HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. II COASTAL-INLAND DIVERGENCE IN THE GARTER SNAKE,THAMNOPHIS ELEGANS

The time-scale for the evolution of additive genetic variance-covariance matrices (G-matrices) is a crucial issue in evolutionary biology. If the evolution of G-matrices is slow enough, we can use standard multivariate equations to model drift and selection response on evolutionary time scales. We compared the G-matrices for meristic traits in two populations of gaiter snakes (Thamnophis elegans) with an apparent separation time of 2 million years. Despite considerable divergence in the meristic traits, foraging habits, and diet, these populations show conservation of structure in their G-matrices. Using Flury's hierarchial approach to matrix comparisons, we found that the populations have retained the principal components (eigenvectors) of their G-matrices, but their eigenvalues have diverged. In contrast, we were unable to reject the hypothesis of equal environmental matrices (E-matrices) for these populations. We propose that a conserved pattern of multivariate stabilizing selection may have contributed to conservation of G- and E-matrix structure during the divergence of these populations.     

Cereal aphids, their parasites and predators caught in cages over oat and winter wheat crops

The trapping of alate aphids in emergence cages each 1 yd² (0–83 m²) over cereal crops from mid-June to the end of July, 1964 to 1971, always revealed colonies of cereal aphids within the crop. Four species, Sitobion avenae, S. fragariae, Metopolophium dirhodum and Rhopalosiphum padi occurred every year in different proportions. Alate aphids from winter wheat were most numerous in 1968 and fewest in 1967. Alatae developed slightly earlier in cages than in the field and peak catches were a few days earlier than in a nearby 12-2 m suction trap. Cereal aphid colonies were adversely affected by bad weather in May, e.g. in 1969, and by predators. Coccinellidae (chiefly Propylea 14-punctata) were the dominant predators in 1971 and 1968, Syrphidae in 1966, 1971 and 1968 and Chrysopidae in 1970. Parasites belonging mainly to the genus Aphidius were numerous every year. When hyperparasites such as Asaphes vulgaris, Lygocerus sp., Conostigmus sp. and Phaenoglyphis sp. were abundant as in 1967, they affected numbers of aphids in the current year and increased them in the following year (1968), possibly by hindering early, heavy parasitism. Hyperparasites could have an important influence in fluctuations of cereal aphid populations from year to year. Aphids of one species or another are always present in cereal crops in sufficient numbers during the summer months to provide copious quantities of honey dew, and this is unlikely to be a limiting factor in the biology of the wheat bulb fly, Leptohylemyia coarctata.     

Irradiation of synchronized cell cultures

Summary When HeLa cells are synchronized by the double thymidine block method, it is shown that the mitotic delay produced by 450 R X-rays is longer when cells are irradiated in G₂ than in G₁ but longer still when they are irradiated in the early part of S. DNA synthesis, measured by³H-Thymidine incorporation, is not reduced considerably (± 25%) and only for a few hours when 600 R are given at this time. A more pronounced inhibition occurs when irradiation is given later in S. There is also no decrease in incorporation of³H-orotic acid in RNA when the cells are irradiated in S or in G₂. These results are discussed and it is concluded that the long mitotic delays cannot he due to a modification of nucleic acids metabolism.Paper read at the 6th Annual Meeting of the European Society for Radiobiology, Interlaken, 5.–8. June, 1968. Round Table: Radiation Effectsin vitro andin vivo. Correlations and Discrepancies.     

Approximating the Non-Null Distribution of the Likelihood Ratio Test Statistic

This paper is concerned with investigation into the behavior of the likelihood ratio test statistic G² when the alternative hypothesis M (QQ) is the true model. Exact moments of G² are computed empirically and three approximations are considered for approximating the non-null distribution of G². Our results show that the two parameter gamma distribution provides a closer approximation to the exact powers of G². A randomized procedure was employed to obtain critical values based on 1000 simulated samples.     

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. I. USING THE FLURY HIERARCHY

The comparison of additive genetic variance-covariance matrices (G-matrices) is an increasingly popular exercise in evolutionary biology because the evolution of the G-matrix is central to the issue of persistence of genetic constraints and to the use of dynamic models in an evolutionary time frame. The comparison of G-matrices is a nontrivial statistical problem because family structure induces nonindependence among the elements in each matrix. Past solutions to the problem of G-matrix comparison have dealt with this problem, with varying success, but have tested a single null hypothesis (matrix equality or matrix dissimilarity). Because matrices can differ in many ways, several hypotheses are of interest in matrix comparisons. Flury (1988) has provided an approach to matrix comparison in which a variety of hypotheses are tested, including the two extreme hypotheses prevalent in the evolutionary literature. The hypotheses are arranged in a hierarchy and involve comparisons of both the principal components (eigenvectors) and eigenvalues of the matrix. We adapt Flury's hierarchy of tests to the problem of comparing G-matrices by using randomization testing to account for nonindependence induced by family structure. Software has been developed for carrying out this analysis for both genetic and phenotypic data. The method is illustrated with a garter snake test case.     

Generating Correlated Binary Variables with Complete Specification of the Joint Distribution

Most statistical methods for the analysis of correlated binary data are based on asymptotic theory. Therefore it is important to generate correlated binary data efficiently for Monte Carlo simulation studies to investigate the finite sample performance of these methods. This article provides a simple method for generating correlated binary data with a given joint distribution. The key idea is to consider k‐variate binary data as a multinomial distribution with 2^k possible outcomes.     

Comparison of genetic (co)variance matrices within and between Scabiosa canescens and S. columbaria

In the current study, we used bootstrap analyses and the common principal component (CPC) method of Flury (1988) to estimate and compare the G ‐matrix of Scabiosa columbaria and S. canescens populations. We found three major patterns in the G ‐matrices: (i) the magnitude of the (co)variances was more variable among characters than among populations, (ii) different populations showed high (co)variance for different characters, and (iii) there was a tendency for S. canescens to have higher genetic (co)variances than S. columbaria. The hypothesis of equal G ‐matrices was rejected in all comparisons and there was no evidence that the matrices differed by a proportional constant in any of the analyses. The two ‘species matrices’ were found to be unrelated, both for raw data and data standardized over populations, and there was significant between‐population variation in the G ‐matrix in both species. Populations of S. canescens showed conservation of structure (principal components) in their G ‐matrices, contrasting with the lack of common structure among the S. columbaria matrices. Given these observations and the results from previous studies, we propose that selection may be responsible for some of the variation between the G ‐matrices, at least in S. columbaria and at the between‐species level.     

A New Variant for Mathematical Analysis of Pulse Cytophotometric Data

The staining of DNA by specific fluorochromes provides a suitable method of receiving histograms in a short time by means of pulse cytometry. They represent the proliferative structure of cell populations at a high degree of statistical security. A method for quantitative determination of cell cycle phases (G_1-, S- and G₂ + M-phase) is presented which includes the fraction of cell debris in the calculation procedure. The advantages of this method are the elimination of overlapping between the fraction of debris and cell cycle phases and the quantitative determination of the fraction of cell debris offers the opportunity to get information on cytolytic potencies. Apart from the calculation of the various cell cycle phases the method provides criteria on the adaptation of mathematical analysis to primary data.     

Measuring Fit of Sequence Data to Phylogenetic Model: Gain of Power Using Marginal Tests

Testing fit of data to model is fundamentally important to any science, but publications in the field of phylogenetics rarely do this. Such analyses discard fundamental aspects of science as prescribed by Karl Popper. Indeed, not without cause, Popper (Unended quest: an intellectual autobiography. Fontana, London, 1976) once argued that evolutionary biology was unscientific as its hypotheses were untestable. Here we trace developments in assessing fit from Penny et al. (Nature 297:197–200, 1982) to the present. We compare the general log-likelihood ratio (the G or G ² statistic) statistic between the evolutionary tree model and the multinomial model with that of marginalized tests applied to an alignment (using placental mammal coding sequence data). It is seen that the most general test does not reject the fit of data to model (P ~ 0.5), but the marginalized tests do. Tests on pairwise frequency (F) matrices, strongly (P < 0.001) reject the most general phylogenetic (GTR) models commonly in use. It is also clear (P < 0.01) that the sequences are not stationary in their nucleotide composition. Deviations from stationarity and homogeneity seem to be unevenly distributed amongst taxa; not necessarily those expected from examining other regions of the genome. By marginalizing the 4 ^t patterns of the i.i.d. model to observed and expected parsimony counts, that is, from constant sites, to singletons, to parsimony informative characters of a minimum possible length, then the likelihood ratio test regains power, and it too rejects the evolutionary model with P ≪ 0.001. Given such behavior over relatively recent evolutionary time, readers in general should maintain a healthy skepticism of results, as the scale of the systematic errors in published trees may really be far larger than the analytical methods (e.g., bootstrap) report.     

Estimation of the Parameters for Tremograms According to the Eskov–Zinchenko Effect

The features of the chaotic dynamics of parameters of the neuromuscular system (tremors) were studied using conventional and novel biological methods based on a multidimensional phase-space representation. The dynamics of involuntary micromovements of limbs (finger tremor) both in the relaxation phase (F = 0) and under static load (F = 3N) was manifested in a change in the number of “coincidences” of randomly selected sample pairs (k) of matrices (15 × 15) in paired comparison of tremograms, which demonstrated the global statistical instability of the samples (statistical distribution functions f(x), spectral densities of signals, and autocorrelation A(t)). The samples that result from one experiment cannot be randomly repeated in the next experiment (with the same homeostasis). This represents a quantitative measure of the Eskov–Zinchenko effect in the analysis of chaotically changing statistical distribution functions of tremogram samples. In this paper, the use of quasi-attractor parameters of tremograms (their areas) is proposed to represent changes in the neuromuscular system when passing from one homeostasis to another (G₁ ≠ G₂).

     

Patterns of allozyme variation in relation to population size of the threatened plantMegaleranthis saniculifolia (Ranunculaceae) in Korea

Patterns of variation at 27 allozyme loci were investigated in the endangered endemic plantMegaleranthis saniculifolia. Levels of allozyme variation (A = 1.47,P = 40%,He = 0.088) were also compared with other endemic plant species. Genetic divergence between populations was very high (G ^st = 0.271 ), with moderate to high interpopulation differentiation, which probably arose through historical bottlenecks in a landscape of habitat fragmentation and/or human influence. The percentage of polymorphic loci, heterozygosity, and mean number of alleles per locus were positively related to population size, probably due to the stochastic loss of rare alleles in the smaller populations. Individuals in the small and marginal populations (TB, KD, and CJ) showed higher proportions of fixed loci. These ecologically marginal populations were typically more distant from the nearest neighboring population and were more genetically distinct from one another. The genetic structure of the current population ofM. saniculifolia is probably the result of local extinctions of intervening populations. This, in turn, is due to the Pleistocene climatic change and increased habitat destruction. A positive association appears to exist between genetic diversity and population size. Although these small population sizes are more sensitive to stochastic events, securing a certain number of individuals from the three larger populations (SB, JB, and TG) could be accomplished as part of a conservation strategy. In addition, it is important to prioritize populations in different regions in order to limit population declines caused by large-scale environmental catastrophes.     

Missing data in craniometrics: a simulation study

Craniometric measurements represent a useful tool for studying the differentiation of mammal populations. However, the fragility of skulls often leads to incomplete data matrices. Damaged specimens or incomplete sets of measurements are usually discarded prior to statistical analysis. We assessed the performance of two strategies that avoid elimination of observations: (1) pairwise deletion of missing cells, and (2) estimation of missing data using available measurements. The effect of these distinct approaches on the computation of inter-individual distances and population differentiation analyses were evaluated using craniometric measurements obtained from insular populations of deer micePeromyscus maniculatus (Wagner, 1845). In our simulations, Euclidean distances were greatly altered by pairwise deletion, whereas Gower’s distance coefficient corrected for missing data provided accurate results. Among the different estimation methods compared in this paper, the regression-based approximations weighted by coefficients of determination (r ²) outperformed the competing approaches. We further show that incomplete sets of craniometric measurements can be used to compute distance matrices, provided that an appropriate coefficient is selected. However, the application of estimation procedures provides a flexible approach that allows researchers to analyse incomplete data sets.     

Catalytic solid substrate–room temperature phosphorimetry for the determination of residual perphenazine based on the electronic effect of rhodamine 6G

The rhodamine 6G⁺‐perphenazine (Rhod 6G⁺–PPH) compound is formed in the ester‐exchange reaction between ‐OH of PPH and ‐COOC₂H₅ of Rhod 6G⁺. PPH was oxidized to a red compound (PPH') in the presence of K₂S₂O₈. Interestingly, the room temperature phosphorescence (RTP) of Rhod 6G⁺ was quenched because the ‐OH of PPH′ reacted with ‐COOC₂H₅ of Rhod 6G⁺–PPH to form Rhod 6G⁺–PPH’ and PPH, which decreased the π‐electron density (δ) of the carbon atom in the Rhod 6G⁺–PPH’ conjugated system and enhanced the nonradiation energy loss of the excited Rhod 6G⁺ of the triplet state. The PPH content was directly proportional to the ΔI_p of the system. Thus, a new catalytic solid‐substrate room temperature phosphorimetry (SSRTP) method was established for the determination of PPH. The method had high sensitivity (the limit of detection was 0.019 fg/spot, corresponding to a concentration of 4.8 × 10^–14 g/mL; the sampling quantity was 0.40 μL/spot), good selectivity, convenience and speed. The analytical results were in accordance with those of high‐performance liquid chromatography (HPLC). The structures of Rhod 6G⁺, PPH and Rhod 6G⁺–PPH were characterized by infrared spectra. The reaction mechanism by which PPH was determined is discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparing molecular measures for detecting inbreeding depression

Correlations between heterozygosity and components of fitness have been investigated in natural populations for over 20 years. Positive correlations between a trait of interest and heterozygosity (usually measured at allozyme loci) are generally recognized as evidence of inbreeding depression. More recently, molecular markers such as microsatellites have been employed for the same purpose. A typical study might use around five to ten markers. In this paper we use a panel of 71 microsatellite loci to: (1) Compare the efficacy of heterozygosity and a related microsatellite‐specific variable, mean d², in detecting inbreeding depression; (2) Examine the statistical power of heterozygosity to detect such associations. We performed our analyses in a wild population of red deer (Cervus elaphus) in which inbreeding depression in juvenile traits had previously been detected using a panel of nine markers. We conclude that heterozygosity‐based measures outperform mean d²‐based measures, but that power to detect heterozygosity‐fitness associations is nonetheless low when ten or fewer markers are typed.     

Estimating overdispersion in sparse multinomial data

Multinomial data arise in many areas of the life sciences, such as mark-recapture studies and phylogenetics, and will often by overdispersed, with the variance being higher than predicted by a multinomial model. The quasi-likelihood approach to modeling this overdispersion involves the assumption that the variance is proportional to that specified by the multinomial model. As this approach does not require specification of the full distribution of the response variable, it can be more robust than fitting a Dirichlet-multinomial model or adding a random effect to the linear predictor. Estimation of the amount of overdispersion is often based on Pearson's statistic X² or the deviance D. For many types of study, such as mark-recapture, the data will be sparse. The estimator based on X² can then be highly variable, and that based on D can have a large negative bias. We derive a new estimator, which has a smaller asymptotic variance than that based on X², the difference being most marked for sparse data. We illustrate the numerical difference between the three estimators using a mark-recapture study of swifts and compare their performance via a simulation study. The new estimator has the lowest root mean squared error across a range of scenarios, especially when the data are very sparse.     

Auswertungs-Verfahren bei Doppelmarkierung mit C14- und H3-Thymidin für exponentielles Wachstum

Zusammenfassung Es wird für rein exponentielles Wachstum ein analytisches Verfahren zur Auswertung von Doppelmarkierungs-Versuchen mit zwei zeitlich auseinanderliegenden Applikationen von C¹⁴- und H³-Thymidin beschrieben. Mit Hilfe dieses Verfahrens können die DNS-Synthesezeit (S) und die Generationsdauer (T) rechnerisch in einem Schritt bestimmt werden, wenn die Zeitdauer für (G+M) angenähert bekannt ist. Unsicherheiten in der Kenntnis des Wertes für (G+M) wirken sich nur in geringem Maße aus. Die Bedeutung des analytischen Verfahrens liegt darin, daß es eine Methode darstellt, welche die Bestimmung von S und T auch für exponentiell wachsende Zellpopulationen in einfacher und exakter Weise erlaubt. Damit kann auch für exponentielles Wachstum neben der Methode der markierten Mitosen ein zweites autoradiographisches Verfahren zur Bestimmung des Zellzyklus angewandt werden.

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An analytic method to evaluate double labelling experiments using C¹⁴- and H³- thymidine for exponential growth

Summary The paper describes an analytic method for the evaluation of experiments by using the double labelling technique (application of C-14- and H-3-thymidine) with exponentially growing cell populations. By the analytic method it is possible to calculate exactly the DNA synthesis time and generation time, if the duration of (G+M) is approximately known. Uncertainty of knowledge of the value for (G+M) is only of minimal influence on the results. Thus it is possible to use beside the method of labelled mitoses the double labelling technique as a second method to determine the cell cycle for exponential growth.

     

POPULATION STRUCTURE OF MORPHOLOGICAL TRAITS IN CLARKIA DUDLEYANA. II. CONSTANCY OF WITHIN-POPULATION GENETIC VARIANCE

Recent quantitative genetic studies have attempted to infer long-term selection responsible for differences in observed phenotypes. These analyses are greatly simplified by the assumption that the within-population genetic variance remains constant through time and over space, or for the multivariate case, that the matrix of additive genetic variances and covariances (G matrix) is constant. We examined differences in G matrices and the association of these differences with differences in multivariate means (Mahalanobis D²) among 11 populations of the California endemic annual plant, Clarkia dudleyana. Based on nine continuous morphological traits, the relationship between Mahalanobis D² and a distance measure summarizing differences in G matrices reflected no concomitant change in (co)variances with changes in means. Based on both broad- and narrow-sense analyses, we found little evidence that G matrices differed between populations. These results suggest that both the additive and nonadditive (co)variances for traits have remained relatively constant despite changes in means.     

THE PROLIFERATION KINETICS OF NHIK 1922 CELLS IN VITRO AND IN SOLID TUMOURS IN ATHYMIC MICE

The proliferation kinetics of cells of the line NHIK 1922 grown in vitro and as solid tumours in the athymic mutant nude mouse has been studied. In vitro, growth curves were determined for exponentially growing populations and for populations synchronized by mitotic selection. The phase durations for these populations were determined by flow cytofluorometric measurements of DNA-histograms and pulsed incorporation of [³H]TdR respectively. The generation time and the phase durations for synchronized populations were found to be about equal to those for exponentially growing populations. The duration of the phases G₁, S and G₂+ M was found to be 8·5–9·5, 11·0–12·0 and 6·0–6·5 hr respectively, i.e. the generation time was 26·5–27·0 hr. The proliferation kinetics in vivo were studied by flow cytofluorometry and by the technique of percentage labelled mitoses. The median duration of S-phase and (G₂+ M)-phase in vivo was found to be approximately the same as that observed in vitro, while the median duration of G₁-phase was found to be approximately 5 hr longer in vivo than under the present in vitro growth conditions. The growth fraction in vivo was estimated to be approximately 50%. The non-proliferative compartment of the tumour cells was found to consist mainly of cells with the DNA-content of cells in G₁-phase. It is concluded that the reduced rate of proliferation of NHIK 1922 cells in vivo is correlated with alterations in the duration of G₁-phase and, hence, the proportion of cells in G₁-phase.     

Cloning and Expression of a Rat Acetylcholinesterase Subunit: Generation of Multiple Molecular Forms and Complementarity with a Torpedo Collagenic Subunit

Abstract: We obtained a cDNA clone encoding one type of catalytic subunit of acetylcholinesterase (AChE) from rat brain (T subunit). The coding sequence shows a high frequency of (G + C) at the third position of the codons (66%), as already noted for several AChEs, in contrast with mammalian butyrylcholinesterase. The predicted primary sequence of rat AChE presents only 11 amino acid differences, including one in the signal peptide, from that of the mouse T subunit. In particular, four alanines in the mouse sequence are replaced by serine or threonine. In northern blots, a rat AChE probe indicates the presence of major 3.2-and 2.4-kb mRNAs, expressed in the CNS as well as in some peripheral tissues, including muscle and spleen. In vivo, we found that the proportions of G₁, G₂, and G₄ forms are highly variable in different brain areas. We did not observe any glycolipid-anchored G₂ form, which would be derived from an H subunit. We expressed the cloned rat AChE in COS cells: The transfected cells produce principally an amphiphilic G₁^a form, together with amphiphilic G₂^a and G₄^a forms, and a nonamphiphilic G₄^na form. The amphiphilic G₁^a and G₂^a forms correspond to type II forms, which are predominant in muscle and brain of higher vertebrates. The cells also release G₄^na, G₂^a, and G₁^a in the culture medium. These experiments show that all the forms observed in the CNS in vivo may be obtained from the T subunit. By cotransfecting COS cells with the rat T subunit and the Torpedo collagenic subunit, we obtained chimeric collagentailed forms. This cross-species complementarity demonstrates that the interaction domains of the catalytic and structural subunits are highly conserved during evolution.