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Abstract：
Generalized linear models (GLMs) are an integral tool in ecology. Like general linear models, GLMs assume linearity, which entails a linear relationship between independent and dependent variables. However, because this assumption acts on the link rather than the natural scale in GLMs, it is more easily overlooked. We reviewed recent ecological literature to quantify the use of linearity. We then used two case studies to confront the linearity assumption via two GLMs fit to empirical data. In the first case study we compared GLMs to generalized additive models (GAMs) fit to mammal relative abundance data. In the second case study we tested for linearity in occupancy models using passerine point-count data. We reviewed 162 studies published in the last 5 years in five leading ecology journals and found less than 15% reported testing for linearity. These studies used transformations and GAMs more often than they reported a linearity test. In the first case study, GAMs strongly out-performed GLMs as measured by AIC in modeling relative abundance, and GAMs helped uncover nonlinear responses of carnivore species to landscape development. In the second case study, 14% of species-specific models failed a formal statistical test for linearity. We also found that differences between linear and nonlinear (i.e., those with a transformed independent variable) model predictions were similar for some species but not for others, with implications for inference and conservation decision-making. Our review suggests that reporting tests for linearity are rare in recent studies employing GLMs. Our case studies show how formally comparing models that allow for nonlinear relationships between the dependent and independent variables has the potential to impact inference, generate new hypotheses, and alter conservation implications. We conclude by suggesting that ecological studies report tests for linearity and use formal methods to address linearity assumption violations in GLMs.
摘要：
广义线性模型(GLM)是生态学中不可或缺的工具。像一般的线性模型一样，GLM假设线性，这需要自变量和因变量之间的线性关系。然而,因为这个假设作用于GLM中的链接而不是自然尺度，它更容易被忽视。我们回顾了最近的生态学文献，以量化线性的使用。然后，我们使用两个案例研究，通过两个GLM拟合经验数据来面对线性假设。在第一个案例研究中，我们将GLM与适合哺乳动物相对丰度数据的广义加性模型（GAM）进行了比较。在第二个案例研究中，我们使用雀形目点数数据测试了占用模型的线性。我们回顾了过去5年在5个领先的生态学期刊上发表的162项研究，发现只有不到15％的人报告了线性测试。这些研究使用转化和GAM的频率比他们报道的线性测试更多。在第一个案例研究中，在建模相对丰度时，GAM强烈优于AIC测得的GLM，和GAMs有助于揭示食肉动物物种对景观发展的非线性响应。在第二个案例研究中，14%的物种特异性模型未能通过正式的线性统计检验。我们还发现线性和非线性之间的差异(即，具有转换后的自变量的那些)模型预测对于某些物种是相似的，而对于其他物种则不是，对推理和保护决策有影响。OurreviewsuggeststhatreportingtestsforlinearityarerareinrecentstudiesemployingGLM.Ourcasestudiesshowshowformallycomparingmodelsthatallowedfor非线性relationshipbetweenthedependentandindependentvariableshasthepotentialtoimpactinference.产生新的假设，并改变保护的含义。最后，我们建议生态研究报告线性测试，并使用正式方法解决GLM中违反线性假设的问题。
