BACKGROUND Red Queen dynamics are defined as long term co-evolutionary dynamics, often with oscillations of genotype abundances driven by fluctuating selection in host-parasite systems. Much of our current understanding of these dynamics is based on theoretical concepts explored in mathematical models that are mostly (i) deterministic, inferring an infinite population size and (ii) evolutionary, thus ecological interactions that change population sizes are excluded. Here, we recall the different mathematical approaches used in the current literature on Red Queen dynamics. We then compare models from game theory (evo) and classical theoretical ecology models (eco-evo), that are all derived from individual interactions and are thus intrinsically stochastic. We assess the influence of this stochasticity through the time to the first loss of a genotype within a host or parasite population. RESULTS The time until the first genotype is lost ("extinction time"), is shorter when ecological dynamics, in the form of a changing population size, is considered. Furthermore, when individuals compete only locally with other individuals extinction is even faster. On the other hand, evolutionary models with a fixed population size and competition on the scale of the whole population prolong extinction and therefore stabilise the oscillations. The stabilising properties of intra-specific competitions become stronger when population size is increased and the deterministic part of the dynamics gain influence. In general, the loss of genotype diversity can be counteracted with mutations (or recombination), which then allow the populations to recurrently undergo negative frequency-dependent selection dynamics and selective sweeps. CONCLUSION Although the models we investigated are equal in their biological motivation and interpretation, they have diverging mathematical properties both in the derived deterministic dynamics and the derived stochastic dynamics. We find that models that do not consider intraspecific competition and that include ecological dynamics by letting the population size vary, lose genotypes - and thus Red Queen oscillations - faster than models with competition and a fixed population size.

中文翻译：

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红皇后动力学在遗传漂移下能存活多长时间？进化模型与生态进化模型的比较分析。

背景技术红色皇后动力学被定义为长期的协同进化动力学，常常伴随着宿主-寄生虫系统中选择波动的基因型丰度振荡。我们目前对这些动力学的大部分理解是基于数学模型中探索的理论概念，这些理论概念主要是（i）确定性的，推断出无限的种群数量，以及（ii）进化，因此排除了改变种群数量的生态相互作用。在这里，我们回想起当前有关“红色女王”动力学的文献中使用的不同数学方法。然后，我们将博弈论（evo）和经典理论生态模型（eco-evo）的模型进行比较，这些模型都是从个体相互作用中得出的，因此具有内在的随机性。我们评估了这种随机性对宿主或寄生虫种群中基因型首次丧失的影响。结果当考虑种群数量变化形式的生态动态时，直到第一个基因型消失的时间（“灭绝时间”）更短。此外，当个体仅与其他个体局部竞争时，灭绝甚至更快。另一方面，具有固定人口规模和整个人口规模竞争的演化模型会延长灭绝的时间，从而稳定振荡。当种群数量增加并且动力学的确定性部分受到影响时，种内竞争的稳定特性变得更强。一般而言，基因型多样性的丧失可以通过突变（或重组）来弥补，然后，这些种群便会反复经历负频率相关的选择动态和选择性扫描。结论尽管我们研究的模型在生物学动机和解释上是相等的，但它们在派生的确定性动力学和派生的随机动力学方面都具有不同的数学性质。我们发现，没有考虑种内竞争的模型，而是通过让种群数量变化，失去基因型以及因此导致红皇后振荡的生态动力学方法，比具有竞争和固定种群数量的模型更快。它们在派生的确定性动力学和派生的随机动力学方面都有不同的数学特性。我们发现，没有考虑种内竞争的模型，而是通过让种群数量变化，失去基因型以及因此导致红皇后振荡的生态动力学方法，比具有竞争和固定种群数量的模型更快。它们在派生的确定性动力学和派生的随机动力学方面都有不同的数学特性。我们发现，没有考虑种内竞争的模型，而是通过让种群数量变化，失去基因型以及因此导致红皇后振荡的生态动力学方法，比具有竞争和固定种群数量的模型更快。