1. Sample size sufficiency is a critical consideration for estimating resource selection functions (RSFs) from GPS-based animal telemetry. Cited thresholds for sufficiency include a number of captured animals and as many relocations per animal N as possible. These thresholds render many RSF-based studies misleading if large sample sizes were truly insufficient, or unpublishable if small sample sizes were sufficient but failed to meet reviewer expectations.
2. We provide the first comprehensive solution for RSF sample size by deriving closed-form mathematical expressions for the number of animals M and the number of relocations per animal N required for model outputs to a given degree of precision. The sample sizes needed depend on just 3 biologically meaningful quantities: habitat selection strength, variation in individual selection and a novel measure of landscape complexity, which we define rigorously. The mathematical expressions are calculable for any environmental dataset at any spatial scale and are applicable to any study involving resource selection (including sessile organisms). We validate our analytical solutions using globally relevant empirical data including 5,678,623 GPS locations from 511 animals from 10 species (omnivores, carnivores and herbivores living in boreal, temperate and tropical forests, montane woodlands, swamps and Arctic tundra).
3. Our analytic expressions show that the required M and N must decline with increasing selection strength and increasing landscape complexity, and this decline is insensitive to the definition of availability used in the analysis. Our results demonstrate that the most biologically relevant effects on the utilization distribution (i.e. those landscape conditions with the greatest absolute magnitude of resource selection) can often be estimated with much fewer than animals.
4. We identify several critical steps in implementing these equations, including (a) a priori selection of expected model coefficients and (b) regular sampling of background (pseudoabsence) data within a given definition of availability. We discuss possible methods to identify a priori expectations for habitat selection coefficients, effects of scale on RSF estimation and caveats for rare species applications. We argue that these equations should be a mandatory component for all future RSF studies.

中文翻译：

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解决资源选择函数的样本量问题

1. 从基于 GPS 的动物遥测中估计资源选择函数 (RSF) 时，样本量的充足性是一个重要的考虑因素。引用的充分性阈值包括捕获的动物数量和每只动物N的尽可能多的重新定位。如果大样本量确实不足，这些阈值会使许多基于 RSF 的研究产生误导，或者如果小样本量足够但未能满足审稿人的期望则无法发表。
2. 我们通过推导动物数量M和每只动物的重新安置数量N 的封闭形式数学表达式，为 RSF 样本量提供了第一个综合解决方案需要模型输出到给定的精度。所需的样本大小仅取决于 3 个具有生物学意义的数量：栖息地选择强度、个体选择的变化以及我们严格定义的景观复杂性的新度量。数学表达式适用于任何空间尺度的任何环境数据集，适用于任何涉及资源选择（包括固着生物）的研究。我们使用全球相关的经验数据验证我们的分析解决方案，包括来自 10 个物种（生活在北方、温带和热带森林、山地林地、沼泽和北极苔原的杂食动物、食肉动物和食草动物）的 511 只动物的 5,678,623 个 GPS 位置。
3. 我们的分析表达式表明，所需的M和N必须随着选择强度的增加和景观复杂性的增加而下降，并且这种下降对分析中使用的可用性定义不敏感。我们的结果表明，对利用分布（即具有最大资源选择绝对量级的景观条件）最具有生物学相关性的影响通常可以用比动物少得多的数量来估计。
4. 我们确定了实施这些方程的几个关键步骤，包括 (a) 对预期模型系数的先验选择和 (b) 在给定的可用性定义内对背景（伪缺失）数据进行定期采样。我们讨论了可能的方法来确定栖息地选择系数的先验期望、规模对 RSF 估计的影响以及稀有物种应用的注意事项。我们认为这些方程应该是所有未来 RSF 研究的强制性组成部分。