Impact of environmental stochastic fluctuations on the evolutionary stability of imitation dynamics.

To show the impact of environmental noise on imitation dynamics, the stochastic stability and stochastic evolutionary stability of a discrete-time imitation dynamics with random payoffs are studied in this paper. Based on the stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model, we extend the concept of stochastic evolutionary stability to the stochastic imitation dynamics, which is defined as a strategy such that, if all the members of the population adopt it, then the probability for any mutant strategy to invade the population successfully under the influence of natural selection is arbitrarily low. Our main results show clearly that the stochastic evolutionary stability of the system depends only on the properties of the mean matrix of the random payoff matrix and is independent of the randomness of the random payoff matrix.

Evolutionary dynamics of cooperation coupled with ecological feedback compensation.

A simple theoretical model (or a demonstrative example) was developed to illustrate how the evolution of cooperation can be affected by the density-dependent survival competition, in which we assume that the fertility of an individual depends only on the pairwise interaction between him and other individuals based on Prisoner's Dilemma game, while its viability is only related to the density-dependent survival competitiveness. Our results show that not only cooperation could be evolutionarily stable if the advantage of cooperators in viability can compensate for the cost they pay for their fertility, but also the long-term stable coexistence of cooperation and defection is possible if none of cooperation and defection is evolutionarily stable. Moreover, for the stochastic evolutionary dynamics in a finite population, our analysis shows that the increase (or decrease) of the survival competitiveness of cooperators (or defectors) should be conductive to the evolutionary emergence of cooperation.

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.

Stochastic replicator dynamics and evolutionary stability.

To develop the concept of evolutionary stability in a stochastic environment, we investigate the continuous-time dynamics of a two-phenotype linear evolutionary game with generally correlated random payoffs in pairwise interactions. By using the Gram-Schmidt orthogonalization procedure and Itô's formula, we deduce a stochastic differential equation for the phenotype frequencies that extends the replicator equation, called the stochastic replicator equation. We give conditions for stochastic stability of a fixation state or a constant interior equilibrium point with respect to the stochastic dynamics of the two phenotypes.

Stochastic evolutionary stability in matrix games with random payoffs.

Evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behavior, but also widely used in economics and social sciences. Recently, in order to reveal the stochastic dynamical properties of evolutionary games in randomly fluctuating environments, the concept of stochastic evolutionary stability based on conditions for stochastic local stability for a fixation state was developed in the context of a symmetric matrix game with two phenotypes and random payoffs in pairwise interactions [Zheng et al., Phys.

Evolutionary game dynamics with non-uniform interaction rates in finite population.

In this study, we extend evolutionary game dynamics with non-uniform interaction rates to the situation with finite population. Our main goal is to show how the fixation probability is influenced by the non-uniform interaction rates under weak selection. Based on the diffusion approximation of the Moran process and assumption of weak selection, the stochastic dynamic properties of a two-phenotype game with non-uniform interaction rates in a finite population are investigated.

Inclusive fitness and Hamilton's rule in a stochastic environment.

The evolution of cooperation in Prisoner's Dilemmas with additive random cost and benefit for cooperation cannot be accounted for by Hamilton's rule based on mean effects transferred from recipients to donors weighted by coefficients of relatedness, which defines inclusive fitness in a constant environment. Extensions that involve higher moments of stochastic effects are possible, however, and these are connected to a concept of random inclusive fitness that is frequency-dependent. This is shown in the setting of pairwise interactions in a haploid population with the same coefficient of relatedness between interacting players.

Hamilton's rule and kin competition in a finite kin population.

Kin selection means that individuals can increase their own inclusive fitness through displaying more altruistically toward their relatives. So, Hamilton's rule says kin selection will work if the coefficient of relatedness exceeds the cost-to-benefit ratio of the altruistic act. However, some studies have shown that the kin competition due to the altruism among relatives can reduce, and even totally negate, the kin-selected benefits of altruism toward relatives.

Weak selection can filter environmental noise in the evolution of animal behavior.

Weak selection is an important assumption in theoretical evolutionary biology, but its biological significance remains unclear. In this study, we investigate the effect of weak selection on stochastic evolutionary stability in a two-phenotype evolutionary game dynamics with a random payoff matrix assuming an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We show that, under weak selection, both stochastic local stability and stochastic evolutionary stability in this system depend on the means of the random payoffs but not on their variances.

Transitions in the cell-fate induction induced by colored noise associated with the inductive stimulus.

The cell-fate induction based on the saddle-node bifurcation is undoubtedly a very important concept in developmental biology, which provides a possible mechanism to explain the intrinsic irreversibility in the developmental process. In this paper, the effect of a colored noise, which is associated with the inductive stimulus, on the saddle-node landscape of cell-fate induction is investigated, especially, the effect of the change of correlation time of colored noise on cell-fate induction. The main results show clearly that the change of correlation time of colored noise could induce the transitions of the system.

6mA-DNA-binding factor Jumu controls maternal-to-zygotic transition upstream of Zelda.

A long-standing question in the field of embryogenesis is how the zygotic genome is precisely activated by maternal factors, allowing normal early embryonic development. We have previously shown that N6-methyladenine (6mA) DNA modification is highly dynamic in early Drosophila embryos and forms an epigenetic mark. However, little is known about how 6mA-formed epigenetic information is decoded.

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution.

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics.

Evolutionary stability concepts in a stochastic environment.

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions.

Limiting similarity of competitive species and demographic stochasticity.

The limiting similarity of competitive species and its relationship with the competitive exclusion principle is still one of the most important concepts in ecology. In the 1970s, May [R. M.

A simple rule of direct reciprocity leads to the stable coexistence of cooperation and defection in the Prisoner's Dilemma game.

The long-term coexistence of cooperation and defection is a common phenomenon in nature and human society. However, none of the theoretical models based on the Prisoner's Dilemma (PD) game can provide a concise theoretical model to explain what leads to the stable coexistence of cooperation and defection in the long-term even though some rules for promoting cooperation have been summarized (Nowak, 2006, Science 314, 1560-1563). Here, based on the concept of direct reciprocity, we develop an elementary model to show why stable coexistence of cooperation and defection in the PD game is possible.

Opting out against defection leads to stable coexistence with cooperation.

Cooperation coexisting with defection is a common phenomenon in nature and human society. Previous studies for promoting cooperation based on kin selection, direct and indirect reciprocity, graph selection and group selection have provided conditions that cooperators outcompete defectors. However, a simple mechanism of the long-term stable coexistence of cooperation and defection is still lacking.

Kinship as a frequency dependent strategy.

Humans divide themselves up into separate cultures, which is a unique and ubiquitous characteristic of our species. Kinship norms are one of the defining features of such societies. Here we show how norms of marital residence can evolve as a frequency-dependent strategy, using real-world cases from southwestern China and an evolutionary game model.

Ci antagonizes Hippo signaling in the somatic cells of the ovary to drive germline stem cell differentiation.

Many stem cell populations are tightly regulated by their local microenvironment (niche), which comprises distinct types of stromal cells. However, little is known about mechanisms by which niche subgroups coordinately determine the stem cell fate. Here we identify that Yki, the key Hippo pathway component, is essential for escort cell (EC) function in promoting germline differentiation in Drosophila ovary.

Dynamic transcriptional symmetry-breaking in pre-implantation mammalian embryo development revealed by single-cell RNA-seq.

During mammalian pre-implantation embryo development, when the first asymmetry emerges and how it develops to direct distinct cell fates remain longstanding questions. Here, by analyzing single-blastomere transcriptome data from mouse and human pre-implantation embryos, we revealed that the initial blastomere-to-blastomere biases emerge as early as the first embryonic cleavage division, following a binomial distribution pattern. The subsequent zygotic transcriptional activation further elevated overall blastomere-to-blastomere biases during the two- to 16-cell embryo stages.

Organizer-derived Bmp2 is required for the formation of a correct Bmp activity gradient during embryonic development.

Bone morphogenetic proteins (Bmps) control dorsoventral patterning of vertebrate embryos through the establishment of a ventrodorsal gradient of the activated downstream cytoplasmic effectors Smad1/5/8. Some Bmp ligands are expressed in the ventral and lateral regions and in the organizer during gastrulation of the embryo, but it remains unclear how organizer-derived Bmps contribute to total Bmp ligand levels and to the establishment of the correct phospho-Smad1/5/8 gradient along the ventrodorsal axis. Here we demonstrate that interference with organizer-specific Bmp2b signalling in zebrafish embryos alters the phospho-Smad1/5/8 gradient throughout the ventrodorsal axis, elevates the levels of the Bmp antagonist Chordin and dorsalizes the embryos.

Cell-surface localization of Pellino antagonizes Toll-mediated innate immune signalling by controlling MyD88 turnover in Drosophila.

Innate immunity mediated by Toll signalling has been extensively studied, but how Toll signalling is precisely controlled in balancing innate immune responses remains poorly understood. It was reported that the plasma membrane localization of Drosophila MyD88 is necessary for the recruitment of cytosolic adaptor Tube to the cell surface, thus contributing to Toll signalling transduction. Here we demonstrate that Drosophila Pellino functions as a negative regulator in Toll-mediated signalling.

Activation of Smurf E3 ligase promoted by smoothened regulates hedgehog signaling through targeting patched turnover.

Hedgehog signaling plays conserved roles in controlling embryonic development; its dysregulation has been implicated in many human diseases including cancers. Hedgehog signaling has an unusual reception system consisting of two transmembrane proteins, Patched receptor and Smoothened signal transducer. Although activation of Smoothened and its downstream signal transduction have been intensively studied, less is known about how Patched receptor is regulated, and particularly how this regulation contributes to appropriate Hedgehog signal transduction.

The niche-dependent feedback loop generates a BMP activity gradient to determine the germline stem cell fate.

Stem cells interact with surrounding stromal cells (or niche) via signaling pathways to precisely balance stem cell self-renewal and differentiation. However, little is known about how niche signals are transduced dynamically and differentially to stem cells and their intermediate progeny and how the fate switch of stem cell to differentiating cell is initiated. The Drosophila ovarian germline stem cells (GSCs) have provided a heuristic model for studying the stem cell and niche interaction.

Stochastic analysis of gene expression.

In this chapter, stochasticity in gene expression is investigated using Ω-expansion technique. Two theoretical models are considered here, one concern the stochastic fluctuations in a single-gene network with negative feedback regulation, and the other the additivity of noise propagation in a protein cascade. All of these theoretical analyses may provide a basic framework for understanding stochastic gene expression.