Recognition-Encoded Molecules: a Minimal Self-Replicator.

Nucleic acids, with their unique duplex structure, which is key for information replication, have sparked interest in self-replication's role in life's origins. Early template-based replicators, initially built on short oligonucleotides, expanded to include peptides and synthetic molecules. We explore here the potential of a class of synthetic duplex-forming oligoanilines, as self-replicators. We have recently developed oligoanilines equipped with 2-trifluoromethylphenol-phosphine oxide H-bond base pairs and we investigate whether the imine formed between aniline and aldehyde complementary monomers can self-replicate. Despite lacking a clear sigmoidal kinetic profile, control experiments with a methylated donor and a competitive inhibitor support self-replication. Further investigations with the reduced aniline dimer demonstrate templated synthesis, revealing a characteristic parabolic growth. After showing sequence selective duplex formation, templated synthesis and the emergence of catalytic function, the self-replication behaviour further suggests that the unique properties of nucleic acids can be paralleled by synthetic recognition-encoded molecules.

Using synthetic dataset for semantic segmentation of the human body in the problem of extracting anthropometric data.

Background: The COVID-19 pandemic highlighted the need for accurate virtual sizing in e-commerce to reduce returns and waste. Existing methods for extracting anthropometric data from images have limitations. This study aims to develop a semantic segmentation model trained on synthetic data that can accurately determine body shape from real images, accounting for clothing. Methods: A synthetic dataset of over 22,000 images was created using NVIDIA Omniverse Replicator, featuring human models in various poses, clothing, and environments. Popular CNN architectures (U-Net, SegNet, DeepLabV3, PSPNet) with different backbones were trained on this dataset for semantic segmentation. Models were evaluated on accuracy, precision, recall, and IoU metrics. The best performing model was tested on real human subjects and compared to actual measurements. Results: U-Net with EfficientNet backbone showed the best performance, with 99.83% training accuracy and 0.977 IoU score. When tested on real images, it accurately segmented body shape while accounting for clothing. Comparison with actual measurements on 9 subjects showed average deviations of -0.24 cm for neck, -0.1 cm for shoulder, 1.15 cm for chest, -0.22 cm for thallium, and 0.17 cm for hip measurements. Discussion: The synthetic dataset and trained models enable accurate extraction of anthropometric data from real images while accounting for clothing. This approach has significant potential for improving virtual fitting and reducing returns in e-commerce. Future work will focus on refining the algorithm, particularly for thallium and hip measurements which showed higher variability.

Interaction intensity in strategic fitness: A quantifying yardstick of selection optimization for evolutionary game.

The notion of the fitness of a strategy has been assimilated as the reproductive success in the evolutionary game. Initially, this fitness was tied to the game's pay-off and the strategy's relative frequency. However, density dependence becomes exigent in order to make ecologically reliable fitness. However, the contributions of each different type of interaction to the species's overall growth process were surprisingly under-explored. This oversight has occasionally led to either more or less prediction of strategy selection compared to the actual possibility. Moreover, density regulation of the population has always been analysed in a general way compared to strategy selection. In this context, our study introduces the concept of mean relative death payoff, which helps in assessing interaction intensity coefficients and integrates them into strategic fitness. Based on this fitness function, we develop the frequency-density replicator dynamics, which eventually provides distinguishing criteria for directional and balancing selection. Our optimized, evolutionarily stable strategy emerges as a superior alternative to the conventional trade-off between selection forces and ecological processes. More significantly, mean relative death pay-off has both conditional and quantitative roles in getting a stable population size. As a case study, we have extensively analysed the evolution of aggression using the Hawk-Dove game. We have shown that pure Dove selection is always beneficial for species growth rather than pure Hawk selection, and the condition of selection is dependent on external mortality pressure. However, the condition of coexistence is independent of external mortality pressure, representing a strong evolutionary selection that optimizes population density governed by interaction intensity.

Evolution of Cooperation in Spatio-Temporal Evolutionary Games with Public Goods Feedback.

In biology, evolutionary game-theoretical models often arise in which players' strategies impact the state of the environment, driving feedback between strategy and the surroundings. In this case, cooperative interactions can be applied to studying ecological systems, animal or microorganism populations, and cells producing or actively extracting a growth resource from their environment. We consider the framework of eco-evolutionary game theory with replicator dynamics and growth-limiting public goods extracted by population members from some external source. It is known that the two sub-populations of cooperators and defectors can develop spatio-temporal patterns that enable long-term coexistence in the shared environment. To investigate this phenomenon and unveil the mechanisms that sustain cooperation, we analyze two eco-evolutionary models: a well-mixed environment and a heterogeneous model with spatial diffusion. In the latter, we integrate spatial diffusion into replicator dynamics. Our findings reveal rich strategy dynamics, including bistability and bifurcations, in the temporal system and spatial stability, as well as Turing instability, Turing-Hopf bifurcations, and chaos in the diffusion system. The results indicate that effective mechanisms to promote cooperation include increasing the player density, decreasing the relative timescale, controlling the density of initial cooperators, improving the diffusion rate of the public goods, lowering the diffusion rate of the cooperators, and enhancing the payoffs to the cooperators. We provide the conditions for the existence, stability, and occurrence of bifurcations in both systems. Our analysis can be applied to dynamic phenomena in fields as diverse as human decision-making, microorganism growth factors secretion, and group hunting.

Revealing the hierarchical structure of microbial communities.

Measuring the dynamics of microbial communities results in high-dimensional measurements of taxa abundances over time and space, which is difficult to analyze due to complex changes in taxonomic compositions. This paper presents a new method to investigate and visualize the intrinsic hierarchical community structure implied by the measurements. The basic idea is to identify significant intersection sets, which can be seen as sub-communities making up the measured communities. Using the subset relationship, the intersection sets together with the measurements form a hierarchical structure visualized as a Hasse diagram. Chemical organization theory (COT) is used to relate the hierarchy of the sets of taxa to potential taxa interactions and to their potential dynamical persistence. The approach is demonstrated on a data set of community data obtained from bacterial 16S rRNA gene sequencing for samples collected monthly from four groundwater wells over a nearly 3-year period (n = 114) along a hillslope area. The significance of the hierarchies derived from the data is evaluated by showing that they significantly deviate from a random model. Furthermore, it is demonstrated how the hierarchy is related to temporal and spatial factors; and how the idea of a core microbiome can be extended to a set of interrelated core microbiomes. Together the results suggest that the approach can support developing models of taxa interactions in the future.

Selectively advantageous instability in biotic and pre-biotic systems and implications for evolution and aging.

Rules of biology typically involve conservation of resources. For example, common patterns such as hexagons and logarithmic spirals require minimal materials, and scaling laws involve conservation of energy. Here a relationship with the opposite theme is discussed, which is the selectively advantageous instability (SAI) of one or more components of a replicating system, such as the cell. By increasing the complexity of the system, SAI can have benefits in addition to the generation of energy or the mobilization of building blocks. SAI involves a potential cost to the replicating system for the materials and/or energy required to create the unstable component, and in some cases, the energy required for its active degradation. SAI is well-studied in cells. Short-lived transcription and signaling factors enable a rapid response to a changing environment, and turnover is critical for replacement of damaged macromolecules. The minimal gene set for a viable cell includes proteases and a nuclease, suggesting SAI is essential for life. SAI promotes genetic diversity in several ways. Toxin/antitoxin systems promote maintenance of genes, and SAI of mitochondria facilitates uniparental transmission. By creating two distinct states, subject to different selective pressures, SAI can maintain genetic diversity. SAI of components of synthetic replicators favors replicator cycling, promoting emergence of replicators with increased complexity. Both classical and recent computer modeling of replicators reveals SAI. SAI may be involved at additional levels of biological organization. In summary, SAI promotes replicator genetic diversity and reproductive fitness, and may promote aging through loss of resources and maintenance of deleterious alleles.

The dynamics of casual groups can keep free-riders at bay.

Understanding the conditions for maintaining cooperation in groups of unrelated individuals despite the presence of non-cooperative members is a major research topic in contemporary biological, sociological, and economic theory. The N-person snowdrift game models the type of social dilemma where cooperative actions are costly, but there is a reward for performing them. We study this game in a scenario where players move between play groups following the casual group dynamics, where groups grow by recruiting isolates and shrink by losing individuals who then become isolates. This describes the size distribution of spontaneous human groups and also the formation of sleeping groups in monkeys. We consider three scenarios according to the probability of isolates joining a group. We find that for appropriate choices of the cost-benefit ratio of cooperation and the aggregation-disaggregation ratio in the formation of casual groups, free-riders can be completely eliminated from the population. If individuals are more attracted to large groups, we find that cooperators persist in the population even when the mean group size diverges. We also point out the remarkable similarity between the replicator equation approach to public goods games and the trait group formulation of structured demes.

Natural gradient ascent in evolutionary games.

We consider evolutionary games with a continuous trait space where the replicator dynamics are restricted to the manifold of multivariate Gaussian distributions. We demonstrate that replicator dynamics are gradient flows with respect to the Fisher information metric. The potential function for these gradient flows is closely related to the mean fitness. Our findings extend previous results on natural gradient ascent in evolutionary games with a finite strategy set. Throughout the paper we pursue an information-geometric point of view on evolutionary games. This sheds a new light on the replicator dynamics as a learning process, realizing the compromise between maximization of the mean fitness and preservation of the diversity.

The shirker's dilemma and the prospect of cooperation in large groups.

Cooperation usually becomes harder to sustain as groups become larger because incentives to shirk increase with the number of potential contributors to collective action. But is this always the case? Here we study a binary-action cooperative dilemma where a public good is provided as long as not more than a given number of players shirk from a costly cooperative task. We find that at the stable polymorphic equilibrium, which exists when the cost of cooperation is low enough, the probability of cooperating increases with group size and reaches a limit of one when the group size tends to infinity. Nevertheless, increasing the group size may increase or decrease the probability that the public good is provided at such an equilibrium, depending on the cost value. We also prove that the expected payoff to individuals at the stable polymorphic equilibrium (i.e., their fitness) decreases with group size. For low enough costs of cooperation, both the probability of provision of the public good and the expected payoff converge to positive values in the limit of large group sizes. However, we also find that the basin of attraction of the stable polymorphic equilibrium is a decreasing function of group size and shrinks to zero in the limit of very large groups. Overall, we demonstrate non-trivial comparative statics with respect to group size in an otherwise simple collective action problem.

Towards a mathematical understanding of invasion resistance in multispecies communities.

Multispecies community composition and dynamics are key to health and disease across biological systems, a prominent example being microbial ecosystems. Explaining the forces that govern diversity and resilience in the microbial consortia making up our body's defences remains a challenge. In this, theoretical models are crucial, to bridge the gap between species dynamics and underlying mechanisms and to develop analytic insight. Here we propose a replicator equation framework to model multispecies dynamics where an explicit notion of invasion resistance of a system emerges and can be studied explicitly. For illustration, we derive the conceptual link between such replicator equation and N microbial species' growth and interaction traits, stemming from micro-scale environmental modification. Within this replicator framework, mean invasion fitness arises, evolves dynamically, and may undergo critical predictable shifts with global environmental changes. This mathematical approach clarifies the key role of this resident system trait for invader success, and highlights interaction principles among N species that optimize their collective resistance to invasion. We propose this model based on the replicator equation as a powerful new avenue to study, test and validate mechanisms of invasion resistance and colonization in multispecies microbial ecosystems and beyond.

The evolution of cooperation in the unidirectional division of labour on a tree network.

Division of labour on complex networks is rarely investigated using evolutionary game theory. We investigate a division of labour where divided roles are assigned to groups on the nodes of a general unidirectional finite tree graph network. From the network's original node, a task flows and is divided along the branches. A player is randomly selected in each group of cooperators and defectors, who receives a benefit from a cooperator in the upstream group and a part of the task. A cooperator completes their part by paying a cost and then passing it downstream until the entire task is completed. Defectors do not do anything and the division of labour stops, causing all groups to suffer losses due to the incomplete task. We develop a novel method to analyse the local stability in this general tree. We discover that not the benefits but the costs of the cooperation influence the evolution of cooperation, and defections in groups that are directly related to that group's task cause damage to players in that group. We introduce two sanction systems, one of which induces the evolution of cooperation more than the system without sanctions, and promote the coexistence of cooperator and defector groups.

Managing ecological thresholds of a risky commons.

Common resources are often overexploited and appear subject to critical transitions from one stable state to another antagonistic state. Many times resulting in tragedy of the commons (TOC)-exploitation of shared resources for personal gain/payoffs, leading to worse outcomes or extinction. An adequate response would be strategic interaction, such as inspection and punishment by institutions to avoid TOC. This strategic interaction is often coupled with dynamically changing common resources. However, effect of strategic interaction in complex, coupled socio-ecological systems is less studied. Here, we develop replicator equations using evolving games in which strategy and common resources co-evolve. We consider the shared commons as fish dynamics governed by the intrinsic growth rate, predation and harvesting. The joint dynamics exhibit an oscillatory TOC, revealing that institutions need to pay special attention to intrinsic growth rate and nonlinear interaction. Our research shows that the co-evolving system exhibits a broader range of dynamics when predation is present compared to the disengaged fishery system. We conclude that the usefulness, chances and challenges of modelling co-evolutionary games to create sustainable systems merit further research.

Multi-objective control optimization of isolated bridge using replicator controller and NSGA-II.

Earthquakes can cause significant damage to constructed structures, leading engineers to design systems that effectively reduce damage and improve real-time vibration control. While base isolation is a commonly used passive method for seismic protection in highway structures, it has limitations such as a lack of immediate adaptation, constrained power dissipation capacity, and poor performance during earthquakes. To address the limitations of passive base isolation bearings, a hybrid control system that includes semi-active MR dampers is being introduced into isolated highway bridge structures. The aim is to enhance vibration reduction and improve overall performance. One of the major challenges in implementing this technology is developing appropriate control algorithms to handle the nonlinear behavior of semi-active devices. This paper proposes an adaptive data-driven control algorithm, informed by evolutionary game theory and a multi-objective optimization process, to optimize the distribution of voltage to semi-active MR dampers based on measurements of the damper's response to input signals. The algorithm is designed to provide optimal seismic protection. The performance of the replicator dynamics in the control system depends on three critical parameters: total population, which represents the total available resources or the sum of actuator forces; growth rate, which is the rate at which resources are distributed among control devices; and the fictitious fitness function, which regulates power consumption. Previous studies used sensitivity analysis to ascertain the best values for population size and growth rate, a time-consuming and unreliable process. This study aims to improve the performance of the system by solving a multi-objective problem. The proposed approach integrates a control algorithm with a multi-objective optimization algorithm, namely NSGA-II, to find Pareto optimal values for all parameters of the replicator dynamics. These parameters include total population, growth rate, and the fictitious function, with the aim of ensuring sustainability. By considering multiple objectives simultaneously, the proposed approach can provide a more comprehensive and effective solution for the bridge control problem. The effectiveness of this proposed approach is demonstrated through sample results Utilizing a case study centered around the Southern California Interstate 91/5 Overcrossing Highway Bridge, which is exposed to seismic activities.

How biological codes break causal chains to enable autonomy for organisms.

Autonomy, meaning freedom from exogenous control, requires independence of both constitution and cybernetic regulation. Here, the necessity of biological codes to achieve both is explained, assuming that Aristotelian efficient cause is 'formal cause empowered by physical force'. Constitutive independence requires closure to efficient causation (in the Rosen sense); cybernetic independence requires transformation of cause-effect into signal-response relations at the organism boundary; the combination of both kinds of independence enables adaptation and evolution. Codes and cyphers translate information from one form of physical embodiment (domain) to another. Because information can only contribute as formal cause to efficient cause within the domain of its embodiment, translation can extend or restrict the range over which information is effective. Closure to efficient causation requires internalised information to be isolated from the cycle of efficient causes that it informs: e.g. Von Neumann self-replicator requires a (template) source of information that is causally isolated from the physical replication system. Life operationalises this isolation with the genetic code translating from the (isolated) domain of codons to that of protein interactions. Separately, cybernetic freedom is achieved at the cell boundary because transducers, which embody molecular coding, translate exogenous information into a domain where it no longer has the power of efficient cause. Information, not efficient cause, passes through the boundary to serve as stimulus for an internally generated response. Coding further extends freedom by enabling historically accumulated information to be selectively transformed into efficient cause under internal control, leaving it otherwise stored inactive. Code-based translation thus enables selective causal isolation, controlling the flow from cause to effect. Genetic code, cell-signalling codes and, in eukaryotes, the histone code, signal sequence based protein sorting and other code-dependent processes all regulate and separate causal chains. The existence of life can be seen as an expression of the power of molecular codes to selectively isolate and thereby organise causal relations among molecular interactions to form an organism.

Age structure, replicator equation, and the prisoner's dilemma.

We investigate the evolutionary dynamics of an age-structured population subject to weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimensional modified replicator equation. The modified replicator equation is then used to investigate cooperation (the prisoner's dilemma) by means of adaptive dynamics. We identify conditions under which age structure is able to promote cooperation. At the end we discuss the relevance of our findings.

Quasi-neutral dynamics in a coinfection system with N strains and asymmetries along multiple traits.

Understanding the interplay of different traits in a co-infection system with multiple strains has many applications in ecology and epidemiology. Because of high dimensionality and complex feedback between traits manifested in infection and co-infection, the study of such systems remains a challenge. In the case where strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Here, we apply singular perturbation theory to many strain parameters simultaneously and advance analytically to obtain their explicit collective dynamics. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) dynamics among N strains, which vary in 5 fitness dimensions: transmissibility, clearance rate of single- and co-infection, transmission probability from mixed coinfection, and co-colonization vulnerability factors encompassing cooperation and competition. This quasi-neutral system is analyzed with a singular perturbation method through an appropriate slow-fast decomposition. The fast dynamics correspond to the embedded neutral system, while the slow dynamics are governed by an N-dimensional replicator equation, describing the time evolution of strain frequencies. The coefficients of this replicator system are pairwise invasion fitnesses between strains, which, in our model, are an explicit weighted sum of pairwise asymmetries along all trait dimensions. Remarkably these weights depend only on the parameters of the neutral system. Such model reduction highlights the centrality of the neutral system for dynamics at the edge of neutrality and exposes critical features for the maintenance of diversity.

Policy choices and compliance behavior in pandemic times.

In this paper, we model an evolutionary noncooperative game between politicians and citizens that, given the level of infection, describes the observed variety of mitigation policies and citizens' compliance during the COVID-19 pandemic period. Our results show that different stable equilibria exist and that different ways/paths exist to reach these equilibria may be present, depending on the choice of parameters. When the parameters are chosen opportunistically, in the short run, our model generates transitions between hard and soft policy measures to deal with the pandemic. In the long-run, convergence is achieved toward one of the possible stable steady states (obey or not obey lockdown rules) as functions of politicians' and citizens' incentives.

Weak selection and stochastic evolutionary stability in a stochastic replicator dynamics.

It is a very challenging problem whether natural selection is able to effectively resist the continuous disturbance of environmental noise such that the direction or outcome of evolution determined by the deterministic selection pressure will not be changed. By analyzing the impact of weak selection on the evolutionary stability of a stochastic replicator dynamics with n possible pure strategies, we found that the weak selection is able to enhance the evolutionary stability, that is, under weak selection, the stochastic evolutionary stability of the system is determined by the mean payoff matrix. This finding strongly implies that the weak selection should be regarded as an important mechanism to ensure evolutionary stability in stochastic environments.

Mean-Field Limits for Entropic Multi-Population Dynamical Systems.

The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution of the labels, the case of different time scales between the agents' locations and labels dynamics is considered. The limit system couples a mean-field-type evolution in the space of positions and an instantaneous optimization of the payoff functional in the space of labels.