Contemporary studies of species coexistence are underpinned by deterministic models that assume that competing species have continuous (i.e., noninteger) densities, live in infinitely large landscapes, and coexist over infinite time horizons. By contrast, in nature, species are composed of discrete individuals subject to demographic stochasticity and occur in habitats of finite size where extinctions occur in finite time. One consequence of these discrepancies is that metrics of species’ coexistence derived from deterministic theory may be unreliable predictors of the duration of species coexistence in nature. These coexistence metrics include invasion growth rates and niche and fitness differences, which are now commonly applied in theoretical and empirical studies of species coexistence. In this study, we tested the efficacy of deterministic coexistence metrics on the duration of species coexistence in a finite world. We introduce new theoretical and computational methods to estimate coexistence times in stochastic counterparts of classic deterministic models of competition. Importantly, we parameterized this model using experimental field data for 90 pairwise combinations of 18 species of annual plants, allowing us to derive biologically informed estimates of coexistence times for a natural system. Strikingly, we found that for species expected to deterministically coexist, community sizes containing only 10 individuals had predicted coexistence times of more than 1000 years. We also found that invasion growth rates explained 60% of the variation in intrinsic coexistence times, reinforcing their general usefulness in studies of coexistence. However, only by integrating information on both invasion growth rates and species' equilibrium population sizes could most (>99%) of the variation in species coexistence times be explained. This integration was achieved with demographically uncoupled single-species models solely determined by the invasion growth rates and equilibrium population sizes. Moreover, because of a complex relationship between niche overlap/fitness differences and equilibrium population sizes, increasing niche overlap and increasing fitness differences did not always result in decreasing coexistence times, as deterministic theory would predict. Nevertheless, our results tend to support the informed use of deterministic theory for understanding the duration of species’ coexistence while highlighting the need to incorporate information on species' equilibrium population sizes in addition to invasion growth rates.

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确定性共存理论在有限世界中重要吗？

当代物种共存研究以确定性模型为基础，这些模型假设竞争物种具有连续（即非整数）密度，生活在无限大的景观中，并在无限的时间范围内共存。相比之下，在自然界中，物种由受人口统计随机性影响的离散个体组成，并出现在有限大小的栖息地中，而灭绝发生在有限的时间内。这些差异的一个结果是，从确定性理论得出的物种共存指标可能无法可靠地预测物种在自然界共存的持续时间。这些共存指标包括入侵增长率以及生态位和适应性差异，这些指标现在普遍应用于物种共存的理论和实证研究。在这项研究中，我们测试了确定性共存指标对有限世界中物种共存持续时间的有效性。我们引入了新的理论和计算方法来估计经典确定性竞争模型的随机对应物的共存时间。重要的是，我们使用 18 种一年生植物的 90 对组合的实验田间数据对该模型进行了参数化，使我们能够推导出自然系统共存时间的生物学估计。引人注目的是，我们发现对于预期确定性共存的物种，仅包含 10 个个体的群落规模预测共存时间超过 1000 年。我们还发现入侵增长率解释了 60% 的内在共存时间变化，加强了它们在共存研究中的普遍用途。然而，只有整合入侵增长率和物种平衡种群规模的信息，才能解释物种共存时间的大部分（>99%）变化。这种整合是通过仅由入侵增长率和平衡种群规模确定的人口统计学上不耦合的单一物种模型实现的。此外，由于生态位重叠/适应度差异与平衡种群规模之间的复杂关系，增加生态位重叠和增加适应度差异并不总是导致共存时间减少，正如确定性理论所预测的那样。尽管如此，我们的结果倾向于支持明智地使用确定性理论来理解物种共存的持续时间，同时强调需要结合物种的信息