Research on hypercycles focuses on cooperative interactions among replicating species, including the emergence of catalytic parasites and catalytic shortcircuits. Further interactions may be expected to arise in cooperative systems. For instance, molecular replicators are subject to mutational processes and ecological species to behavioural shifts due to environmental and ecological changes. Such changes could involve switches from cooperative to antagonistic interactions, in what we call a functional shift. In this article, we investigate a model for a two-member hypercycle model, considering that one species performs a functional shift. First, we introduce the model dynamics without functional shifts to illustrate the dynamics only considering obligate and facultative cooperation. Then, two more cases maintaining cross-catalysis are considered: (i) a model describing the dynamics of ribozymes where a fraction of the population of one replicator degrades the other molecular species while the other fraction still receives catalytic aid; and (ii) a system in which a given fraction of the population predates on the cooperating species while the rest of the population still receives aid. We have characterised the key bifurcation parameters determining extinction, survival, and coexistence of species. We show that predation, regardless of the fraction that benefits from it, does not significantly change dynamics with respect to the degradative case (i), thus conserving dynamics and bifurcations. Their biological significance is interpreted, and their potential implications for the dynamics of early replicators and ecological species are outlined.

中文翻译：

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两种物种超循环中的功能转变建模

对超循环的研究侧重于复制物种之间的合作相互作用，包括催化寄生虫和催化短路的出现。在合作系统中可能会出现进一步的交互。例如，由于环境和生态变化，分子复制子会受到突变过程和生态物种的行为改变的影响。这种变化可能涉及从合作互动到对抗互动的转变，我们称之为功能转变. 在本文中，我们研究了一个二元超循环模型，考虑到一个物种执行功能转变。首先，我们介绍没有功能转移的模型动力学，以说明仅考虑专职和兼性合作的动力学。然后，考虑另外两种保持交叉催化的情况：（i）描述核酶动力学的模型，其中一个复制子的一部分种群降解其他分子种类，而另一部分仍然接受催化辅助；(ii) 一种系统，在该系统中，一定比例的种群先于合作物种，而其余种群仍接受援助。我们已经描述了决定物种灭绝、生存和共存的关键分叉参数。我们表明捕食，无论从中受益的分数如何，都不会显着改变关于退化情况 (i) 的动态，从而保持动态和分叉。解释了它们的生物学意义，并概述了它们对早期复制者和生态物种动态的潜在影响。