Phenotypic plasticity of growth trajectory and ontogenic allometry in response to density for eucalyptus hybrid clones and families

BACKGROUND: and Aims Response to density is a crucial aspect of the ecology of trees in forests and plantations. Few studies have investigated the genetics of plasticity in response to density for growth traits such as height and circumference through development. METHODS: Two experiments were carried out in the field, the first with full-sib families of Eucalyptus urophylla x E. grandis hybrids, and the second with clones of E. tereticornis x E. grandis hybrids planted across a range of densities (625, 1111 and 2500 trees ha-1). Height, circumference and stem taper were measured through development in both experiments. Variance components were estimated and a repeated measure approach for plasticity and three different methods were used to compare the variance-covariance matrix across densities. KEY RESULTS: Genetic variance was significantly different from zero but the density x genotype interaction was significant only for clone experiments at the adult stage. Significant plasticity for three traits in both experiments was found. In the clone experiments, a significant clone x time x density interaction was found, suggesting that plasticity for growth and stem form is under genetic control. In both experiments, density did not affect environmental correlation, which remained high throughout tree development. The impact of density on genetic correlation was marked in the clone experiment, with a reduced value at lower density, but was not observed in the family trial. The differences between clones and family are mainly explained by the distribution of genetic variation within and among genotypes. CONCLUSIONS: The results suggest that plasticity for growth traits and form of tropical Eucalyptus species is under genetic control and that the environment changes genetic co-variation through ontogeny. The findings confirm that a tree population with a narrow genetic basis (represented by clones) is sensitive to a changing environment, whereas a population with a broader genetic basis (full-sib family here) exhibits a more stable reaction.     

Probability density functions for axial ratios of sectioning profiles of anisotropically arranged elliptical microvessels

The article theoretically regards probability density functions (PDFs) for axial ratio (X/Y) of sectioning profiles of elliptical microvessels (MVs) arranged with anisotropy in a biological tissue volume. A technique for the PDF_X/Y calculations in anisotropy of the elliptical MVs is described. The essence of this technique is introducing anisotropy in PDF(α,φ), i.e. the function of the joint distribution of the polar and planar angles α and φ, which define mutual orientation of the elliptical MVs and sectioning planes. With the aid of this technique, the anisotropy cases are studied with PDF(α,φ) given by pair combinations of the following distributions: (i) a uniform distribution of the angles α and/or φ, (ii) the angle α distribution with , and (iii) Gaussian distributions of the α or φ values. Specifically, PDF_X/Y curves are obtained for MVs with the true, or three-dimensional, axial ratio X₀/Y₀=2.0, and the anisotropy effects on the X/Y expected frequencies are analysed. Conclusions of this analysis, the PDF_X/Y calculation technique, and the PDF_X/Y curves obtained are useful for stereological reconstruction of anisotropically organised microcirculatory networks, with an ellipticity of their MVs being taken into consideration.     

The relationship between growth and allometry

The asymptotic allometric equations are derived by considering the relative growth of different physiological and anatomical quantities. The growth rate is assumed to be proportional to the value of the quantity, where the proportion coefficient depends on time. The allometric exponents are calculated for some organs of man and compared with the experimental values for primates. The exponents are generally time-dependent during the growth. The effect of the choice of the origin of time axis on the asymptotic allometric exponents is studied.     

A computer program for the graphical and iterative fitting of probability density functions to biological data.

A tutorially-assisted, interactive program, written for a Digital Equipment Corporation LAB-11 minicomputer (PDP-11/20, is described which allows a user to fit (with or without automatic estimation of initial parameter values), by a method of nonlinear least squres, any one of seven different types of probability density functions (p.d.f.'s) to an empirical frequency distribution; the latter of which may be input to the program or formed by the program whenever it is furnished a series of times between events. The iteratively-obtained, "best fit" p.d.f. is displayed on a two color, point-plot display against the background of a point-plot histogram. By selecting any one of nine output modes, the user is allowed: (1) to view histograms successively on the point-plot display, (2) to generate selected p.d.f.'s (3) to "force" p.d.f.'s having known parameters through the histogram data, (4) to obtain Chi-square (x2) and Kolmogorov-Smionov estimates of the goodness of fit to the data, and (5) to apply a special test [Williams and Kloot, 1953] in order to determine whether the least squares estimates of two candidate models are statistically different. The resident driver program and the four overlayable program segments are written in standard FORTRAN IV; except for two plot routines, which are written in PDP-11 assembly language.     

Scoring functions for cryoEM density fitting

In fitting atomic structures into cryoEM density maps of macromolecular assemblies, the cross-correlation function (CCF) is the most prevalent method of scoring the goodness-of-fit. However, there are still many possible, less studied ways of scoring fits. In this paper, we introduce four scores new to cryoEM fitting and compare their performance to three known scores. Our benchmark consists of (a) 4 protein assemblies with simulated maps at 5-20 ? resolution, including the heptameric ring of GroEL; and (b) 4 experimental maps of GroEL at ～6-23 ? resolution with corresponding fitted atomic models. We perturb each fit 1000 times and assess each new fit with each score. The correlation between a score and the Cα RMSD of each fit from the "correctly" fitted structure shows that the CCF is one of the best scores, but in certain situations could be augmented or even replaced by other scores. For instance, our implementation of a score based on mutual information outperforms or is comparable to the CCF in almost all test cases, and our new "envelope score" works as well as the CCF at sub-nanometer resolution but is an order of magnitude faster to calculate. The results also suggest that the width of the Gaussian function used to blur the atomic structure into a density map can significantly affect the fitting process. Finally, we show that our score-testing method, when combined with the Laplacian CCF or the mutual information scores, can be used as a statistical tool for improving cryoEM density fitting.     

Bivariate and multivariate growth allometry: statistical and biological considerations

Bivariate and multivariate analyses of 55 cranial dimensions were completed on ontogenetic series of Pygmy chimpanzees ( Pan paniscus ), Common chimpanzees ( Pan troglodytes ), and gorillas ( Gorilla gorilla ). Subanalyses described here were specifically designed to compare and crosscheck quantitative assessments of relative growth as determined using the bivariate and multivariate (principal components analysis—PCA) approaches. Results indicate a strong concordance between the bivariate and multivariate patterns, empirically supporting the claim that PCA provides an effective multivariate approach to analysing growth allometry. Comparison of bivariate and multivariate results also suggests that in multi-group PCA, the first component summarizes shape variation resulting from the sharing and extension of common patterns of growth allometry, while the second and subsequent components summarize shape variation resulting from divergent growth trajectories, reflected in bivariate comparisons as either vertical shifts and/or slope differences. Examination of non-normalized first component loadings, plus a comparison with estimates of logarithmic growth in the cranial dimensions, reveals that the non-normalized loadings are proportional to coefficients of specific growth. This finding further links the bivariate and multivariate approaches, grounding both in Huxley's theoretical notions of multiplicative and relative growth.     

Risk functions and expected spike density functions for neurons in the cat cochlear nucleus

The temporal properties of spontaneous and (or) evoked discharges of 157 neurons localized in dorsal cochlear nucleus of anaesthetized cats have been studied. Tone bursts were presented at stimulus best frequency in a free field from the side of ipsilateral ear. About half of cells were characterized by paused or build-up types of the discharge. For all such units a long lasting post-spike decrease in excitability could be seen from the analysis of hazard functions of spontaneous and evoked activity. As a result, the time dependence of conditional probability of the first crossing of the threshold (under condition of an absence of previous response spikes) or expecting probability function (EPF) were over the usual peristimulus histograms. Units with chopper discharges usually did not demonstrate alternative peaks in EPF. We interpreted this fact as evidence that chopper discharge pattern is a result of strong post spike decrease in excitability. Such pattern doesn't demonstrate an existence of real periodicity of the unit. In primary-like units the hazard functions demonstrated only minor after-spike decrease of excitability, and the EPFs were similar to the initial part of peristimulus histograms. Type II units (presumably inhibitory cells) were characterized by non-monotonous hazard functions and by a tendency to burst response patterns. In some cells, we observed a tendency to existence of real intrinsic oscillations both in the EPFs and hazard functions.     

The effects of hybridization on growth allometry and craniofacial form in Sulawesi macaques

The present research investigates the effects of hybridization between Macaca maurus and M. tonkeana on adult male form and patterns of growth allometry. Comparisons of adult hybrid mean phenotypic values with the adult averages of the parental species indicate a condition of heterosis for cranial vault length and crown-rump length. Negative heterosis is indicated for body mass. Regression parameters describing growth allometry are generated for four craniofacial measurement variables and one body measurement using both least squares and reduced major axis regression. Comparisons of hybrid and parental regression slopes and intercepts using analysis of covariance and t-tests suggest that there is a hybrid pattern of growth allometry characterized by an increase in regression slope values coupled with lower intercept values compared to those of the parental species and the parental averages for most regression parameters. Multivariate analyses of the adult and ontogenetic morphometric data indicate significant differences across species taxa in form and shape during development and adulthood. Our finding of significant differences between hybrids and their parental taxa in growth allometry and craniofacial form and shape during development challenges the assumption often made regarding the reproductive and taxonomic significance of observed ontogenetic divergence between Neandertals and modern humans. We propose that anthropological primatology, with its goal of developing nonhuman primate models for investigating human evolution, can provide a biologically relevant means by which to empirically estimate the taxonomic significance of morphological and ontogenetic divergence observed in the hominid fossil record.     

Otolith allometry informs age and growth of long-lived Quillback Carpiodes cyprinus

Environmental Biology of Fishes - The carpsuckers, which include Quillback Carpiodes cyprinus, river carpsucker Carpiodes carpio, and highfin carpsucker Carpiodes velifer, are ictiobine catostomids...     

Model of hidden heterogeneity in longitudinal data

Variables measured in longitudinal studies of aging and longevity do not exhaust the list of all factors affecting health and mortality transitions. Unobserved factors generate hidden variability in susceptibility to diseases and death in populations and in age trajectories of longitudinally measured indices. Effects of such heterogeneity can be manifested not only in observed hazard rates but also in average trajectories of measured indices. Although effects of hidden heterogeneity on observed mortality rates are widely discussed, their role in forming age patterns of other aging-related characteristics (average trajectories of physiological state, stress resistance, etc.) is less clear. We propose a model of hidden heterogeneity to analyze its effects in longitudinal data. The approach takes the presence of hidden heterogeneity into account and incorporates several major concepts currently developing in aging research (allostatic load, aging-associated decline in adaptive capacity and stress-resistance, age-dependent physiological norms). Simulation experiments confirm identifiability of model's parameters.     

Low density lipoprotein heterogeneity in spontaneously hypercholesterolemic pigs

We previously described a strain of spontaneously hypercholesterolemic pigs carrying an apo-B allele termed Lpb ⁵. Lpb ⁵ pigs are heterogeneous with respect to the severity of their hypercholesterolemia. We have termed Lpb ⁵ pigs with severe hypercholesterolemia Lpb 5.1 pigs, and those with moderate hypercholesterolemia Lpb 5.2, Lpb 5.1 animals have a dramatic increase in buoyant LDL relative to dense LDL, with a buoyant-to-dense LDL ratio of 2.2. In contrast, Lpb 5.2 and control pigs have buoyant-to-dense LDL ratios of 0.7 and 0.5 respectively. This ratio appears to be a stable characteristic of the Lpb 5.1 phenotype because sexually mature boars have a dramatic decrease in total plasma cholesterol concentration with no decrease in their ratio of buoyant-to-dense LDL. We have previously demonstrated a fourteen-fold overproduction of buoyant LDL in the Lpb 5.1 pigs, with very little conversion of dense LDL to buoyant LDL. In the current work, very low density lipoprotein (VLDL) turnover experiments were conducted to determine whether VLDL conversion to buoyant LDL was increased in the Lpb 5.1 pigs. VLDL conversion to buoyant LDL could not account for the increased production of buoyant LDL in Lpb 5.1 pigs. Thus, we cannot account for the increased production of buoyant LDL in the Lpb 5.1 pigs from any measurable plasma lipoprotein source. We have therefore termed this production of buoyant LDL in the Lpb 5.1 pigs direct buoyant LDL production.     

Development of a useful technique for analyzing behavioral teratologic data

Two measures of postnatal development are described in this paper: the PAC50 and AD50. These measures proved to be more sensitive than the use of means in the evaluation of three radiation studies involving postnatal developmental evaluation. PAC50 is the percent of achievement of a goal by litters or offspring in an experimental group at the age when 50% of the control litters or offspring attain that goal. AD50 is the age (acquisition day) at which 50% of the litters or offspring in each group attain a specified developmental goal. This methodology is a useful technique for analyzing selected behavioral data following in utero X-irradiation and may prove to be a sensitive means of determining postnatal alteration due to prenatal exposure to a variety of suspect agents.     

Low density lipoprotein heterogeneity in the cebus monkey

In studies of cebus monkey plasma lipoproteins, we have used an ultracentrifugally generated density gradient to isolate two distinct species of low density lipoproteins (LDL). Compositional analyses revealed that each of the ultracentrifugally isolated fractions was enriched in cholesteryl esters and contained a single apolipoprotein which in terms of its mobility on SDS gels corresponded to apolipoprotein B-100, the major apolipoprotein of human LDL. Hydrodynamic measurements carried out in the analytical ultracentrifuge showed that F1.20 values were 30.0 for LDL1 and 23.5 for LDL2. In a solution of density 1.0069 g/ml, the sedimentation rates were 5.9 and 7.2 S for LDL1 and LDL2, respectively. In addition to sedimentation velocity data, we describe a new approach for using these same data to obtain calculated values for molecular weight. The hydrated densities calculated for the two fractions were 1.033 and 1.045 g/ml and calculated molecular weights were 3.08 million for LDL1 and 2.42 million for LDL2. Hydrated density values were in excellent agreement with those calculated from compositional data. Electron microscopy data showed that LDL1 had a larger mean diameter of 26.7 nm than LDL2 which had a diameter of 19.3 nm. Native gel electrophoretic analyses of the two LDL fractions in 3.5% acrylamide showed that, consistent with its size, LDL1 had slower mobility than LDL2.     

A useful method for the analysis of growth studies

A group of parsimonious models for the analysis of animal growth curves is presented. The effects of correlations between the successive weights are reduced by analyzing the weight gained between the different weighing times. A model is developed for the resulting two-way table of group average gain curves (group by periods), using the two-way table modeling techniques proposed by Mandel. The coefficients in the fitted model are examined to determine what functions of the weight gain measurements will summarize the characteristics of the curves. In the second part of the analysis these statistics are computed for each animal and analyzed to determine the effects of the design variables on the growth of the animals. Experience has shown that in many instances total weight gain summarizes all the information in the curve. The conditions under which total gain provides an adequate summary are discussed. The model has been used in the analysis of rat, dog, hamster, guinea pig and swine growth curves. An example is included to illustrate the utility of the proposed approach.     

Stochastic ontogenetic allometry: the statistical dynamics of relative growth

Background

In the absence of stochasticity, allometric growth throughout ontogeny is axiomatically described by the logarithm-transformed power-law model, , where and are the logarithmic sizes of two traits at any given time t. Realistically, however, stochasticity is an inherent property of ontogenetic allometry. Due to the inherent stochasticity in both and , the ontogenetic allometry coefficients, and k, can vary with t and have intricate temporal distributions that are governed by the central and mixed moments of the random ontogenetic growth functions, and . Unfortunately, there is no probabilistic model for analyzing these informative ontogenetic statistical moments.

Methodology/Principal Findings

This study treats and as correlated stochastic processes to formulate the exact probabilistic version of each of the ontogenetic allometry coefficients. In particular, the statistical dynamics of relative growth is addressed by analyzing the allometric growth factors that affect the temporal distribution of the probabilistic version of the relative growth rate, , where is the expected value of the ratio of stochastic to stochastic , and and are the numerator and the denominator of , respectively. These allometric growth factors, which provide important insight into ontogenetic allometry but appear only when stochasticity is introduced, describe the central and mixed moments of and as differentiable real-valued functions of t.

Conclusions/Significance

Failure to account for the inherent stochasticity in both and leads not only to the miscalculation of k, but also to the omission of all of the informative ontogenetic statistical moments that affect the size of traits and the timing and rate of development of traits. Furthermore, even though the stochastic process and the stochastic process are linearly related, k can vary with t.