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1. Beyond simple adaptation: Incorporating other evolutionary processes and concepts into eco‐evolutionary dynamics

   https://doi.org/10.1111/ele.14197  

   Yamamichi, Masato; Ellner, Stephen P.; Hairston, Nelson G. (September 2023, Ecology Letters)

   Studies of eco‐evolutionary dynamics have integrated evolution with ecological processes at multiple scales (populations, communities and ecosystems) and with multiple interspecific interactions (antagonistic, mutualistic and competitive). However, evolution has often been conceptualised as a simple process: short‐term directional adaptation that increases population growth. Here we argue that diverse other evolutionary processes, well studied in population genetics and evolutionary ecology, should also be considered to explore the full spectrum of feedback between ecological and evolutionary processes. Relevant but underappreciated processes include (1) drift and mutation, (2) disruptive selection causing lineage diversification or speciation reversal and (3) evolution driven by relative fitness differences that may decrease population growth. Because eco‐evolutionary dynamics have often been studied by population and community ecologists, it will be important to incorporate a variety of concepts in population genetics and evolutionary ecology to better understand and predict eco‐evolutionary dynamics in nature. 

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2. On the Constructor–Blocker game

   https://doi.org/10.1002/jgt.23186  

   Balogh, József; Chen, Ce; English, Sean (March 2025, Journal of Graph Theory)

   Abstract In the Constructor–Blocker game, two players, Constructor and Blocker, alternately claim unclaimed edges of the complete graph . For given graphs and , Constructor can only claim edges that leave her graph ‐free, while Blocker has no restrictions. Constructor's goal is to build as many copies of as she can, while Blocker attempts to minimize the number of copies of in Constructor's graph. The game ends once there are no more edges that Constructor can claim. The score of the game is the number of copies of in Constructor's graph at the end of the game when both players play optimally and Constructor plays first. In this paper, we extend results of Patkós, Stojaković and Vizer on to many pairs of and : We determine when and , also when both and are odd cycles, using Szemerédi's Regularity Lemma. We also obtain bounds of when and . 

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3. Extending eco‐evolutionary theory with oligomorphic dynamics

   https://doi.org/10.1111/ele.14183  

   Lion, Sébastien; Sasaki, Akira; Boots, Mike (February 2023, Ecology Letters)

   Abstract Understanding the interplay between ecological processes and the evolutionary dynamics of quantitative traits in natural systems remains a major challenge. Two main theoretical frameworks are used to address this question, adaptive dynamics and quantitative genetics, both of which have strengths and limitations and are often used by distinct research communities to address different questions. In order to make progress, new theoretical developments are needed that integrate these approaches and strengthen the link to empirical data. Here, we discuss a novel theoretical framework that bridges the gap between quantitative genetics and adaptive dynamics approaches. ‘Oligomorphic dynamics’ can be used to analyse eco‐evolutionary dynamics across different time scales and extends quantitative genetics theory to account for multimodal trait distributions, the dynamical nature of genetic variance, the potential for disruptive selection due to ecological feedbacks, and the non‐normal or skewed trait distributions encountered in nature. Oligomorphic dynamics explicitly takes into account the effect of environmental feedback, such as frequency‐ and density‐dependent selection, on the dynamics of multi‐modal trait distributions and we argue it has the potential to facilitate a much tighter integration between eco‐evolutionary theory and empirical data. 

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4. Instance-dependent Sample Complexity Bounds for Zero-sum Matrix Games

   Maiti, Arnab; Jamieson, Kevin; Ratliff, Lillian J. (January 2023, Proceedings of Machine Learning Research)

   Francisco Ruiz, Jennifer Dy (Ed.)

   We study the sample complexity of identifying an approximate equilibrium for two-player zero-sum n × 2 matrix games. That is, in a sequence of repeated game plays, how many rounds must the two players play before reaching an approximate equilibrium (e.g., Nash)? We derive instance-dependent bounds that define an ordering over game matrices that captures the intuition that the dynamics of some games converge faster than others. Specifically, we consider a stochastic observation model such that when the two players choose actions i and j, respectively, they both observe each other’s played actions and a stochastic observation Xij such that E [Xij ] = Aij . To our knowledge, our work is the first case of instance-dependent lower bounds on the number of rounds the players must play before reaching an approximate equilibrium in the sense that the number of rounds depends on the specific properties of the game matrix A as well as the desired accuracy. We also prove a converse statement: there exist player strategies that achieve this lower bound. 

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5. Nonequilibrium statistical mechanics of money/energy exchange models

   https://doi.org/10.1088/1751-8121/ad369b  

   Miao, Maggie; Makarov, Dmitrii E; Blom, Kristian (April 2024, Journal of Physics A: Mathematical and Theoretical)

   Abstract Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations. In fact, a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model and its extensions using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing ‘unfair’ exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the ‘ground state’ (i.e. with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant’s wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game. The time evolution of a player’s wealth in this case can be thought of as a ‘chemical reaction’, where a transition between ‘reactants’ (rich state) and ‘products’ (poor state) involves crossing a large free energy barrier. We thus analyze the trajectories generated from the game using ideas from the theory of transition paths and highlight non-Markovian effects in the barrier crossing dynamics. 

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