Stochastic Evolutionary Model Research Articles

The Stochastic Evolution Game of Knowledge Sharing in the Infrastructure PPP Supply Chain Network

Due to the complexity and randomness of environmental change, the knowledge-sharing behavior of members in the PPP supply chain will be affected by random disturbance factors. Traditional evolutionary game models cannot describe this effect. In this study, Gaussian white noise is introduced into the stochastic evolutionary game model of PPP supply chain knowledge sharing. The numerical simulation of the model is carried out to analyze the influence of parameter changes on the strategy selection of enterprise groups. The result shows that the strong knowledge power enterprise group is more sensitive with the variation of parameters than that of the weak knowledge power enterprise group. However, the weak enterprise group has a more vital willingness to share knowledge. Incentive measures can increase the knowledge-sharing benefits and promote the strong knowledge powerful enterprise group toward the sharing strategy. Increasing the mutual trust coefficient, reducing the sharing cost, and improving the enterprise’s transformation ability will help both sides to evolve into the sharing strategy more quickly. This study would have significance for PPP project performance and industry innovation.

Effective Boundary of Innovation Subsidy: Searching by Stochastic Evolutionary Game Model

Relationship between innovation subsidies and corporate strategic choices has been extensively studied. Public innovation subsidies are by no means a certain value, existing in the form of an effective range instead. This means that the public innovation subsidies existing within the reasonable range can achieve the same incentive effect. So, what is the reasonable range or the effective boundaries of public innovation subsidies to promote enterprises that adopt cooperation strategies? There is no definite answer. Based on classical game theory, a stochastic evolutionary game model is proposed in this paper, which takes into account the influence of random disturbance on the strategy evolution process. An effective boundary of public innovation subsidy is provided as the main contribution based on a mature game scenario. A set of experimental data is subsequently selected as the sample for numerical simulation and result verification. The results showed that the probability of noncooperation within the effective value range will successfully converge to zero, which also means that the agents will adopt a collaborative cooperation strategy. The regulation effect of the combination of multiple variables is also discussed.

Optimal Decision Making Approach for Cyber Security Defense Using Evolutionary Game

At present, there are many techniques for cyber security defense such as firewall, intrusion detection and cryptography. Despite decades of studies and experiences on this issue, there still exists a problem that we always pay great attention to technology while overlooking strategy. In the traditional warfare, the level of decision-making and the formulation of optimal strategies have a great effect on the warfare result. Similarly, the timeliness and quality of decision-making in cyber attack-defense also make great significance. Since the attackers and defenders are oppositional, the selection of optimal defense strategy with the maximum payoff is difficult. To solve this problem, the stochastic evolutionary game model is utilized to simulate the dynamic adversary of cyber attack-defense. We add the parameter $\lambda $ to the Logit Quantal Response Dynamics (LQRD) equation to quantify the cognitive differences of real-world players. By calculating the evolutionary stable equilibrium, the best decision-making approach is proposed, which makes a balance between defense cost and benefit. Cases studies on ransomware indicate that the proposed approach can help the defender predict possible attack action, select the related optimal defense strategy over time, and gain the maximum defense payoff.

Study on Stochastic Differential Game Model in Network Attack and Defense

In recent years, evolutionary game theory has been gradually applied to analyze and predict network attack and defense for maintaining cybersecurity. The traditional deterministic game model cannot accurately describe the process of actual network attack and defense due to changing in the set of attack-defense strategies and external factors (such as the operating environment of the system). In this paper, we construct a stochastic evolutionary game model by the stochastic differential equation with Markov property. The evolutionary equilibrium solution of the model is found and the stability of the model is proved according to the knowledge of the stochastic differential equation. And we apply the explicit Euler numerical method to analyze the evolution of the strategy selection of the players for different problem situations. The simulation results show that the stochastic evolutionary game model proposed in this paper can get a steady state and obtain the optimal defense strategy under the action of the stochastic disturbance factor. In addition, compared with other kinds of literature, we can conclude that the return on security investment of this model is better, and the strategy selection of the attackers and defenders in our model is more suitable for actual network attack and defense.

Exit from equilibrium in coordination games under probit choice

We consider a model of stochastic evolution under the probit choice rule. In the small noise double limit, where first the noise level in agents' decisions is taken to zero, and then the population size to infinity, escape from and transitions between equilibria can be described in terms of solutions to continuous optimal control problems. We use results from optimal control theory to solve the exit cost problem. This is used to determine the most likely exit paths from the initial basin of attraction and also to assess the expected time until the evolutionary process leaves the basin of attraction of a stable equilibrium in a class of three-strategy coordination games.

Substantive Innovation or Strategic Innovation? Research on Multiplayer Stochastic Evolutionary Game Model and Simulation

Innovation subsidy is of great significance to promoting enterprise innovation development. However, in recent years, the frequent occurrence of R&D subsidy deception in China has greatly reduced effectiveness of innovation. From the perspective of the strategic choice motivation of the innovation subject (including the enterprises, research institutions, and local governments), this paper constructs a multiplayer stochastic evolutionary game model. The influence of each variable on the subject strategy adoption is analyzed by simulation. There are two important findings in this paper. First, the paper confirms that there is an optimal boundary for the high subsidies received by enterprises and academic institutions, and the “subsidy boundary” is solved through the model. Second, this paper analyzes the effectiveness of the regulation of each variable through simulation and provides management and policy implications.

Modeling Tumor Evolutionary Dynamics to Predict Clinical Outcomes for Patients with Metastatic Colorectal Cancer: A Retrospective Analysis.

Over 50% of colorectal cancer patients develop resistance after a transient response to therapy. Understanding tumor resistance from an evolutionary perspective leads to better predictions of treatment outcomes. The objectives of this study were to develop a computational framework to analyze tumor longitudinal measurements and recapitulate the individual evolutionary dynamics in metastatic colorectal cancer (mCRC) patients. A stochastic modeling framework was developed to depict the whole spectrum of tumor evolution prior to diagnosis and during and after therapy. The evolutionary model was optimized using a nonlinear mixed effect (NLME) method based on the longitudinal measurements of liver metastatic lesions from 599 mCRC patients. The deterministic limits in the NLME model were applied to optimize the stochastic model for each patient. Cox proportional hazards models coupled with the least absolute shrinkage and selection operator (LASSO) algorithm were applied to predict patients' progression-free survival (PFS) and overall survival (OS). The stochastic evolutionary model well described the longitudinal profiles of tumor sizes. The evolutionary parameters optimized for each patient indicated substantial interpatient variability. The number of resistant subclones at diagnosis was found to be a significant predictor to survival, and the hazard ratios with 95% CI were 1.09 (0.79-1.49) and 1.54 (1.01-2.34) for patients with three or more resistant subclones. Coupled with several patient characteristics, evolutionary parameters strongly predict patients' PFS and OS. A stochastic computational framework was successfully developed to recapitulate individual patient evolutionary dynamics, which could predict clinical survival outcomes in mCRC patients. SIGNIFICANCE: A data analysis framework depicts the individual evolutionary dynamics of mCRC patients and can be generalized to project patient survival outcomes.

Stochastic Evolution of Pancreatic Cancer Metastases During Logistic Clonal Expansion.

Despite recent progress in diagnostic and multimodal treatment approaches, most cancer deaths are still caused by metastatic spread and the subsequent growth of tumor cells in sites distant from the primary organ. So far, few quantitative studies are available that allow for the estimation of metastatic parameters and the evaluation of alternative treatment strategies. Most computational studies have focused on situations in which the tumor cell population expands exponentially over time; however, tumors may eventually be subject to resource and space limitations so that their growth patterns deviate from exponential growth to adhere to density-dependent growth models. In this study, we developed a stochastic evolutionary model of cancer progression that considers alterations in metastasis-related genes and intercellular growth competition leading to density effects described by logistic growth. Using this stochastic model, we derived analytical approximations for the time between the initiation of tumorigenesis and diagnosis, the expected number of metastatic sites, the total number of metastatic cells, the size of the primary tumor, and survival. Furthermore, we investigated the effects of drug administration and surgical resection on these quantities and predicted outcomes for different treatment regimens. Parameter values used in the analysis were estimated from data obtained from a pancreatic cancer rapid autopsy program. Our theoretical approach allows for flexible modeling of metastatic progression dynamics.

Branching Stochastic Evolutionary Models of Cell Populations

This review paper surveys results on branching stochastic models with and without immigration published during the past nine years. Studies of this class of stochastic models were motivated by the quantitative analysis of the dynamics of population of cells of the central nervous system, called the terminally differentiated oligodendrocytes, and their progenitor cells. We focus on original ideasspecifically developed for Sevastyanov branching processes allowing the contribution of an external cellular compartment (e.g., stem cells) via anonhomogeneous Poisson immigration process. Limiting distributions are discribed in the subcritical, critical and supercritical cases for various immigration rates.

On a Skorokhod problem with small double limit

We consider a model of stochastic evolution with combinatorial effects of homogenization and large deviations principle for Markov processes which move in a domain with boundary and which be subject to oblique reflection at the boundary. Our analysis focuses on behavior in small perturbations for reflecting stochastic differential equations with two dependencies parameters in order to explicit the associated rate function. Here, we suppose that the homogenization parameter converges sufficiently quickly more than the large deviations parameter.

The replicator dynamics for multilevel selection in evolutionary games.

We consider a stochastic model for evolution of group-structured populations in which interactions between group members correspond to the Prisoner's Dilemma or the Hawk-Dove game. Selection operates at two organization levels: individuals compete with peer group members based on individual payoff, while groups also compete with other groups based on average payoff of group members. In the Prisoner's Dilemma, this creates a tension between the two levels of selection, as defectors are favored at the individual level, whereas groups with at least some cooperators outperform groups of defectors at the between-group level. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time behavior of solutions of our equation, finding a threshold intensity of between-group selection required to sustain density steady states and the survival of cooperation. When all-cooperator groups are most fit, the average and most abundant group compositions at steady state range from featuring all-defector groups when individual-level selection dominates to featuring all-cooperator groups when group-level selection dominates. When the most fit groups have a mix of cooperators and defectors, then the average and most abundant group compositions always feature a smaller fraction of cooperators than required for the optimal mix, even in the limit where group-level selection is infinitely stronger than individual-level selection. In such cases, the conflict between the two levels of selection cannot be decoupled, and cooperation cannot be sustained at all in the case where between-group competition favors an even mix of cooperators and defectors.

Generation of Level- k LGT Networks.

Phylogenetic networks provide a mathematical model to represent the evolution of a set of species where, apart from speciation, reticulate evolutionary events have to be taken into account. Among these events, lateral gene transfers need special consideration due to the asymmetry in the roles of the species involved in such an event. To take into account this asymmetry, LGT networks were introduced. Contrarily to the case of phylogenetic trees, the combinatorial structure of phylogenetic networks is much less known and difficult to describe. One of the approaches in the literature is to classify them according to their level and find generators of the given level that can be used to recursively generate all networks. In this paper, we adapt the concept of generators to the case of LGT networks. We show how these generators, classified by their level, give rise to simple LGT networks of the specified level, and how any LGT network can be obtained from these simple networks, that act as building blocks of the generic structure. The stochastic models of evolution of phylogenetic networks are also much less studied than those for phylogenetic trees. In this setting, we introduce a novel two-parameter model that generates LGT networks. Finally, we present some computer simulations using this model in order to investigate the complexity of the generated networks, depending on the parameters of the model.

Promotion of cooperation in evolutionary game dynamics under asymmetric information

The emergence and abundance of cooperation in the population of selfish individuals is a challenging problem in evolutionary dynamics. Here we propose two asymmetric information systems in which individuals adopt two different rules to update their strategies. One of the stochastic evolutionary models is mixed by aspiration-driven rule and local information-driven rule, while the other model is mixed by local rule and imitation-driven rule. The proposed heterogeneous systems promote at least one kind of individuals’ cooperation. Compared with the standard imitation dynamics and local dynamics, there is always a non-zero probability to support the formation of cooperation in the system with the aspiration and other rules. Furthermore, the more aspiration-driven individuals lead to higher fraction of local-driven cooperators. In the other case, the invasion of individuals who use local information is conductive to promoting the imitation-driven ones’ cooperation. In both heterogeneous systems, we find that the individuals who use less information are more likely to cooperate than the ones who use higher information.

Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects.

Quantifying codon usage in signal peptides: Gene expression and amino acid usage explain apparent selection for inefficient codons

The Sec secretion pathway is found across all domains of life. A critical feature of Sec secreted proteins is the signal peptide, a short peptide with distinct physicochemical properties located at the N-terminus of the protein. Previous work indicates signal peptides are biased towards translationally inefficient codons, which is hypothesized to be an adaptation driven by selection to improve the efficacy and efficiency of the protein secretion mechanisms. We investigate codon usage in the signal peptides of E. coli using the Codon Adaptation Index (CAI), the tRNA Adaptation Index (tAI), and the ribosomal overhead cost formulation of the stochastic evolutionary model of protein production rates (ROC-SEMPPR). Comparisons between signal peptides and 5′-end of cytoplasmic proteins using CAI and tAI are consistent with a preference for inefficient codons in signal peptides. Simulations reveal these differences are due to amino acid usage and gene expression – we find these differences disappear when accounting for both factors. In contrast, ROC-SEMPPR, a mechanistic population genetics model capable of separating the effects of selection and mutation bias, shows codon usage bias (CUB) of the signal peptides is indistinguishable from the 5′-ends of cytoplasmic proteins. Additionally, we find CUB at the 5′-ends is weaker than later segments of the gene. Results illustrate the value in using models grounded in population genetics to interpret genetic data. We show failure to account for mutation bias and the effects of gene expression on the efficacy of selection against translation inefficiency can lead to a misinterpretation of codon usage patterns.

Modeling the Subclonal Evolution of Cancer Cell Populations.

Increasing evidence shows that tumor clonal architectures are often the consequence of a complex branching process, yet little is known about the expected dynamics and extent to which these divergent subclonal expansions occur. Here, we develop and implement more than 88,000 instances of a stochastic evolutionary model simulating genetic drift and neoplastic progression. Under different combinations of population genetic parameter values, including those estimated for colorectal cancer and glioblastoma multiforme, the distribution of sizes of subclones carrying driver mutations had a heavy right tail at the time of tumor detection, with only 1 to 4 dominant clones present at ≥10% frequency. In contrast, the vast majority of subclones were present at <10% frequency, many of which had higher fitness than currently dominant clones. The number of dominant clones (≥10% frequency) in a tumor correlated strongly with the number of subclones (<10% of the tumor). Overall, these subclones were frequently below current standard detection thresholds, frequently harbored treatment-resistant mutations, and were more common in slow-growing tumors.Significance: The model presented in this paper addresses tumor heterogeneity by framing expectations for the number of resistant subclones in a tumor, with implications for future studies of the evolution of therapeutic resistance. Cancer Res; 78(3); 830-9. ©2017 AACR.

Extinction dynamics from metastable coexistences in an evolutionary game.

Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We investigate the most probable extinction trajectory under such fluctuations by mapping a stochastic evolutionary model to a problem of classical mechanics using the Wentzel-Kramers-Brillouin (WKB) approximation. Our results show that more abundant types in a coexistence may be more likely to go extinct first, in good agreement with previous results. The distance between the coexistence and extinction points is not a good predictor of extinction either. Instead, the WKB method correctly predicts the type going extinct first.

Genomic plasticity and rapid host switching can promote the evolution of generalism: a case study in the zoonotic pathogen Campylobacter

Horizontal gene transfer accelerates bacterial adaptation to novel environments, allowing selection to act on genes that have evolved in multiple genetic backgrounds. This can lead to ecological specialization. However, little is known about how zoonotic bacteria maintain the ability to colonize multiple hosts whilst competing with specialists in the same niche. Here we develop a stochastic evolutionary model and show how genetic transfer of host segregating alleles, distributed as predicted for niche specifying genes, and the opportunity for host transition could interact to promote the emergence of host generalist lineages of the zoonotic bacterium Campylobacter. Using a modelling approach we show that increasing levels of homologous recombination enhance the efficiency with which selection can fix combinations of beneficial alleles, speeding adaptation. We then show how these predictions change in a multi-host system, with low levels of recombination, consistent with real r/m estimates, increasing the standing variation in the population, allowing a more effective response to changes in the selective landscape. Our analysis explains how observed gradients of host specialism and generalism can evolve in a multihost system through the transfer of ecologically important loci among coexisting strains.

When agreement-accepting free-riders are a necessary evil for the evolution of cooperation

Agreements and commitments have provided a novel mechanism to promote cooperation in social dilemmas in both one-shot and repeated games. Individuals requesting others to commit to cooperate (proposers) incur a cost, while their co-players are not necessarily required to pay any, allowing them to free-ride on the proposal investment cost (acceptors). Although there is a clear complementarity in these behaviours, no dynamic evidence is currently available that proves that they coexist in different forms of commitment creation. Using a stochastic evolutionary model allowing for mixed population states, we identify non-trivial roles of acceptors as well as the importance of intention recognition in commitments. In the one-shot prisoner’s dilemma, alliances between proposers and acceptors are necessary to isolate defectors when proposers do not know the acceptance intentions of the others. However, when the intentions are clear beforehand, the proposers can emerge by themselves. In repeated games with noise, the incapacity of proposers and acceptors to set up alliances makes the emergence of the first harder whenever the latter are present. As a result, acceptors will exploit proposers and take over the population when an apology-forgiveness mechanism with too low apology cost is introduced, and hence reduce the overall cooperation level.

Differential Equations with Small Stochastic Additions Under Poisson Approximation Conditions

The methods proposed in the paper allow us to investigate the model of stochastic evolution, which includes Markov switchings, and to identify big jumps of disturbing process in the limiting equation. Big jumps of this type may describe rare catastrophic events in different applied problems. We consider the case where system disturbance is defined by impulse process in nonclassical approximation scheme. Particular attention is paid to the asymptotic behavior of the generator of the evolutionary system under examination.