Consumer-resource Model Research Articles

Ecosystem stability relies on diversity difference between trophic levels

The stability of ecological communities has a profound impact on humans, ranging from individual health influenced by the microbiome to ecosystem services provided by fisheries. A long-standing goal of ecology is the elucidation of the interplay between biodiversity and ecosystem stability, with some ecologists warning of instability due to loss of species diversity while others arguing that greater diversity will instead lead to instability. Here, by considering a minimal two-level ecosystem with multiple predator and prey species, we show that stability does not depend on absolute diversity but rather on diversity differences between levels. We found that increasing diversity in either level first destabilizes but then stabilizes the community (i.e., a reentrant stability transition). We therefore find that it is the diversity difference between levels that is the key to stability, with the least stable communities having similar diversities in different levels. An analytical stability criterion is derived, demonstrating quantitatively that the critical diversity difference is determined by the correlation between how one level affects another and how it is affected in turn. Our stability criterion also applies to consumer-resource models with other forms of interaction such as cross-feeding. Finally, we show that stability depends on diversity differences in ecosystems with three trophic levels. Our finding of a nonmonotonic dependence of stability on diversity provides a natural explanation for the variety of diversity-stability relationships reported in the literature, and emphasizes the significance of level structure in predicting complex community behaviors.

MacArthur’s consumer-resource model: a 'Rosetta Stone' for competitive interactions

MacArthur’s consumer-resource model: a 'Rosetta Stone' for competitive interactions

Predicting metabolite response to dietary intervention using deep learning.

Due to highly personalized biological and lifestyle characteristics, different individuals may have different metabolite responses to specific foods and nutrients. In particular, the gut microbiota, a collection of trillions of microorganisms living in the gastrointestinal tract, is highly personalized and plays a key role in the metabolite responses to foods and nutrients. Accurately predicting metabolite responses to dietary interventions based on individuals' gut microbial compositions holds great promise for precision nutrition. Existing prediction methods are typically limited to traditional machine learning models. Deep learning methods dedicated to such tasks are still lacking. Here we develop a method McMLP (Metabolite response predictor using coupled Multilayer Perceptrons) to fill in this gap. We provide clear evidence that McMLP outperforms existing methods on both synthetic data generated by the microbial consumer-resource model and real data obtained from six dietary intervention studies. Furthermore, we perform sensitivity analysis of McMLP to infer the tripartite food-microbe-metabolite interactions, which are then validated using the ground-truth (or literature evidence) for synthetic (or real) data, respectively. The presented tool has the potential to inform the design of microbiota-based personalized dietary strategies to achieve precision nutrition.

Resource-based modelling approach to studying evolutionary rescue.

In this paper, we present an in-depth investigation into the dynamics of evolutionary rescue using a resource-based modelling approach. Utilizing classical consumer-resource models, we aim to understand how species can adapt to abrupt environmental changes that alter the availability of substitutable resources. Through both analytical solutions and simulation-based techniques, we explore the conditions under which populations can recover from critical sizes and avoid extinction. Our findings highlight the importance of minimum viable population sizes, mutation rates, and the adaptive capacity of metabolic strategies in influencing population resilience. We demonstrate that while increased mutation rates can facilitate faster recovery by enabling populations to evolve new metabolic strategies suited to the altered resource landscape, populations starting with smaller sizes or facing severe reductions in resource availability are more susceptible to extinction. This study offers valuable insights into the interplay between ecological dynamics and evolutionary mechanisms, providing a comprehensive framework for predicting population persistence and informing conservation strategies under changing environmental conditions.

Microbial Dormancy Supports Multi-Species Coexistence Under Resource Fluctuations.

The ability for microbes to enter dormant states is adaptive under resource fluctuations and has been linked to the maintenance of diversity. Nevertheless, the mechanism by which microbial dormancy gives rise to the density-dependent feedbacks required for stable coexistence under resource fluctuations is not well understood. Via analysis of consumer-resource models, we show that the stable coexistence of dormancy and non-dormancy strategists is a consequence of the former benefiting more from resource fluctuations while simultaneously reducing overall resource variability, which sets up the requisite negative frequency dependence. Moreover, we find that dormants can coexist alongside gleaner and opportunist strategies in a competitive-exclusion-defying case of three species coexistence on a single resource. This multi-species coexistence is typically characterised by non-simple assembly rules that cannot be predicted from pairwise competition outcomes. The diversity maintained via this three-way trade-off represents a novel phenomenon that is ripe for further theoretical and empirical inquiry.

Plant antagonistic facilitation across environmental gradients: a soil-resource ecosystem engineering model.

Theory questions the persistence of nonreciprocal interactions in which one plant has a positive net effect on a neighbor that, in return, has a negative net impact on its benefactor - a phenomenon known as antagonistic facilitation. We develop a spatially explicit consumer-resource model for belowground plant competition between ecosystem engineers, plants able to mine resources and make them available for any other plant in the community, and exploiters. We use the model to determine in what environmental conditions antagonistic facilitation via soil-resource engineering emerges as an optimal strategy. Antagonistic facilitation emerges in stressful environments where ecosystem engineers' self-benefits from mining resources outweigh the competition with opportunistic neighbors. Among all potential causes of stress considered in the model, the key environmental parameter driving changes in the interaction between plants is the proportion of the resource that becomes readily available for plant consumption in the absence of any mining activity. Our results align with theories of primary succession and the stress gradient hypothesis. However, we find that the total root biomass and its spatial allocation through the root system, often used to measure the sign of the interaction between plants, do not predict facilitation reliably.

Nutrient competition predicts gut microbiome restructuring under drug perturbations.

Human gut commensal bacteria are routinely exposed to various stresses, including therapeutic drugs, and collateral effects are difficult to predict. To systematically interrogate community-level effects of drug perturbations, we screened stool-derived in vitro communities with 707 clinically relevant small molecules. Across ∼5,000 community-drug interaction conditions, compositional and metabolomic responses were predictably impacted by nutrient competition, with certain species exhibiting improved growth due to adverse impacts on competitors. Changes to community composition were generally reversed by reseeding with the original community, although occasionally species promotion was long-lasting, due to higher-order interactions, even when the competitor was reseeded. Despite strong selection pressures, emergence of resistance within communities was infrequent. Finally, while qualitative species responses to drug perturbations were conserved across community contexts, nutrient competition quantitatively affected their abundances, consistent with predictions of consumer-resource models. Our study reveals that quantitative understanding of the interaction landscape, particularly nutrient competition, can be used to anticipate and potentially mitigate side effects of drug treatment on the gut microbiota.

Quantifying massively parallel microbial growth with spatially mediated interactions.

Quantitative understanding of microbial growth is an essential prerequisite for successful control of pathogens as well as various biotechnology applications. Even though the growth of cell populations has been extensively studied, microbial growth remains poorly characterised at the spatial level. Indeed, even isogenic populations growing at different locations on solid growth medium typically show significant location-dependent variability in growth. Here we show that this variability can be attributed to the initial physiological states of the populations, the interplay between populations interacting with their local environment and the diffusion of nutrients and energy sources coupling the environments. We further show how the causes of this variability change throughout the growth of a population. We use a dual approach, first applying machine learning regression models to discover that location dominates growth variability at specific times, and, in parallel, developing explicit population growth models to describe this spatial effect. In particular, treating nutrient and energy source concentration as a latent variable allows us to develop a mechanistic resource consumer model that captures growth variability across the shared environment. As a consequence, we are able to determine intrinsic growth parameters for each local population, removing confounders common to location-dependent variability in growth. Importantly, our explicit low-parametric model for the environment paves the way for massively parallel experimentation with configurable spatial niches for testing specific eco-evolutionary hypotheses.

On the Dynamics of Mortality and the Ephemeral Nature of Mammalian Megafauna.

AbstractEnergy flow through consumer-resource interactions is largely determined by body size. Allometric relationships govern the dynamics of populations by impacting rates of reproduction as well as alternative sources of mortality, which have differential impacts on smaller to larger organisms. Here we derive and investigate the timescales associated with four alternative sources of mortality for terrestrial mammals: mortality from starvation, mortality associated with aging, mortality from consumption by predators, and mortality introduced by anthropogenic subsidized harvest. The incorporation of these allometric relationships into a minimal consumer-resource model illuminates central constraints that may contribute to the structure of mammalian communities. Our framework reveals that while starvation largely impacts smaller-bodied species, the allometry of senescence is expected to be more difficult to observe. In contrast, external predation and subsidized harvest have greater impacts on the populations of larger-bodied species. Moreover, the inclusion of predation mortality reveals mass thresholds for mammalian herbivores, where dynamic instabilities may limit the feasibility of megafaunal populations. We show how these thresholds vary with alternative predator-prey mass relationships, which are not well understood within terrestrial systems. Finally, we use our framework to predict the harvest pressure required to induce mass-specific extinctions, which closely align with previous estimates of anthropogenic megafaunal exploitation in both paleontological and historical contexts. Together our results underscore the tenuous nature of megafaunal populations and how different sources of mortality may contribute to their ephemeral nature over evolutionary time.

Spatiotemporal patterns in a diffusive resource–consumer model with distributed memory and maturation delay

In this paper, we propose a diffusive consumer–resource model in which the consumer is involved with spatiotemporal memory and the resource has maturation delay. Firstly, for the case without maturation delay, the influence of the spatiotemporal distributed memory on the stability of the positive steady state is investigated. It has been shown that memory delay can induce Turing bifurcation for the negative memory-based diffusion coefficient and induce Hopf bifurcation for the positive memory-based diffusion coefficient. Then the joint effect of the memory delay and the maturation delay on the stability of the positive steady state is investigated and it has been shown that the joint effect of the memory delay and the maturation delay can induce more complicated spatiotemporal dynamics via Turing–Hopf bifurcation and double Hopf bifurcation. Finally, we apply our theoretical analysis results to a consumer–resource model with Holling-II type functional response to illustrate the existence of the different spatiotemporal patterns.

Phase Transition to Chaos in Complex Ecosystems with Nonreciprocal Species-Resource Interactions.

Nonreciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of nonreciprocity in the context of theoretical ecology by analyzing a generalization of MacArthur's consumer-resource model with asymmetric interactions between species and resources. Using a mixture of analytic cavity calculations and numerical simulations, we show that such ecosystems generically undergo a phase transition to chaotic dynamics as the amount of nonreciprocity is increased. We analytically construct the phase diagram for this model and show that the emergence of chaos is controlled by a single quantity: the ratio of surviving species to surviving resources. We also numerically calculate the Lyapunov exponents in the chaotic phase and carefully analyze finite-size effects. Our findings show how nonreciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.

Resource competition predicts assembly of gut bacterial communities in vitro.

Microbial community dynamics arise through interspecies interactions, including resource competition, cross-feeding and pH modulation. The individual contributions of these mechanisms to community structure are challenging to untangle. Here we develop a framework to estimate multispecies niche overlaps by combining metabolomics data of individual species, growth measurements in spent media and mathematical models. We applied our framework to an in vitro model system comprising 15 human gut commensals in complex media and showed that a simple model of resource competition accounted for most pairwise interactions. Next, we built a coarse-grained consumer-resource model by grouping metabolomic features depleted by the same set of species and showed that this model predicted the composition of 2-member to 15-member communities with reasonable accuracy. Furthermore, we found that incorporation of cross-feeding and pH-mediated interactions improved model predictions of species coexistence. Our theoretical model and experimental framework can be applied to characterize interspecies interactions in bacterial communities in vitro.

Emergent competition shapes top-down versus bottom-up control in multi-trophic ecosystems.

Ecosystems are commonly organized into trophic levels-organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic structure, diversity, and competition shapes the properties of ecosystems. To address this problem, we analyze a generalized Consumer Resource Model with three trophic levels using the zero-temperature cavity method and numerical simulations. We derive the corresponding mean-field cavity equations and show that intra-trophic diversity gives rise to an effective "emergent competition" term between species within a trophic level due to feedbacks mediated by other trophic levels. This emergent competition gives rise to a crossover from a regime of top-down control (populations are limited by predators) to a regime of bottom-up control (populations are limited by primary producers) and is captured by a simple order parameter related to the ratio of surviving species in different trophic levels. We show that our theoretical results agree with empirical observations, suggesting that the theoretical approach outlined here can be used to understand complex ecosystems with multiple trophic levels.

Pairing metagenomics and metaproteomics to characterize ecological niches and metabolic essentiality of gut microbiomes.

The genome of a microorganism encodes its potential functions that can be implemented through expressed proteins. It remains elusive how a protein's selective expression depends on its metabolic essentiality to microbial growth or its ability to claim resources as ecological niches. To reveal a protein's metabolic or ecological role, we developed a computational pipeline, which pairs metagenomics and metaproteomics data to quantify each protein's gene-level and protein-level functional redundancy simultaneously. We first illustrated the idea behind the pipeline using simulated data of a consumer-resource model. We then validated it using real data from human and mouse gut microbiome samples. In particular, we analyzed ABC-type transporters and ribosomal proteins, confirming that the metabolic and ecological roles predicted by our pipeline agree well with prior knowledge. Finally, we performed in vitro cultures of a human gut microbiome sample and investigated how oversupplying various sugars involved in ecological niches influences the community structure and protein abundance. The presented results demonstrate the performance of our pipeline in identifying proteins' metabolic and ecological roles, as well as its potential to help us design nutrient interventions to modulate the human microbiome.

Reciprocal inhibition and competitive hierarchy cause negative biodiversity-ecosystem function relationships.

The relationship between biodiversity and ecosystem function (BEF) captivates ecologists, but the factors responsible for the direction of this relationship remain unclear. While higher ecosystem functioning at higher biodiversity levels ('positive BEF') is not universal in nature, negative BEF relationships seem puzzlingly rare. Here, we develop a dynamical consumer-resource model inspired by microbial decomposer communities in pitcher plant leaves to investigate BEF. We manipulate microbial diversity via controlled colonization and measure their function as total ammonia production. We test how niche partitioning among bacteria and other ecological processes influence BEF in the leaves. We find that a negative BEF can emerge from reciprocal interspecific inhibition in ammonia production causing a negative complementarity effect, or from competitive hierarchies causing a negative selection effect. Absent these factors, a positive BEF was the typical outcome. Our findings provide a potential explanation for the rarity of negative BEF in empirical data.

Multi-scale effects of habitat loss and the role of trait evolution.

Habitat loss (HL) is a major cause of species extinctions. Although the effects of HL beyond the directly impacted area have been previously observed, they have not been modelled explicitly, especially in an eco-evolutionary context. To start filling this gap, we study a two-patch deterministic consumer-resource model, with one of the patches experiencing loss of resources as a special case of HL. Our model allows foraging and mating within a patch as well as between patches. We then introduce heritable variation in consumer traits related to resource utilization and patch use to investigate eco-evolutionary dynamics and compare results with constant and no trait variation scenarios. Our results show that HL in one patch can indeed reduce consumer densities in the neighbouring patch but can also increase consumer densities in the neighbouring patch when the resources are overexploited. Yet at the landscape scale, the effect of HL on consumer densities is consistently negative. Patch isolation increases consumer density in the patch experiencing HL but has generally negative effects on the neighbouring patch, with context-dependent results at the landscape scale. With high cross-patch dependence and coupled foraging and mating preferences, local HL can sometimes even lead to landscape-level consumer extinction. Eco-evolutionary dynamics can rescue consumers from such extinction in some cases if their death rates are sufficiently small. More generally, trait evolution had positive or negative effects on equilibrium consumer densities after HL, depending on the evolving trait and the spatial scale considered. In summary, our findings show that HL at a local scale can affect the neighbouring patch and the landscape as a whole, where heritable trait variation can, in some cases, alleviate the impact of HL. We thus suggest joint consideration of multiple spatial scales and trait variation when assessing and predicting the impacts of HL.

Our fragile future under the cumulative cultural evolution of two technologies

We derive and analyse a model with unusual features characterizing human activities over the long-run. First, human population dynamics draw heavily on consumer–resource modelling in ecology in that humans must consume biological resources to produce new humans. Second, the model also draws heavily from economic growth theory in that humans do not simply consume biological resources; they also produce the resources they consume. Finally, humans use two types of technology. Consumption technology affects the rate at which humans can extract resources. Production technology controls how effectively humans convert labour into new resources. The dynamics of both types of technology are subject to cumulative cultural evolutionary processes that allow both technological progress and regress. The resulting model exhibits a wide range of dynamical regimes. That said, the system is routinely sensitive to initial conditions, with wildly different outcomes given the same parameter values. Moreover, the system exhibits a basic fragility in the sense that human activities often lead to the endogenous extinction of the human species. This can happen gently, or it can follow periods of explosive human activity with super-exponential growth that ends in collapse. This article is part of the theme issue ‘Evolution and sustainability: gathering the strands for an Anthropocene synthesis’.

Geometry of ecological coexistence and niche differentiation.

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze consumer resource models using geometric arguments. This has led to broadly applicable principles such as Tilman's R^{*} and species coexistence cones. Here, we extend these arguments by constructing a geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species which may coexist and enumerate ecologically stable steady states and transitions between them. Collectively, these results provide a framework for understanding the role of species traits within niche theory.

The evolutionary dynamics of plastic foraging and its ecological consequences: a resource-consumer model

The evolutionary dynamics of plastic foraging and its ecological consequences: a resource-consumer model

Aquatic insects balance growth with future supply of algal food resources

Many consumers depend on the contemporaneous growth of their food resources. For example, Tanytarsus gracilentus midges feed on algae, and because midge generation time is much longer than that of algae, individual midges benefit not just from the standing stock but also from the growth of algae during their lifespans. This implies that an intermediate consumption rate maximizes midge somatic growth: low consumption rates constrain midge growth because they do not fully utilize the available food, whereas high consumption rates suppress algal biomass growth and consequently limit future food availability. An experiment manipulating midge presence and initial algal abundance showed that midges can suppress algal growth, as measured by changes in algal gross primary production (GPP). We also found a positive relationship between GPP and midge growth. A consumer–resource model fit to the experimental data showed a hump‐shaped relationship between midge consumption rates and their somatic growth. In the model, predicted midge somatic growth rates were only positively associated with GPP when their consumption rate was below the value that optimized midge growth. Therefore, midges did not overexploit algae in the experiment. This work highlights the balance that consumers which depend on contemporaneous resource growth might have to strike between short‐term growth and future food availability, and the benefits for consumers when they ‘manage' their resources well.