Using neural ordinary differential equations to predict complex ecological dynamics from population density data.

Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modelling bias due to simplifying assumptions or unaccounted factors, limiting their predictive power. Neural ordinary differential equations (NODEs) have surged as a machine-learning algorithm that preserves the dynamic nature of the data (Chen et al. 2018 Adv. Neural Inf. Process. Syst.). Although preserving the dynamics in the data is an advantage, the question of how NODEs perform as a forecasting tool of ecological communities is unanswered. Here, we explore this question using simulated time series of competing species in a time-varying environment. We find that NODEs provide more precise forecasts than autoregressive integrated moving average (ARIMA) models. We also find that untuned NODEs have a similar forecasting accuracy to untuned long-short term memory neural networks and both are outperformed in accuracy and precision by empirical dynamical modelling . However, we also find NODEs generally outperform all other methods when evaluating with the interval score, which evaluates precision and accuracy in terms of prediction intervals rather than pointwise accuracy. We also discuss ways to improve the forecasting performance of NODEs. The power of a forecasting tool such as NODEs is that it can provide insights into population dynamics and should thus broaden the approaches to studying time series of ecological communities.

The three-species problem: Incorporating competitive asymmetry and intransitivity in modern coexistence theory.

While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three-species competitive communities are a bridge to more-diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three-species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet-wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three-species competition outcomes.

Eco-evolutionary emergence of macroecological scaling in plankton communities.

Macroecological scaling patterns, such as between prey and predator biomass, are fundamental to our understanding of the rules of biological organization and ecosystem functioning. Although these scaling patterns are ubiquitous, how they arise is poorly understood. To explain these patterns, we used an eco-evolutionary predator-prey model parameterized using data for phytoplankton and zooplankton. We show that allometric scaling relationships at lower levels of biological organization, such as body-size scaling of nutrient uptake and predation, give rise to scaling relationships at the food web and ecosystem levels. Our predicted macroecological scaling exponents agree well with observed values across ecosystems. Our findings explicitly connect scaling relationships at different levels of biological organization to ecological and evolutionary mechanisms, yielding testable hypotheses for how observed macroecological patterns emerge.

The ecological causes of functional distinctiveness in communities.

Recent work has shown that evaluating functional trait distinctiveness, the average trait distance of a species to other species in a community offers promising insights into biodiversity dynamics and ecosystem functioning. However, the ecological mechanisms underlying the emergence and persistence of functionally distinct species are poorly understood. Here, we address the issue by considering a heterogeneous fitness landscape whereby functional dimensions encompass peaks representing trait combinations yielding positive population growth rates in a community. We identify four ecological cases contributing to the emergence and persistence of functionally distinct species. First, environmental heterogeneity or alternative phenotypic designs can drive positive population growth of functionally distinct species. Second, sink populations with negative population growth can deviate from local fitness peaks and be functionally distinct. Third, species found at the margin of the fitness landscape can persist but be functionally distinct. Fourth, biotic interactions (positive or negative) can dynamically alter the fitness landscape. We offer examples of these four cases and guidelines to distinguish between them. In addition to these deterministic processes, we explore how stochastic dispersal limitation can yield functional distinctiveness. Our framework offers a novel perspective on the relationship between fitness landscape heterogeneity and the functional composition of ecological assemblages.

Life-history responses to temperature and seasonality mediate ectotherm consumer-resource dynamics under climate warming.

Climate warming is altering life cycles of ectotherms by advancing phenology and decreasing generation times. Theoretical models provide powerful tools to investigate these effects of climate warming on consumer-resource population dynamics. Yet, existing theory primarily considers organisms with simplified life histories in constant temperature environments, making it difficult to predict how warming will affect organisms with complex life cycles in seasonal environments. We develop a size-structured consumer-resource model with seasonal temperature dependence, parameterized for a freshwater insect consuming zooplankton. We simulate how climate warming in a seasonal environment could alter a key life-history trait of the consumer, number of generations per year, mediating responses of consumer-resource population sizes and consumer persistence. We find that, with warming, consumer population sizes increase through multiple mechanisms. First, warming decreases generation times by increasing rates of resource ingestion and growth and/or lengthening the growing season. Second, these life-history changes shorten the juvenile stage, increasing the number of emerging adults and population-level reproduction. Unstructured models with similar assumptions found that warming destabilized consumer-resource dynamics. By contrast, our size-structured model predicts stability and consumer persistence. Our study suggests that, in seasonal environments experiencing climate warming, life-history changes that lead to shorter generation times could delay population extinctions.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly.

AbstractHow is trait diversity in a community apportioned between and within coevolving species? Disruptive selection may result in either a few species with large intraspecific trait variation (ITV) or many species with different mean traits but little ITV. Similar questions arise in spatially structured communities: heterogeneous environments could result in either a few species that exhibit local adaptation or many species with different mean traits but little local adaptation. To date, theory has been well-equipped to either include ITV or to dynamically determine the number of coexisting species, but not both. Here, we devise a theoretical framework that combines these facets and apply it to the above questions of how trait variation is apportioned within and between species in unstructured and structured populations, using two simple models of Lotka-Volterra competition. For unstructured communities, we find that as the breadth of the resource spectrum increases, ITV goes from being unimportant to crucial for characterizing the community. For spatially structured communities on two patches, we find no local adaptation, symmetric local adaptation, or asymmetric local adaptation, depending on how much the patches differ. Our framework provides a general approach to incorporate ITV in models of eco-evolutionary community assembly.

A general framework for species-abundance distributions: Linking traits and dispersal to explain commonness and rarity.

Species-abundance distributions (SADs) describe the spectrum of commonness and rarity in a community. Beyond the universal observation that most species are rare and only a few common, more-precise description of SAD shape is controversial. Furthermore, the mechanisms behind SADs and how they vary along environmental gradients remain unresolved. We lack a general, non-neutral theory of SADs. Here, we develop a trait-based framework, focusing on a local community coupled to the region by dispersal. The balance of immigration and exclusion determines abundances, which vary over orders-of-magnitude. The local trait-abundance distribution (TAD) reflects a transformation of the regional TAD. The left-tail of the SAD depends on scaling exponents of the exclusion function and the regional species pool. More-complex local dynamics can lead to multimodal TADs and SADs. Connecting SADs with trait-based ecological theory provides a way to generate more-testable hypotheses on the controls over commonness and rarity in communities.

How the resource supply distribution structures competitive communities.

Competition is a pervasive interaction known to structure ecological communities. The Lotka-Volterra (LV) model has been foundational for our understanding of competition, and trait-based LV models have been used to model community assembly and eco-evolutionary phenomena like diversification. The intrinsic growth rate function is determined by the underlying resource distribution and is a key determinant of the resulting diversity, traits and abundances of species. In these models, the width of the resource distribution relative to the width of the competition kernel has been identified as a key parameter that leads to diversification. However, studies have only investigated the impact of width at just a few discrete values, while also often assuming the intrinsic growth rate function to be unimodal. Thus, the impact of the underlying resource distribution's width and shape together remains incompletely explored, particularly for large, diverse communities. In this study, we vary its width continuously for two shapes (unimodal and bimodal) to explore its impact on community structure. When the resource distribution is very narrow in both the unimodal bimodal cases, competition is strong, leading to exclusion of all but the best-adapted species. Wider resource distributions allow stable coexistence, where the traits of the species depend on the shape of the resource distribution. Extremely wide resource distributions support a diverse community, where the strength of competition ultimately determines the diversity and traits of coexisting species, but their abundances reflect the underlying resource distribution. Further, competition acts to maximize the use of available resources among the competing species. For large communities, the shape of resource distribution becomes immaterial and the width determines the diversity. These results affirm and extend our understanding of limiting similarity.

Resource Competition and Host Feedbacks Underlie Regime Shifts in Gut Microbiota.

AbstractThe spread of an enteric pathogen in the human gut depends on many interacting factors, including pathogen exposure, diet, host gut environment, and host microbiota, but how these factors jointly influence infection outcomes remains poorly characterized. Here we develop a model of host-mediated resource competition between mutualistic and pathogenic taxa in the gut that aims to explain why similar hosts, exposed to the same pathogen, can have such different infection outcomes. Our model successfully reproduces several empirically observed phenomena related to transitions between healthy and infected states, including (1) the nonlinear relationship between pathogen inoculum size and infection persistence, (2) the elevated risk of chronic infection during or after treatment with broad-spectrum antibiotics, (3) the resolution of gut dysbiosis with fecal microbiota transplants, and (4) the potential protection from infection conferred by probiotics. We then use the model to explore how host-mediated interventions-namely, shifts in the supply rates of electron donors (e.g., dietary fiber) and respiratory electron acceptors (e.g., oxygen)-can potentially be used to direct gut community assembly. Our study demonstrates how resource competition and ecological feedbacks between the host and the gut microbiota can be critical determinants of human health outcomes. We identify several testable model predictions ready for experimental validation.

Climate Change-Driven Regime Shifts in a Planktonic Food Web.

AbstractPredicting how food webs will respond to global environmental change is difficult because of the complex interplay between the abiotic forcing and biotic interactions. Mechanistic models of species interactions in seasonal environments can help understand the effects of global change in different ecosystems. Seasonally ice-covered lakes are warming faster than many other ecosystems and undergoing pronounced food web changes, making the need to forecast those changes especially urgent. Using a seasonally forced food web model with a generalist zooplankton grazer and competing cold-adapted winter and warm-adapted summer phytoplankton, we show that with declining ice cover, the food web moves through different dynamic regimes, from annual to biennial cycles, with decreasing and then disappearing winter phytoplankton blooms and a shift of maximum biomass to summer season. Interestingly, when predator-prey interactions were not included, a declining ice cover did not cause regime shifts, suggesting that both are needed for regime transitions. A cluster analysis of long-term data from Lake Baikal, Siberia, supports the model results, revealing a change from regularly occurring winter blooms of endemic diatoms to less frequent winter bloom years with decreasing ice cover. Together, the results show that even gradual environmental change, such as declining ice cover duration, may cause discontinuous or abrupt transitions between dynamic regimes in food webs.

Ecological limits to evolutionary rescue.

Environments change, for both natural and anthropogenic reasons, which can threaten species persistence. Evolutionary adaptation is a potentially powerful mechanism to allow species to persist in these changing environments. To determine the conditions under which adaptation will prevent extinction (evolutionary rescue), classic quantitative genetics models have assumed a constantly changing environment. They predict that species traits will track a moving environmental optimum with a lag that approaches a constant. If fitness is negative at this lag, the species will go extinct. There have been many elaborations of these models incorporating increased genetic realism. Here, we review and explore the consequences of four ecological complications: non-quadratic fitness functions, interacting density- and trait-dependence, species interactions and fundamental limits to adaptation. We show that non-quadratic fitness functions can result in evolutionary tipping points and existential crises, as can the interaction between density- and trait-dependent mortality. We then review the literature on how interspecific interactions affect adaptation and persistence. Finally, we suggest an alternative theoretical framework that considers bounded environmental change and fundamental limits to adaptation. A research programme that combines theory and experiments and integrates across organizational scales will be needed to predict whether adaptation will prevent species extinction in changing environments. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

Nitrogen limitation inhibits marine diatom adaptation to high temperatures.

Ongoing climate change is shifting species distributions and increasing extinction risks globally. It is generally thought that large population sizes and short generation times of marine phytoplankton may allow them to adapt rapidly to global change, including warming, thus limiting losses of biodiversity and ecosystem function. Here, we show that a marine diatom survives high, previously lethal, temperatures after adapting to above-optimal temperatures under nitrogen (N)-replete conditions. N limitation, however, precludes thermal adaptation, leaving the diatom vulnerable to high temperatures. A trade-off between high-temperature tolerance and increased N requirements may explain why N limitation inhibited adaptation. Because oceanic N limitation is common and likely to intensify in the future, the assumption that phytoplankton will readily adapt to rising temperatures may need to be reevaluated.

Microbial cross-feeding promotes multiple stable states and species coexistence, but also susceptibility to cheaters.

Mutualism, interspecific cooperation that yields reciprocal benefits, can promote species coexistence, enhancing biodiversity. As a specific form of mutualism, cross-feeding, where each of two mutualists produces a resource the other one needs, has been broadly studied. However, few theoretical studies have examined competition between cross-feeding mutualists and cheaters, who do not synthesize resources themselves. In this paper we study a model with two mutualists, a cheater, two micronutrients that are synthesized and exchanged by the mutualists, and one macronutrient that is only from external supply. We investigate the coexistence of the species in the framework of resource competition theory. In particular, we examine the effect of the mutualists' synthesis rates on their coexistence. In the absence of cheaters, multiple stable states occur if the synthesis rates are high, and higher synthesis rates increase the possibility that mutualists coexist. However, when the cheater is present, higher synthesis rates promote invasion by the cheater: If the cheater is superior on all three resources, it will either persist with at most one mutualist or even trigger extinction of all three species; if the cheater is only superior on the macronutrient, both mutualists may still coexist with the cheater. Our results provide a framework for further study on more complex mutualistic networks and real microbial communities.

Regional neutrality evolves through local adaptive niche evolution.

Biodiversity in natural systems can be maintained either because niche differentiation among competitors facilitates stable coexistence or because equal fitness among neutral species allows for their long-term cooccurrence despite a slow drift toward extinction. Whereas the relative importance of these two ecological mechanisms has been well-studied in the absence of evolution, the role of local adaptive evolution in maintaining biological diversity through these processes is less clear. Here we study the contribution of local adaptive evolution to coexistence in a landscape of interconnected patches subject to disturbance. Under these conditions, early colonists to empty patches may adapt to local conditions sufficiently fast to prevent successful colonization by other preadapted species. Over the long term, the iteration of these local-scale priority effects results in niche convergence of species at the regional scale even though species tend to monopolize local patches. Thus, the dynamics evolve from stable coexistence through niche differentiation to neutral cooccurrence at the landscape level while still maintaining strong local niche segregation. Our results show that neutrality can emerge at the regional scale from local, niche-based adaptive evolution, potentially resolving why ecologists often observe neutral distribution patterns at the landscape level despite strong niche divergence among local communities.

Evolutionarily stable communities: a framework for understanding the role of trait evolution in the maintenance of diversity.

Biological diversity depends on the interplay between evolutionary diversification and ecological mechanisms allowing species to coexist. Current research increasingly integrates ecology and evolution over a range of timescales, but our common conceptual framework for understanding species coexistence requires better incorporation of evolutionary processes. Here, we focus on the idea of evolutionarily stable communities (ESCs), which are theoretical endpoints of evolution in a community context. We use ESCs as a unifying framework to highlight some important but under-appreciated theoretical results, and we review empirical research relevant to these theoretical predictions. We explain how, in addition to generating diversity, evolution can also limit diversity by reducing the effectiveness of coexistence mechanisms. The coevolving traits of competing species may either diverge or converge, depending on whether the number of species in the community is low (undersaturated) or high (oversaturated) relative to the ESC. Competition in oversaturated communities can lead to extinction or neutrally coexisting, ecologically equivalent species. It is critical to consider trait evolution when investigating fundamental ecological questions like the strength of different coexistence mechanisms, the feasibility of ecologically equivalent species, and the interpretation of different patterns of trait dispersion.

Plant Strategies along Resource Gradients.

Plants present a variety of defensive strategies against herbivores, broadly classified into tolerance and resistance. Since resource availability can also limit plant growth, we expect plant allocation to resource acquisition and defense to vary along resource gradients. Yet, the conditions under which one defensive strategy is favored over the other are unclear. Here, we use an eco-evolutionary model to investigate plant adaptive allocation to resource acquisition, tolerance, and resistance along a resource gradient in a simple food web module inspired by plankton communities where plants compete for a single resource and are grazed on by a shared herbivore. We show that undefended, acquisition-specialist strategies dominate under low resource supplies. Conversely, high resource supplies, which lead to high herbivore abundance because of trophic transfers, result in either the dominance of very resistant strategies or coexistence between a completely resistant strategy and a fast-growing, tolerant one. We also explore the consequences of this adaptive allocation on species biomasses. Finally, we compare our predictions to a more traditional, density-independent optimization model. We show that density dependence mediated by resources and herbivores is the cause of the increase in plant resistance along the resource gradient, as the optimization model would instead have favored tolerance.

How leaking and overproducing resources affect the evolutionary robustness of cooperative cross-feeding.

Cooperative cross-feeding, a resource-exchange mutualism between microbes, is ubiquitous; however, models suggest it should be susceptible to cheating. Recent work suggested two novel mechanisms that could allow cross-feeders to exclude cheaters, even in the absence of tight coupling between cooperative organisms. The first is pattern formation, where cross-feeders form regular patterns so that their resources are separated and cheaters cannot obtain both. The second mechanism is neighbor uncertainty, where demographic stochasticity separates resources so cheaters cannot obtain both. Here we use a stochastic spatial model to test whether those mechanisms are evolutionarily stable, or whether they will collapse under gradual evolution towards reduced resource production. The answer depends on whether a microbe can make the resource for itself without sharing it. If it cannot (i.e. if producing more of a resource means sharing more of a resource), then both mechanisms continue to function. In this case, resource production directly benefits the individual, and cooperation is a byproduct. If microbes can make the resource without sharing it (i.e. if production is an altruistic trait), then neighbor uncertainty completely fails, and pattern formation is weakened. In this case, the costly trait has no direct benefit to the individual, and can only persist if cooperative organisms become associated with their partner. Thus, the novel mechanisms, which operate without tight associations, falter. These results have implications for synthetic ecology, as they suggest that how cross-feeding is engineered will impact its evolutionary stability.

Rapid thermal adaptation in a marine diatom reveals constraints and trade-offs.

Rapid evolution in response to environmental change will likely be a driving force determining the distribution of species across the biosphere in coming decades. This is especially true of microorganisms, many of which may evolve in step with warming, including phytoplankton, the diverse photosynthetic microbes forming the foundation of most aquatic food webs. Here we tested the capacity of a globally important, model marine diatom Thalassiosira pseudonana, for rapid evolution in response to temperature. Selection at 16 and 31°C for 350 generations led to significant divergence in several temperature response traits, demonstrating local adaptation and the existence of trade-offs associated with adaptation to different temperatures. In contrast, competitive ability for nitrogen (commonly limiting in marine systems), measured after 450 generations of temperature selection, did not diverge in a systematic way between temperatures. This study shows how rapid thermal adaptation affects key temperature and nutrient traits and, thus, a population's long-term physiological, ecological, and biogeographic response to climate change.

Local interactions and self-organized spatial patterns stabilize microbial cross-feeding against cheaters.

Mutualisms are ubiquitous, but models predict they should be susceptible to cheating. Resolving this paradox has become relevant to synthetic ecology: cooperative cross-feeding, a nutrient-exchange mutualism, has been proposed to stabilize microbial consortia. Previous attempts to understand how cross-feeders remain robust to non-producing cheaters have relied on complex behaviour (e.g. cheater punishment) or group selection. Using a stochastic spatial model, we demonstrate two novel mechanisms that can allow cross-feeders to outcompete cheaters, rather than just escape from them. Both mechanisms work through the spatial segregation of the resources, which prevents individual cheaters from acquiring the resources they need to reproduce. First, if microbe dispersal is low but resources are shared widely, then the cross-feeders self-organize into stable spatial patterns. Here the cross-feeders can build up where the resource they need is abundant, and send their resource to where their partner is, separating resources at regular intervals in space. Second, if dispersal is high but resource sharing is local, then random variation in population density creates small-scale variation in resource density, separating the resources from each other by chance. These results suggest that cross-feeding may be more robust than previously expected and offer strategies to engineer stable consortia.

How spatial structure and neighbor uncertainty promote mutualists and weaken black queen effects.

The ubiquity of cooperative cross-feeding (a resource-exchange mutualism) raises two related questions: Why is cross-feeding favored over self-sufficiency, and how are cross-feeders protected from non-producing cheaters? The Black Queen Hypothesis suggests that if leaky resources are costly, then there should be selection for either gene loss or self-sufficiency, but selection against mutualistic inter-dependency. Localized interactions have been shown to protect mutualists against cheaters, though their effects in the presence of self-sufficient organisms are not well understood. Here we develop a stochastic spatial model to examine how spatial effects alter the predictions of the Black Queen Hypothesis. Microbes need two essential resources to reproduce, which they can produce themselves (at a cost) or take up from neighbors. Additionally, microbes need empty sites to give birth into. Under well mixed mean-field conditions, the cross-feeders will always be displaced by a non-producer and a self-sufficient microbe. However, localized interactions have two effects that favor production. First, a microbe that interacts with a small number of neighbors will not always receive the essential resources it needs; this effect slightly harms cross-feeders but greatly harms non-producers. Second, microbes tend to displace other microbes that produce resources they need; this effect also slightly harms cross-feeders but greatly harms non-producers. Our work therefore suggests localized interactions produce an accelerating cost of non-production. Thus, the right trade-off between the cost of producing resources and the cost of sometimes being resource-limited can favor mutualistic inter-dependence over both self-sufficiency and non-production.