Ecologists have long sought a way to explain how the remarkable biodiversity observed in nature is maintained. On the one hand, simple models of interacting competitors cannot produce the stable persistence of very large ecological communities. On the other hand, neutral models, in which species do not interact and diversity is maintained by immigration and speciation, yield unrealistically small fluctuations in population abundance, and a strong positive correlation between a species' abundance and its age, contrary to empirical evidence. Models allowing for the robust persistence of large communities of interacting competitors are lacking. Here we show that very diverse communities could persist thanks to the stabilizing role of higher-order interactions, in which the presence of a species influences the interaction between other species. Although higher-order interactions have been studied for decades, their role in shaping ecological communities is still unclear. The inclusion of higher-order interactions in competitive network models stabilizes dynamics, making species coexistence robust to the perturbation of both population abundance and parameter values. We show that higher-order interactions have strong effects in models of closed ecological communities, as well as of open communities in which new species are constantly introduced. In our framework, higher-order interactions are completely defined by pairwise interactions, facilitating empirical parameterization and validation of our models.

How the coexistence of many species is maintained is a fundamental and unresolved question in ecology. Coexistence is a puzzle because we lack a mechanistic understanding of the variation in species presence and abundance. Whether variation in ecological communities is driven by deterministic or random processes is one of the most controversial issues in ecology. Here, I study the variation of species presence and abundance in microbial communities from a macroecological standpoint. I identify three macroecological laws that quantitatively characterize the fluctuation of species abundance across communities and over time. Using these three laws, one can predict species’ presence and absence, diversity, and commonly studied macroecological patterns. I show that a mathematical model based on environmental stochasticity, the stochastic logistic model, quantitatively predicts the three macroecological laws, as well as non-stationary properties of community dynamics.

Networks composed of distinct, densely connected subsystems are called modular. In ecology, it has been posited that a modular organization of species interactions would benefit the dynamical stability of communities, even though evidence supporting this hypothesis is mixed. Here we study the effect of modularity on the local stability of ecological dynamical systems, by presenting new results in random matrix theory, which are obtained using a quaternionic parameterization of the cavity method. Results show that modularity can have moderate stabilizing effects for particular parameter choices, while anti-modularity can greatly destabilize ecological networks.

Despite decades of research, how mammalian cell size is controlled remains unclear because of the difficulty of directly measuring growth at the single-cell level. Here we report direct measurements of single-cell volumes over entire cell cycles on various mammalian cell lines and primary human cells. We find that, in a majority of cell types, the volume added across the cell cycle shows little or no correlation to cell birth size, a homeostatic behavior called “adder”. This behavior involves modulation of G1 or S-G2 duration and modulation of growth rate. The precise combination of these mechanisms depends on the cell type and the growth condition. We have developed a mathematical framework to compare size homeostasis in datasets ranging from bacteria to mammalian cells. This reveals that a near-adder behavior is the most common type of size control and highlights the importance of growth rate modulation to size control in mammalian cells.

Empirical evidence suggesting that living systems might operate in the vicinity of critical points, at the borderline between order and disorder, has proliferated in recent years, with examples ranging from spontaneous brain activity to flock dynamics. However, a well-founded theory for understanding how and why interacting living systems could dynamically tune themselves to be poised in the vicinity of a critical point is lacking. Here we use tools from statistical mechanics and information theory to show that complex adaptive or evolutionary systems can be much more efficient in coping with diverse heterogeneous environmental conditions when operating at criticality. Analytical as well as computational evolutionary and adaptive models vividly illustrate that a community of such systems dynamically self-tunes close to a critical state as the complexity of the environment increases while they remain noncritical for simple and predictable environments. A more robust convergence to criticality emerges in coevolutionary and coadaptive setups in which individuals aim to represent other agents in the community with fidelity, thereby creating a collective critical ensemble and providing the best possible tradeoff between accuracy and flexibility. Our approach provides a parsimonious and general mechanism for the emergence of critical-like behavior in living systems needing to cope with complex environments or trying to efficiently coordinate themselves as an ensemble.evolution | adaptation | self-organization P hysical systems undergo phase transitions from ordered to disordered states on changing control parameters (1, 2). Critical points, with all their remarkable properties (1, 2), are only observed upon parameter fine tuning. This is in sharp contrast to the ubiquity of critical-like behavior in complex living matter. Indeed, empirical evidence has proliferated that living systems might operate at criticality (3)-i.e. at the borderline between order and disorder-with examples ranging from spontaneous brain behavior (4) to gene expression patterns (5), cell growth (6), morphogenesis (7), bacterial clustering (8), and flock dynamics (9). Even if none of these examples is fully conclusive and even if the meaning of "criticality" varies across these works, the criticality hypothesis-as a general strategy for the organization of living matter-is a tantalizing idea worthy of further investigation.Here we present a framework for understanding how selftuning to criticality can arise in living systems. Unlike models of self-organized criticality in which some inanimate systems are found to become critical in a mechanistic way (10), our focus here is on general adaptive or evolutionary mechanisms, specific to biological systems. We suggest that the drive to criticality arises from functional advantages of being poised in the vicinity of a critical point.However, why is a living system fitter when it is critical? Living systems need to perceive and respond to environmental cues and to interact with other similar entities. In...

The role of species interactions in controlling the interplay between the stability of ecosystems and their biodiversity is still not well understood. The ability of ecological communities to recover after small perturbations of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the conditions change (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strengths and ecological network structure on the volume of parameter space leading to feasible equilibria. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence. We show that feasibility is determined by few quantities describing the interactions, yielding a nontrivial complexity–feasibility relationship. Analysing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions.

The simplest theories often have much merit and many limitations, and in this vein, the value of Neutral Theory (NT) of biodiversity has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain several patterns observed in the organization of ecosystems. Among ecologists, it had a polarizing effect: There were a few ecologists who were enthusiastic, and there were a larger number who firmly opposed it. Physicists and mathematicians, instead, welcomed the theory with excitement. Indeed, NT spawned several theoretical studies that attempted to explain empirical data and predicted trends of quantities that had not yet been studied. While there are a few reviews of NT oriented towards ecologists, our goal here is to review the quantitative aspects of NT and its extensions for physicists who are inter- problems remain unresolved. Furthermore, we hope that this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. We propose to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: we also discuss new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models. CONTENTS

The mean size of exponentially dividing Escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time, and individual growth rate are only starting to be characterized. Recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables. Here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times. We found that scaling relations based on the means collapse both size and doubling-time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means. Our data on these joint fluctuations highlight the importance of cell individuality: Single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the "division hazard rate function," which defines the probability rate of dividing as a function of measurable parameters. This "model free" approach gives a rationale for the universal body-size distributions observed in microbial ecosystems across many microbial species, presumably dividing with multiple mechanisms. Additionally, our experiments show a crossover between fast and slow growth in the relation between individual-cell growth rate and division time, which can be understood in terms of different regimes of genome replication control.