Fox David R, Ridsdill-Smith James
IPP&P Biometrics Unit, CSIRO Centre for Mediterranean Agricultural Research, Private Bag, 6014, PO Wembley, WA, Australia.
Division of Entomology, CSIRO Centre for Mediterranean Agricultural Research, Private Bag, PO, 6014, Wembley, WA, Australia.
Oecologia. 1995 Sep;103(4):435-443. doi: 10.1007/BF00328681.
We have examined a number of statistical issues associated with methods for evaluating different tests of density dependence. The lack of definitive standards and benchmarks for conducting simulation studies makes it difficult to assess the performance of various tests. The biological researcher has a bewildering choice of statistical tests for testing density dependence and the list is growing. The most recent additions have been based on computationally intensive methods such as permutation tests and boot-strapping. We believe the computational effort and time involved will preclude their widespread adoption until: (1) these methods have been fully explored under a wide range of conditions and shown to be demonstrably superior than other, simpler methods, and (2) general purpose software is made available for performing the calculations. We have advocated the use of Bulmer's (first) test as a de facto standard for comparative studies on the grounds of its simplicity, applicability, and satisfactory performance under a variety of conditions. We show that, in terms of power, Bulmer's test is robust to certain departures from normality although, as noted by other authors, it is affected by temporal trends in the data. We are not convinced that the reported differences in power between Bulmer's test and the randomisation test of Pollard et al. (1987) justifies the adoption of the latter. Nor do we believe a compelling case has been established for the parametric bootstrap likelihood ratio test of Dennis and Taper (1994). Bulmer's test is essentially a test of the serial correlation in the (log) abundance data and is affected by the presence of autocorrelated errors. In such cases the test cannot distinguish between the autoregressive effect in the errors and a true density dependent effect in the time series data. We suspect other tests may be similarly affected, although this is an area for further research. We have also noted that in the presence of autocorrelation, the type I error rates can be substantially different from the assumed level of significance, implying that in such cases the test is based on a faulty significance region. We have indicated both qualitatively and quantitatively how autoregressive error terms can affect the power of Bulmer's test, although we suggest that more work is required in this area. These apparent inadequacies of Bulmer's test should not be interpreted as a failure of the statistical procedure since the test was not intended to be used with autocorrelated error terms.
我们研究了一些与评估密度依赖不同检验方法相关的统计问题。进行模拟研究缺乏明确的标准和基准，这使得评估各种检验的性能变得困难。生物学研究者在用于检验密度依赖的统计检验方面面临令人眼花缭乱的选择，而且这个列表还在不断增加。最新增加的检验方法基于计算密集型方法，如置换检验和自助法。我们认为，在以下情况出现之前，所涉及的计算工作量和时间将阻碍它们的广泛采用：（1）这些方法在广泛的条件下得到充分探索，并被证明明显优于其他更简单的方法；（2）有通用软件可用于进行计算。我们主张将布尔默（首次提出的）检验用作比较研究的事实上的标准，理由是它简单、适用，并且在各种条件下表现令人满意。我们表明，就检验功效而言，布尔默检验对于某些偏离正态性的情况具有稳健性，不过，正如其他作者所指出的，它会受到数据中时间趋势的影响。我们不相信布尔默检验与波拉德等人（1987年）的随机化检验之间所报告的功效差异能成为采用后者的理由。我们也不认为丹尼斯和塔珀（1994年）的参数自助似然比检验有令人信服的依据。布尔默检验本质上是对（对数）丰度数据中序列相关性的检验，并且会受到自相关误差存在的影响。在这种情况下，该检验无法区分误差中的自回归效应和时间序列数据中真正的密度依赖效应。我们怀疑其他检验可能也会受到类似影响，尽管这是一个有待进一步研究的领域。我们还注意到，在存在自相关的情况下，第一类错误率可能与假定的显著性水平有很大差异，这意味着在这种情况下，检验所基于的显著性区域是错误的。我们已经定性和定量地指出了自回归误差项如何影响布尔默检验的功效，不过我们建议在这个领域还需要做更多工作。布尔默检验这些明显的不足之处不应被解释为统计程序的失败，因为该检验并非旨在用于带有自相关误差项的数据。
