Understanding how stochastic fluctuations in the environment influence population dynamics is crucial for sustainable management of biological diversity. However, because species do not live in isolation, this requires knowledge of how species interactions influence population dynamics. In addition, spatial processes play an important role in shaping population dynamics. It is therefore important to improve our understanding of how these different factors act together to shape patterns of abundance across space within and among species. Here, we present a new analytical model for understanding patterns of covariation in space between interacting species in a stochastic environment. We show that the correlation between two species in how they experience the same environmental conditions determines how correlated fluctuations in their densities would be in the absence of competition. In other words, without competition, synchrony between the species is driven by the environment, similar to the Moran effect within a species. Competition between the two species causes their abundances to become less positively or more negatively correlated. The same strength of competition has a greater negative effect on the correlation between species when one of them has a more variable growth rate than the other. In addition, dispersal or other movement weakens the effect of competition on the interspecific correlation. Finally, we show that movement increases the distance over which the species are (positively or negatively) correlated, an effect that is stronger when the species are competitors, and that there is a close connection between the spatial scaling of population synchrony within a species and between species. Our results show that the relationships between the different factors influencing interspecific correlations in abundance are not simple linear ones, but this model allows us to disentangle them and predict how they will affect population fluctuations in different situations.

中文翻译：

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波动环境中竞争物种的空间协变

了解环境中的随机波动如何影响种群动态对于生物多样性的可持续管理至关重要。然而，由于物种不是孤立生活的，这需要了解物种相互作用如何影响种群动态。此外，空间过程在塑造人口动态方面发挥着重要作用。因此，重要的是要提高我们对这些不同因素如何共同作用以塑造物种内部和物种之间的空间丰度模式的理解。在这里，我们提出了一种新的分析模型，用于理解随机环境中相互作用物种之间空间的协变模式。我们表明，两个物种在如何经历相同的环境条件方面的相关性决定了在没有竞争的情况下它们的密度波动的相关性。换句话说，没有竞争，物种之间的同步是由环境驱动的，类似于物种内部的莫兰效应。这两个物种之间的竞争导致它们的丰度变得不那么正相关或更加负相关。当其中一个物种的增长率比另一个变化更大时，相同的竞争强度对物种之间的相关性具有更大的负面影响。此外，分散或其他运动削弱了竞争对种间相关性的影响。最后，我们表明运动增加了物种（正或负）相关的距离，当物种是竞争者时，这种效应会更强，并且物种内部和物种之间的种群同步空间尺度之间存在密切联系。我们的结果表明，影响种间丰度相关性的不同因素之间的关系不是简单的线性关系，但该模型使我们能够解开它们并预测它们将如何影响不同情况下的种群波动。