Session G37: Ecological Dynamics II

Microbial community dynamics in-silico, in-vitro, and in-vivo

Thousands of microbial species coexist in the human gut or in a gram of soil, but what maintains community diversity is still unclear. Experiments show that tens of species can coexist under simple conditions, e.g., where a single carbon source is provided. The complexity of the structure of these communities reflects the hidden complexity of the network of inter-species interactions and of the chemical and physical environment, which are constantly altered by bacterial growth phases. In this talk, I will discuss how the statistical properties of environmental variability can give rise to regularities in community variation. By studying this connection, I will show how relatively simple models of stochastic population dynamics can capture patterns of variability in empirical and experimental communities. I will then discuss how current theoretical ecology frameworks fail to predict reproducible experimental patterns of diversity and composition.   

Diversity begets stability: sublinear growth and competitive coexistence across ecosystems

The unfolding global biodiversity crisis brings special urgency to understanding how diverse ecosystems are naturally stabilized. Whereas conventional wisdom and empirical observation suggest that stability increases with diversity, ecological theory has long made the opposite prediction, leading to the longstanding "diversity-stability debate". Here we show this puzzle is resolved through a model where growth scales as a sublinear power law with biomass (exponent < 1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions in a community with sublinear growth do not lead to exclusion, but instead promote stability at higher diversity. Our model realigns theory with classic observations and large-scale macroecological patterns. However, it makes an unsettling prediction: biodiversity loss may accelerate the destabilization of ecosystems.   

Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions

Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity 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 non-reciprocity 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 non-reciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.   

Evolution of division of labor in a response threshold model

This work explores the evolving division of labor in a response threshold model. As we know,

division of labor is central to driving cooperative structures in societies, bacterial communities, and insect colonies.

Starting from the simplest case of an unstructured population with fixed response thresholds, we can derive threshold prescriptions to ensure division of labor. We derive mean-field equations for

the stimulus dynamics and show that they exhibit complex attractors through period-doubling bifurcation cascades when the noise disrupting the thresholds is small. In addition, we show how

the fixed threshold can be set to ensure specialization in both the transient and equilibrium regimes

of the stimulus dynamics. Using the framework of structured populations, we then address the fundamental question of determining the underlying conditions that lead to the division of labor from a homogeneous population. In the formulation, a group fitness function, W(T), acts as a guiding force that shapes the distribution of tasks among individuals while maximizing the collective work output of the group. The perfect division of labor, guided by specific threshold prescriptions, constitutes a global optimum of W(T). Our results demonstrate the emergence of an imperfect division of labor, which contrasts sharply with a previous study that found no such specialization. The degeneracy of the global fitness optimum is responsible for such an outcome, in which a fraction of agents act as generalists.    

Linear response theory for eco-evolutionary dynamics

Ecological and evolutionary processes often unfold on overlapping timescales, making an integrated theory of eco-evolutionary dynamics indispensable. Traditional evolutionary theories typically focus on single-species dynamics and only crudely account for niche-based competition. Conversely, niche theory captures ecological interactions but lacks evolutionary processes. Here, we bridge this gap by incorporating evolutionary dynamics into niche theory. Our framework models mutations as small phenotypic perturbations to existing species and computes the community's linear response to such perturbations. This approach illuminates two key aspects of eco-evolutionary processes. First, it mathematically decomposes a mutant's fitness into three easily interpretable components: strategy (competitive ability), innovation (novelty), and naive fitness (mortality/maintenance rate). Each of these components have clear geometric interpretations as vectors in niche space. Second, our theory can predict how a successful mutant will affect the community, including changes in species abundances and resource levels. We illustrate the explanatory power of our framework using a variety of consumer-resource models, including the MacArthur, linear resource, and microbial consumer resource models.   

Horizontal transfer of phage-defense genes can stably maintain their diversity in a microbial pan-genome despite continuous extinction and turnover of genomes

Phages and their bacterial hosts are locked in an evolutionary competition which in small and closed systems typically results in an extinction of one or the other. To resist phages bacteria have evolved numerous defense systems, which nevertheless are still susceptible to specific phage anti-defense mechanisms. These defense/anti-defense systems are a major element of microbial genetic diversity and have been demonstrated to propagate between strains by horizontal gene transfer (HGT). It has been proposed that the totality of defense systems found in microbial communities collectively form a distributed "pan-immune" system with individual elements moving between strains with via ubiquitous HGT. Here, we formulate a Lotka-Volterra type model of a host/phage system interacting via a combinatorial variety of defense/anti-defense systems and show that HGT enables stable maintenance of diverse defense/anti-defense genes in the microbial pan-genome even when individual microbial strains inevitably undergo extinction leaving only few descendants that survive thanks to immunity acquired through HGT. This mechanism of persistence for the pan-immune gene pool is fundamentally similar to the "island migration" model of ecological diversity, with genes moving between genomes instead of species migrating between islands.   

Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations

Stochastic reaction-diffusion (SRD) systems serve as versatile models for many complex physical, societal, and ecological systems. The effective coarse-grained reaction rates in continuum descriptions for such systems represent macroscopic parameters that need to be either measured experimentally or determined numerically. In an agent-based Monte Carlo simulation of SRD systems, the control parameters are the prescribed microscopic probabilities for certain events to happen. They ultimately define the large-scale behavior and long-time states of the system, as well as relaxation rates and other relevant time scales such as oscillation frequencies. To match the results of numerical simulations to experiments, a mapping is required between the microscopic probabilities that define a Monte Carlo simulation and the macroscopic reaction rates. This constitutes in general a non-trivial problem, and there exists no systematic method to obtain the functional dependence of the macroscopic rates on the microscopic probabilities and interaction rules. Here we introduce an algorithmic approach using Monte Carlo simulations to evaluate the macroscopic reaction rates by counting how many events occur per simulation timestep. Our technique is first tested on known simple examples such as simple birth reactions, coagulation, and pair annihilation. We then investigate how the microscopic reaction probabilities become coarse-grained into macroscopic rates in more complicated models such as the Lotka-Volterra predator-prey model, the rock-paper-scissors or cyclic Lotka-Volterra model, and the May-Leonard model for cyclic competition of three species. This work aims towards a deeper understanding of coarse-graining in SRD systems with a focus on ecological systems, and improved Monte Carlo simulation techniques to fit experimental or observational data.   

A framework for the interaction between wildlife and spatial hazards

One of the major challenges in conservation and movement ecology is to understand the mechanisms through which spatial interventions due to human development can affect wildlife. An important example is the development of road infrastructure leading to wildlife-vehicle accidents. Modern tracking technology increasingly provides high-resolution datasets of the movement patterns of animals at various spatiotemporal scales, but theory lags behind in providing an understanding of how patterns lead to interactions. We develop a general theory for the interactions between a moving agent and a hazardous domain. Landscape scale motion is represented by stochastic differential equations, whereas interaction events are represented by stopping times for this process. Statistics of these stopping times provide trajectory-level information about the use of space in the vicinity of a hazard. General results about the distribution of interaction times can be derived, with particular emphasis on the case of range-resident motion, exemplified by the Ornstein-Uhlenbeck processes. Incorporating intrinsic sources of mortality allows for evaluation of the reduction in lifespan associated to the introduction of the spatial hazard. The importance of considering inhomogeneous use of space is highlighted by comparison with reflected Brownian motion. We discuss the connection with data and simulations, as well as possible extensions to include autocorrelation in noise.   

Tweets vs Pathogen Spread: A Case Study of COVID-19 in American States

The concept of the mutual influence that awareness and disease may exert on each other has recently presented significant challenges. The actions individuals take to prevent contracting a disease and their level of awareness can profoundly affect the dynamics of its spread. Simultaneously, disease outbreaks impact how people become aware. In response, we initially propose a null model that couples two Susceptible-Infectious-Recovered (SIR) dynamics and analyze it using a mean-field approach. Subsequently, we explore the parameter space to quantify the effects of this mutual influence on various observables. Finally, based on this null model, we conduct an empirical analysis of Twitter data related to COVID-19 and confirmed cases within American states.

Our findings indicate that in specific regions of the parameter space, it is possible to suppress the epidemic by increasing awareness, and we investigate phase transitions. Furthermore, our model demonstrates the ability to alter the dominant population group by adjusting parameters throughout the course of the outbreak. Additionally, using the model, we assign a set of parameters to each state, revealing that these parameters change at different pandemic peaks. Notably, a robust correlation emerges between the ranking of states’ Twitter activity, as gathered from empirical data, and the immunity parameters assigned to each state using our model. This observation underscores the pivotal role of sustained awareness transitioning from the initial to the subsequent peaks in the disease progression.   

Quantifying noise effects on networked epidemic transmission through structural predictability

Estimating networked transmission dynamics of infectious diseases from noisy surveillance data remains a persistent challenge in modern epidemiology. Key parameters are derived from time series data to inform policymakers about disease trends and assess public health interventions. However, the accuracy of these inferences critically hinges on reliable data sources. In this work, we established a dual equivalence between epidemic dynamics stability to noise and network structural predictability. Specifically, we have demonstrated the equivalence of epidemic dynamics stability concerning data noise and structural noise. The stability of epidemic dynamics, in the context of structural noise, can be quantified using network predictability measures. Leveraging this connection, we utilize network predictability to characterize the stability of disease spread dynamics, allowing us to assess the impact of noise on model predictions. Network predictability reflects the limit of accuracy in forecasting missing links, showcasing structural and functional traits. Existing studies lack precision, a distinct definition, and an explanation of predictability. Our approach links network dynamics stability and predictability, introducing a precise, non-training metric. By building upon the discoveries related to predictability, we can quantify the extent to which noise affects the network in the dynamics of disease transmission.   

Morphodynamics of bacterial communities proliferating in three dimensions

In nature, bacteria often grow as communities in three-dimensional (3D) environments, with multiple different cell types cooperating or competing for resources. While many studies have investigated how proliferation drives the spatial organization of multi-strain/species communities in two dimensions, little is known about the morphology of these communities in 3D. Here, we use two different strains of E. coli suspended in a transparent jammed packing of microgel particles to investigate the morphodynamics of communities with multiple cell types proliferating in 3D. Unexpectedly, even though the strains are initially well-mixed, we find that they proliferate into single-strain microcolonies within the overall community, with the size and shape of each microcolony determined by the initial cell density and colony width. We rationalize these results by considering the interplay between proliferation, competition for space, and nutrients. Taken together, our results help to shed new light on the morphodynamics of mixed microbial communities, as well as other forms of proliferating active matter, in 3D.