Current theories of bacterial growth physiology demonstrate impressive predictive power but are often phenomenological, lacking mechanistic detail. Incorporating such details would significantly enhance our ability to predict and control bacterial growth under varying environmental conditions. The "Flux Controlled Regulation" (FCR) model serves as a reference framework, linking ribosome allocation to translation efficiency through a steady-state assumption. However, it neglects ppGpp-mediated nutrient sensing and transcriptional regulation of ribosomal operons. Here, we propose a mechanistic model that extends the FCR framework by incorporating three key components: (i) the amino acid pool, (ii) ppGpp sensing of translation elongation rate, and (iii) transcriptional regulation of protein allocation by ppGpp-sensitive promoters. Our model aligns with observed steady-state growth laws and makes testable predictions for unobserved quantities. We show that during environmental changes, the incoherent feedback between sensing and regulation generates oscillatory relaxation dynamics, a behavior that we support by new and existing experimental data.

The ecological dynamics of interacting predator and prey populations can display sustained oscillations, as for instance predicted by the Rosenzweig-MacArthur predator-prey model. The presence of demographic stochasticity, due to the finiteness of population sizes, alters the amplitude and frequency of these oscillations. Here we present a method for characterizing the effects of demographic stochasticity on the limit cycle attractor of the Rosenzweig-MacArthur. We show that an angular Brownian motion well describes the frequency oscillations. In the vicinity of the bifurcation point, we obtain an analytical approximation for the angular diffusion constant. This approximation accurately captures the effect of demographic stochasticity across parameter values.

The structure and diversity of microbial communities are intrinsically hierarchical due to the shared evolutionary history of their constituents. This history is typically captured through taxonomic assignment and phylogenetic reconstruction, sources of information that are frequently used to group microbes into higher levels of organization in experimental and natural communities. Connecting community diversity to the joint ecological dynamics of the abundances of these groups is a central problem of community ecology. However, how microbial diversity depends on the scale of observation at which groups are defined has never been systematically examined. Here, we used a macroecological approach to quantitatively characterize the structure and diversity of microbial communities among disparate environments across taxonomic and phylogenetic scales. We found that measures of biodiversity at a given scale can be consistently predicted using a minimal model of ecology, the Stochastic Logistic Model of growth (SLM). This result suggests that the SLM is a more appropriate null-model for microbial biodiversity than alternatives such as the Unified Neutral Theory of Biodiversity. Extending these within-scale results, we examined the relationship between measures of biodiversity calculated at different scales (e.g. genus vs. family), an empirical pattern previously evaluated in the context of the Diversity Begets Diversity (DBD) hypothesis (Madi et al., 2020). We found that the relationship between richness estimates at different scales can be quantitatively predicted assuming independence among community members, demonstrating that the DBD can be sufficiently explained using the SLM as a null model of ecology. Contrastingly, only by including correlations between the abundances of community members (e.g. as the consequence of interactions) can we predict the relationship between estimates of diversity at different scales. The results of this study characterize novel microbial patterns across scales of organization and establish a sharp demarcation between recently proposed macroecological patterns that are not and are affected by ecological interactions.

Ecology has historically benefited by characterizing statistical patterns of biodiversity within and across communities. This approach, encompassed by the discipline of macroecology, has achieved considerable success in microbial ecology in recent years. Macroecological approaches have identified universal patterns of diversity and abundance that can be captured by effective models that do not include explicit interactions between community members. Experimentation has simultaneously played a crucial role in the development of our understanding of the ecology of microbes, as the advent of highly replicated time-series has allowed researchers to investigate how ecological forces govern community dynamics. However, there remains a gap between microbial experiments performed in the laboratory and macroecological patterns documented in natural systems, as we do not know if and how experimental manipulations produce macroecological effects. Here, we work to bridge the gap between the experimental manipulation of communities and their macroecological consequences. Using high-replication time-series of experimental microbial communities, we demonstrate that macroecological laws observed in nature can be readily recapitulated in a laboratory setting and unified under the Stochastic Logistic Model of growth (SLM). We found that demographic manipulations and their effect on community-level variation can alter empirical patterns in a manner that diverges from predictions obtained from the SLM. By incorporating experimental details (e.g., number of migrants), we were able to restore the predictive capacity of the SLM by linking demographic manipulations with macroecological effects. Finally, we demonstrate the extent that experimental manipulations are capable of altering macroecological patterns under the SLM, establishing a demarcation between macroecological outcomes we can and cannot observe in a laboratory setting.

The assumption of constant population size is central in population genetics. It led to a large body of results that is robust to modeling choices and that has proven successful to understand evolutionary dynamics. In reality, allele frequencies and population size are both determined by the interaction between a population and the environment. Relaxing the constant-population assumption has two big drawbacks. It increases the technical difficulty of the analysis, and it requires specifying a mechanism for the saturation of the population size, possibly making the results contingent on model details. Here we develop a framework that encompasses a great variety of systems with an arbitrary mechanism for population growth limitation. By using techniques based on scale separation for stochastic processes, we are able to calculate analytically properties of evolutionary trajectories, such as the fixation probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three parameters related to the intergeneration timescale, the invasion fitness, and the carrying capacity of the strains. In other words, different systems, such as Lotka-Volterra or a chemostat model (contained in our framework), share the same evolutionary outcomes after a proper remapping of their parameters. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of invasion fitness.

The horizontal transfer of genes is fundamental for the eco-evolutionary dynamics of microbial communities, such as oceanic plankton, soil, and the human microbiome. In the case of an acquired beneficial gene, classic population genetics would predict a genome-wide selective sweep, whereby the genome spreads clonally within the community and together with the beneficial gene, removing genome diversity. Instead, several sources of metagenomic data show the existence of “gene-specific sweeps”, whereby a beneficial gene spreads across a bacterial community, maintaining genome diversity. Several hypotheses have been proposed to explain this process, including the decreasing gene flow between ecologically distant populations, frequency-dependent selection from linked deleterious allelles, and very high rates of horizontal gene transfer. Here, we propose an additional possible scenario grounded in eco-evolutionary principles. Specifically, we show by a mathematical model and simulations that a metacommunity where species can occupy multiple patches, acting together with a realistic (moderate) HGT rate, helps maintain genome diversity. Assuming a scenario of patches dominated by single species, our model predicts that diversity only decreases moderately upon the arrival of a new beneficial gene, and that losses in diversity can be quickly restored. We explore the generic behaviour of diversity as a function of three key parameters, frequency of insertion of new beneficial genes, migration rates and horizontal transfer rates.Our results provides a testable explanation for how diversity can be maintained by gene-specific sweeps even in the absence of high horizontal gene transfer rates.

Real-world datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this Letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high dimensionality of sequences' space.

Microbial communities are found throughout the biosphere, from human guts to glaciers, from soil to activated sludge. Understanding the statistical properties of such diverse communities can pave the way to elucidate the common mechanisms ...Multiple ecological forces act together to shape the composition of microbial communities. Phyloecology approaches—which combine phylogenetic relationships between species with community ecology—have the potential to disentangle such forces but are often ...

Understanding the evolutionary stability of cooperation is a central problem in biology, sociology, and economics. There exist only a few known mechanisms that guarantee the existence of cooperation and its robustness to cheating. Here, we introduce a mechanism for the emergence of cooperation in the presence of fluctuations. We consider agents whose wealth changes stochastically in a multiplicative fashion. Each agent can share part of her wealth as a public good, which is equally distributed among all the agents. We show that, when agents operate with long-time horizons, cooperation produces an advantage at the individual level, as it effectively screens agents from the deleterious effect of environmental fluctuations.

Multiple ecological forces act together to shape the composition of microbial communities. Phyloecology approaches-which combine phylogenetic relationships between species with community ecology-have the potential to disentangle such forces but are often hard to connect with quantitative predictions from theoretical models. On the other hand, macroecology, which focuses on statistical patterns of abundance and diversity, provides natural connections with theoretical models but often neglects interspecific correlations and interactions. Here, we propose a unified framework combining both such approaches to analyze microbial communities. In particular, by using both cross-sectional and longitudinal metagenomic data for species abundances, we reveal the existence of an empirical macroecological law establishing that correlations in species-abundance fluctuations across communities decay from positive to null values as a function of phylogenetic dissimilarity in a consistent manner across ecologically distinct microbiomes. We formulate three variants of a mechanistic model-each relying on alternative ecological forces-that lead to radically different predictions. From these analyses, we conclude that the empirically observed macroecological pattern can be quantitatively explained as a result of shared population-independent fluctuating resources, i.e., environmental filtering and not as a consequence of, e.g., species competition. Finally, we show that the macroecological law is also valid for temporal data of a single community and that the properties of delayed temporal correlations can be reproduced as well by the model with environmental filtering.

In many natural environments, microorganisms decompose microscale resource patches made of complex organic matter. The growth and collapse of populations on these resource patches unfold within spatial ranges of a few hundred micrometers or less, making such microscale ecosystems hotspots of heterotrophic metabolism. Despite the potential importance of patch-level dynamics for the large-scale functioning of heterotrophic microbial communities, we have not yet been able to delineate the ecological processes that control natural populations at the microscale. Here, we address this challenge by characterizing the natural marine communities that assembled on over 1,000 individual microscale particles of chitin, the most abundant marine polysaccharide. Using low-template shotgun metagenomics and imaging, we find significant variation in microscale community composition despite the similarity in initial species pools across replicates. Chitin-degrading taxa that were rare in seawater established large populations on a subset of particles, resulting in a wide range of predicted chitinolytic abilities and biomass at the level of individual particles. We show, through a mathematical model, that this variability can be attributed to stochastic colonization and historical contingencies affecting the tempo of growth on particles. We find evidence that one biological process leading to such noisy growth across particles is differential predation by temperate bacteriophages of chitin-degrading strains, the keystone members of the community. Thus, initial stochasticity in assembly states on individual particles, amplified through ecological interactions, may have significant consequences for the diversity and functionality of systems of microscale patches.

Summary Growth and division are central to cell size. Bacteria achieve size homeostasis by dividing when growth has added a constant size since birth, termed the “adder” principle, by unknown mechanisms [1–4]. Growth is well known to be regulated by ppGpp, which controls anything from ribosome production to metabolic enzyme activity and replication initiation, and whose absence or excess can induce the stress response, filamentation, and yield growth-arrested miniature cells [5–8]. These observations raise unresolved questions about the relation between ppGpp and size homeostasis mechanisms during normal exponential growth. Here, to untangle effects of ppGpp and nutrients, we gained control of cellular ppGpp by inducing the synthesis and hydrolysis enzymes RelA and Mesh1. We found that ppGpp not only exerts control over the growth rate, but also over cell division and hence the steady state cell size. The added size responds rapidly to changes in the ppGpp level, aided by transiently accelerated or delayed divisions, and establishes its new constant value while the growth rate still adjusts. Moreover, the magnitude of the added size and resulting steady-state birth size correlate consistently with the ppGpp level, rather than with the growth rate, which results in cells of different size that grow equally fast. Our findings suggest that ppGpp serves as a critical regulator that coordinates cell size and growth control.

The large taxonomic variability of microbial community composition is a consequence of the combination of environmental variability, mediated through ecological interactions, and stochasticity. Most of the analysis aiming to infer the biological factors determining this difference in community structure start by quantifying how much communities are similar in their composition, trough beta-diversity metrics. The central role that these metrics play in microbial ecology does not parallel with a quantitative understanding of their relationships and statistical properties. In particular, we lack a framework that reproduces the empirical statistical properties of beta-diversity metrics. Here we take a macroecological approach and introduce a model to reproduce the statistical properties of community similarity. The model is based on the statistical properties of individual communities and on a single tunable parameter, the correlation of species' carrying capacities across communities, which sets the difference of two communities. The model reproduces quantitatively the empirical values of several commonly-used beta-diversity metrics, as well as the relationships between them. In particular, this modeling framework naturally reproduces the negative correlation between overlap and dissimilarity, which has been observed in both empirical and experimental communities and previously related to the existence of universal features of community dynamics. In this framework, such correlation naturally emerges due to the effect of random sampling.

Physics can be seen as a conceptual approach to scientific problems, a method for discovery, but teaching this aspect of our discipline can be a challenge. We report on a first-time remote teaching experience for a computational physics third-year physics laboratory class taught in the first part of the 2020 COVID-19 pandemic (March-May 2020). To convey a 'physics of data' approach to data analysis and data-driven physical modeling we used interdisciplinary data sources, with an openended 'COVID-19 data challenge' project as the core of the course. COVID-19 epidemiological data provided an ideal setting for motivating the students to deal with complex problems, where there is no unique or preconceived solution. Our results indicate that such problems yield qualitatively different improvements compared to close-ended projects, as well as point to critical aspects in using these problems as a teaching strategy. By breaking the students' expectations of unidirectionality, remote teaching provided unexpected opportunities to promote active work and active learning.

Growing cells adopt common basic strategies to achieve optimal resource allocation under limited resource availability. Our current understanding of such "growth laws" neglects degradation, assuming that it occurs slowly compared to the cell cycle duration. Here we argue that this assumption cannot hold at slow growth, leading to important consequences. We propose a simple framework showing that at slow growth protein degradation is balanced by a fraction of "maintenance" ribosomes. Consequently, active ribosomes do not drop to zero at vanishing growth, but as growth rate diminishes, an increasing fraction of active ribosomes performs maintenance. Through a detailed analysis of compiled data, we show that the predictions of this model agree with data from E. coli and S. cerevisiae. Intriguingly, we also find that protein degradation increases at slow growth, which we interpret as a consequence of active waste management and/or recycling. Our results highlight protein turnover as an underrated factor for our understanding of growth laws across kingdoms.

Marco Cosentino Lagomarsino, 2 Guglielmo Pacifico, Valerio Firmano, Edoardo Bella, Pietro Benzoni, Jacopo Grilli, Federico Bassetti, Fabrizio Capuani, Pietro Cicuta, and Marco Gherardi IFOM Foundation, FIRC Institute of Molecular Oncology, Milan, Italy Dipartimento di Fisica, Università degli Studi di Milano, and I.N.F.N, via Celoria 16 Milano, Italy∗ Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16 Milano, Italy The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy. Politecnico di Milano, Piazza Leonardo da Vinci 32, Milano, Italy I.N.F.N. Sezione di Roma Sapienza. Piazzale Aldo Moro 2, Roma, Italy Cavendish Laboratory, Cambridge University, Cambridge, United Kingdom

Microbial communities found in nature are composed of many rare species and few abundant ones, as reflected by their heavy-tailed abundance distributions. How a large number of species can coexist in those complex communities and why they are dominated by rare species is still not fully understood. We show how heavy-tailed distributions arise as an emergent property from large communities with many interacting species in population-level models. To do so we rely on stochastic logistic and generalized Lotka-Volterra models for which we introduce a global maximal capacity. This maximal capacity accounts for the fact that communities are limited by available resources and space. In a parallel ‘ad-hoc’ approach, we obtain heavy-tailed abundance distributions from non-interacting models through specific distributions of the parameters. We expect both mechanisms, interactions between many species and specific parameter distributions, to be relevant to explain the observed heavy tails.

Growing cells adopt common basic strategies to achieve optimal resource allocation under limited resource availability. Our current understanding of such “growth laws” neglects degradation, assuming that it occurs slowly compared to the cell cycle duration. Here we argue that this assumption cannot hold at slow growth, leading to important consequences. We propose a simple framework showing that at slow growth protein degradation is balanced by a fraction of “maintenance” ribosomes. Consequently, active ribosomes do not drop to zero at vanishing growth, but as growth rate diminishes, an increasing fraction of active ribosomes performs maintenance. Through a detailed analysis of compiled data, we show that the predictions of this model agree with data from E. coli and S. cerevisiae. Intriguingly, we also find that protein degradation increases at slow growth, which we interpret as a consequence of active waste management and/or recycling. Our results highlight protein turnover as an underrated factor for our understanding of growth laws across kingdoms.

The most fundamental questions in microbial ecology concern the diversity and variability of communities. Their composition varies widely across space and time, as a result of a nontrivial combination of stochastic and deterministic processes. The interplay between nonlinear community dynamics and environmental fluctuations determines the rich statistical structure of community variability. We analyze long time series of individual human gut microbiomes and compare intra- and intercommunity dissimilarity under a macroecological framework. We show that most taxa have large but stationary fluctuations over time, while a minority of taxa display rapid changes in average abundance that cluster in time, suggesting the presence of alternative stable states. We disentangle interindividual variability in a stochastic component and a deterministic one, the latter recapitulated by differences in carrying capacities. Last, by combining environmental fluctuations and alternative stable states, we introduce a model that quantitatively predicts the statistical properties of both intra- and interindividual community variability, therefore summarizing variation in a unique macroecological framework.

The assumption of constant population size is central in population genetics. It led to a large body of results, that are robust to modeling choices and that have proven successful to understand evolutionary dynamics. In reality, allele frequencies and population size are both determined by the interaction between a population and the environment. Including explicitly the demographic factors and life-history traits that determine the eco-evolutionary dynamics makes the analysis difficult and the results contingent on model details. Here, we develop a framework that encompasses a great variety of systems with arbitrary population dynamics and competition between species. By using techniques based on scale separation for stochastic processes, we are able to calculate analytically evolutionary properties, such as the fixation probability. Remarkably, these properties assume a universal form with respect to our framework, which depends on only three life-history traits related to the inter-generation timescale, the invasion fitness, and the carrying capacity of the alleles. In other words, different systems, such as Lotka-Volterra or a chemostat model, share the same evolutionary outcomes after mapping the parameters of the models into three effective life-history traits. An important and surprising consequence of our results is that the direction of selection can be inverted, with a population evolving to reach lower values of invasion fitness.