Error, Bias, and Long-Branch Attraction in Data for Two Chloroplast Photosystem Genes in Seed Plants

Sequences of two chloroplast photosystem genes, psaA and psbB, together comprising about 3,500 bp, were obtained for all five major groups of extant seed plants and several outgroups among other vascular plants. Strongly supported, but significantly conflicting, phylogenetic signals were obtained in parsimony analyses from partitions of the data into first and second codon positions versus third positions. In the former, both genes agreed on a monophyletic gymnosperms, with Gnetales closely related to certain conifers. In the latter, Gnetales are inferred to be the sister group of all other seed plants, with gymnosperms paraphyletic. None of the data supported the modern ‘‘anthophyte hypothesis,’’ which places Gnetales as the sister group of flowering plants. A series of simulation studies were undertaken to examine the error rate for parsimony inference. Three kinds of errors were examined: random error, systematic bias (both properties of finite data sets), and statistical inconsistency owing to long-branch attraction (an asymptotic property). Parsimony reconstructions were extremely biased for third-position data for psbB. Regardless of the true underlying tree, a tree in which Gnetales are sister to all other seed plants was likely to be reconstructed for these data. None of the combinations of genes or partitions permits the anthophyte tree to be reconstructed with high probability. Simulations of progressively larger data sets indicate the existence of long-branch attraction (statistical inconsistency) for third-position psbB data if either the anthophyte tree or the gymnosperm tree is correct. This is also true for the anthophyte tree using either psaA third positions or psbB first and second positions. A factor contributing to bias and inconsistency is extremely short branches at the base of the seed plant radiation, coupled with extremely high rates in Gnetales and nonseed plant outgroups. M. J. Sanderson,* M. F. Wojciechowski,*† J.-M. Hu,* T. Sher Khan,* and S. G. Brady

The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Assessment of lifetime cumulative sun exposure using a self-administered questionnaire : reliability of two approaches

Few studies have evaluated the reliability of lifetime sun exposure estimated from inquiring about the number of hours people spent outdoors in a given period on a typical weekday or weekend day (the time-based approach). Some investigations have suggested that women have a particularly difficult task in estimating time outdoors in adulthood due to their family and occupational roles. We hypothesized that people might gain additional memory cues and estimate lifetime hours spent outdoors more reliably if asked about time spent outdoors according to specific activities (an activity-based approach). Using self-administered, mailed questionnaires, test-retest responses to time-based and to activity-based approaches were evaluated in 124 volunteer radiologic technologist participants from the United States: 64 females and 60 males 48 to 80 years of age. Intraclass correlation coefficients (ICC) were used to evaluate the test-retest reliability of average number of hours spent outdoors in the summer estimated for each approach. We tested the differences between the two ICCs, corresponding to each approach, using a t test with the variance of the difference estimated by the jackknife method. During childhood and adolescence, the two approaches gave similar ICCs for average numbers of hours spent outdoors in the summer. By contrast, compared with the time-based approach, the activity-based approach showed significantly higher ICCs during adult ages (0.69 versus 0.43, P = 0.003) and over the lifetime (0.69 versus 0.52, P = 0.05); the higher ICCs for the activity-based questionnaire were primarily derived from the results for females. Research is needed to further improve the activity-based questionnaire approach for long-term sun exposure assessment. (Cancer Epidemiol Biomarkers Prev 2009;18(2):464–71)

Interleaved PC-OFDM to reduce peak-to-average power ratio

Parallel combinatory orthogonal frequency division multiplexing (PC-OFDM yields lower maximum peak-to-average power ratio (PAR), high bandwidth efficiency and lower bit error rate (BER) on Gaussian channels compared to OFDM systems. However, PC-OFDM does not improve the statistics of PAR significantly. In this chapter, the use of a set of fixed permutations to improve the statistics of the PAR of a PC-OFDM signal is presented. For this technique, interleavers are used to produce K-1 permuted sequences from the same information sequence. The sequence with the lowest PAR, among K sequences is chosen for the transmission. The PAR of a PC-OFDM signal can be further reduced by 3-4 dB by this technique. Mathematical expressions for the complementary cumulative density function (CCDF)of PAR of PC-OFDM signal and interleaved PC-OFDM signal are also presented.