Environmental fluctuations can shape replicator dynamics, with important consequences for both prebiotic and modern ecosystems. However, it remains unclear how simple replicators can acquire and use information about fluctuating environments, given that such information processing is often assumed to require sophisticated mechanisms for sensing and control. Here, we show that even simple replicator networks can increase productivity by exploiting environmental information in a functional way. Using a model of autocatalytic replicators in a flow reactor, we derive an information-theoretic decomposition of productivity, with separate contributions from environmental uncertainty, side information, and distribution mismatch. We derive optimal strategies and universal bounds on the benefit of information and compare our findings with existing work, including “Kelly gambling” in information theory. By applying our framework to a model of real-world molecular replicators, we demonstrate the benefits of internal memory and propose an experimental setup for detecting functional information in a minimal chemical system.

Mutualistic interactions are widespread in nature, from plant communities and microbiomes to human organizations. Along with competition for resources, cooperative interactions shape biodiversity and contribute to the robustness of complex ecosystems. We present a stochastic neutral theory of cooperator species. Our model shares with the classic neutral theory of biodiversity the assumption that all species are equivalent, but crucially differs in requiring cooperation between species for replication. With low migration, our model displays a bimodal species-abundance distribution, with a high-abundance mode associated with a core of cooperating species. This core is responsible for maintaining a diverse pool of long-lived species, which are present even at very small migration rates. We derive analytical expressions of the steady-state species abundance distribution, as well as scaling laws for diversity, number of species, and residence times. With high migration, our model recovers the results of classic neutral theory. We briefly discuss implications of our analysis for research on the microbiome, synthetic biology, and the origin of life.

Harvesting free energy from the environment is essential for the operation of many biological and artificial systems. We use techniques from stochastic thermodynamics to investigate the maximum rate of harvesting achievable by optimizing a set of reactions in a Markovian system, possibly under various kinds of topological, kinetic, and thermodynamic constraints. This question is relevant for the optimal design of new harvesting devices as well as for quantifying the efficiency of existing systems. We first demonstrate that the maximum harvesting rate can be expressed as a constrained convex optimization problem. We illustrate it on bacteriorhodopsin, a light -driven proton pump from Archaea, which we find is close to optimal under realistic conditions. In our second result, we solve the optimization problem in closed -form in three physically meaningful limiting regimes. These closed -form solutions are illustrated on two idealized models of unicyclic harvesting systems.

We explore the application of a new theory of Semantic Information to the well-motivated problem of a resource foraging agent. Semantic information is defined as the subset of correlations, measured via the transfer entropy, between agent $A$ and environment $E$ that is necessary for the agent to maintain its viability $V$. Viability, in turn, is endogenously defined as opposed to the use of exogenous quantities like utility functions. In our model, the forager's movements are determined by its ability to measure, via a sensor, the presence of an individual unit of resource, while the viability function is its expected lifetime. Through counterfactual interventions -- scrambling the correlations between agent and environment via noising the sensor -- we demonstrate the presence of a critical value of the noise parameter, $\eta_c$, above which the forager's expected lifetime is dramatically reduced. On the other hand, for $\eta < \eta_c$ there is little-to-no effect on its ability to survive. We refer to this boundary as the semantic threshold, quantifying the subset of agent-environment correlations that the agent actually needs to maintain its desired state of staying alive. Each bit of information affects the agent's ability to persist both above and below the semantic threshold. Modeling the viability curve and its semantic threshold via forager/environment parameters, we show how the correlations are instantiated. Our work provides a useful model for studies of established agents in terms of semantic information. It also shows that such semantic thresholds may prove useful for understanding the role information plays in allowing systems to become autonomous agents.

Harvesting free energy from the environment is essential for the operation of many biological and artificial systems. We investigate the maximum rate of harvesting achievable by optimizing a set of reactions in a Markovian system, possibly given topological, kinetic, and thermodynamic constraints. We show that the maximum harvesting rate can be expressed as a variational principle, which we solve in closed-form for three physically meaningful regimes. Our approach is relevant for optimal design and for quantifying efficiency of existing reactions. Our results are illustrated on bacteriorhodopsin, a light-driven proton pump from Archae, which is found to be close to optimal under realistic conditions.

Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are driven by cooperative and symmetric interactions between these species. For an isolated population, we determine the probability to reach fixation, where only one species remains, as a function of the initial concentrations of the two species, as well as the time to reach fixation. The latter scales exponentially with the population size. When members of each species migrate into the population at rate λ and replace a randomly selected individual, surprisingly rich dynamics ensues. Ostensibly, the population reaches a steady state, but the steady-state population distribution undergoes a unimodal to trimodal transition as the migration rate decreases below a critical value λ c . In the low-migration regime, λ < λ c , the steady state is not truly steady, but instead strongly fluctuates between near-fixation states, where the population consists of mostly A’s or of mostly B’s. The characteristic time scale of these fluctuations diverges as λ −1 . Thus in spite of the cooperative interaction, a typical snapshot of the population will contain almost all A’s or almost all B’s.

Cooperative interactions pervade the dynamics of a broad rage of many-body systems, such as ecological communities, the organization of social structures, and economic webs. In this work, we investigate the dynamics of a simple population model that is driven by cooperative and symmetric interactions between two species. We develop a mean-field and a stochastic description for this cooperative two-species reaction scheme. For an isolated population, we determine the probability to reach a state of fixation, where only one species survives, as a function of the initial concentrations of the two species. We also determine the time to reach the fixation state. When each species can migrate into the population and replace a randomly selected individual, the population reaches a steady state. We show that this steady-state distribution undergoes a unimodal to trimodal transition as the migration rate is decreased beyond a critical value. In this low-migration regime, the steady state is not truly steady, but instead fluctuates strongly between near-fixation states of the two species. The characteristic time scale of these fluctuations diverges as $\lambda^{-1}$.

Have you ever taken a disputed decision by tossing a coin and checking its landing side? This ancestral "heads or tails" practice is still widely used when facing undecided alternatives since it relies on the intuitive fairness of equiprobability. However, it critically disregards an interesting third outcome: the possibility of the coin coming at rest on its edge. Provided this evident yet elusive possibility, previous works have already focused on capturing all three landing probabilities of thick coins, but have only succeeded computationally as an exact and fully grounded analytical solution still evades the physics community. In this work we combine the classical equations of collisions with a statistical-mechanics approach to derive the exact analytical outcome probabilities of the partially inelastic coin toss. We validate the theoretical prediction by comparing it to previously reported simulations and experimental data; we discuss the moderate discrepancies arising at the highly inelastic regime; we describe the differences with previous, approximate models; and we finally propose the optimal geometry for the fair, cylindrical three-sided die based on the current results.

Multicellular entities are characterized by intricate spatial patterns, intimately related to the functions they perform. These patterns are often created from isotropic embryonic structures, without external information cues guiding the symmetry breaking process. Mature biological structures also display characteristic scales with repeating distributions of signals or chemical species across space. Many candidate patterning modules have been used to explain processes during development and typically include a set of interacting and diffusing chemicals or agents known as morphogens. Great effort has been put forward to better understand the conditions in which pattern-forming processes can occur in the biological domain. However, evidence and practical knowledge allowing us to engineer symmetry-breaking is still lacking. Here we follow a different approach by designing a synthetic gene circuit in E. coli that implements a local activation long-range inhibition mechanism. The synthetic gene network implements an artificial differentiation process that changes the physicochemical properties of the agents. Using both experimental results and modeling, we show that the proposed system is capable of symmetry-breaking leading to regular spatial patterns during colony growth. Studying how these patterns emerge is fundamental to further our understanding of the evolution of biocomplexity and the role played by self-organization. The artificial system studied here and the engineering perspective on embryogenic processes can help validate developmental theories and identify universal properties underpinning biological pattern formation, with special interest for the area of synthetic developmental biology.

Multicellular entities are characterized by exquisite spatial patterns, intimately related to the functions they perform. Oftentimes these patterns emerge as periodic structures with a well-defined characteristic scale. A candidate mechanism to explain their origins was early introduced by Alan Turing through the interaction and diffusion of two so called . Unfortunately, most available evidence for Turing patterns in biology is usually obscured by the tangled nature of regulatory phenomena, making difficult to validate Turing’s proposal in developmental processes. Here we follow a different approach, by designing synthetic genetic circuits in engineered strains that implement the essential activator-inhibitor motif (AIM) using a two-cell consortium. The two diffusible compartments are one cell type (activator, small-diffusion component) and a small signal molecule (a homoserine lactone, acting as the fast-diffusing inhibitor). Using both experimental results, we show that the AIM is capable of generating diffusion-induced instabilities leading to regular spatial patterns. The artificial construction taken here can help validate developmental theories and identify universal properties underpinning biological pattern formation. The implications of the work for the area of synthetic developmental biology are outlined.

We investigate the dynamics of the voter model in which the population itself changes endogenously via the birth-death process. There are two species of voters, labeled A and B, and the population of each species can grow or shrink by the birth-death process at equal rates b. Individuals of opposite species also undergo voter model dynamics in which an AB pair can equiprobably become AA or BB with rate v-neutral evolution. In the limit b/v -> infinity, the distribution of consensus times varies as t(-3) and the probability that the population size equals n at the moment of consensus varies as n(-3). As the birth/death rate b is increased, fixation occurs more more quickly; that is, population fluctuations promote consensus.

Habitat loss is known to pervade extinction thresholds in metapopulations. Such thresholds result from a loss of stability that can eventually lead to collapse. Several models have been developed to understand the nature of these transitions and how are they affected by the locality of interactions, fluctuations, or external drivers. Most models consider the impact of grazing or aridity as a control parameter that can trigger sudden shifts, once critical values are reached. Others explore instead the role played by habitat loss and fragmentation. Here we consider a minimal model incorporating facilitation along with habitat destruction, with the aim of understanding how local cooperation and habitat loss interact with each other. An explicit mathematical model is derived, along with a spatially explicit simulation model. It is found that a catastrophic shift is expected for increasing levels of habitat loss, but the breakpoint dynamics becomes continuous when dispersal is local. Under these conditions, spatial patchiness is found and the qualitative change from discontinuous to continuous results from a universal behaviour found in a broad class of nonlinear ecological systems (Weissmann and Shnerb, 2014; Martin et al. PNAS (2015) E1828-E1836). Our results suggest that species exhibiting facilitation and displaying short-range dispersal will be markedly more capable of dealing with habitat destruction, also avoiding catastrophic tipping points.

Liquid neural networks (or “liquid brains”) are a widespread class of cognitive living networks characterised by a common feature: the agents (ants or immune cells, for example) move in space. Thus, no fixed, long-term agent-agent connections are maintained, in contrast with standard neural systems. How is this class of systems capable of displaying cognitive abilities, from learning to decision-making? In this paper, the collective dynamics, memory and learning properties of liquid brains is explored under the perspective of statistical physics. Using a comparative approach, we review the generic properties of three large classes of systems, namely: standard neural networks (“solid brains”), ant colonies and the immune system. It is shown that, despite their intrinsic physical differences, these systems share key properties with standard neural systems in terms of formal descriptions, but strongly depart in other ways. On one hand, the attractors found in liquid brains are not always based on connection weights but instead on population abundances. However, some liquid systems use fluctuations in ways similar to those found in cortical networks, suggesting a relevant role of criticality as a way of rapidly reacting to external signals.

Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constraints for these systems remain an open question. This is largely due to the lack of a general theory of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements falling under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Secondly, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics. Finally, we comment and discuss where further research should be focused on.

Mutualistic networks have been shown to involve complex patterns of interactions among animal and plant species, including a widespread presence of nestedness. The nested structure of these webs seems to be positively correlated with higher diversity and resilience. Moreover, these webs exhibit marked measurable structural patterns, including broad distributions of connectivity, strongly asymmetrical interactions and hierarchical organization. Hierarchical organization is an especially interesting property, since it is positively correlated with biodiversity and network resilience, thus suggesting potential selection processes favouring the observed web organization. However, here we show that all these structural quantitative patterns-and nestedness in particular-can be properly explained by means of a very simple dynamical model of speciation and divergence with no selection-driven coevolution of traits. The agreement between observed and modelled networks suggests that the patterns displayed by real mutualistic webs might actually represent evolutionary spandrels.

Although the presence of vast amounts of plastic in the open ocean has generated great concern due to its potential ecological consequences, recent studies reveal that its measured abundance is much smaller than expected. Regional and global studies indicate that the difference between expected and actual estimates is enormous, suggesting that a large part of the plastic has been degraded by either physical and biotic processes. A paradoxical observation is the lack of a trend in plastic accumulation found in the North Atlantic Subtropical Gyre, despite the rapid increase in plastic production and disposal. In this paper we show, using mathematical and computer models, that this observation could be explained by the nonlinear coupling between plastic (as a resource) and an evolved set of organisms (the consumers) capable of degrading it. The result is derived using two different resource-consumer mathematical approaches as well as a spatially-dependent plastic-microbial model incorporating a minimal hydrodynamical coupling with a two-dimensional fluid. The potential consequences of the evolution of marine plastic garbage and its removal are outlined.

It has been suggested that major transitions in evolution require the emergence of novelties, often associated to the cooperative behaviour of previously existing objects or agents. A key innovation involves the first cooperative interactions among molecules in a prebiotic biosphere. One of the simplest scenarios includes two molecular species capable of helping each other forming a catalytic loop or hypercycle. The second order kinetics of the hypercycle implies a hyperbolic growth dynamics, capable of overcoming some selection barriers associated to non-cooperative molecular systems. Moreover, it has been suggested that molecular replicators might have benefited from a limited diffusion associated to their attachment to surfaces: evolution and escape from extinction might have been tied to living on a surface. In this paper we propose a field theoretical model of the hypercycle involving reaction and diffusion through the use of a many-body Hamiltonian. This treatment allows a characterisation of the spatially correlated dynamics of the system, where the critical dimension is found to be $d_c=2$. We discuss the role of surface dynamics as a selective advantage for the system's survival.