Modeling spatial evolution of multi-drug resistance under drug environmental gradients.

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria based on a drug-concentration rescaling approach. We show how the resistance to drugs in space, and the consequent adaptation of growth rate, is governed by a Price equation with diffusion, integrating features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Although in many evolution models, per capita growth rate is a natural surrogate for fitness, in spatially-extended, potentially heterogeneous habitats, fitness is an emergent property that potentially reflects additional complexities, from boundary conditions to the specific spatial variation of growth rates. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem, λ1. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits to the relative advantage of each mutant across the environment. Our approach allows one to predict the precise outcomes of selection among mutants over space, ultimately from comparing their λ1 values, which encode a critical interplay between growth functions, movement traits, habitat size and boundary conditions. Such mathematical understanding opens new avenues for multi-drug therapeutic optimization.

Triggering Toll-Like Receptor 5 signaling during pneumococcal superinfection prevents the selection of antibiotic resistance.

Toll-like receptor 5 (TLR5) signaling plays a key role in antibacterial defenses. We previously showed that respiratory administration of flagellin, a potent TLR5 agonist, in combination with amoxicillin improves the treatment of primary pneumonia or superinfection caused by amoxicillin-sensitive or -resistant Streptococcus pneumoniae. Here, the impact of adjunct flagellin therapy on antibiotic dose/regimen and the selection of antibiotic-resistant S. pneumoniae was investigated using superinfection with isogenic antibiotic-sensitive and -resistant bacteria and population dynamics analysis. Our findings demonstrate that flagellin allows for a 200-fold reduction in the antibiotic dose, achieving the same therapeutic effect observed with antibiotic alone. Adjunct treatment also reduced the selection of antibiotic-resistant bacteria in contrast to the antibiotic monotherapy. Finally, we developed a mathematical model that captured the population dynamics and estimated a 20-fold enhancement immune-modulatory factor on bacterial clearance. This work paves the way for the development of host-directed therapy and refinement of treatment by modeling.

Pneumococcus and the stress-gradient hypothesis: A trade-off links R0 and susceptibility to co-colonization across countries.

Modern molecular technologies have revolutionized our understanding of bacterial epidemiology, but reported data across studies and different geographic endemic settings remain under-integrated in common theoretical frameworks. Pneumococcus serotype co-colonization, caused by the polymorphic bacteria Streptococcus pneumoniae, has been increasingly investigated and reported in recent years. While the global genomic diversity and serotype distribution of S. pneumoniae have been well-characterized, there is limited information on how co-colonization patterns vary globally, critical for understanding the evolution and transmission dynamics of the bacteria. Gathering a rich dataset of cross-sectional pneumococcal colonization studies in the literature, we quantified patterns of transmission intensity and co-colonization prevalence variation in children populations across 17 geographic locations. Linking these data to an SIS model with cocolonization under the assumption of quasi-neutrality among multiple interacting strains, our analysis reveals strong patterns of negative co-variation between transmission intensity (R0) and susceptibility to co-colonization (k). In line with expectations from the stress-gradient-hypothesis in ecology (SGH), pneumococcus serotypes appear to compete more in co-colonization in high-transmission settings and compete less in low-transmission settings, a trade-off which ultimately leads to a conserved ratio of single to co-colonization µ=1/(R0-1)k. From the mathematical model's behavior, such conservation suggests preservation of 'stability-diversity-complexity' regimes in coexistence of similar co-colonizing strains. We find no major differences in serotype compositions across studies, pointing to adaptation of the same set of serotypes across variable environments as an explanation for their differential interaction in different transmission settings. Our work highlights that the understanding of transmission patterns of Streptococcus pneumoniae from global scale epidemiological data can benefit from simple analytical approaches that account for quasi-neutrality among strains, co-colonization, as well as variable environmental adaptation.

Quasi-neutral dynamics in a coinfection system with N strains and asymmetries along multiple traits.

Understanding the interplay of different traits in a co-infection system with multiple strains has many applications in ecology and epidemiology. Because of high dimensionality and complex feedback between traits manifested in infection and co-infection, the study of such systems remains a challenge. In the case where strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Here, we apply singular perturbation theory to many strain parameters simultaneously and advance analytically to obtain their explicit collective dynamics. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) dynamics among N strains, which vary in 5 fitness dimensions: transmissibility, clearance rate of single- and co-infection, transmission probability from mixed coinfection, and co-colonization vulnerability factors encompassing cooperation and competition. This quasi-neutral system is analyzed with a singular perturbation method through an appropriate slow-fast decomposition. The fast dynamics correspond to the embedded neutral system, while the slow dynamics are governed by an N-dimensional replicator equation, describing the time evolution of strain frequencies. The coefficients of this replicator system are pairwise invasion fitnesses between strains, which, in our model, are an explicit weighted sum of pairwise asymmetries along all trait dimensions. Remarkably these weights depend only on the parameters of the neutral system. Such model reduction highlights the centrality of the neutral system for dynamics at the edge of neutrality and exposes critical features for the maintenance of diversity.

Disentangling how multiple traits drive 2 strain frequencies in SIS dynamics with coinfection.

A general theory for competitive dynamics among many strains at the epidemiological level is required to understand polymorphisms in virulence, transmissibility, antibiotic resistance and other biological traits of infectious agents. Mathematical coinfection models have addressed specific systems, focusing on the criteria leading to stable coexistence or competitive exclusion, however, due to their complexity and nonlinearity, analytical solutions in coinfection models remain rare. Here we study a 2-strain Susceptible-Infected-Susceptible (SIS) compartmental model with co-infection/co-colonization, incorporating five strain fitness dimensions under the same framework: variation in transmissibility, duration of carriage, pairwise susceptibilities to coinfection, coinfection duration, and transmission priority effects from mixed coinfection. Taking advantage of a singular perturbation approach, under the assumption of strain similarity, we expose how strain dynamics on a slow timescale are explicitly governed by a replicator equation which encapsulates all traits and their interplay. This allows to predict explicitly not only the final epidemiological outcome of a given 2-player competition, but moreover, their entire frequency dynamics as a direct function of their relative variation and of strain-transcending global parameters. Based on mutual invasion fitnesses, we analyze and report rigorous results on transition phenomena in the 2-strain system, strongly mediated via endemic coinfection prevalence. We show that coinfection is not always a promoter of coexistence; instead, its effect to favour or prevent polymorphism is non-monotonic and depends on the type and level of phenotypic differentiation between strains. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with theoretical and practical applications in epidemiology, ecology and evolution.

Renal control of disease tolerance to malaria.

Malaria, the disease caused by Plasmodium spp. infection, remains a major global cause of morbidity and mortality. Host protection from malaria relies on immune-driven resistance mechanisms that kill Plasmodium However, these mechanisms are not sufficient per se to avoid the development of severe forms of disease. This is accomplished instead via the establishment of disease tolerance to malaria, a defense strategy that does not target Plasmodium directly. Here we demonstrate that the establishment of disease tolerance to malaria relies on a tissue damage-control mechanism that operates specifically in renal proximal tubule epithelial cells (RPTEC). This protective response relies on the induction of heme oxygenase-1 (HMOX1; HO-1) and ferritin H chain (FTH) via a mechanism that involves the transcription-factor nuclear-factor E2-related factor-2 (NRF2). As it accumulates in plasma and urine during the blood stage of Plasmodium infection, labile heme is detoxified in RPTEC by HO-1 and FTH, preventing the development of acute kidney injury, a clinical hallmark of severe malaria.

Predicting N-Strain Coexistence from Co-colonization Interactions: Epidemiology Meets Ecology and the Replicator Equation.

Multi-type infection processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to analyze and to understand on a fundamental level. Here, we study a multi-strain susceptible-infected-susceptible model with coinfection. A host already colonized by one strain can become more or less vulnerable to co-colonization by a second strain, as a result of facilitating or competitive interactions between the two. Fitness differences between N strains are mediated through [Formula: see text] altered susceptibilities to secondary infection that depend on colonizer-cocolonizer identities ([Formula: see text]). By assuming strain similarity in such pairwise traits, we derive a model reduction for the endemic system using separation of timescales. This 'quasi-neutrality' in trait space sets a fast timescale where all strains interact neutrally, and a slow timescale where selective dynamics unfold. We find that these slow dynamics are governed by the replicator equation for N strains. Our framework allows to build the community dynamics bottom-up from only pairwise invasion fitnesses between members. We highlight that mean fitness of the multi-strain network, changes with their individual dynamics, acts equally upon each type, and is a key indicator of system resistance to invasion. By uncovering the link between N-strain epidemiological coexistence and the replicator equation, we show that the ecology of co-colonization relates to Fisher's fundamental theorem and to Lotka-Volterra systems. Besides efficient computation and complexity reduction for any system size, these results open new perspectives into high-dimensional community ecology, detection of species interactions, and evolution of biodiversity.

Integrating Antimicrobial Therapy with Host Immunity to Fight Drug-Resistant Infections: Classical vs. Adaptive Treatment.

Antimicrobial resistance of infectious agents is a growing problem worldwide. To prevent the continuing selection and spread of drug resistance, rational design of antibiotic treatment is needed, and the question of aggressive vs. moderate therapies is currently heatedly debated. Host immunity is an important, but often-overlooked factor in the clearance of drug-resistant infections. In this work, we compare aggressive and moderate antibiotic treatment, accounting for host immunity effects. We use mathematical modelling of within-host infection dynamics to study the interplay between pathogen-dependent host immune responses and antibiotic treatment. We compare classical (fixed dose and duration) and adaptive (coupled to pathogen load) treatment regimes, exploring systematically infection outcomes such as time to clearance, immunopathology, host immunization, and selection of resistant bacteria. Our analysis and simulations uncover effective treatment strategies that promote synergy between the host immune system and the antimicrobial drug in clearing infection. Both in classical and adaptive treatment, we quantify how treatment timing and the strength of the immune response determine the success of moderate therapies. We explain key parameters and dimensions, where an adaptive regime differs from classical treatment, bringing new insight into the ongoing debate of resistance management. Emphasizing the sensitivity of treatment outcomes to the balance between external antibiotic intervention and endogenous natural defenses, our study calls for more empirical attention to host immunity processes.

Transmission Fitness in Co-colonization and the Persistence of Bacterial Pathogens.

Humans are often colonized by polymorphic bacteria such as Streptococcus pneumoniae, Bordetella pertussis, Staphylococcus Aureus, and Haemophilus influenzae. Two co-colonizing pathogen clones may interact with each other upon host entry and during within-host dynamics, ranging from competition to facilitation. Here we examine the significance of these exploitation strategies for bacterial spread and persistence in host populations. We model SIS epidemiological dynamics to capture the global behavior of such multi-strain systems, focusing on different parameters of single and dual colonization. We analyze the impact of heterogeneity in clearance and transmission rates of single and dual colonization and find the criteria under which these asymmetries enhance endemic persistence. We obtain a backward bifurcation near [Formula: see text] if the reproductive value of the parasite in dually infected hosts is sufficiently higher than that in singly infected ones. In such cases, the parasite is able to persist even in sub-threshold conditions, and reducing the basic reproduction number below 1 would be insufficient for elimination. The fitness superiority in co-colonized hosts can be attained by lowering net parasite clearance rate ([Formula: see text]), by increasing transmission rate ([Formula: see text]), or both, and coupling between these traits critically constrains opportunities of pathogen survival in the [Formula: see text] regime. Finally, using an adaptive dynamics approach, we verify that despite their importance for sub-threshold endemicity, traits expressed exclusively in coinfection should generally evolve independently of single infection traits. In particular, for [Formula: see text] a saturating parabolic or hyperbolic function of [Formula: see text], co-colonization traits evolve to an intermediate optimum (evolutionarily stable strategy, ESS), determined only by host lifespan and the trade-off parameters linking [Formula: see text] and [Formula: see text]. Our study invites more empirical attention to the dynamics and evolution of parasite life-history traits expressed exclusively in coinfection.

How direct competition shapes coexistence and vaccine effects in multi-strain pathogen systems.

We describe an integrated modeling framework for understanding strain coexistence in polymorphic pathogen systems. Previous studies have debated the utility of neutral formulations and focused on cross-immunity between strains as a major stabilizing mechanism. Here we convey that direct competition for colonization mediates stable coexistence only when competitive abilities amongst pathogen clones satisfy certain pairwise asymmetries. We illustrate our ideas with nested SIS models of single and dual colonization, applied to polymorphic pneumococcal bacteria. By fitting the models to cross-sectional prevalence data from Portugal (before and after the introduction of a seven-valent pneumococcal conjugate vaccine), we are able to not only statistically compare neutral and non-neutral epidemiological formulations, but also estimate vaccine efficacy, transmission and competition parameters simultaneously. Our study highlights that the response of polymorphic pathogen populations to interventions holds crucial information about strain interactions, which can be extracted by suitable nested modeling.

A theoretical framework to identify invariant thresholds in infectious disease epidemiology.

Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena - such as the epidemic and reinfection thresholds - remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems.

Unveiling time in dose-response models to infer host susceptibility to pathogens.

The biological effects of interventions to control infectious diseases typically depend on the intensity of pathogen challenge. As much as the levels of natural pathogen circulation vary over time and geographical location, the development of invariant efficacy measures is of major importance, even if only indirectly inferrable. Here a method is introduced to assess host susceptibility to pathogens, and applied to a detailed dataset generated by challenging groups of insect hosts (Drosophila melanogaster) with a range of pathogen (Drosophila C Virus) doses and recording survival over time. The experiment was replicated for flies carrying the Wolbachia symbiont, which is known to reduce host susceptibility to viral infections. The entire dataset is fitted by a novel quantitative framework that significantly extends classical methods for microbial risk assessment and provides accurate distributions of symbiont-induced protection. More generally, our data-driven modeling procedure provides novel insights for study design and analyses to assess interventions.

Revisiting the diffusion approximation to estimate evolutionary rates of gene family diversification.

Genetic diversity in multigene families is shaped by multiple processes, including gene conversion and point mutation. Because multi-gene families are involved in crucial traits of organisms, quantifying the rates of their genetic diversification is important. With increasing availability of genomic data, there is a growing need for quantitative approaches that integrate the molecular evolution of gene families with their higher-scale function. In this study, we integrate a stochastic simulation framework with population genetics theory, namely the diffusion approximation, to investigate the dynamics of genetic diversification in a gene family. Duplicated genes can diverge and encode new functions as a result of point mutation, and become more similar through gene conversion. To model the evolution of pairwise identity in a multigene family, we first consider all conversion and mutation events in a discrete manner, keeping track of their details and times of occurrence; second we consider only the infinitesimal effect of these processes on pairwise identity accounting for random sampling of genes and positions. The purely stochastic approach is closer to biological reality and is based on many explicit parameters, such as conversion tract length and family size, but is more challenging analytically. The population genetics approach is an approximation accounting implicitly for point mutation and gene conversion, only in terms of per-site average probabilities. Comparison of these two approaches across a range of parameter combinations reveals that they are not entirely equivalent, but that for certain relevant regimes they do match. As an application of this modelling framework, we consider the distribution of nucleotide identity among VSG genes of African trypanosomes, representing the most prominent example of a multi-gene family mediating parasite antigenic variation and within-host immune evasion.

The impact of mutation and gene conversion on the local diversification of antigen genes in African trypanosomes.

Patterns of genetic diversity in parasite antigen gene families hold important information about their potential to generate antigenic variation within and between hosts. The evolution of such gene families is typically driven by gene duplication, followed by point mutation and gene conversion. There is great interest in estimating the rates of these processes from molecular sequences for understanding the evolution of the pathogen and its significance for infection processes. In this study, a series of models are constructed to investigate hypotheses about the nucleotide diversity patterns between closely related gene sequences from the antigen gene archive of the African trypanosome, the protozoan parasite causative of human sleeping sickness in Equatorial Africa. We use a hidden Markov model approach to identify two scales of diversification: clustering of sequence mismatches, a putative indicator of gene conversion events with other lower-identity donor genes in the archive, and at a sparser scale, isolated mismatches, likely arising from independent point mutations. In addition to quantifying the respective probabilities of occurrence of these two processes, our approach yields estimates for the gene conversion tract length distribution and the average diversity contributed locally by conversion events. Model fitting is conducted using a Bayesian framework. We find that diversifying gene conversion events with lower-identity partners occur at least five times less frequently than point mutations on variant surface glycoprotein (VSG) pairs, and the average imported conversion tract is between 14 and 25 nucleotides long. However, because of the high diversity introduced by gene conversion, the two processes have almost equal impact on the per-nucleotide rate of sequence diversification between VSG subfamily members. We are able to disentangle the most likely locations of point mutations and conversions on each aligned gene pair.

Linking the antigen archive structure to pathogen fitness in African trypanosomes.

Systems that generate antigenic variation enable pathogens to evade host immune responses and are intricately interwoven with major pathogen traits, such as host choice, growth, virulence and transmission. Although much is understood about antigen switching at the molecular level, little is known about the cross-scale links between these molecular processes and the larger-scale within and between host population dynamics that they must ultimately drive. Inspired by the antigenic variation system of African trypanosomes, we apply modelling approaches to our expanding understanding of the organization and expression of antigen repertoires, and explore links across these scales. We predict how pathogen population processes are determined by underlying molecular genetics and infer resulting selective pressures on important emergent repertoire traits.

Towards a mathematical understanding of invasion resistance in multispecies communities.

Multispecies community composition and dynamics are key to health and disease across biological systems, a prominent example being microbial ecosystems. Explaining the forces that govern diversity and resilience in the microbial consortia making up our body's defences remains a challenge. In this, theoretical models are crucial, to bridge the gap between species dynamics and underlying mechanisms and to develop analytic insight. Here we propose a replicator equation framework to model multispecies dynamics where an explicit notion of invasion resistance of a system emerges and can be studied explicitly. For illustration, we derive the conceptual link between such replicator equation and N microbial species' growth and interaction traits, stemming from micro-scale environmental modification. Within this replicator framework, mean invasion fitness arises, evolves dynamically, and may undergo critical predictable shifts with global environmental changes. This mathematical approach clarifies the key role of this resident system trait for invader success, and highlights interaction principles among N species that optimize their collective resistance to invasion. We propose this model based on the replicator equation as a powerful new avenue to study, test and validate mechanisms of invasion resistance and colonization in multispecies microbial ecosystems and beyond.

Modeling spatial evolution of multi-drug resistance under drug environmental gradients.

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.

Slow growing behavior in African trypanosomes during adipose tissue colonization.

When Trypanosoma brucei parasites, the causative agent of sleeping sickness, colonize the adipose tissue, they rewire gene expression. Whether this adaptation affects population behavior and disease treatment remained unknown. By using a mathematical model, we estimate that the population of adipose tissue forms (ATFs) proliferates slower than blood parasites. Analysis of the ATFs proteome, measurement of protein synthesis and proliferation rates confirm that the ATFs divide on average every 12 h, instead of 6 h in the blood. Importantly, the population of ATFs is heterogeneous with parasites doubling times ranging between 5 h and 35 h. Slow-proliferating parasites remain capable of reverting to the fast proliferation profile in blood conditions. Intravital imaging shows that ATFs are refractory to drug treatment. We propose that in adipose tissue, a subpopulation of T. brucei parasites acquire a slow growing behavior, which contributes to disease chronicity and treatment failure.

Price equation captures the role of drug interactions and collateral effects in the evolution of multidrug resistance.

Bacterial adaptation to antibiotic combinations depends on the joint inhibitory effects of the two drugs (drug interaction [DI]) and how resistance to one drug impacts resistance to the other (collateral effects [CE]). Here we model these evolutionary dynamics on two-dimensional phenotype spaces that leverage scaling relations between the drug-response surfaces of drug-sensitive (ancestral) and drug-resistant (mutant) populations. We show that evolved resistance to the component drugs - and in turn, the adaptation of growth rate - is governed by a Price equation whose covariance terms encode geometric features of both the two-drug-response surface (DI) in ancestral cells and the correlations between resistance levels to those drugs (CE). Within this framework, mean evolutionary trajectories reduce to a type of weighted gradient dynamics, with the drug interaction dictating the shape of the underlying landscape and the collateral effects constraining the motion on those landscapes. We also demonstrate how constraints on available mutational pathways can be incorporated into the framework, adding a third key driver of evolution. Our results clarify the complex relationship between drug interactions and collateral effects in multidrug environments and illustrate how specific dosage combinations can shift the weighting of these two effects, leading to different and temporally explicit selective outcomes.

The ratio of single to co-colonization is key to complexity in interacting systems with multiple strains.

The high number and diversity of microbial strains circulating in host populations have motivated extensive research on the mechanisms that maintain biodiversity. However, much of this work focuses on strain-specific and cross-immunity interactions. Another less explored mode of pairwise interaction is via altered susceptibilities to co-colonization in hosts already colonized by one strain. Diversity in such interaction coefficients enables strains to create dynamically their niches for growth and persistence, and "engineer" their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability-complexity regimes in such multi-player endemic systems remain poorly understood. In a recent study (Madec & Gjini, Bulletin of Mathematical Biology, 82), we obtained an analytic representation for N-type coexistence in an SIS epidemiological model with co-colonization. We mapped multi-strain dynamics to a replicator equation using timescale separation. Here, we examine what drives coexistence regimes in such co-colonization system. We find the ratio of single to co-colonization, µ, critically determines the type of equilibrium and number of coexisting strains, and encodes a trade-off between overall transmission intensity R 0 and mean interaction coefficient in strain space, k. Preserving a given coexistence regime, under fixed trait variation, requires balancing between higher mean competition in favorable environments, and higher cooperation in harsher environments, and is consistent with the stress gradient hypothesis. Multi-strain coexistence tends to steady-state attractors for small µ, whereas as µ increases, dynamics tend to more complex attractors. Following strain frequencies, evolutionary dynamics in the system also display contrasting patterns with µ, interpolating between multi-stable and fluctuating selection for cooperation and mean invasion fitness, in the two extremes. This co-colonization framework could be applied more generally, to study invariant principles in collective coexistence, and to quantify how critical shifts in community dynamics get potentiated by mean-field and environmental gradients.