Many major questions in the theory of evolutionary dynamics can in a meaningful sense be mapped to analyses of stochastic trajectories in game theoretic contexts. Often the approach is to analyze small numbers of distinct populations and/or to assume dynamics occur within a regime of population sizes large enough that deterministic trajectories are an excellent approximation of reality. The addition of ecological factors, termed "eco-evolutionary dynamics", further complicates the dynamics and results in many problems which are intractable or impractically messy for current theoretical methods. However, an analogous but underexplored approach is to analyze these systems with an eye primarily towards uncertainty in the models themselves. In the language of researchers in Reinforcement Learning and adjacent fields, a Partially Observable Markov Process. Here we introduce a duality which maps the complexity of accounting for both ecology and individual genotypic/phenotypic types onto a problem of accounting solely for underlying information-theoretic computations rather than drawing physical boundaries which do not change the computations. Armed with this equivalence between computation and the relevant biophysics, which we term Taak-duality, we attack the problem of "directed evolution" in the form of a Partially Observable Markov Decision Process. This provides a tractable case of studying eco-evolutionary trajectories of a highly general type, and of analyzing questions of potential limits on the efficiency of evolution in the directed case.

翻译：摘要：进化动力学理论中的许多主要问题，在某种意义上可以映射为博弈论背景下随机轨迹的分析。常见方法是分析少量不同种群，或假设群体规模足够大，使得确定性轨迹能极好地近似真实动态。引入生态因素（即"生态进化动力学"）会进一步复杂化动态过程，导致许多问题在当前理论方法下难以处理或过于杂乱。然而，一个类似但未被充分探索的方法是，以模型自身不确定性为主要着眼点来分析这些系统。用强化学习及相关领域研究者的术语来说，这属于部分可观测马尔可夫过程。本文引入一种对偶性，将同时考虑生态和个体基因型/表型类型的复杂性，映射为仅需考虑底层信息论计算的问题，而非划定不改变计算的物理边界。借助这种计算与相关生物物理之间的等价性（我们称之为塔克对偶性），我们以部分可观测马尔可夫决策过程的形式攻克了"定向进化"问题。这为研究高度普适类型的生态进化轨迹，以及分析定向情形下进化效率的潜在极限问题，提供了一个可处理的案例。