Les Houches Lectures on Community Ecology: From Niche Theory to Statistical Mechanics.

Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years, there has been a growing theoretical and experimental interest in these problems from the physics and quantitative biology communities. Here, we give an overview of community ecology, highlighting the deep connections between ecology and statistical physics. We start by introducing the two classes of mathematical models that have served as the workhorses of community ecology: Consumer Resource Models (CRM) and the generalized Lotka-Volterra models (GLV). We place a special emphasis on graphical methods and general principles. We then review recent works showing a deep and surprising connection between ecological dynamics and constrained optimization. We then shift our focus by analyzing these same models in "high-dimensions" (i.e. in the limit where the number of species and resources in the ecosystem becomes large) and discuss how such complex ecosystems can be analyzed using methods from the statistical physics of disordered systems such as the cavity method and Random Matrix Theory.

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.

Metabolic similarity and the predictability of microbial community assembly.

When microbial communities form, their composition is shaped by selective pressures imposed by the environment. Can we predict which communities will assemble under different environmental conditions? Here, we hypothesize that quantitative similarities in metabolic traits across metabolically similar environments lead to predictable similarities in community composition. To that end, we measured the growth rate and by-product profile of a library of proteobacterial strains in a large number of single nutrient environments. We found that growth rates and secretion profiles were positively correlated across environments when the supplied substrate was metabolically similar. By analyzing hundreds of in-vitro communities experimentally assembled in an array of different synthetic environments, we then show that metabolically similar substrates select for taxonomically similar communities. These findings lead us to propose and then validate a comparative approach for quantitatively predicting the effects of novel substrates on the composition of complex microbial consortia.

Midwave resonant cavity infrared detectors (RCIDs) with suppressed background noise.

We report a resonant cavity infrared detector (RCID) with an InAsSb/InAs superlattice absorber with a thickness of only ≈ 100 nm, a 33-period GaAs/Al0.92Ga0.08As distributed Bragg reflector bottom mirror, and a Ge/SiO2/Ge top mirror. At a low bias voltage of 150 mV, the external quantum efficiency (EQE) reaches 58% at the resonance wavelength λres ≈ 4.6 µm, with linewidth δλ = 19-27 nm. The thermal background current for a realistic system scenario with f/4 optic that views a 300 K scene is estimated by integrating the photocurrent generated by background spanning the entire mid-IR spectral band (3-5 µm). The resulting specific detectivity is a factor of 3 lower than for a state-of-the-art broadband HgCdTe device at 300 K, where dark current dominates the noise. However, at 125 K where the suppression of background noise becomes critical, the estimated specific detectivity D* of 5.5 × 1012 cm Hz½/W is more than 3× higher. This occurs despite a non-optimal absorber cut-off that causes the EQE to decrease rapidly with decreasing temperature, e.g., to 33% at 125 K. The present RCID's advantage over the broadband device depends critically on its low EQE at non-resonance wavelengths: ≤ 1% in the range 3.9-5.5 µm. Simulations using NRL MULTIBANDS indicate that impact ionization in the bottom contact and absorber layers dominates the dark current at near ambient temperatures. We expect future design modifications to substantially enhance D* throughout the investigated temperature range of 100-300 K.

Emergent competition shapes the ecological properties of multi-trophic ecosystemss.

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 find that intra-trophic diversity gives rise to "emergent competition" 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.

Diverse communities behave like typical random ecosystems.

In 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory. Yet, it remains unclear if and when we can treat real communities as random ecosystems. Here, we draw on recent progress in random matrix theory and statistical physics to extend May's approach to generalized consumer-resource models. We show that in diverse ecosystems adding even modest amounts of noise to consumer preferences results in a transition to "typicality," where macroscopic ecological properties of communities are indistinguishable from those of random ecosystems, even when resource preferences have prominent designed structures. We test these ideas using numerical simulations on a wide variety of ecological models. Our work offers an explanation for the success of random consumer resource models in reproducing experimentally observed ecological patterns in microbial communities and highlights the difficulty of scaling up bottom-up approaches in synthetic ecology to diverse communities.

Beam stability of buried-heterostructure quantum cascade lasers employing HVPE regrowth.

Measurements of beam stability for mid-infrared (IR)-emitting quantum cascade lasers (QCLs) are important for applications that require the beam to travel through air to remote targets, such as free-space communication links. We report beam-quality measurement results of narrow-ridge, 4.6 µm-emitting buried-heterostructure (BH) QCLs fabricated using ICP etching and HVPE regrowth. Beam-quality measurements under QCW operation exhibit M2 < 1.2 up to 1 W for ∼5 µm-wide ridges. 5 µm-wide devices display some small degree of centroid motion with increasing output power (< 0.125 mrad), which corresponds to a targeting error of ∼1.25 cm over a distance of 100 m.

Niche Theory for Mutualism: A Graphical Approach to Plant-Pollinator Network Dynamics.

AbstractContemporary niche theory is a useful framework for understanding how organisms interact with each other and with their shared environment. Its graphical representation, popularized by Tilman's resource ratio hypothesis, facilitates analysis of the equilibrium structure of complex dynamical models, including species coexistence. This theory has been applied primarily to resource competition since its early beginnings. Here, we integrate mutualism into niche theory by expanding Tilman's graphical representation to the analysis of consumer-resource dynamics of plant-pollinator networks. We graphically explain the qualitative phenomena previously found by numerical simulations, including the effects on community dynamics of nestedness, adaptive foraging, and pollinator invasions. Our graphical approach promotes the unification of niche and network theories and deepens the synthesis of different types of interactions within a consumer-resource framework.

Tregs self-organize into a computing ecosystem and implement a sophisticated optimization algorithm for mediating immune response.

Regulatory T cells (Tregs) play a crucial role in mediating immune response. Yet an algorithmic understanding of the role of Tregs in adaptive immunity remains lacking. Here, we present a biophysically realistic model of Treg-mediated self-tolerance in which Tregs bind to self-antigens and locally inhibit the proliferation of nearby activated T cells. By exploiting a duality between ecological dynamics and constrained optimization, we show that Tregs tile the potential antigen space while simultaneously minimizing the overlap between Treg activation profiles. We find that for sufficiently high Treg diversity, Treg-mediated self-tolerance is robust to fluctuations in self-antigen concentrations but lowering the Treg diversity results in a sharp transition-related to the Gardner transition in perceptrons-to a regime where changes in self-antigen concentrations can result in an autoimmune response. We propose an experimental test of this transition in immune-deficient mice and discuss potential implications for autoimmune diseases.

The Minimum Environmental Perturbation Principle: A New Perspective on Niche Theory.

AbstractFifty years ago, Robert MacArthur showed that stable equilibria optimize quadratic functions of the population sizes in several important ecological models. Here, we generalize this finding to a broader class of systems within the framework of contemporary niche theory and precisely state the conditions under which an optimization principle (not necessarily quadratic) can be obtained. We show that conducting the optimization in the space of environmental states instead of population sizes leads to a universal and transparent physical interpretation of the objective function. Specifically, the equilibrium state minimizes the perturbation of the environment induced by the presence of the competing species, subject to the constraint that no species has a positive net growth rate. We use this "minimum environmental perturbation principle" to make new predictions for evolution and community assembly, where the minimum perturbation increases monotonically under invasion by new species. We also describe a simple experimental setting where the conditions of validity for this optimization principle have been empirically tested.

Effect of Resource Dynamics on Species Packing in Diverse Ecosystems.

The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e., the number of surviving species cannot exceed the number of resources). An open question is to understand if and how different resource dynamics affect this bound. Here, we analyze a generalized consumer resource model with externally supplied resources and show that-in contrast to self-renewing resources-species can occupy only half of all available environmental niches. This motivates us to construct a new schema for classifying ecosystems based on species packing properties.

The Nanomechanical Bit.

The applicability of nanomechanical devices for computational approaches is reviewed. The focus is on the representation and processing of information based on nanomechanical bits. Several device concepts are discussed ranging from nano-electromechanical systems in silicon to circuits based on carbon nano-tube switches, combinations of nanomechanical resonators and traditional transistors, and integration into a computing architecture. The strengths of mechanical systems include their scalability, robustness to external electrical shocks, and their low-energy consumption. Hence, they may lead the way to new forms of ultradense memory and alternative routes of computing. In conjunction with quantum mechanical single electron circuits, nano-electromechanical systems may also have potential for quantum computational circuits.

Data-driven modeling reveals a universal dynamic underlying the COVID-19 pandemic under social distancing.

We show that the COVID-19 pandemic under social distancing exhibits universal dynamics. The cumulative numbers of both infections and deaths quickly cross over from exponential growth at early times to a longer period of power law growth, before eventually slowing. In agreement with a recent statistical forecasting model by the IHME, we show that this dynamics is well described by the erf function. Using this functional form, we perform a data collapse across countries and US states with very different population characteristics and social distancing policies, confirming the universal behavior of the COVID-19 outbreak. We show that the predictive power of statistical models is limited until a few days before curves flatten, forecast deaths and infections assuming current policies continue and compare our predictions to the IHME models. We present simulations showing this universal dynamics is consistent with disease transmission on scale-free networks and random networks with non-Markovian transmission dynamics.

The Community Simulator: A Python package for microbial ecology.

Natural microbial communities contain hundreds to thousands of interacting species. For this reason, computational simulations are playing an increasingly important role in microbial ecology. In this manuscript, we present a new open-source, freely available Python package called Community Simulator for simulating microbial population dynamics in a reproducible, transparent and scalable way. The Community Simulator includes five major elements: tools for preparing the initial states and environmental conditions for a set of samples, automatic generation of dynamical equations based on a dictionary of modeling assumptions, random parameter sampling with tunable levels of metabolic and taxonomic structure, parallel integration of the dynamical equations, and support for metacommunity dynamics with migration between samples. To significantly speed up simulations using Community Simulator, our Python package implements a new Expectation-Maximization (EM) algorithm for finding equilibrium states of community dynamics that exploits a recently discovered duality between ecological dynamics and convex optimization. We present data showing that this EM algorithm improves performance by between one and two orders compared to direct numerical integration of the corresponding ordinary differential equations. We conclude by listing several recent applications of the Community Simulator to problems in microbial ecology, and discussing possible extensions of the package for directly analyzing microbiome compositional data.

A minimal model for microbial biodiversity can reproduce experimentally observed ecological patterns.

Surveys of microbial biodiversity such as the Earth Microbiome Project (EMP) and the Human Microbiome Project (HMP) have revealed robust ecological patterns across different environments. A major goal in ecology is to leverage these patterns to identify the ecological processes shaping microbial ecosystems. One promising approach is to use minimal models that can relate mechanistic assumptions at the microbe scale to community-level patterns. Here, we demonstrate the utility of this approach by showing that the Microbial Consumer Resource Model (MiCRM) - a minimal model for microbial communities with resource competition, metabolic crossfeeding and stochastic colonization - can qualitatively reproduce patterns found in survey data including compositional gradients, dissimilarity/overlap correlations, richness/harshness correlations, and nestedness of community composition. By using the MiCRM to generate synthetic data with different environmental and taxonomical structure, we show that large scale patterns in the EMP can be reproduced by considering the energetic cost of surviving in harsh environments and HMP patterns may reflect the importance of environmental filtering in shaping competition. We also show that recently discovered dissimilarity-overlap correlations in the HMP likely arise from communities that share similar environments rather than reflecting universal dynamics. We identify ecologically meaningful changes in parameters that alter or destroy each one of these patterns, suggesting new mechanistic hypotheses for further investigation. These findings highlight the promise of minimal models for microbial ecology.

The in vivo genetic program of murine primordial lung epithelial progenitors.

Multipotent Nkx2-1-positive lung epithelial primordial progenitors of the foregut endoderm are thought to be the developmental precursors to all adult lung epithelial lineages. However, little is known about the global transcriptomic programs or gene networks that regulate these gateway progenitors in vivo. Here we use bulk RNA-sequencing to describe the unique genetic program of in vivo murine lung primordial progenitors and computationally identify signaling pathways, such as Wnt and Tgf-ß superfamily pathways, that are involved in their cell-fate determination from pre-specified embryonic foregut. We integrate this information in computational models to generate in vitro engineered lung primordial progenitors from mouse pluripotent stem cells, improving the fidelity of the resulting cells through unbiased, easy-to-interpret similarity scores and modulation of cell culture conditions, including substratum elastic modulus and extracellular matrix composition. The methodology proposed here can have wide applicability to the in vitro derivation of bona fide tissue progenitors of all germ layers.

Machine Learning as Ecology.

Machine learning methods have had spectacular success on numerous problems. Here we show that a prominent class of learning algorithms - including Support Vector Machines (SVMs) - have a natural interpretation in terms of ecological dynamics. We use these ideas to design new online SVM algorithms that exploit ecological invasions, and benchmark performance using the MNIST dataset. Our work provides a new ecological lens through which we can view statistical learning and opens the possibility of designing ecosystems for machine learning.

Environmental boundary conditions for the origin of life converge to an organo-sulfur metabolism.

It has been suggested that a deep memory of early life is hidden in the architecture of metabolic networks, whose reactions could have been catalyzed by small molecules or minerals before genetically encoded enzymes. A major challenge in unravelling these early steps is assessing the plausibility of a connected, thermodynamically consistent proto-metabolism under different geochemical conditions, which are still surrounded by high uncertainty. Here we combine network-based algorithms with physico-chemical constraints on chemical reaction networks to systematically show how different combinations of parameters (temperature, pH, redox potential and availability of molecular precursors) could have affected the evolution of a proto-metabolism. Our analysis of possible trajectories indicates that a subset of boundary conditions converges to an organo-sulfur-based proto-metabolic network fuelled by a thioester- and redox-driven variant of the reductive tricarboxylic acid cycle that is capable of producing lipids and keto acids. Surprisingly, environmental sources of fixed nitrogen and low-potential electron donors are not necessary for the earliest phases of biochemical evolution. We use one of these networks to build a steady-state dynamical metabolic model of a protocell, and find that different combinations of carbon sources and electron donors can support the continuous production of a minimal ancient 'biomass' composed of putative early biopolymers and fatty acids.

Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions.

Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints, of which QP is a special case, and consumer resource models describing ecological dynamics. Combining this duality with a recent "cavity solution," we analyze high-dimensional, random QP where the optimization function and constraints are drawn randomly. Our theory shows remarkable agreement with numerics and points to a deep connection between optimization, dynamical systems, and ecology.

The thermodynamic uncertainty relation in biochemical oscillations.

Living systems regulate many aspects of their behaviour through periodic oscillations of molecular concentrations, which function as 'biochemical clocks.' The chemical reactions that drive these clocks are intrinsically stochastic at the molecular level, so that the duration of a full oscillation cycle is subject to random fluctuations. Their success in carrying out their biological function is thought to depend on the degree to which these fluctuations in the cycle period can be suppressed. Biochemical oscillators also require a constant supply of free energy in order to break detailed balance and maintain their cyclic dynamics. For a given free energy budget, the recently discovered 'thermodynamic uncertainty relation' yields the magnitude of period fluctuations in the most precise conceivable free-running clock. In this paper, we show that computational models of real biochemical clocks severely underperform this optimum, with fluctuations several orders of magnitude larger than the theoretical minimum. We argue that this suboptimal performance is due to the small number of internal states per molecule in these models, combined with the high level of thermodynamic force required to maintain the system in the oscillatory phase. We introduce a new model with a tunable number of internal states per molecule and confirm that it approaches the optimal precision as this number increases.