Significance: Recently, evidence has been mounting that biological systems might operate at the borderline between order and disorder, i.e., near a critical point. A general mathematical framework for understanding this common pattern, explaining the possible origin and role of criticality in living adaptive and evolutionary systems, is still missing. We rationalize this apparently ubiquitous criticality in terms of adaptive and evolutionary functional advantages. We provide an analytical framework, which demonstrates that the optimal response to broadly different changing environments occurs in systems organizing spontaneously—through adaptation or evolution—to the vicinity of a critical point. Furthermore, criticality turns out to be the evolutionary stable outcome of a community of individuals aimed at communicating with each other to create a collective entity.

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 toward ecologists, the goal here is to review the quantitative aspects of NT and its extensions for physicists who are interested in learning what NT is, what its successes are, and what important problems remain unresolved. Furthermore, this review could also be of interest to theoretical ecologists because many potentially interesting results are buried in the vast NT literature. It is proposed to make these more accessible by extracting them and presenting them in a logical fashion. The focus of this review is broader than NT: new, more recent approaches for studying ecological systems and how one might introduce realistic non-neutral models are also discussed.

Significance: The past few decades have seen an intensification of international food trade and the increase in the number of countries that depend on food imports. As an effect of the associated globalization of food, local shocks in food production, combined with the adoption of new national or regional energy and trade policies, have recently led to global food crises. Here we develop a framework to investigate the coupled global food–population dynamics, and evaluate the effect of international trade on global food security. We find that, as the dependency on trade increases, the global food system is losing resilience and is becoming increasingly unstable and susceptible to conditions of crisis.

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.