Department of Environmental Sciences, University of Toledo, 2801 W. Bancroft Street, MS# 604, Toledo, OH, USA.
Great Lakes Environmental Research Laboratory, National Oceanic and Atmospheric Administration, Ann Arbor, MI, USA.
Water Res. 2019 Oct 15;163:114855. doi: 10.1016/j.watres.2019.114855. Epub 2019 Jul 13.
Using cross-sectional data for making ecological inference started as a practical means of pooling data to enable meaningful empirical model development. For example, limnologists routinely use sample averages from numerous individual lakes to examine patterns across lakes. The basic assumption behind the use of cross-lake data is often that responses within and across lakes are identical. As data from multiple study units across a wide spatiotemporal scale are increasingly accessible for researchers, an assessment of this assumption is now feasible. In this study, we demonstrate that this assumption is usually unjustified, due largely to a statistical phenomenon known as the Simpson's paradox. Through comparisons of a commonly used empirical model of the effect of nutrients on algal growth developed using several data sets, we discuss the cognitive importance of distinguishing factors affecting lake eutrophication operating at different spatial and temporal scales. Our study proposes the use of the Bayesian hierarchical modeling approach to properly structure the data analysis when data from multiple lakes are employed.
利用横剖数据进行生态推断最初是一种实用的方法，可以汇集数据以支持有意义的经验模型开发。例如，湖沼学家通常使用来自多个个体湖泊的样本平均值来研究湖泊之间的模式。跨湖数据使用背后的基本假设通常是，湖泊内和湖泊之间的反应是相同的。随着越来越多的研究人员可以获得广泛时空尺度上的多个研究单元的数据，现在可以对这一假设进行评估。在这项研究中，我们表明，由于一种称为辛普森悖论的统计现象，这一假设通常是没有根据的。通过比较使用多个数据集开发的一种常用的营养物质对藻类生长影响的经验模型，我们讨论了区分影响湖泊富营养化的因素的认知重要性，这些因素在不同的时空尺度上起作用。我们的研究提出了在使用多个湖泊的数据时，使用贝叶斯层次建模方法来正确构建数据分析的建议。
