The presence and establishment of a tree species at a particular spatial location is influenced by multiple physiological and environmental filters such as propagule pressure (seed availability), light and moisture availability, and slope and elevation. However, a less understood environmental filter to species-specific establishment is competition or facilitation between dominant tree species. For example, certain tree species may compete for resources at spatial locations where such resources are scarce while less competition may occur at resource-rich areas. Using data from the Forest Inventory and Analysis (FIA) program of the United States Department of Agriculture (USDA) Forest Service, we develop a multivariate spatial Bernoulli model to investigate the space-varying relationship between extant tree species in Utah. Additionally, we propose a novel modeling strategy that explains the spatially varying relationships by regressing the associated between-species correlation matrix on available covariate data. Positive definite conditions of the covariate-varying correlation matrix are ensured by defining the regression in terms of the unique partial correlation matrix. Results indicate that correlations between species are dependent upon elevation.

中文翻译：

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犹他州优势树种之间的空间和协变量关系

树木在特定空间位置的存在和建立受到多种生理和环境过滤器（例如繁殖压力（种子可用性），光照和水分可用性以及坡度和海拔）的影响。但是，对于特定树种的建立缺乏了解的环境过滤器是优势树种之间的竞争或促进。例如，某些树种可能会在资源稀缺的空间位置竞争资源，而在资源丰富的区域可能发生较少竞争。使用来自美国农业部（USDA）森林服务局的森林清单和分析（FIA）计划的数据，我们开发了一个多元空间伯努利模型来研究犹他州现存树种之间的空间变化关系。另外，我们提出了一种新颖的建模策略，该算法通过对可用协变量数据上的相关物种间相关矩阵进行回归来解释空间变化的关系。通过根据唯一的部分相关矩阵定义回归，可以确保协变量变化相关矩阵的正定条件。结果表明，物种之间的相关性取决于海拔。