Life history complementarity and the maintenance of biodiversity.

Life history, the schedule of when and how fast organisms grow, die and reproduce, is a critical axis along which species differ from each other1-4. In parallel, competition is a fundamental mechanism that determines the potential for species coexistence5-8. Previous models of stochastic competition have demonstrated that large numbers of species can persist over long timescales, even when competing for a single common resource9-12, but how life history differences between species increase or decrease the possibility of coexistence and, conversely, whether competition constrains what combinations of life history strategies complement each other remain open questions. Here we show that specific combinations of life history strategy optimize the persistence times of species competing for a single resource before one species overtakes its competitors. This suggests that co-occurring species would tend to have such complementary life history strategies, which we demonstrate using empirical data for perennial plants.

Universal abundance fluctuations across microbial communities, tropical forests, and urban populations.

The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to understand each individual system, a unified analysis of different complex populations is lacking; such an analysis could deepen our understanding of each system and facilitate cross-pollination of tools and insights across fields. Here, we use a shared framework to analyze time-series data of the human gut microbiome, tropical forest, and urban employment. We demonstrate that a single, three-parameter model of stochastic population dynamics can reproduce the empirical distributions of population abundances and fluctuations in all three datasets. The three parameters characterizing a species measure its mean abundance, deterministic stability, and stochasticity. Our analysis reveals that, despite the vast differences in scale, all three systems occupy a similar region of parameter space when time is measured in generations. In other words, although the fluctuations observed in these systems may appear different, this difference is primarily due to the different physical timescales associated with each system. Further, we show that the distribution of temporal abundance fluctuations is described by just two parameters and derive a two-parameter functional form for abundance fluctuations to improve risk estimation and forecasting.

Sparsity of higher-order landscape interactions enables learning and prediction for microbiomes.

Microbiome engineering offers the potential to leverage microbial communities to improve outcomes in human health, agriculture, and climate. To translate this potential into reality, it is crucial to reliably predict community composition and function. But a brute force approach to cataloging community function is hindered by the combinatorial explosion in the number of ways we can combine microbial species. An alternative is to parameterize microbial community outcomes using simplified, mechanistic models, and then extrapolate these models beyond where we have sampled. But these approaches remain data-hungry, as well as requiring an a priori specification of what kinds of mechanisms are included and which are omitted. Here, we resolve both issues by introducing a mechanism-agnostic approach to predicting microbial community compositions and functions using limited data. The critical step is the identification of a sparse representation of the community landscape. We then leverage this sparsity to predict community compositions and functions, drawing from techniques in compressive sensing. We validate this approach on in silico community data, generated from a theoretical model. By sampling just [Formula: see text]1% of all possible communities, we accurately predict community compositions out of sample. We then demonstrate the real-world application of our approach by applying it to four experimental datasets and showing that we can recover interpretable, accurate predictions on composition and community function from highly limited data.

Metabolic Trade-Offs Can Reverse the Resource-Diversity Relationship.

AbstractFor species that partition resources, the classic expectation is that increasing resource diversity allows for increased species diversity. On the other hand, for neutral species, such as those competing equally for a single resource, diversity reflects a balance between the rate of introduction of novelty (e.g., by immigration or speciation) and the rate of extinction. Recent models of microbial metabolism have identified scenarios where metabolic trade-offs among species partitioning multiple resources can produce emergent neutral-like dynamics. In this hybrid scenario, one might expect that both resource diversity and immigration will act to boost species diversity. We show, however, that the reverse may be true: when metabolic trade-offs hold and population sizes are sufficiently large, increasing resource diversity can act to reduce species diversity, sometimes drastically. This reversal is explained by a generic transition between neutral- and niche-like dynamics, driven by the diversity of resources. The inverted resource-diversity relationship that results may be a signature of consumer-resource systems with strong metabolic trade-offs.

A Spatial Signal of Niche Differentiation in Tropical Forests.

AbstractExplaining diversity in tropical forests remains a challenge in community ecology. Theory tells us that species differences can stabilize communities by reducing competition, while species similarities can promote diversity by reducing fitness differences and thus prolonging the time to competitive exclusion. Combined, these processes may lead to clustering of species such that species are niche differentiated across clusters and share a niche within each cluster. Here, we characterize this partial niche differentiation in a tropical forest in Panama by measuring spatial clustering of woody plants and relating these clusters to local soil conditions. We find that species were spatially clustered and the clusters were associated with specific concentrations of soil nutrients, reflecting the existence of nutrient niches. Species were almost twice as likely to recruit in their own nutrient niche. A decision tree algorithm showed that local soil conditions correctly predicted the niche of the trees with up to 85% accuracy. Iron, zinc, phosphorus, manganese, and soil pH were among the best predictors of species clusters.

Stability criteria for the consumption and exchange of essential resources.

Models of consumer effects on a shared resource environment have helped clarify how the interplay of consumer traits and resource supply impact stable coexistence. Recent models generalize this picture to include the exchange of resources alongside resource competition. These models exemplify the fact that although consumers shape the resource environment, the outcome of consumer interactions is context-dependent: such models can have either stable or unstable equilibria, depending on the resource supply. However, these recent models focus on a simplified version of microbial metabolism where the depletion of resources always leads to consumer growth. Here, we model an arbitrarily large system of consumers governed by Liebig's law, where species require and deplete multiple resources, but each consumer's growth rate is only limited by a single one of these resources. Resources that are taken up but not incorporated into new biomass are leaked back into the environment, possibly transformed by intracellular reactions, thereby tying the mismatch between depletion and growth to cross-feeding. For this set of dynamics, we show that feasible equilibria can be either stable or unstable, again depending on the resource environment. We identify special consumption and production networks which protect the community from instability when resources are scarce. Using simulations, we demonstrate that the qualitative stability patterns derived analytically apply to a broader class of network structures and resource inflow profiles, including cases where multiple species coexist on only one externally supplied resource. Our stability criteria bear some resemblance to classic stability results for pairwise interactions, but also demonstrate how environmental context can shape coexistence patterns when resource limitation and exchange are modeled directly.

Emergent neutrality in consumer-resource dynamics.

Neutral theory assumes all species and individuals in a community are ecologically equivalent. This controversial hypothesis has been tested across many taxonomic groups and environmental contexts, and successfully predicts species abundance distributions across multiple high-diversity communities. However, it has been critiqued for its failure to predict a broader range of community properties, particularly regarding community dynamics from generational to geological timescales. Moreover, it is unclear whether neutrality can ever be a true description of a community given the ubiquity of interspecific differences, which presumably lead to ecological inequivalences. Here we derive analytical predictions for when and why non-neutral communities of consumers and resources may present neutral-like outcomes, which we verify using numerical simulations. Our results, which span both static and dynamical community properties, demonstrate the limitations of summarizing distributions to detect non-neutrality, and provide a potential explanation for the successes of neutral theory as a description of macroecological pattern.

Translucent windows: how uncertainty in competitive interactions impacts detection of community pattern.

Traits can provide a window into the mechanisms that maintain coexistence among competing species. Recent theory suggests that competitive interactions will lead to groups, or clusters, of species with similar traits. However, theoretical predictions typically assume complete knowledge of the map between competition and measured traits. These assumptions limit the plausible application of these patterns for inferring competitive interactions in nature. Here, we relax these restrictions and find that the clustering pattern is robust to contributions of unknown or unobserved niche axes. However, it may not be visible unless measured traits are close proxies for niche strategies. We conclude that patterns along single niche axes may reveal properties of interspecific competition in nature, but detecting these patterns requires natural history expertise firmly tying traits to niches.

Born to Run? Quantifying the Balance of Prior Bias and New Information in Prey Escape Decisions.

Animal behaviors can often be challenging to model and predict, though optimality theory has improved our ability to do so. While many qualitative predictions of behavior exist, accurate quantitative models, tested by empirical data, are often lacking. This is likely due to variation in biases across individuals and variation in the way new information is gathered and used. We propose a modeling framework based on a novel interpretation of Bayes's theorem to integrate optimization of energetic constraints with both prior biases and specific sources of new information gathered by individuals. We present methods for inferring distributions of prior biases within populations rather than assuming known priors, as is common in Bayesian approaches to modeling behavior, and for evaluating the goodness of fit of overall model descriptions. We apply this framework to predict optimal escape during predator-prey encounters, based on prior biases and variation in what information prey use. Using this approach, we collected and analyzed data characterizing white-tailed deer (Odocoileus virginianus) escape behavior in response to human approaches. We found that distance to predator alone was not sufficient to predict deer flight response and show that the inclusion of additional information is necessary. We also compared differences in the inferred distributions of prior biases across different populations and discuss the possible role of human activity in influencing these distributions.

Backbones of evolutionary history test biodiversity theory for microbes.

Identifying the ecological and evolutionary mechanisms that determine biological diversity is a central question in ecology. In microbial ecology, phylogenetic diversity is an increasingly common and relevant means of quantifying community diversity, particularly given the challenges in defining unambiguous species units from environmental sequence data. We explore patterns of phylogenetic diversity across multiple bacterial communities drawn from different habitats and compare these data to evolutionary trees generated using theoretical models of biodiversity. We have two central findings. First, although on finer scales the empirical trees are highly idiosyncratic, on coarse scales the backbone of these trees is simple and robust, consistent across habitats, and displays bursts of diversification dotted throughout. Second, we find that these data demonstrate a clear departure from the predictions of standard neutral theories of biodiversity and that an alternative family of generalized models provides a qualitatively better description. Together, these results lay the groundwork for a theoretical framework to connect ecological mechanisms to observed phylogenetic patterns in microbial communities.

Reinterpreting maximum entropy in ecology: a null hypothesis constrained by ecological mechanism.

Simplified mechanistic models in ecology have been criticised for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in ecology to make predictions constrained by just a handful of state variables, like total abundance or species richness. But an outstanding question remains: what principle tells us which state variables to constrain? Here we attempt to solve both problems simultaneously, by translating a given set of mechanisms into the state variables to be used in MaxEnt, and then using this MaxEnt theory as a null model against which to compare mechanistic predictions. In particular, we identify the sufficient statistics needed to parametrise a given mechanistic model from data and use them as MaxEnt constraints. Our approach isolates exactly what mechanism is telling us over and above the state variables alone.

Species-abundance distributions under colored environmental noise.

Natural communities at all spatiotemporal scales are subjected to a wide variety of environmental pressures, resulting in random changes in the demographic rates of species populations. Previous analyses have examined the effects of such environmental variance on the long-term growth rate and time to extinction of single populations, but studies of its effects on the diversity of communities remain scarce. In this study, we construct a new master-equation model incorporating demographic and environmental variance and use it to examine how statistical patterns of diversity, as encapsulated by species-abundance distributions (SADs), are altered by environmental variance. Unlike previous diffusion models with environmental variance uncorrelated in time (white noise), our model allows environmental variance to be correlated at different timescales (colored noise), thus facilitating representation of phenomena such as yearly and decadal changes in climate. We derive an exact analytical expression for SADs predicted by our model together with a close approximation, and use them to show that the main effect of adding environmental variance is to increase the proportion of abundant species, thus flattening the SAD relative to the log-series form found in the neutral case. This flattening effect becomes more prominent when environmental variance is more correlated in time and has greater effects on species' demographic rates, holding all other factors constant. Furthermore, we show how our model SADs are consistent with those from diffusion models near the white noise limit. The mathematical techniques we develop are catalysts for further theoretical work exploring the consequences of environmental variance for biodiversity.

Maintenance of biodiversity on islands.

MacArthur and Wilson's theory of island biogeography predicts that island species richness should increase with island area. This prediction generally holds among large islands, but among small islands species richness often varies independently of island area, producing the so-called 'small-island effect' and an overall biphasic species-area relationship (SAR). Here, we develop a unified theory that explains the biphasic island SAR. Our theory's key postulate is that as island area increases, the total number of immigrants increases faster than niche diversity. A parsimonious mechanistic model approximating these processes reproduces a biphasic SAR and provides excellent fits to 100 archipelago datasets. In the light of our theory, the biphasic island SAR can be interpreted as arising from a transition from a niche-structured regime on small islands to a colonization-extinction balance regime on large islands. The first regime is characteristic of classic deterministic niche theories; the second regime is characteristic of stochastic theories including the theory of island biogeography and neutral theory. The data furthermore confirm our theory's key prediction that the transition between the two SAR regimes should occur at smaller areas, where immigration is stronger (i.e. for taxa that are better dispersers and for archipelagos that are less isolated).

Comparing process-based and constraint-based approaches for modeling macroecological patterns.

Ecological patterns arise from the interplay of many different processes, and yet the emergence of consistent phenomena across a diverse range of ecological systems suggests that many patterns may in part be determined by statistical or numerical constraints. Differentiating the extent to which patterns in a given system are determined statistically, and where it requires explicit ecological processes, has been difficult. We tackled this challenge by directly comparing models from a constraint-based theory, the Maximum Entropy Theory of Ecology (METE) and models from a process-based theory, the size-structured neutral theory (SSNT). Models from both theories were capable of characterizing the distribution of individuals among species and the distribution of body size among individuals across 76 forest communities. However, the SSNT models consistently yielded higher overall likelihood, as well as more realistic characterizations of the relationship between species abundance and average body size of conspecific individuals. This suggests that the details of the biological processes contain additional information for understanding community structure that are not fully captured by the METE constraints in these systems. Our approach provides a first step towards differentiating between process- and constraint-based models of ecological systems and a general methodology for comparing ecological models that make predictions for multiple patterns.

Reproducing static and dynamic biodiversity patterns in tropical forests: the critical role of environmental variance.

Ecological communities are subjected to stochasticity in the form of demographic and environmental variance. Stochastic models that contain only demographic variance (neutral models) provide close quantitative fits to observed species-abundance distributions (SADs) but substantially underestimate observed temporal species-abundance fluctuations. To provide a holistic assessment of whether models with demographic and environmental variance perform better than neutral models, the fit of both to SADs and temporal species-abundance fluctuations at the same time has to be tested quantitatively. In this study, we quantitatively test how closely a model with demographic and environmental variance reproduces total numbers of species, total abundances, SADs and temporal species-abundance fluctuations for two tropical forest tree communities, using decadal data from long-term monitoring plots and considering individuals larger than two size thresholds for each community. We find that the model can indeed closely reproduce these static and dynamic patterns of biodiversity in the two communities for the two size thresholds, with better overall fits than corresponding neutral models. Therefore, our results provide evidence that stochastic models incorporating demographic and environmental variance can simultaneously capture important static and dynamic biodiversity patterns arising in tropical forest communities.

A mean field model for competition: from neutral ecology to the Red Queen.

Individual species are distributed inhomogeneously over space and time, yet, within large communities of species, aggregated patterns of biodiversity seem to display nearly universal behaviour. Neutral models assume that an individual's demographic prospects are independent of its species identity. They have successfully predicted certain static, time-independent patterns. But they have generally failed to predict temporal patterns, such as species ages or population dynamics. We construct a new, multispecies framework incorporating competitive differences between species, and assess the impact of this competition on static and dynamic patterns of biodiversity. We solve this model exactly for the special case of a Red Queen hypothesis, where fitter species are continually arising. The model predicts more realistic species ages than neutral models, without greatly changing predictions for static species abundance distributions. Our modelling approach may allow users to incorporate a broad range of ecological mechanisms.

Species ages in neutral biodiversity models.

Biogeography seeks to understand the mechanisms that drive biodiversity across long temporal and large spatial scales. Theoretical models of biogeography can be tested by comparing their predictions of quantities such as species ages against empirical estimates. It has previously been claimed that the neutral theory of biodiversity and biogeography predicts species ages that are unrealistically long. Any improved theory of biodiversity must rectify this problem, but first it is necessary to quantify the problem precisely. Here we provide analytical expressions for species ages in neutral biodiversity communities. We analyse a spatially implicit metacommunity model and solve for both the zero-sum and non-zero-sum cases. We explain why our new expressions are, in the context of biodiversity, usually more appropriate than those previously imported from neutral molecular evolution. Because of the time symmetry of the spatially implicit neutral model, our expressions also lead directly to formulas for species persistence times and species lifetimes. We use our new expressions to estimate species ages of forest trees under a neutral model and find that they are about an order of magnitude shorter than those predicted previously but still unrealistically long. In light of our results, we discuss different models of biogeography that may solve the problem of species ages.

Moving beyond the mean: an analysis of faecal corticosterone metabolites shows substantial variability both within and across white-tailed deer populations.

Glucocorticoid (GC) levels have significant impacts on the health and behaviour of wildlife populations and are involved in many essential body functions including circadian rhythm, stress physiology and metabolism. However, studies of GCs in wildlife often focus on estimating mean hormone levels in populations, or a subset of a population, rather than on assessing the entire distribution of hormone levels within populations. Additionally, explorations of population GC data are limited due to the tradeoff between the number of individuals included in studies and the amount of data per individual that can be collected. In this study, we explore patterns of GC level distributions in three white-tailed deer (Odocoileus virginianus) populations using a non-invasive, opportunistic sampling approach. GC levels were assessed by measuring faecal corticosterone metabolite levels ('fCMs') from deer faecal samples throughout the year. We found both population and seasonal differences in fCMs but observed similarly shaped fCM distributions in all populations. Specifically, all population fCM cumulative distributions were found to be very heavy-tailed. We developed two toy models of acute corticosterone elevation in an effort to recreate the observed heavy-tailed distributions. We found that, in all three populations, cumulative fCM distributions were better described by an assumption of large, periodic spikes in corticosterone levels every few days, as opposed to an assumption of random spikes in corticosterone levels. The analyses presented in this study demonstrate the potential for exploring population-level patterns of GC levels from random, opportunistically sampled data. When taken together with individual-focused studies of GC levels, such analyses can improve our understanding of how individual hormone production scales up to population-level patterns.

Processes governing species richness in communities exposed to temporal environmental stochasticity: A review and synthesis of modelling approaches.

Research into the processes governing species richness has often assumed that the environment is fixed, whereas realistic environments are often characterised by random fluctuations over time. This temporal environmental stochasticity (TES) changes the demographic rates of species populations, with cascading effects on community dynamics and species richness. Theoretical and applied studies have used process-based mathematical models to determine how TES affects species richness, but under a variety of frameworks. Here, we critically review such studies to synthesise their findings and draw general conclusions. We first provide a broad mathematical framework encompassing the different ways in which TES has been modelled. We then review studies that have analysed models with TES under the assumption of negligible interspecific interactions, such that a community is conceptualised as the sum of independent species populations. These analyses have highlighted how TES can reduce species richness by increasing the frequency at which a species becomes rare and therefore prone to extinction. Next, we review studies that have relaxed the assumption of negligible interspecific interactions. To simplify the corresponding models and make them analytically tractable, such studies have used mean-field theory to derive fixed parameters representing the typical strength of interspecific interactions under TES. The resulting analyses have highlighted community-level effects that determine how TES affects species richness, for species that compete for a common limiting resource. With short temporal correlations of environmental conditions, a non-linear averaging effect of interspecific competition strength over time gives an increase in species richness. In contrast, with long temporal correlations of environmental conditions, strong selection favouring the fittest species between changes in environmental conditions results in a decrease in species richness. We compare such results with those from invasion analysis, which examines invasion growth rates (IGRs) instead of species richness directly. Qualitative differences sometimes arise because the IGR is the expected growth rate of a species when it is rare, which does not capture the variation around this mean or the probability of the species becoming rare. Our review elucidates key processes that have been found to mediate the negative and positive effects of TES on species richness, and by doing so highlights key areas for future research.