Diversity begets stability: Sublinear growth and competitive coexistence across ecosystems.

The worldwide loss of species diversity brings urgency to understanding how diverse ecosystems maintain stability. Whereas early ecological ideas and classic observations suggested that stability increases with diversity, ecological theory makes the opposite prediction, leading to the long-standing "diversity-stability debate." Here, we show that this puzzle can be resolved if growth scales as a sublinear power law with biomass (exponent <1), exhibiting a form of population self-regulation analogous to models of individual ontogeny. We show that competitive interactions among populations with sublinear growth do not lead to exclusion, as occurs with logistic growth, but instead promote stability at higher diversity. Our model realigns theory with classic observations and predicts large-scale macroecological patterns. However, it makes an unsettling prediction: Biodiversity loss may accelerate the destabilization of ecosystems.

Pathways for socio-economic system transitions expressed as a Markov chain.

Cross-impact balance (CIB) analysis provides a system-theoretical view of scenarios useful for investigating complex socio-economic systems. CIB can synthesize a variety of qualitative or quantitative inputs and return information suggestive of system evolution. Current software tools for CIB are limited to identifying system attractors as well as describing system evolution from only one scenario of initial conditions at a time. Through this study, we enhance CIB by developing and applying a method that considers all possible system evolutions as transitions in a Markov chain. We investigated a simple three-variable system (27 possible scenarios) of the demographic transition and were able to generally replicate the findings of traditional CIB. Through our experiments with four possible approaches to produce CIB Markov chains, we found that information about transition pathways is gained; however, information about system attractors may be lost. Through a comparison of model results to a recent literature review on human demography, we found that low-income countries are more likely to remain stuck in a demographic trap if economic development is not prioritized alongside educational gains. Future work could test our comparative methodological findings for systems comprised of more than three variables.

Diversity enables the jump towards cooperation for the Traveler's Dilemma.

Social dilemmas are situations in which collective welfare is at odds with individual gain. One widely studied example, due to the conflict it poses between human behaviour and game theoretic reasoning, is the Traveler's Dilemma. The dilemma relies on the players' incentive to undercut their opponent at the expense of losing a collective high payoff. Such individual incentive leads players to a systematic mutual undercutting until the lowest possible payoff is reached, which is the game's unique Nash equilibrium. However, if players were satisfied with a high payoff -that is not necessarily higher than their opponent's- they would both be better off individually and collectively. Here, we explain how it is possible to converge to this cooperative high payoff equilibrium. Our analysis focuses on decomposing the dilemma into a local and a global game. We show that players need to escape the local maximisation and jump to the global game, in order to reach the cooperative equilibrium. Using a dynamic approach, based on evolutionary game theory and learning theory models, we find that diversity, understood as the presence of suboptimal strategies, is the general mechanism that enables the jump towards cooperation.

RAFFT: Efficient prediction of RNA folding pathways using the fast Fourier transform.

We propose a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. This heuristic is inspired by the kinetic partitioning mechanism, by which molecules follow alternative folding pathways to their native structure, some much faster than others. Similarly, our algorithm RAFFT starts by generating an ensemble of concurrent folding pathways ending in multiple metastable structures, which is in contrast with traditional thermodynamic approaches that find single structures with minimal free energies. When we constrained the algorithm to predict only 50 structures per sequence, near-native structures were found for RNA molecules of length ≤ 200 nucleotides. Our heuristic has been tested on the coronavirus frameshifting stimulation element (CFSE): an ensemble of 68 distinct structures allowed us to produce complete folding kinetic trajectories, whereas known methods require evaluating millions of sub-optimal structures to achieve this result. Thanks to the fast Fourier transform on which RAFFT (RNA folding Algorithm wih Fast Fourier Transform) is based, these computations are efficient, with complexity [Formula: see text].

Diffusion approximations in population genetics and the rate of Muller's ratchet.

The Wright-Fisher binomial model of allele frequency change is often approximated by a scaling limit in which selection, mutation and drift all decrease at the same 1/N rate. This construction restricts the applicability of the resulting 'Wright-Fisher diffusion equation' to the weak selection, weak mutation regime of evolution. We argue that diffusion approximations of the Wright-Fisher model can be used more generally, for instance in cases where genetic drift is much weaker than selection. One important example of this regime is Muller's ratchet phenomenon, whereby deleterious mutations slowly but irreversibly accumulate through rare stochastic fluctuations. Using a modified diffusion equation we derive improved analytical estimates for the mean click time of the ratchet.

aRNAque: an evolutionary algorithm for inverse pseudoknotted RNA folding inspired by Lévy flights.

BACKGROUND: We study in this work the inverse folding problem for RNA, which is the discovery of sequences that fold into given target secondary structures. RESULTS: We implement a Lévy mutation scheme in an updated version of aRNAque an evolutionary inverse folding algorithm and apply it to the design of RNAs with and without pseudoknots. We find that the Lévy mutation scheme increases the diversity of designed RNA sequences and reduces the average number of evaluations of the evolutionary algorithm. Compared to antaRNA, aRNAque CPU time is higher but more successful in finding designed sequences that fold correctly into the target structures. CONCLUSION: We propose that a Lévy flight offers a better standard mutation scheme for optimizing RNA design. Our new version of aRNAque is available on GitHub as a python script and the benchmark results show improved performance on both Pseudobase++ and the Eterna100 datasets, compared to existing inverse folding tools.

The cost of noise: Stochastic punishment falls short of sustaining cooperation in social dilemma experiments.

Identifying mechanisms able to sustain costly cooperation among self-interested agents is a central problem across social and biological sciences. One possible solution is peer punishment: when agents have an opportunity to sanction defectors, classical behavioral experiments suggest that cooperation can take root. Overlooked from standard experimental designs, however, is the fact that real-world human punishment-the administration of justice-is intrinsically noisy. Here we show that stochastic punishment falls short of sustaining cooperation in the repeated public good game. As punishment noise increases, we find that contributions decrease and punishment efforts intensify, resulting in a 45% drop in gains compared to a noiseless control. Moreover, we observe that uncertainty causes a rise in antisocial punishment, a mutually harmful behavior previously associated with societies with a weak rule of law. Our approach brings to light challenges to cooperation that cannot be explained by economic rationality and strengthens the case for further investigations of the effect of noise-and not just bias-on human behavior.

Natural Selection beyond Life? A Workshop Report.

Natural selection is commonly seen not just as an explanation for adaptive evolution, but as the inevitable consequence of "heritable variation in fitness among individuals". Although it remains embedded in biological concepts, such a formalisation makes it tempting to explore whether this precondition may be met not only in life as we know it, but also in other physical systems. This would imply that these systems are subject to natural selection and may perhaps be investigated in a biological framework, where properties are typically examined in light of their putative functions. Here we relate the major questions that were debated during a three-day workshop devoted to discussing whether natural selection may take place in non-living physical systems. We start this report with a brief overview of research fields dealing with "life-like" or "proto-biotic" systems, where mimicking evolution by natural selection in test tubes stands as a major objective. We contend the challenge may be as much conceptual as technical. Taking the problem from a physical angle, we then discuss the framework of dissipative structures. Although life is viewed in this context as a particular case within a larger ensemble of physical phenomena, this approach does not provide general principles from which natural selection can be derived. Turning back to evolutionary biology, we ask to what extent the most general formulations of the necessary conditions or signatures of natural selection may be applicable beyond biology. In our view, such a cross-disciplinary jump is impeded by reliance on individuality as a central yet implicit and loosely defined concept. Overall, these discussions thus lead us to conjecture that understanding, in physico-chemical terms, how individuality emerges and how it can be recognised, will be essential in the search for instances of evolution by natural selection outside of living systems.

Why are viral genomes so fragile? The bottleneck hypothesis.

If they undergo new mutations at each replication cycle, why are RNA viral genomes so fragile, with most mutations being either strongly deleterious or lethal? Here we provide theoretical and numerical evidence for the hypothesis that genetic fragility is partly an evolutionary response to the multiple population bottlenecks experienced by viral populations at various stages of their life cycles. Modelling within-host viral populations as multi-type branching processes, we show that mutational fragility lowers the rate at which Muller's ratchet clicks and increases the survival probability through multiple bottlenecks. In the context of a susceptible-exposed-infectious-recovered epidemiological model, we find that the attack rate of fragile viral strains can exceed that of more robust strains, particularly at low infectivities and high mutation rates. Our findings highlight the importance of demographic events such as transmission bottlenecks in shaping the genetic architecture of viral pathogens.

Quasi-species evolution maximizes genotypic reproductive value (not fitness or flatness).

Growing efforts to measure fitness landscapes in molecular and microbial systems are motivated by a longstanding goal to predict future evolutionary trajectories. Sometimes under-appreciated, however, is that the fitness landscape and its topography do not by themselves determine the direction of evolution: under sufficiently high mutation rates, populations can climb the closest fitness peak (survival of the fittest), settle in lower regions with higher mutational robustness (survival of the flattest), or even fail to adapt altogether (error catastrophes). I show that another measure of reproductive success, Fisher's reproductive value, resolves the trade-off between fitness and robustness in the quasi-species regime of evolution: to forecast the motion of a population in genotype space, one should look for peaks in the (mutation-rate dependent) landscape of genotypic reproductive values-whether or not these peaks correspond to local fitness maxima or flat fitness plateaus. This new landscape picture turns quasi-species dynamics into an instance of non-equilibrium dynamics, in the physical sense of Markovian processes, potential landscapes, entropy production, etc.

Parameters and determinants of responses to selection in antibody libraries.

The sequences of antibodies from a given repertoire are highly diverse at few sites located on the surface of a genome-encoded larger scaffold. The scaffold is often considered to play a lesser role than highly diverse, non-genome-encoded sites in controlling binding affinity and specificity. To gauge the impact of the scaffold, we carried out quantitative phage display experiments where we compare the response to selection for binding to four different targets of three different antibody libraries based on distinct scaffolds but harboring the same diversity at randomized sites. We first show that the response to selection of an antibody library may be captured by two measurable parameters. Second, we provide evidence that one of these parameters is determined by the degree of affinity maturation of the scaffold, affinity maturation being the process by which antibodies accumulate somatic mutations to evolve towards higher affinities during the natural immune response. In all cases, we find that libraries of antibodies built around maturated scaffolds have a lower response to selection to other arbitrary targets than libraries built around germline-based scaffolds. We thus propose that germline-encoded scaffolds have a higher selective potential than maturated ones as a consequence of a selection for this potential over the long-term evolution of germline antibody genes. Our results are a first step towards quantifying the evolutionary potential of biomolecules.

A non-equilibrium formulation of food security resilience.

Resilience, the ability to recover from adverse events, is of fundamental importance to food security. This is especially true in poor countries, where basic needs are frequently threatened by economic, environmental and health shocks. An empirically sound formalization of the concept of food security resilience, however, is lacking. Here, we introduce a general non-equilibrium framework for quantifying resilience based on the statistical notion of persistence. Our approach can be applied to any food security variable for which high-frequency time-series data are available. We illustrate our method with per capita kilocalorie availability for 161 countries between 1961 and 2011. We find that resilient countries are not necessarily those that are characterized by high levels or less volatile fluctuations of kilocalorie intake. Accordingly, food security policies and programmes will need to be tailored not only to welfare levels at any one time, but also to long-run welfare dynamics.

Limiting fitness distributions in evolutionary dynamics.

Natural selection works on variation in fitness, but how should we measure "variation" to predict the rate of future evolution? Fisher's fundamental theorem of natural selection provides the short-run answer: the instantaneous rate of growth of a population's mean fitness is its variance in fitness. This identity captures an important feature of the evolutionary process, but, because it does not specify how the variance itself evolves in time, it cannot be used to predict evolutionary dynamics in the long run. In this paper we reconsider the problem of computing evolutionary trajectories from limited statistical information. We identify the feature of fitness distributions which controls their late-time evolution: their (suitably defined) tail indices. We show that the location, scale and shape of the fitness distribution can be predicted far into the future from the measurement of this tail index at some initial time. Unlike the "fitness waves" studied in the literature, this pattern encompasses both positive and negative selection and is not restricted to rapidly adapting populations. Our results are well supported by numerical simulations, both from the Wright-Fisher model and from a less structured genetic algorithm.

Minimum relative entropy distributions with a large mean are Gaussian.

Entropy optimization principles are versatile tools with wide-ranging applications from statistical physics to engineering to ecology. Here we consider the following constrained problem: Given a prior probability distribution q, find the posterior distribution p minimizing the relative entropy (also known as the Kullback-Leibler divergence) with respect to q under the constraint that mean(p) is fixed and large. We show that solutions to this problem are approximately Gaussian. We discuss two applications of this result. In the context of dissipative dynamics, the equilibrium distribution of a Brownian particle confined in a strong external field is independent of the shape of the confining potential. We also derive an H-type theorem for evolutionary dynamics: The entropy of the (standardized) distribution of fitness of a population evolving under natural selection is eventually increasing in time.

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes.

Ecosystems exhibit surprising regularities in structure and function across terrestrial and aquatic biomes worldwide. We assembled a global data set for 2260 communities of large mammals, invertebrates, plants, and plankton. We find that predator and prey biomass follow a general scaling law with exponents consistently near ¾. This pervasive pattern implies that the structure of the biomass pyramid becomes increasingly bottom-heavy at higher biomass. Similar exponents are obtained for community production-biomass relations, suggesting conserved links between ecosystem structure and function. These exponents are similar to many body mass allometries, and yet ecosystem scaling emerges independently from individual-level scaling, which is not fully understood. These patterns suggest a greater degree of ecosystem-level organization than previously recognized and a more predictive approach to ecological theory.

Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks.

The financial crisis illustrated the need for a functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult to model analytically, most recent studies of this problem have relied on numerical simulations. Here we report analytical results in a network model of interbank lending based on directly relevant financial parameters, such as interest rates and leverage ratios. We obtain a closed-form formula for the "critical degree" (the number of creditors per bank below which an individual shock can propagate throughout the network), and relate failures distributions to network topologies, in particular scalefree ones. Our criterion for the onset of contagion turns out to be isomorphic to the condition for cooperation to evolve on graphs and social networks, as recently formulated in evolutionary game theory. This remarkable connection supports recent calls for a methodological rapprochement between finance and ecology.

Gauge symmetries in spin-foam gravity: the case for "cellular quantization".

The spin-foam approach to quantum gravity rests on a quantization of BF theory using 2-complexes and group representations. We explain why, in dimension three and higher, this spin-foam quantization must be amended to be made consistent with the gauge symmetries of discrete BF theory. We discuss a suitable generalization, called "cellular quantization," which (1) is finite, (2) produces a topological invariant, (3) matches with the properties of the continuum BF theory, and (4) corresponds to its loop quantization. These results significantly clarify the foundations--and limitations--of the spin-foam formalism and open the path to understanding, in a discrete setting, the symmetry-breaking which reduces BF theory to gravity.

Tailoring diffusion in analog spacetimes.

Diffusive transport is characterized by the scaling law (length)^{2}∝(time). In this paper we show that this relationship is significantly altered in curved analog spacetimes. This circumstance provides an opportunity to tailor diffusion: by a suitable design of the analog metric, it is possible to create materials where diffusion is either faster or slower than in normal media, as desired. This prediction can, in principle, be tested experimentally with optical analogs, curved graphene sheets, and so on (indeed with any analog spacetime).