What do we really know about the signalling role of plumage colour in blue tits? A case study of impediments to progress in evolutionary biology

Evolutionary biologists seek to explain the origin and maintenance of phenotypes, and a substantial portion of this research is accomplished by thorough study of individual species. For instance, many researchers study individual species to understand evolution of ornamental traits which appear to be products of sexual selection. I explored our understanding of sexual ornaments in a well‐studied vertebrate species that may serve as a case study for research programs in evolutionary biology. I attempted to located all published papers examining plumage colour and variables related to sexual selection hypotheses in a common European songbird, the blue tit (Cyanistes caeruleus). Researchers have estimated over 1200 statistical relationships with plumage colour of blue tits in 52 studies. However, of the approximately 1000 main‐effect relationships from the 48 studies that are candidates for inclusion in this meta‐analysis, more than 400 were reported without details of strength and direction. Circumstantial evidence suggests that an unknown number of other estimated effects remain unpublished. Missing information is a substantial barrier to interpretation of these papers and to meta‐analytic synthesis. Examination and analysis of funnel plots indicated that unpublished effects may be a biased sample of all effects, especially for comparisons of plumage colour to age and individual quality, and possibly also to measures of mate choice. Further, type I error was likely elevated by the large number of statistical comparisons evaluated, the frequent use of iterative model‐building procedures, and a willingness to interpret a wide variety of results as support for a hypothesis. Type I errors were made more problematic because blue tit plumage researchers only rarely have attempted to replicate important findings in their own work or that of others. Replication is essential to drawing robust scientific conclusions, especially in probabilistic systems with moderate to weak effects or a likelihood of bias. Last, researchers studying blue tit plumage have often developed ad hoc explanations for deviations of results from their predictions. Revising hypotheses in light of data is appropriate, but these revised hypotheses were rarely tested with new data. The only highly robust conclusion supported by meta‐analysis is that male blue tits have plumage that reflects more light in the ultraviolet and yellow wavelengths than the plumage of females. Various other effects, including condition‐dependence of plumage colour expression and a tendency for females to adjust the sex ratio of their offspring in response to male colour, remain uncertain. These obstacles to progress in the blue tit plumage literature are likely common in evolutionary biology, and so I recommend changes to incentive structures which may improve progress towards scientific understanding in this discipline.     

A Note on the Log‐Rank Test in Life Table Analysis with Correlated Observations

Survival data consisting of independent sets of correlated failure times may arise in many situations. For example, we may take repeated observations of the failure time of interest from each patient or observations of the failure time on siblings, or consider the failure times on littermates in toxicological experiments. Because the failure times taken on the same patient or related family members or from the same litter are likely correlated, use of the classical log‐rank test in these situations can be quite misleading with respect to type I error. To avoid this concern, this paper develops two closed‐form asymptotic summary tests, that account for the intraclass correlation between the failure times within patients or units. In fact, one of these two test includes the classical log‐rank test as a special case when the intraclass correlation equals 0. Furthermore, to evaluate the finite‐sample performance of the two tests developed here, this paper applies Monte Carlo simulation and notes that they can actually perform quite well in a variety of situations considered here.     

Testing Equality between Two Diagnostic Procedures in Paired‐Sample Ordinal Data

When a new diagnostic procedure is developed, it is important to assess whether the diagnostic accuracy of the new procedure is different from that of the standard procedure. For paired‐sample ordinal data, this paper develops two test statistics for testing equality of the diagnostic accuracy between two procedures without assuming any parametric models. One is derived on the basis of the probability of correctly identifying the case for a randomly selected pair of a case and a non‐case over all possible cutoff points, and the other is derived on the basis of the sensitivity and specificity directly. To illustrate the practical use of the proposed test procedures, this paper includes an example regarding the use of digitized and plain films for screening breast cancer. This paper also applies Monte Carlo simulation to evaluate the finite sample performance of the two statistics developed here and notes that they can perform well in a variety of situations. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact test, the exact chi‐squared test and the exact likelihood ratio test are popular and can be implemented in software StatXact. In this paper we investigate which test is the best in small samples in terms of the unconditional exact power. In equal sample cases it is proved that the three tests produce the same unconditional exact power. A symmetry of the unconditional exact power is also found. In unequal sample cases the unconditional exact powers of the three tests are computed and compared. In most cases the Fisher's exact test turns out to be best, but we characterize some cases in which the exact likelihood ratio test has the highest unconditional exact power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reproducibility of species lists,visual cover estimates and frequency methods for recording high‐mountain vegetation

Question: When multiple observers record the same spatial units of alpine vegetation, how much variation is there in the records and what are the consequences of this variation for monitoring schemes to detect changes? Location: One test summit in Switzerland (Alps) and one test summit in Scotland (Cairngorm Mountains). Method: Eight observers used the GLORIA protocols for species composition and visual cover estimates in percentages on large summit sections (>100 m²) and species composition and frequency in nested quadrats (1 m²). Results: The multiple records from the same spatial unit for species composition and species cover showed considerable variation in the two countries. Estimates of pseudo‐turnover of composition and coefficients of variation of cover estimates for vascular plant species in 1 m × 1‐m quadrats showed less variation than in previously published reports, whereas our results in larger sections were broadly in line with previous reports. In Scotland, estimates for bryophytes and lichens were more variable than for vascular plants. Conclusions: Statistical power calculations indicated that unless large numbers of plots were used, changes in cover or frequency were only likely to be detected for abundant species (exceeding 10% cover) or if relative changes were large (50% or more). Lower variation could be reached with the point method and with larger numbers of small plots. However, as summits often strongly differ from each other, supplementary summits cannot be considered as a way of increasing statistical power without introducing a supplementary component of variance into the analysis and hence into the power calculations.