Estimating phylogenetic inertia in Tithonia (Asteraceae): a comparative approach

Abstract.— Phylogenetic inertia is a difficult issue in evolutionary biology because we have yet to reach a consensus about how to measure it. In this study a comparative approach is used to evaluate phylogenetic inertia in 14 demographic and morphological characters in 10 species and one subspecies of the genus Tithonia (Asteraceae). Three different methods, autocorrelational analysis, phylogenetic correlograms, and ancestor-state reconstruction, were used to evaluate phylogenetic inertia in these traits. Results were highly dependent on the method applied. Autoregression and phylogenetic eigenvector regression (PVR) methods found more inertia in morphological traits. In contrast, phylogenetic correlograms and ancestor-state reconstruction suggest that morphological characters exhibit less phylogenetic inertia than demographic ones. The differences between results are discussed and methods are compared in an effort to understand phylogenetic inertia more thoroughly.     

Minimax D-optimal designs for the logistic model

We propose an algorithm for constructing minimax D-optimal designs for the logistic model when only the ranges of the values for both parameters are assumed known. Properties of these designs are studied and compared with optimal Bayesian designs and Sitter's (1992, Biometrics, 48, 1145-1155) minimax D-optimal kk-designs. Examples of minimax D-optimal designs are presented for the logistic and power logistic models, including a dose-response design for rheumatoid arthritis patients.     

Weighted p-value adjustments for animal carcinogenicity trend test

A typical animal carcinogenicity experiment routinely analyzes approximately 10-30 tumor sites. Comparisons of tumor responses between dosed and control groups and dose-related trend tests are often evaluated for each individual tumor site/type separately. p-Value adjustment approaches have been proposed for controlling the overall Type I error rate or familywise error rate (FWE). However, these adjustments often result in reducing the power to detect a dose effect. This paper proposes using weighted adjustments by assuming that each tumor can be classified as either class A or class B based on prior considerations. The tumors in class A, which are considered as more critical endpoints, are given less adjustment. Two weighted methods of adjustments are presented, the weighted p adjustment and weighted alpha adjustment. A Monte Carlo simulation shows that both weighted adjustments control the FWE well. Furthermore, the power increases if a treatment-dependent tumor is analyzed as in class A tumors and the power decreases if it is analyzed as in class B tumors. A data set from a National Toxicology Program (NTP) 2-year animal carcinogenicity experiment with 13 tumor types/sites observed in male mice was analyzed using the proposed methods. The modified poly-3 test was used to test for increased carcinogenicity since it has been adopted by the NTP as a standard test for a dose-related trend. The unweighted adjustment analysis concluded that there was no statistically significant dose-related trend. Using the Food and Drug Administration classification scheme for the weighted adjustment analyses, two rare tumors (with background rates of 1% or less) were analyzed as class A tumors and 11 common tumors (with background rates higher than 1%) as class B. Both weighted analyses showed a significant dose-related trend for one rare tumor.     

Imaging cytosolic free-calcium distribution and oscillations in pollen tubes with confocal microscopy: A comparison of different dyes and loading methods

Summary A steep, oscillating tip-focused gradient in cytosolic free calcium ([Ca²⁺]_c) has been implicated in pollen tube growth. Further understanding of the biological causes and consequences of these processes relies on the precise imaging of [Ca²⁺]_c during the different growth phases. In this work, the minimum technical requirements for confocal [Ca²⁺]_c imaging ofAgapanthus umbellatus pollen tubes were examined. A range of dyes, dye forms, and loading methods were compared. Non-ratio and ratio imaging were critically analysed, in terms of the detection of the [Ca²⁺]_c gradient and its fluctuations over time. Both ratiometric and nonratiornetric methods detected relative changes in [Ca²⁺]_c. However, visualisation of the [Ca²⁺]_c gradient, with an accurate spatial definition, was only possible with ratiometric methods. The gradient observed in this study ranged from 1.8 M (tip) to 180–220 nM (basal level), within the first 4–10 m. Apical [Ca²⁺]_c fluctuations with an amplitude between 415 nM and 1.8 M showed a period of 40 to 75 s. All protocols for dye-loading proved to have strengths and weaknesses. Thus, the choice of a dye and its loading procedure should consider the required imaging period, extent of sequestration, effect on cell performance and viability, ease of loading procedure, and aim of the study. The present study constitutes an examination of the [Ca²⁺]_c gradient in pollen tubes by these criteria.Abbreviations CLSM confocal laser scanning microscope - [Ca²⁺]_c cytosolic free calcium - PT pollen tube Dedicated to Professor Walter Gustav Url on the occasion of his 70th birthday     

Direct Calculation of a Tree Length Using a Distance Matrix

Comparative studies of tree-building methods have shown minimum evolution to be in general an accurate criterion for selecting a true tree. To improve the use of this criterion, this paper proposes a method for rapidly and directly calculating a length of a dichotomous tree without having to resort to branch length calculations. This direct calculation (DC) method applies to the complete final topology, giving equal importance to each branch after a dichotomy. According to this method, the tree length S _DC is S _DC =∑ _i ∑ _j (D _ij /2 ^Bij ) = (∑ _i<j ∑D _ij 2 ^Bmax−Bij )/2 ^{Bmax −1} where D _ij is the observed distance between taxa i and j, B _ij is the number of branches connecting i and j, Bmax is the greatest B _ij in the tree, and the powers of two are due to the dichotomy of the tree. This tree length expression may be used as a rapid method for selecting the shortest tree from a set of hypothetical or subobtimal trees. Received: 2 March 2000 / Accepted: 24 March 2000     

Sampling effort, regression method, and the shape and slope of size–abundance relations

1. Despite a substantial body of work there remains much disagreement about the form of the relationship between organism abundance and body size. In an attempt at resolving these disagreements the shape and slope of samples from simulated and real abundance–mass distributions were assessed by ordinary least squares regression (OLS) and the reduced major axis method (RMA).
2. It is suggested that the data gathered by ecologists to assess these relationships are usually truncated in respect of density. Under these conditions RMA gives slope estimates which are consistently closer to the true slopes than OLS regression.
3. The triangular relationships reported by some workers are found over smaller mass and abundance ranges than linear relations. Scatter in slope estimates is much greater and positive slopes more common at small sample sizes and sample ranges. These results support the notion that inadequate and truncated sampling is responsible for much of the disagreement reported in the literature.
4. The results strongly support the notion that density declines with increasing body mass in a broad, linear band with a slope around −1. However there is some evidence to suggest that this overall relation results from a series of component relations with slopes which differ from the overall slope.     

Biofumigation potential of brassicas

The relationship of global climate change to plant growth and the role of forests as sites of carbon sequestration have encouraged the refinement of the estimates of root biomass and production. However, tremendous controversy exists in the literature as to which is the best method to determine fine root biomass and production. This lack of consensus makes it difficult for researchers to determine which methods are most appropriate for their system. The sequential root coring method was the most commonly used method to collect root biomass data in the past and is still commonly used. But within the last decade the use of minirhizotrons has become a favorite method of many researchers. In addition, due to the high labor-intensive requirements of many of the direct approaches to determine root biomass, there has been a shift to develop indirect methods that would allow fine root biomass and production to be predicted using data on easily monitored variables that are highly correlated to root dynamics. Discussions occur as to which method should be used but without gathering data from the same site using different methods, these discussions can be futile. This paper discusses and compares the results of the most commonly used direct and indirect methods of determining root biomass and production: sequential root coring, ingrowth cores, minirhizotrons, carbon fluxes approach, nitrogen budget approach and correlations with abiotic resources. No consistent relationships were apparent when comparing several sites where at least one of the indirect and direct methods were used on the same site. Until the different root methods can be compared to some independently derived root biomass value obtained from total carbon budgets for systems, one root method cannot be stated to be the best and the method of choice will be determined from researcher's personal preference, experiences, equipment, and/or finances.     

Rapid Evaluation of Least-Squares and Minimum-Evolution Criteria on Phylogenetic Trees

We present fast new algorithms for evaluating trees with respectto least squares and minimum evolution (ME), the most commonlyused criteria for inferring phylogenetic trees from distancedata. The new algorithms include an optimal O(N2) time algorithmfor calculating the edge (branch or internode) lengths on atree according to ordinary or unweighted least squares (OLS);an O(N3) time algorithm for edge lengths under weighted leastsquares (WLS) including the Fitch-Margoliash method; and anoptimal O(N4) time algorithm for generalized least-squares (GLS)edge lengths (where N is the number of taxa in the tree). TheME criterion is based on the sum of edge lengths. Consequently,the edge lengths algorithms presented here lead directly toO(N2), O(N3), and O(N4) time algorithms for ME under OLS, WLS,and GLS, respectively. All of these algorithms are as fast asor faster than any of those previously published, and the algorithmsfor OLS and GLS are the fastest possible (with respect to orderof computational complexity). A major advantage of our new methodsis that they are as well adapted to multifurcating trees asthey are to binary trees. An optimal algorithm for determiningpath lengths from a tree with given edge lengths is also developed.This leads to an optimal O(N2) algorithm for OLS sums of squaresevaluation and corresponding O(N3) and O(N4) time algorithmsfor WLS and GLS sums of squares, respectively. The GLS algorithmis time-optimal if the covariance matrix is already inverted.The speed of each algorithm is assessed analytically—thespeed increases we calculate are confirmed by the dramatic speedincreases resulting from their implementation in PAUP* 4.0.The new algorithms enable far more extensive tree searches andstatistical evaluations (e.g., bootstrap, parametric bootstrap,or jackknife) in the same amount of time. Hopefully, the fastalgorithms for WLS and GLS will encourage the use of these criteriafor evaluating trees and their edge lengths (e.g., for approximatedivergence time estimates), since they should be more statisticallyefficient than OLS.