed point sensitivity analysis of interacting structured populations.

Sensitivity analysis of structured populations is a useful tool in population ecology. Historically, methodological development of sensitivity analysis has focused on the sensitivity of eigenvalues in linear matrix models, and on single populations. More recently there have been extensions to the sensitivity of nonlinear models, and to communities of interacting populations. Here we derive a fully general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations. Our method yields the response of an arbitrary function of the stage class abundances to perturbations of any model parameters. As a demonstration, we apply this sensitivity analysis to a two-species model of ontogenetic niche shift where each species has two stage classes, juveniles and adults. In the context of this model, we demonstrate that our theory is quite robust to violating two of its technical assumptions: the assumption that the community is at a point equilibrium and the assumption of infinitesimally small parameter perturbations. Our results on the sensitivity of a community are also interpreted in a niche theoretical context: we determine how the niche of a structured population is composed of the niches of the individual states, and how the sensitivity of the community depends on niche segregation.

Behavioural synchronisation between different groups of dogs and wolves and their owners/handlers: Exploring the effect of breed and human interaction.

Dogs have previously been shown to synchronise their behaviour with their owner and the aim of this study was to test the effect of immediate interactions, breed, and the effects of domestication. The behavioural synchronisation test was conducted in outdoor enclosures and consisted of 30 s where the owner/handler was walking and 30 s of standing still. Three studies were conducted to explore the effect of immediate interaction (study A), the effect of breed group (study B), and the effect of domestication (study C). In study A, a group of twenty companion dogs of various breeds were tested after three different human interaction treatments: Ignore, Pet, and Play. The results showed that dogs adjusted their movement pattern to align with their owner's actions regardless of treatment. Furthermore, exploration, eye contact, and movement were all influenced by the owners moving pattern, and exploration also decreased after the Play treatment. In study B, the synchronisation test was performed after the Ignore treatment on three groups: 24 dogs of ancient dog breeds, 17 solitary hunting dogs, and 20 companion dogs (data from study A). Irrespective of the group, all dogs synchronised their moving behaviour with their owner. In addition, human walking positively influenced eye contact behaviour while simultaneously decreasing exploration behaviour. In study C, a group of six socialised pack-living wolves and six similarly socialised pack-living dogs were tested after the Ignore treatment. Interestingly, these animals did not alter their moving behaviour in response to their handler. In conclusion, dogs living together with humans synchronise with their owner's moving behaviour, while wolves and dogs living in packs do not. Hence, the degree of interspecies behavioural synchronisation may be influenced by the extent to which the dogs are immersed in everyday life with humans.