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Dhaker Kroumi

Publications and source records attributed to Dhaker Kroumi.

8 recordsLinked to original sources
arXiv2026

Phenotypic Assortment and the Evolution of Cooperation in Finite Periodic Phenotype Spaces

We study the evolution of cooperation in a finite haploid population whose individuals carry both a strategy and a phenotype on a finite periodic space. Cooperators help with a probability that decays exponentially with phenotypic distance, generating graded phenotype-dependent assortment. Under weak selection and a large-population mutation scaling, we combine coalescent arguments with the spectral representation of a random walk on the discrete torus to derive an explicit benefit-to-cost threshold for cooperation to be favored in stationary abundance. Stronger phenotypic discrimination and higher phenotype-space dimension strictly lower this threshold, whereas strategy mutation raises it. In contrast, phenotype mutation has a nonmonotone effect: the threshold diverges for both very rare and very rapid phenotype mutation and therefore attains at least one minimum at an intermediate rate. The high-mutation inhibition results from mixing on the finite phenotype space and distinguishes the periodic model from its unbounded-lattice counterpart.

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arXiv2026

The evolution of cooperation under imperfect phenotypic recognition

Phenotypic similarity is a classical mechanism for the evolution of cooperation. Most existing models assume a binary rule in which individuals cooperate only with others of the same phenotype. This assumption is biologically restrictive, since recognition and discrimination are often gradual rather than all-or-nothing. In this paper, we extend the multidimensional phenotype-space model of cooperation by allowing the probability of helping to decline with phenotypic distance. In a large population under weak selection with mutation in both strategy and phenotype, we derive a generalized threshold for selection to favor the abundance of cooperation and express it using a new Laplace-type transform. We show that this threshold decreases strictly as discrimination becomes sharper, meaning that exact phenotype matching is the most favorable limit within this family of recognition rules. We also show that the threshold decreases strictly with phenotype-space dimension, meaning that higher-dimensional phenotype spaces promote cooperation even when recognition is imperfect. Our asymptotic analysis further shows that low phenotype mutations strongly inhibit cooperation, whereas sufficiently high phenotype mutations drive the threshold toward its minimal value. However, high strategy mutation makes cooperation harder to maintain.

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arXiv2025

Sensitivity-Driven Migration and the Evolution of Cooperation in Multi-Player Games on Structured Populations

Cooperation often depends on individuals avoiding exploitation and interacting preferentially with other cooperators. We explore how context-dependent migration influences the evolution of cooperation in spatially structured populations. Individuals interact in small groups through public goods games and reproduce with possible dispersal. Cooperators migrate more frequently when surrounded by defectors, while defectors disperse uniformly. This behavioral asymmetry reflects realistic differences in mobility and social responsiveness. Our results show that conditional migration can promote cooperation by enabling cooperators to escape defector-rich environments and cluster together. The effectiveness of this mechanism depends on baseline migration rates, group size, and the sensitivity of cooperators to local conditions. We identify parameter ranges where cooperation is favored even under conditions that would typically hinder its evolution. These findings highlight how behavioral plasticity and dispersal strategies can interact with population structure to support the emergence of cooperation.

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arXiv2023

Evolutionary game with stochastic payoffs in a finite island model

In this paper, we consider a two-player two-strategy game with random payoffs in a population subdivided into $d$ demes, each containing $N$ individuals at the beginning of any given generation and experiencing local extinction and recolonization with some fixed probability $m$ after reproduction and selection among offspring. Within each deme, offspring engage in random pairwise interactions, and the payoffs are assumed to have means and variances proportional to the inverse of the population size. By verifying the conditions given in Ethier and Nagylaki (1980) to approximate Markov chains with two time scales, we establish that the discrete-time evolutionary dynamics with $Nd$ generations as unit of time converges to a continuous-time diffusion as $d\rightarrow\infty$. The infinitesimal mean and variance of this diffusion are expressed in terms of the population-scaled means and variances of the payoffs besides identity-by-descent measures between offspring in the same deme in a neutral population. We show that the probability for a strategy to fix in the population starting from an initial frequency $(Nd)^{-1}$ generally increases as the payoffs to that strategy exhibit less variability or the payoffs to the other strategy more variability. As a result, differences in variability can make this fixation probability for cooperation larger than the corresponding one for defection. As the deme-scaled extinction rate $\nu=mN$ decreases for $N$ large enough and $m$ small enough, creating a higher level of identity among offspring within demes, the differences between the population-scaled variances of the payoffs for interacting offspring of different types increases this effect to a greater extent than the differences for interacting offspring of the same type.

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arXiv2023

Stochastic viability in an island model with partial dispersal : Approximation by a diffusion process in the limit of a large number of islands

In this paper, we study a finite population undergoing discrete, nonoverlapping generations, that is structured into $D$ demes, each containing $N$ individuals of two possible types, $A$ and $B$, whose viability coefficients, $s_A$ and $s_B$, respectively, vary randomly from one generation to the next. We assume that the means, variances and covariance of the viability coefficients are inversely proportional to the number of demes $D$, while higher-order moments are negligible in comparison to $1/D$. We use a discrete-time Markov chain with two time scales to model the evolutionary process, and we demonstrate that as the number of demes $D$ approaches infinity, the accelerated Markov chain converges to a diffusion process for any deme size $N\geq 2$. This diffusion process allows us to evaluate the fixation probability of type $A$ following its introduction as a single mutant in a population that was fixed for type $B$. We explore the impact of increasing the variability in the viability coefficients on this fixation probability. At least when $N$ is large enough, it is shown that increasing this variability for type $B$ or decreasing it for type $A$ leads to an increase in the fixation probability of a single $A$. The effect of the population-scaled variances, $\sigma^2_A$ and $\sigma^2_B$, can even cancel the effects of the population-scaled means, $\mu_A$ and $\mu_B$. We also show that the fixation probability of a single $A$ increases as the deme-scaled migration rate increases. Moreover, this probability is higher for type $A$ than for type $B$ if the population-scaled geometric mean is higher for type $A$ than for type $B$, which means that $\mu_A-\sigma_A^2/2>\mu_B-\sigma_B^2/2$.

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arXiv2022

Average abundancy of cooperation in multi-player games with random payoffs

We consider interactions between players in groups of size $d\geq2$ with payoffs that not only depend on the strategies used in the group but also fluctuate at random over time. An individual can adopt either cooperation or defection as strategy and the population is updated from one-time step to the next by a birth-death event according to a Moran model. Assuming recurrent symmetric mutation and payoffs with expected values, variances, and covariances of the same small order, we derive a first-order approximation of the average abundance of cooperation in the selection-mutation equilibrium. We show that increasing the variance of any payoff for defection or decreasing the variance of any payoff for cooperation increases the average abundance of cooperation. As for the effect of the covariance between any payoff for cooperation and any payoff for defection, we show that it depends on the number of cooperators in the group associated with these payoffs. We study in particular the public goods game, the stag hunt game, and the snowdrift game, all social dilemmas based on random benefit $b$ and cost $c$ for cooperation. We show that a decrease in the scaled variance of $b$ or $c$, or an increase in their scaled covariance, makes it easier for weak selection to favor the abundance of cooperation in the stag hunt game and the snowdrift game. The same conclusion holds for the public goods game except that the covariance of $b$ has no effect on the average abundance of $C$. On the other hand, increasing the scaled mutation rate or the group size can enhance or lessen the condition for weak selection to favor the abundance of $C$.

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arXiv2022

Combinatorial Properties of primitive words with Non-primitive Product

Let $\mathcal{A}$ be an alphabet of size $n\ge 2$. In this paper, we give a complete description of primitive words $p\neq q$ over an alphabet $\mathcal{A}$ of size $n\geq2$ such that $pq$ is non-primitive and $|p|=2|q|$. In particular, if $l$ is s a positive integer, we count the cardinality of the set $\mathcal{E}(l,\mathcal{A})$ of all couples $(p,q)$ of primitive words such that $|p|=2|q|=2l$ and $pq$ is non-primitive. Then we give a combinatorial formula for this cardinality and its asymptotic behavior, as $l$ or $n$ goes to infinity.

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