Learning enables adaptation in cooperation for multi-player stochastic games

Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g. the ‘tragedy of the commons’), modulate their behaviours to adapt to the fluctuation of the environment has not yet been addressed satisfactorily. Using evolutionary game theory, we develop a framework of stochastic games that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviours can evolve in the ever-changing group interaction environment. When the action choices of players are just slightly influenced by past reinforcements, we construct an analytical condition to determine whether cooperation can be favoured over defection. Intuitively, this condition reveals why and how the environment can mediate cooperative dilemmas. Under our model architecture, we also compare this learning mechanism with two non-learning decision rules, and we find that learning significantly improves the propensity for cooperation in weak social dilemmas, and, in sharp contrast, hinders cooperation in strong social dilemmas. Our results suggest that in complex social–ecological dilemmas, learning enables the adaptation of individuals to varying environments.     

The organization and control of an evolving interdependent population

Starting with Darwin, biologists have asked how populations evolve from a low fitness state that is evolutionarily stable to a high fitness state that is not. Specifically of interest is the emergence of cooperation and multicellularity where the fitness of individuals often appears in conflict with that of the population. Theories of social evolution and evolutionary game theory have produced a number of fruitful results employing two-state two-body frameworks. In this study, we depart from this tradition and instead consider a multi-player, multi-state evolutionary game, in which the fitness of an agent is determined by its relationship to an arbitrary number of other agents. We show that populations organize themselves in one of four distinct phases of interdependence depending on one parameter, selection strength. Some of these phases involve the formation of specialized large-scale structures. We then describe how the evolution of independence can be manipulated through various external perturbations.     

Directional reversals enable Myxococcus xanthus cells to produce collective one-dimensional streams during fruiting-body formation

The formation of a collectively moving group benefits individuals within a population in a variety of ways. The surface-dwelling bacterium Myxococcus xanthus forms dynamic collective groups both to feed on prey and to aggregate during times of starvation. The latter behaviour, termed fruiting-body formation, involves a complex, coordinated series of density changes that ultimately lead to three-dimensional aggregates comprising hundreds of thousands of cells and spores. How a loose, two-dimensional sheet of motile cells produces a fixed aggregate has remained a mystery as current models of aggregation are either inconsistent with experimental data or ultimately predict unstable structures that do not remain fixed in space. Here, we use high-resolution microscopy and computer vision software to spatio-temporally track the motion of thousands of individuals during the initial stages of fruiting-body formation. We find that cells undergo a phase transition from exploratory flocking, in which unstable cell groups move rapidly and coherently over long distances, to a reversal-mediated localization into one-dimensional growing streams that are inherently stable in space. These observations identify a new phase of active collective behaviour and answer a long-standing open question in Myxococcus development by describing how motile cell groups can remain statistically fixed in a spatial location.     

Defining the surface binding energy in dynamic Monte Carlo simulation for reactive sputtering of compounds

In Monte Carlo simulations of reactive sputtering, it is commonly assumed that the surface binding energy (SBE) for the different phases in the target exhibits a linear behaviour in the transition between the metal mode and the compound mode. In this work we study how the transition between the two modes takes place, and more specifically attempt to experimentally identify how the SBE for the different phases behaves in the transition between the two modes. In essence, this is done by comparing XPS measurements of the aluminium 2p binding energy on samples comprising pure aluminium, stoichiometric aluminium nitride and aluminium oxide with the corresponding measurements on understoichiometric aluminium nitride samples. In this work, it is assumed that the binding energy of the core level is directly correlated to the SBE of the phase in question. That is to say, if the aluminium 2p binding energy in aluminium nitride exhibits a constant and discrete value independent of the nitrogen concentration, the SBE for the compound exhibits a constant and discrete value independent of the surface concentration of nitrogen. It was found by the XPS measurement that the aluminium 2p binding energy in aluminium nitride exhibits a constant and discrete value independent of the nitrogen concentration in the samples and it was, therefore, concluded that the SBE for the different phases exhibits constant and discrete values independent of the surface concentration of nitrogen. The discrete behaviour of the SBE was implemented in the TRIDYN program and the results from these simulations were compared with simulations in which it is assumed that the SBE of the different phases exhibits a linear behaviour in the transition between the metal mode and the compound mode.     

Microscopic Phase-field Simulation of Competition Mechanism Between L12 and D022 Structure in Ni-Cr-Al Alloy

Simulations are performed on temporal evolution of atom morphology and ordering parameters of Ni-14.5 Cr-16.5 Al alloy during early precipitation process at different temperatures based on microscopic phase-field theory; the relationship between precipitation sequence and mechanism of L12 and D022 structure and precipitation temperature are illuminated. The nonstoichiometric ordered L12 phases appear first with congruent ordering＋spinodal decomposition mechanism which is then followed by precipitation of D022 phases at ordering domain boundaries of L12 phases by spinodal decomposition mechanism at 1073 K and 1223 K. The nonstoichiometric L12 phases transform to stoichiometric ordering phases gradually. The incubation period of L12 and D022 phases is shorter at 1073 K than that 1223 K, and growth speed is higher at 1073 K. At 1373 K, L12 and D022 phases appear simultaneously by non-classical nucleation and growth mechanism. After that the particles of D022 phases diminish and disappear gradually; L12 phases grow and single L12 phases are remained at last.     

Anomalous diffusion of heterogeneous populations characterized by normal diffusion at the individual level

The characterization of the dispersal of populations of non-identical individuals is relevant to most ecological and epidemiological processes. In practice, the movement is quantified by observing relatively few individuals, and averaging to estimate the rate of dispersal of the population as a whole. Here, we show that this can lead to serious errors in the predicted movement of the population if the individuals disperse at different rates. We develop a stochastic model for the diffusion of heterogeneous populations, inspired by the movement of the parasitic nematode Phasmarhabditis hermaphrodita. Direct observations of this nematode in homogeneous and heterogeneous environments reveal a large variation in individual behaviour within the population as reflected initially in the speed of the movement. Further statistical analysis shows that the movement is characterized by temporal correlations and in a heterogeneously structured environment the correlations that occur are of shorter range compared with those in a homogeneous environment. Therefore, by using the first-order correlated random walk techniques, we derive an effective diffusion coefficient for each individual, and show that there is a significant variation in this parameter among the population that follows a gamma distribution. Based on these findings, we build a new dispersal model in which we maintain the classical assumption that individual movement can be described by normal diffusion, but due to the variability in individual dispersal rates, the diffusion coefficient is not constant at the population level and follows a continuous distribution. The conclusions and methodology presented are relevant to any heterogeneous population of individuals with widely different diffusion rates.     

Emergent multicellular life cycles in filamentous bacteria owing to density-dependent population dynamics

Filamentous bacteria are the oldest and simplest known multicellular life forms. By using computer simulations and experiments that address cell division in a filamentous context, we investigate some of the ecological factors that can lead to the emergence of a multicellular life cycle in filamentous life forms. The model predicts that if cell division and death rates are dependent on the density of cells in a population, a predictable cycle between short and long filament lengths is produced. During exponential growth, there will be a predominance of multicellular filaments, while at carrying capacity, the population converges to a predominance of short filaments and single cells. Model predictions are experimentally tested and confirmed in cultures of heterotrophic and phototrophic bacterial species. Furthermore, by developing a formulation of generation time in bacterial populations, it is shown that changes in generation time can alter length distributions. The theory predicts that given the same population growth curve and fitness, species with longer generation times have longer filaments during comparable population growth phases. Characterization of the environmental dependence of morphological properties such as length, and the number of cells per filament, helps in understanding the pre-existing conditions for the evolution of developmental cycles in simple multicellular organisms. Moreover, the theoretical prediction that strains with the same fitness can exhibit different lengths at comparable growth phases has important implications. It demonstrates that differences in fitness attributed to morphology are not the sole explanation for the evolution of life cycles dominated by multicellularity.     

Application of surface behaviour diagrams to the study of hydration of phosphoric acid-anodized aluminium

The hydration of aluminium surfaces prepared for adhesive bonding by anodization in phosphoric acid has been studied using surface behaviour diagrams. These surface behaviour diagrams, which are similar to phase diagrams for equilibrium bulk phases, trace the evolution of the aluminium adherend surface composition, obtained by X-ray photoelectron spectroscopy, during the hydration process. When supplemented with high-resolution scanning electron micrographs and Auger depth profiles, the surface behaviour diagrams show that hydration proceeds in three steps. The first step is reversible and consists of the adsorption of water by the monolayer of AlPO₄ initially present on the surface. It involves no change in the oxide morphology. The second, which appears to be rate-controlling, involves the slow dissolution of the phosphate followed by rapid hydration of the exposed alumina to the oxyhydroxide, boehmite. During this stage, extensive morphological changes occur as the boehmite fills the pore cells and bridges the whiskers of the original surface. The third step consists of the nucleation and growth of the trihydroxide, bayerite, on top of the boehmite. Using these results as examples, we propose the surface behaviour diagram approach as a new tool for the study of surface reactions in general.     

Microscopic Phase-field Simulation of Competition Mechanism Between Ll_2 and D0_(22) Structure in Ni-Cr-Al Alloy

Simulations are performed on temporal evolution of atom morphology and ordering parameters of Ni-14.5 Cr-16.5 Al alloy during early precipitation process at different temperatures based on microscopic phase-field theory; the relationship between precipitation sequence and mechanism of L12 and D022 structure and precipitation temperature are illuminated. The nonstoichiometric ordered L12 phases appear first with congruent ordering+spinodal decomposition mechanism which is then followed by precipitation of D022 phases at ordering domain boundaries of L12 phases by spinodal decomposition mechanism at 1073 K and 1223 K. The nonstoichiometric Ll2 phases transform to stoichiometric ordering phases gradually. The incubation period of L12 and D022 phases is shorter at 1073 K than that 1223 K, and growth speed is higher at 1073 K. At 1373 K, L12 and D022 phases appear simultaneously by non-classical nucleation and growth mechanism. After that the particles of D022 phases diminish and disappear gradually; L12 phases grow and single L12 phases are remained at last.     

Modelling emergence of oscillations in communicating bacteria: a structured approach from one to many cells

Population-level measurements of phenotypic behaviour in biological systems may not necessarily reflect individual cell behaviour. To assess qualitative changes in the behaviour of a single cell, when alone and when part of a community, we developed an agent-based model describing the metabolic states of a population of quorum-coupled cells. The modelling is motivated by published experimental work of a synthetic genetic regulatory network (GRN) used in Escherichia coli cells that exhibit oscillatory behaviour across the population. To decipher the mechanisms underlying oscillations in the system, we investigate the behaviour of the model via numerical simulation and bifurcation analysis. In particular, we study the effect of an increase in population size as well as the spatio-temporal behaviour of the model. Our results demonstrate that oscillations are possible only in the presence of a high concentration of the coupling chemical and are due to a time scale separation in key regulatory components of the system. The model suggests that the population establishes oscillatory behaviour as the system''s preferred stable state. This is achieved via an effective increase in coupling across the population. We conclude that population effects in GRN design need to be taken into consideration and be part of the design process. This is important in planning intervention strategies or designing specific cell behaviours.     

Vaccination strategies when vaccines are scarce: on conflicts between reducing the burden and avoiding the evolution of escape mutants

When vaccine supply is limited but population immunization urgent, the allocation of the available doses needs to be carefully considered. One aspect of dose allocation is the time interval between the first and the second injections in two-dose vaccines. By stretching this interval, more individuals can be vaccinated with the first dose more quickly, which can be beneficial in reducing case numbers, provided a single dose is sufficiently effective. On the other hand, there has been concern that intermediate levels of immunity in partially vaccinated individuals may favour the evolution of vaccine escape mutants. In that case, a large fraction of half-vaccinated individuals would pose a risk—but only if they encounter the virus. This raises the question whether there is a conflict between reducing the burden and the risk of vaccine escape evolution or not. We develop an SIR-type model to assess the population-level effects of the timing of the second dose. Trade-offs can occur both if vaccine escape evolution is more likely or if it is less likely in half-vaccinated than in unvaccinated individuals. Their presence or absence depends on the efficacies for susceptibility and transmissibility elicited by a single dose.     

FATIGUE CRACK GROWTH DUE TO TWO SUCCESSIVE SINGLE OVERLOADS

The behaviour of fatigue growth and cyclic tip deformation of long cracks due to two successive single overloads was investigated both experimentally and numerically. The results show the effect of the ratio of the second and first overloads, and the crack increment between the two overloads. The contributions of both crack tip blunting and residual stress fields were separated and accommodated in a previously developed crack tip deformation parameter, which was utilized to predict the resulting fatigue crack growth behaviour. The following trends were experimentally observed. Should the ratio of the second and first overloads not be less than one, fatigue crack growth rates followed the predictions based on the second overload. Otherwise, either of the following two situations resulted: (1) when the two overloads were closely applied, the second overload caused an initial acceleration in growth rates followed by a behaviour controlled by the first overload; (2) when the second overload was applied after the crack growth had reached its minimum rate due to the first overload, more retardation in growth rate was observed. Based on the model developed in the paper, it is possible to enhance the retardation effect of an overload if this overload is preceded by another overload. This enhancement depends on the ratio of the two overloads and the crack increment between them.     

THE DEVELOPMENT OF STRESSES AND THEIR DISTRIBUTION IN TWO-PHASE ALLOYS DURING CYCLIC LOADING

A finite element program calculates the cyclic behaviour of the individual component phases of a multiphase material using a master curve observed in uniaxial cyclic stress tests. The fatigue behaviour of the two-phase alloys was characterized by visualizing the evolution of the phase stress (denoted by an average effective stress and an hydrostatic stress) during cyclic loading. The evolution procedure shows a unique fatigue behaviour of the in situ component phases, which differs from that observed in uniaxial or multiaxial fatigue tests of the single phase material. The fatigue damage on a microstructural scale was identified by the distributions of the plastic strain accumulated during cyclic loading and the stress triaxility in the component phases.     

Cell lineage tracing in the developing enteric nervous system: superstars revealed by experiment and simulation

Cell lineage tracing is a powerful tool for understanding how proliferation and differentiation of individual cells contribute to population behaviour. In the developing enteric nervous system (ENS), enteric neural crest (ENC) cells move and undergo massive population expansion by cell division within self-growing mesenchymal tissue. We show that single ENC cells labelled to follow clonality in the intestine reveal extraordinary and unpredictable variation in number and position of descendant cells, even though ENS development is highly predictable at the population level. We use an agent-based model to simulate ENC colonization and obtain agent lineage tracing data, which we analyse using econometric data analysis tools. In all realizations, a small proportion of identical initial agents accounts for a substantial proportion of the total final agent population. We term these individuals superstars. Their existence is consistent across individual realizations and is robust to changes in model parameters. This inequality of outcome is amplified at elevated proliferation rate. The experiments and model suggest that stochastic competition for resources is an important concept when understanding biological processes which feature high levels of cell proliferation. The results have implications for cell-fate processes in the ENS.     

Selection methods regulate evolution of cooperation in digital evolution

A key, yet often neglected, component of digital evolution and evolutionary models is the ‘selection method’ which assigns fitness (number of offspring) to individuals based on their performance scores (efficiency in performing tasks). Here, we study with formal analysis and numerical experiments the evolution of cooperation under the five most common selection methods (proportionate, rank, truncation-proportionate, truncation-uniform and tournament). We consider related individuals engaging in a Prisoner''s Dilemma game where individuals can either cooperate or defect. A cooperator pays a cost, whereas its partner receives a benefit, which affect their performance scores. These performance scores are translated into fitness by one of the five selection methods. We show that cooperation is positively associated with the relatedness between individuals under all selection methods. By contrast, the change in the performance benefit of cooperation affects the populations’ average level of cooperation only under the proportionate methods. We also demonstrate that the truncation and tournament methods may introduce negative frequency-dependence and lead to the evolution of polymorphic populations. Using the example of the evolution of cooperation, we show that the choice of selection method, though it is often marginalized, can considerably affect the evolutionary dynamics.     

Fatigue crack growth analysis of 2024 T3 aluminium specimens under aircraft service spectra

The fatigue crack growth behaviour of 2024 T3 aluminium was investigated experimentally. The fatigue experiments were performed under constant stress amplitude, constant amplitude with single and multiple overloads and aircraft service spectra. The fatigue spectra used correspond to the air-to-air, air-to-ground and instrumentation and navigation flight phases. They were applied for different stress levels. In total 11 different random flight service spectra were examined. The retardation effects caused by the overloads on the fatigue crack growth behaviour and the fatigue crack growth under aircraft service spectra were predicted using an in-house-developed code. The code makes use of the strip plastic zone approximation to account for material hardening effects along the path of prospective crack growth. Crack growth is treated incrementally and corresponds to failure of material elements ahead of an existing crack after a certain critical number of fatigue cycles. For the simulation of irregular service spectra by equivalent sequences of distinguished stress cycles a modified rainflow counting method is utilized. Spectrum simulation accounts also for non-linearity in fatigue damage accumulation and load sequence effects. The computed fatigue curves fit well with the experimental results.     

International Entrepreneurial Culture and Growth of International New Ventures

A premise in the international new venture (INV) literature is that a strong entrepreneurial orientation distinguishes an INV’s behaviour over time. Employing the concept of international entrepreneurial culture (IEC), which provides a holistic operationalisation of international entrepreneurship, we provide evidence from a longitudinal case study of four Finnish INVs as they grow over time. The findings suggest that various IEC dimensions affect the growth of INVs across their different phases. Although international motivation, innovation propensity, risk attitude, market orientation and proactiveness positively affect advancement through the early INV growth phases, their effect is negative in the later phases. International learning and networking positively affect INV growth throughout all its phases. The motivation of INVs towards the global rather than the international marketplace largely dictates a born global instead of a born international path. The contribution of the study is that it suggests that the nature and intensity of the “entrepreneurialness” of INVs change during their growth. The findings challenge the implicit rationale in the literature, according to which INVs consistently exhibit a strong entrepreneurial orientation. It is advisable to harness most aspects of entrepreneurialness during the later phases of born global firms.     

Ordering structured populations in multiplayer cooperation games

Spatial structure greatly affects the evolution of cooperation. While in two-player games the condition for cooperation to evolve depends on a single structure coefficient, in multiplayer games the condition might depend on several structure coefficients, making it difficult to compare different population structures. We propose a solution to this issue by introducing two simple ways of ordering population structures: the containment order and the volume order. If population structure is greater than population structure in the containment or the volume order, then can be considered a stronger promoter of cooperation. We provide conditions for establishing the containment order, give general results on the volume order, and illustrate our theory by comparing different models of spatial games and associated update rules. Our results hold for a large class of population structures and can be easily applied to specific cases once the structure coefficients have been calculated or estimated.     

Computationally efficient framework for diagnosing,understanding and predicting biphasic population growth

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for the commonly encountered situation involving two phases. Biphasic population growth occurs over a massive range of spatial and temporal scales, ranging from microscopic growth of tumours over several days, to decades-long regrowth of corals in coral reefs that can extend for hundreds of kilometres. Different mathematical models and statistical methods are used to diagnose, understand and predict biphasic growth. Common approaches can lead to inaccurate predictions of future growth that may result in inappropriate management and intervention strategies being implemented. Here, we develop a very general computationally efficient framework, based on profile likelihood analysis, for diagnosing, understanding and predicting biphasic population growth. The two key components of the framework are as follows: (i) an efficient method to form approximate confidence intervals for the change point of the growth dynamics and model parameters and (ii) parameter-wise profile predictions that systematically reveal the influence of individual model parameters on predictions. To illustrate our framework we explore real-world case studies across the life sciences.     

Conformity enhances network reciprocity in evolutionary social dilemmas

The pursuit of highest payoffs in evolutionary social dilemmas is risky and sometimes inferior to conformity. Choosing the most common strategy within the interaction range is safer because it ensures that the payoff of an individual will not be much lower than average. Herding instincts and crowd behaviour in humans and social animals also compel to conformity in their own right. Motivated by these facts, we here study the impact of conformity on the evolution of cooperation in social dilemmas. We show that an appropriate fraction of conformists within the population introduces an effective surface tension around cooperative clusters and ensures smooth interfaces between different strategy domains. Payoff-driven players brake the symmetry in favour of cooperation and enable an expansion of clusters past the boundaries imposed by traditional network reciprocity. This mechanism works even under the most testing conditions, and it is robust against variations of the interaction network as long as degree-normalized payoffs are applied. Conformity may thus be beneficial for the resolution of social dilemmas.