Cumulative t-link threshold models for the genetic analysis of calving ease scores

In this study, a hierarchical threshold mixed model based on a cumulative t-link specification for the analysis of ordinal data or more, specifically, calving ease scores, was developed. The validation of this model and the Markov chain Monte Carlo (MCMC) algorithm was carried out on simulated data from normally and t₄ (i.e. a t-distribution with four degrees of freedom) distributed populations using the deviance information criterion (DIC) and a pseudo Bayes factor (PBF) measure to validate recently proposed model choice criteria. The simulation study indicated that although inference on the degrees of freedom parameter is possible, MCMC mixing was problematic. Nevertheless, the DIC and PBF were validated to be satisfactory measures of model fit to data. A sire and maternal grandsire cumulative t-link model was applied to a calving ease dataset from 8847 Italian Piemontese first parity dams. The cumulative t-link model was shown to lead to posterior means of direct and maternal heritabilities (0.40 ± 0.06, 0.11 ± 0.04) and a direct maternal genetic correlation (-0.58 ± 0.15) that were not different from the corresponding posterior means of the heritabilities (0.42 ± 0.07, 0.14 ± 0.04) and the genetic correlation (-0.55 ± 0.14) inferred under the conventional cumulative probit link threshold model. Furthermore, the correlation (> 0.99) between posterior means of sire progeny merit from the two models suggested no meaningful rerankings. Nevertheless, the cumulative t-link model was decisively chosen as the better fitting model for this calving ease data using DIC and PBF.     

Flexible cloglog links for binomial regression models as an alternative for imbalanced medical data

The complementary log-log link was originally introduced in 1922 to R. A. Fisher, long before the logit and probit links. While the last two links are symmetric, the complementary log-log link is an asymmetrical link without a parameter associated with it. Several asymmetrical links with an extra parameter were proposed in the literature over last few years to deal with imbalanced data in binomial regression (when one of the classes is much smaller than the other); however, these do not necessarily have the cloglog link as a special case, with the exception of the link based on the generalized extreme value distribution. In this paper, we introduce flexible cloglog links for modeling binomial regression models that include an extra parameter associated with the link that explains some unbalancing for binomial outcomes. For all cases, the cloglog is a special case or the reciprocal version loglog link is obtained. A Bayesian Markov chain Monte Carlo inference approach is developed. Simulations study to evaluate the performance of the proposed algorithm is conducted and prior sensitivity analysis for the extra parameter shows that a uniform prior is the most convenient for all models. Additionally, two applications in medical data (age at menarche and pulmonary infection) illustrate the advantages of the proposed models.     

A simple predictive density based on the p*-formula

The predictive density proposed by Harris (1989) is based onintegrating the density for a new observation with respect tothe estimated sampling distribution of the maximum likelihoodestimator of the unknown parameter. This has good properties,but is rather complicated to compute even for simple models.An approximation to the Harris proposal is considered whichconsists of approximating the sampling distribution of the maximumlikelihood estimator of the unknown parameter by Barndorff-Nielsen's(1983) p*-formula, and then using a Laplace approximation withO(n^–1) correction terms for integrating out the parameter.The result can generally be expressed in terms of standard likelihoodderivatives, and takes a quite simple form for exponential familiesand for location models.     

Unequal group variances in microarray data analyses

Motivation: In searching for differentially expressed (DE) genesin microarray data, we often observe a fraction of the genesto have unequal variability between groups. This is not an issuein large samples, where a valid test exists that uses individualvariances separately. The problem arises in the small-samplesetting, where the approximately valid Welch test lacks sensitivity,while the more sensitive moderated t-test assumes equal variance. Methods: We introduce a moderated Welch test (MWT) that allowsunequal variance between groups. It is based on (i) weightingof pooled and unpooled standard errors and (ii) improved estimationof the gene-level variance that exploits the information fromacross the genes. Results: When a non-trivial proportion of genes has unequalvariability, false discovery rate (FDR) estimates based on thestandard t and moderated t-tests are often too optimistic, whilethe standard Welch test has low sensitivity. The MWT is shownto (i) perform better than the standard t, the standard Welchand the moderated t-tests when the variances are unequal betweengroups and (ii) perform similarly to the moderated t, and betterthan the standard t and Welch tests when the group variancesare equal. These results mean that MWT is more reliable thanother existing tests over wider range of data conditions. Availability: R package to perform MWT is available at http://www.meb.ki.se/~yudpaw Contact: yudi.pawitan{at}ki.se Supplementary information: Supplementary data are availableat Bioinformatics online. Associate Editor: Martin Bishop     

Non-uniform survival rate of heterodimerization links in the evolution of the yeast protein-protein interaction network

Protein-protein interaction networks (PINs) are scale-free networks with a small-world property. In a small-world network, the average cluster coefficient () is much higher than in a random network, but the average shortest path length () is similar between the two networks. To understand the evolutionary mechanisms shaping the structure of PINs, simulation studies using various network growth models have been performed. It has been reported that the heterodimerization (HD) model, in which a new link is added between duplicated nodes with a uniform probability, could reproduce scale-freeness and a high . In this paper, however, we show that the HD model is unsatisfactory, because (i) to reproduce the high in the yeast PIN, a much larger number (n(HI)) of HD links (links between duplicated nodes) are required than the estimated number of n(HI) in the yeast PIN and (ii) the spatial distribution of triangles in the yeast PIN is highly skewed but the HD model cannot reproduce the skewed distribution. To resolve these discrepancies, we here propose a new model named the non-uniform heterodimerization (NHD) model. In this model, an HD link is preferentially attached between duplicated nodes when they share many common neighbors. Simulation studies demonstrated that the NHD model can successfully reproduce the high , the low n(HI), and the skewed distribution of triangles in the yeast PIN. These results suggest that the survival rate of HD links is not uniform in the evolution of PINs, and that an HD link between high-degree nodes tends to be evolutionarily conservative. The non-uniform survival rate of HD links can be explained by assuming a low mutation rate for a high-degree node, and thus this model appears to be biologically plausible.     

Relationship between Plant Weight and Growing Period for Vegetable Crops in the United Kingdom

A generalized equation is derived that relates total dry matterproduction to time from emergence for crops grown in the fieldwith adequate water and nutrients. It is: w+K₁lnw+W₀=K₂t where w is the plant dry weight in t ha^–1, t is time indays after emergence, K₂ and K₁ are constants and W₀ equals–(w₀+K₁lnw₀) where w₀ is the value of w at the start ofthe growing period. The increases in the dry matter of 18 different types of vegetablecrop were measured at intervals during growth in the field.In every case the data fitted the equation very satisfactorilywith K₁ set equal to 1 t ha^–1. The fitted values of K₂were similar for many crops; those of W₀ varied considerablybut were always similar to the values calculated from the individualseed weight and the plant population. Good fits were also obtainedwhen time in days was replaced with cumulative evaporation froman open water surface. It is concluded that the growth-time curves of many differentvegetable crops can be described by the same simple equationand that the variation between curves can be largely attributedto differences in seed weight and plant population.     

Maternal corticosteroids influence primary offspring sex ratio in a free-ranging passerine bird

When fitness benefits of investment in sons and daughters differ,animals are predicted to manipulate the sex ratio of their offspring.Sex ratio manipulation occurs in many taxa, but the mechanismsunderlying the phenomenon in vertebrates remain largely unknown.Factors favoring skewed sex ratios, such as reduced maternalcondition or food availability, also induce elevated corticosteroids.Recent experimental studies support a causal relationship betweencorticosteroids and sex ratio. Evidence of a natural correlationbetween maternal corticosteroids and offspring sex ratio hasbeen lacking, however. Without such evidence, the importanceof corticosteroids in influencing sex ratios in natural populationswas unknown. We measured baseline corticosteroids in 19 free-rangingfemale white-crowned sparrows (Zonotrichia leucophrys) and thesex ratios of their offspring. Females with high corticosteroidsproduced more daughters than females with low hormone levels.We then conducted a controlled, field-based experiment investigatingthe effects of moderately increased maternal corticosteroidson offspring sex ratios to determine if the observed correlationreflects a causal relationship between maternal corticosteroidsand offspring sex ratio. Hormone-implanted females producedmore female embryos than control females. These findings providethe first evidence of a natural correlation between maternalcorticosteroids and offspring sex ratios in free-ranging birds,and the first experimental evidence of a causal link betweenmoderate increases in corticosteroids and biased primary sexratios.     

Semiparametric regression estimation in the presence of dependent censoring

We propose a semiparametric estimation procedure for estimatingthe regression of an outcome Y, measured at the end of a fixedfollow-up period, on baseline explanatory variables X, measuredprior to start of follow-up, in the presence of dependent censoringgiven X. The proposed estimators are consistent when the dataare ‘missing at random’ but not ‘missing completelyat random’ (Rubin, 1976), and do not require full specificationof the complete data likelihood. Specifically, we assume thatthe probability of censoring at time t is independent of theoutcome Y conditional on the recorded history up to t of a vectorof time-dependent covariates that are correlated with Y. Ourestimators can be used to adjust for dependent censoring andnonrandom noncompliance in randomised trials studying the effectof a treatment on the mean of a response variable of interest.Even with independent censoring, our methods allow the investigatorto increase efficiency by exploiting the correlation of theoutcome with a vector of time-dependent covariates.     

Generalized varying coefficient models for longitudinal data

We propose a generalization of the varying coefficient modelfor longitudinal data to cases where not only current but alsorecent past values of the predictor process affect current response.More precisely, the targeted regression coefficient functionsof the proposed model have sliding window supports around currenttime t. A variant of a recently proposed two-step estimationmethod for varying coefficient models is proposed for estimationin the context of these generalized varying coefficient models,and is found to lead to improvements, especially for the caseof additive measurement errors in both response and predictors.The proposed methodology for estimation and inference is alsoapplicable for the case of additive measurement error in thecommon versions of varying coefficient models that relate onlycurrent observations of predictor and response processes toeach other. Asymptotic distributions of the proposed estimatorsare derived, and the model is applied to the problem of predictingprotein concentrations in a longitudinal study. Simulation studiesdemonstrate the efficacy of the proposed estimation procedure.     

Late Transplanting and the Yield of Phaseolus vulgaris L.

The prediction that very high seed yields of dry beans (Phaseolusvulgaris L.) would be produced by the delayed transplantingof large plants has been tested in a factorial experiment withfour dates of transplanting and eight plant populations. Therewere significant differences in yield between transplantingdates and between population densities, and there was a significantdate-density interaction. At low plant densities (up to about30 plants m^–2) the three transplanted treatments yieldedless than the hand-sown controls, and late transplanting yieldedless than early. At the highest density the situation was reversed;all three transplanted treatments out-yielded the controls andlate transplanting tended to out-yield plants transplanted early.The biggest yield was 340 g seed m^–2 from a transplantedcrop grown at 35 plants m^–2. The data on yield fitted a modified rectangular hyperbola ofthe form where y is yield per unit area, p is the number of plants perunit area, t is the number of days between sowing and transplanting,and B_o, n, m, and p are arbitrary parameters. This equationaccounted for 91 per cent of the variation in yield with t andp. It is suggested that late transplanting had adverse effects,due to transplanting ‘shock’ and which were mostmarked at low plant densities; and beneficial effects, ascribableto an effect on plant ‘plasticity’, which were mostmarked at high plant densities. Possible physiological mechanismsof these effects are discussed. Phaseolus vulgaris, yield, density, transplanting     

棉铃虫成虫对性信息素的电生理和行为反应研究

通过EAG和风洞实验,研究了棉铃虫雌雄成虫对性信息素组分和诱芯(Z-11-16Ald∶Z-9-16Ald=97∶3)的电生理反应。其中棉铃虫雌、雄蛾对诱芯的平均EAG反应测定值分别为1.06mV和4.32mV,分别高出对照(无性信息素空白诱芯)0.67mV和0.366mV,差异均达到极显著水平(雌蛾：t＝25.020, P≤0.01;雄蛾：t＝44.269,P≤0.01);棉铃虫雌蛾对性信息素组分(Z-11-16-Ald和Z-9.16Ald)的EAG反应值随浓度增加而增加;雄蛾在被剪除触角后与雌蛾不能正常交配,而雌蛾在被剪除触角后仍有40%的交配率,比正常雌雄蛾的交配率(70%)有所下降;在风洞实验中,雄蛾没有顺风远离诱源的飞行行为,趋向诱源的比率为81.8%,与对照有显著差异。研究表明性信息素组分对棉铃虫的交配活动有明显的影响。     

Time to Seed Death as a Function of the Gibbs Free Energy of Water Vapour: Practical and Theoretical Implications

Time (t) to loss of seed viability (e.g. log t or log ) is modelledin the literature as the sum of a moisture term and a quadratictemperature term, f(T,T²). The coefficients inf(T,T²) have beenshown to be ‘identical’ in orthodox seeds. I postulatethat this identity is due to a parameter common to all seedsand, consistent with that hypothesis, report a close correlation(R²=0.9998) between f(T,T²) and the Gibbs free energy of watervapour, G, over the temperature range 0–90 °C. Thehypothesis has the statistical advantage of reducing the numberof independent variables from two to one, without changing thefit. This is demonstrated from analysis of data for lettuceand barley. An explanation for this correlation of time to seeddeath with G is that water vapour is the proximate source ofenergy leading to decomposition of individual molecules, withthe ultimate result of seed death. Copyright 1999 Annals ofBotany Company Seed longevity, temperature effect, Gibbs free energy of water vapour, moisture-temperature interactions, Hordeum vulgare L., barley, Lactuca sativa L., lettuce.     

Local trophodynamics and the interaction of marine mammals and fisheries in the Benguela ecosystem

1. A method for finding the consequences of long-term generalized press perturbations in multispecies ecological communities, with relatively modest requirements for data, is explicated. The approach uses energetic and allometric reasoning to set some parameter values for which data are not available. The remaining unknown parameters are treated as random variables, enabling the calculation of probability distributions for the outcomes that are of interest.
2. The method is used to investigate the effect of a cull of fur seals on fisheries in the Benguela ecosystem, using a 29-species foodweb for that system. In the case of Cape fur seals treated here, it is found that a cull of seals is more likely to be detrimental to total yields from all exploited species than it is to be beneficial.
3. The influence of weak links on the effects of a cull is investigated. Using both consumption by each species and consumption of each species to define link strength, a clear threshold in link strength is found, indicating that 44% of all links could be deleted from the foodweb without affecting the predictions significantly. Even using a criterion based on consumption by each species alone (conventional dietary proportion data), about the same number of links can be deleted without seriously affecting the predictions of the model. This is a very helpful (and encouraging) result for the design of an observational protocol for systematic efforts to gather data for multispecies modelling.     

A New Species of Abietaceous Gone from the Lower Greensand of the Isle of Wight

An account is given of a hitherto undescribed species of Pityostrobusthe specimens of which come from the Lower Greensand of theIsle of Wight and for which the name Pityostrobus jacksoni issuggested. Structurally it has the general characters of thecones of the modern genus Pinus but no immediate affinity toan individual species of that genus is proposed. As a highlycharacteristic feature of the cone the seed-scale complexespossess much inflated apophyses, definite bract scales are alsopresent. The information obtained from sections through variousplanes is embodied in a reconstruction of one seed-scale complextogether with its bract scale.     

Studies on cutin-esterase I. Preparation of cutin and its fatty acid component from tomato fruit peel

Examination was made of the fatty acid component of tomato cutinvia gas-liquid chromatography and thin layer chromatography.Dihydroxyeicosanoic acid was identified as a major componentof tomato cutinic acid in contrast with the results of BAKERand MARTIN (1) who recognized 10,16-dihydroxyhexadecanoic acidas the dominant acid of cutin in all plants tested. On the thinlayer chromatograms we found more than nine kinds of fatty acidsin the cutin hydrolysate which was saponified with ethanol-potashsolution. The gas-liquid chromatogram for trimethylsilyl etherderivatives of methyl cutinate showed somewhat different results,i.e., unsaturated decanoic, t_R 1.4, unsaturated stearic, t_R4.2 and unsaturated octadecanedioic acid, t_R 16.0 as unsaturatedfatty acids. Two more than C₂₂-hydroxyfatty acids were recognizedas minor components. Beside these components, octanoic, t_R 0.9,hydroxydecanoic, t_R 7.0 and cis-epoxy-hydroxyoctadecanoic acid,t_R 18.7 were identified. The biosynthesis of cutin is positednot to be fulfilled or to be delayed due to less lipoxidaseactivity in tomato fruit. ¹Biological Laboratory, Research Department, Nihon Noyaku Co.Ltd., Kawachinagano, Osaka, Japan (Received December 8, 1969; )     

Small Sample Correction for the Variance of GEE Estimators

When clustered multinomial responses are fit using the generalized logistic link, Morel (1989) introduced a small sample correction in the Taylor series based estimator of the covariance matrix of the parameter estimates. The correction reduces the bias of the Type I error rates in small samples and guarantees positive definiteness of the estimated variance‐covariance matrix. It is well known that small sample bias in the use of the Delta method persists in any application of the Generalized Estimating Equations (GEE) methodology. In this article, we extend the correction originally suggested for the generalized logistic link, to other link functions and distributions, when parameters are estimated by GEE. In a Monte Carlo study with correlated data generated under different sampling schemes, the small sample correction has been shown to be effective in reducing the Type I error rates when the number of clusters is relatively small.     

A Canopy Photosynthesis Model for the Dynamics of Size Structure and Self-thinning in Plant Populations

A dynamic model for growth and mortality of individual plantsin a stand was developed, based on the process of canopy photosynthesis,and assuming an allometric relationship between plant heightand weight, i.e. allocation growth pattern of plant height andstem diameter. Functions G(t, x), for the mean growth rate ofindividuals of size x at time t, and M(t,x), for the mortalityrate of individuals of size x at time t, were developed fromthis model and used in simulations. The dynamics of size structurewere simulated, combining the continuity equation model, a simpleversion of the diffusion model, with these functions. Simulationsreproduced several well-documented phenomena: (1) size variabilityin terms of coefficient of variation and skewness of plant weightincreases at first with stand development and then stabilisesor decreases with an onset of intensive self-thinning; (2) duringthe course of self-thinning, there is a power relationship betweendensity and biomass per unit ground area, irrespective of theinitial density and of the allocation-growth pattern in termsof the allometric parameter relating plant height and weight.The following were further shown by simulation: (a) competitionbetween individuals in a crowded stand is never completely one-sidedbut always asymmetrically two-sided, even though competitionis only for light; (b) plants of ‘height-growth’type exhibit a greater asymmetry in competition than plantsof ‘diameter-growth’ type, (c) the effect of competitionon the growth of individuals in a crowded stand converges toa stationary state, even when the stand structure still changesgreatly. All of these theoretical results can explain recentempirical results obtained from several natural plant communities.Finally, a new, general functional form for G(t, x) in a crowdedstand is proposed based on these theoretical results, insteadof a priori or empirical growth and competition functions. Canopy photosynthesis, competition mode, continuity equation, self-thinning, simulation, size distribution     

Adenine nucleotide-creatine-phosphate module in myocardial metabolic system explains fast phase of dynamic regulation of oxidative phosphorylation

Computational models of a large metabolic system can be assembled from modules that represent a biological function emerging from interaction of a small subset of molecules. A "skeleton model" is tested here for a module that regulates the first phase of dynamic adaptation of oxidative phosphorylation (OxPhos) to demand in heart muscle cells. The model contains only diffusion, mitochondrial outer membrane (MOM) permeation, and two isoforms of creatine kinase (CK), in cytosol and mitochondrial intermembrane space (IMS), respectively. The communication with two neighboring modules occurs via stimulation of mitochondrial ATP production by ADP and P_i from the IMS and via time-varying cytosolic ATP hydrolysis during contraction. Assuming normal cytosolic diffusion and high MOM permeability for ADP, the response time of OxPhos (t_mito; generalized time constant) to steps in cardiac pacing rate is predicted to be 2.4 s. In contrast, with low MOM permeability, t_mito is predicted to be 15 s. An optimized MOM permeability of 21 µm/s gives t_mito = 3.7 s, in agreement with experiments on rabbit heart with blocked glycolytic ATP synthesis. The model correctly predicts a lower t_mito if CK activity is reduced by 98%. Among others, the following predictions result from the model analysis: 1) CK activity buffers large ADP oscillations; 2) ATP production is pulsatile in beating heart, although it adapts slowly to demand with "time constant" 14 heartbeats; 3) if the muscle isoform of CK is overexpressed, OxPhos reacts slower to changing workload; and 4) if mitochondrial CK is overexpressed, OxPhos reacts faster. systems biology; computational model; creatine kinase; phosphocreatine shuttle; regulatory module; mitochondrial membrane permeability; oxygen consumption     

Leaf Growth in Cotton (Gossypium hirsutum L.) 2. The Influence of Temperature, Light, Water Stress and Root Restriction on the Growth and Initiation of Leaves

The rate parameters R₁, R₂, I/LI and I/t_0.5, which characterizethe growth in area of successive main-stem leaves, probablyall have the same temperature response. Temperature thereforeonly operates on the time scale. Water stress reduces both therelative growth rate and the advance of developmental age, thelatter however to a lesser extent than the former. The effectof root restriction is explained as resulting from mineral shortage. Gossypium hirsutum L., cotton, leaf growth, leaf initiation, relative growth rate, temperature, light, water stress, root restriction     

Consistency of the Asymptotic Quasi-Likelihood Estimate on Linear Models

Consider a model y_t = f_t(θ) + M_t, 0 ⩽ t ⩽ T where θ∈ Θ in an unknown parameter, f_t(θ) is a linear predictable process, M_t is a martingale difference, and the nature of E(M²_t/ℱ_t—1) is unknown. This paper presents an estimating procedure for θ based on the asymptotic quasi-likelihood methodology. Conditions under which the asymptotic quasi-likelihood estimate converges to the true parameter θ₀ are discussed. This method is applied to several simulated examples, and estimates of the unknown parameter are obtained by means of a two-stage technique. Comparison is made between the estimates obtained via this method and those obtained via the ordinary least squares method. Discussion is provided on the application of the model.