Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.     

Sensitivity of Bayes estimators to hyper-parameters with an application to maximum yield from fisheries

Priors are seldom unequivocal and an important component of Bayesian modeling is assessment of the sensitivity of the posterior to the specified prior distribution. This is especially true in fisheries science where the Bayesian approach has been promoted as a rigorous method for including existing information from previous surveys and from related stocks or species. These informative priors may be highly contested by various interest groups. Here, formulae for the first and second derivatives of Bayes estimators with respect to hyper-parameters of the joint prior density are given. The formula for the second derivative provides a correction to a previously published result. The formulae are shown to reduce to very convenient and easily implemented forms when the hyper-parameters are for exponential family marginal priors. For model parameters with such priors it is shown that the ratio of posterior variance to prior variance can be interpreted as the sensitivity of the posterior mean to the prior mean. This methodology is applied to a nonlinear state-space model for the biomass of South Atlantic albacore tuna and sensitivity of the maximum sustainable yield to the prior specification is examined.     

Simplivariate models: ideas and first examples

One of the new expanding areas in functional genomics is metabolomics: measuring the metabolome of an organism. Data being generated in metabolomics studies are very diverse in nature depending on the design underlying the experiment. Traditionally, variation in measurements is conceptually broken down in systematic variation and noise where the latter contains, e.g. technical variation. There is increasing evidence that this distinction does not hold (or is too simple) for metabolomics data. A more useful distinction is in terms of informative and non-informative variation where informative relates to the problem being studied. In most common methods for analyzing metabolomics (or any other high-dimensional x-omics) data this distinction is ignored thereby severely hampering the results of the analysis. This leads to poorly interpretable models and may even obscure the relevant biological information. We developed a framework from first data analysis principles by explicitly formulating the problem of analyzing metabolomics data in terms of informative and non-informative parts. This framework allows for flexible interactions with the biologists involved in formulating prior knowledge of underlying structures. The basic idea is that the informative parts of the complex metabolomics data are approximated by simple components with a biological meaning, e.g. in terms of metabolic pathways or their regulation. Hence, we termed the framework 'simplivariate models' which constitutes a new way of looking at metabolomics data. The framework is given in its full generality and exemplified with two methods, IDR analysis and plaid modeling, that fit into the framework. Using this strategy of 'divide and conquer', we show that meaningful simplivariate models can be obtained using a real-life microbial metabolomics data set. For instance, one of the simple components contained all the measured intermediates of the Krebs cycle of E. coli. Moreover, these simplivariate models were able to uncover regulatory mechanisms present in the phenylalanine biosynthesis route of E. coli.     

A pedagogical walkthrough of computational modeling and simulation of Wnt signaling pathway using static causal models in MATLAB

The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.     

Efficient Markov chain Monte Carlo implementation of Bayesian analysis of additive and dominance genetic variances in noninbred pedigrees

Accurate and fast computation of quantitative genetic variance parameters is of great importance in both natural and breeding populations. For experimental designs with complex relationship structures it can be important to include both additive and dominance variance components in the statistical model. In this study, we introduce a Bayesian Gibbs sampling approach for estimation of additive and dominance genetic variances in the traditional infinitesimal model. The method can handle general pedigrees without inbreeding. To optimize between computational time and good mixing of the Markov chain Monte Carlo (MCMC) chains, we used a hybrid Gibbs sampler that combines a single site and a blocked Gibbs sampler. The speed of the hybrid sampler and the mixing of the single-site sampler were further improved by the use of pretransformed variables. Two traits (height and trunk diameter) from a previously published diallel progeny test of Scots pine (Pinus sylvestris L.) and two large simulated data sets with different levels of dominance variance were analyzed. We also performed Bayesian model comparison on the basis of the posterior predictive loss approach. Results showed that models with both additive and dominance components had the best fit for both height and diameter and for the simulated data with high dominance. For the simulated data with low dominance, we needed an informative prior to avoid the dominance variance component becoming overestimated. The narrow-sense heritability estimates in the Scots pine data were lower compared to the earlier results, which is not surprising because the level of dominance variance was rather high, especially for diameter. In general, the hybrid sampler was considerably faster than the blocked sampler and displayed better mixing properties than the single-site sampler.     

Studies on some genetic parameters of rice (Oryza sativa L.)

Summary In order to utilize the available useful variation in breeding rice to improve yield and quality of grain, the performance of a wide range of rice germ plasm comprising 30 varieties was evaluated in northern India, a major rice growing belt. Plant performance revealed high genetic divergence and phenotypic variability in the crop, with the maximum range of variation being for grain number per panicle and the minimum for grain dimensions. There were also significant differences among varietal means for ten phenotypic traits. Genotypic and phenotypic variance contributed profoundly to the variance of the phenotypic traits studied, but, since genetic variability in the traits related to yield was considerable, there is scope for further improvement in yielding ability. Grain number per panicle, number of effective tillers per plant and culm length exhibit high heritability, and genotypic coefficient of variation and therefore a high genetic advance. Thus, selection for these traits would be effective in crop improvement. Moreover, grain number per panicle shows a significant positive correlation with yield, and this trait could profitably form a reliable index for the yielding capacity of this crop.     

Trait diversity, heritability and genetic advance in selected germplasm lines of tef

The genetic improvement of the Ethiopian cereal, tef, Eragrostis tef (Zucc.) Trotter, depends upon the variability in the indigenous germplasm. A bi-replicated randomized complete block field experiment was, therefore, carried out at Debre Zeit and Alem Tena in Ethiopia during the 1996 main season to study the pheno-morphic and agronomic trait diversity in 320 tef germplasm lines. All of the 17 traits assessed showed substantial (p < or = 0.001) variation among the lines. Genotypes and locations interacted significantly (p < or = 0.05) on 11 of the traits. At about 50% similarity level, the tef lines grouped into six major clusters of nine to 243 lines. Five principal components (PCs) extracted about 71% of the entire variation of the lines. About 28% of the total variance explained by the first PC was due chiefly to variation in main shoot culm length, diameters of the two basal culm internodes, panicle length and grain yield/panicle. About 16% of the whole variance explained by the second PC originated mainly from variation in the length of the first and second basal culm internodes, grain yield/plant, and peduncle length. The third PC accounting for about 12% of the entire variance resulted largely from variation in harvest index and shoot phytomass yield/plant. Across traits, the phenotypic and genotypic coefficients of variation varied in that order from about 2% for grain yield/panicle to 58% for number of fertile tillers/plant, and from less than 1% for diameters of the two basal culm internodes and grain yield/panicle to 35% for panicle length. Estimates of broad sense heritability and genetic advance (as ratio of the mean) were highest for panicle length (71%) and number of fertile tillers/plant (21%), respectively. But both of these were lowest for the second basal culm internode diameter (< 1%). Overall, the study confirmed that tef is a highly versatile crop with broad trait diversity in the germplasm, and this offers ample opportunities for improvement through breeding.     

Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses

Throughout the last two decades, Bayesian statistical methods have proliferated throughout ecology and evolution. Numerous previous references established both philosophical and computational guidelines for implementing Bayesian methods. However, protocols for incorporating prior information, the defining characteristic of Bayesian philosophy, are nearly nonexistent in the ecological literature. Here, I hope to encourage the use of weakly informative priors in ecology and evolution by providing a ‘consumer's guide’ to weakly informative priors. The first section outlines three reasons why ecologists should abandon noninformative priors: 1) common flat priors are not always noninformative, 2) noninformative priors provide the same result as simpler frequentist methods, and 3) noninformative priors suffer from the same high type I and type M error rates as frequentist methods. The second section provides a guide for implementing informative priors, wherein I detail convenient ‘reference’ prior distributions for common statistical models (i.e. regression, ANOVA, hierarchical models). I then use simulations to visually demonstrate how informative priors influence posterior parameter estimates. With the guidelines provided here, I hope to encourage the use of weakly informative priors for Bayesian analyses in ecology. Ecologists can and should debate the appropriate form of prior information, but should consider weakly informative priors as the new ‘default’ prior for any Bayesian model.     

Genomic prediction of cotton fibre quality and yield traits using Bayesian regression methods

Genomic selection or genomic prediction (GP) has increasingly become an important molecular breeding technology for crop improvement. GP aims to utilise genome-wide marker data to predict genomic breeding value for traits of economic importance. Though GP studies have been widely conducted in various crop species such as wheat and maize, its application in cotton, an essential renewable textile fibre crop, is still significantly underdeveloped. We aim to develop a new GP-based breeding system that can improve the efficiency of our cotton breeding program. This article presents a GP study on cotton fibre quality and yield traits using 1385 breeding lines from the Commonwealth Scientific and Industrial Research Organisation (CSIRO, Australia) cotton breeding program which were genotyped using a high-density SNP chip that generated 12,296 informative SNPs. The aim of this study was twofold: (1) to identify the models and data sources (i.e. genomic and pedigree) that produce the highest prediction accuracies; and (2) to assess the effectiveness of GP as a selection tool in the CSIRO cotton breeding program. The prediction analyses were conducted under various scenarios using different Bayesian predictive models. Results highlighted that the model combining genomic and pedigree information resulted in the best cross validated prediction accuracies: 0.76 for fibre length, 0.65 for fibre strength, and 0.64 for lint yield. Overall, this work represents the largest scale genomic selection studies based on cotton breeding trial data. Prediction accuracies reported in our study indicate the potential of GP as a breeding tool for cotton. The study highlighted the importance of incorporating pedigree and environmental factors in GP models to optimise the prediction performance.Subject terms: Plant breeding, Genome     

Analysis of the benefits to wheat yield from assimilates stored prior to grain filling in a range of environments*

Grain yields of rainfed agriculture in Australia are often low and vary substantially from season to season. Assimilates stored prior to grain filling have been identified as important contributors to grain yield in such environments, but quantifying their benefit has been hampered by inadequate methods and large seasonal variability. APSIM-Nwheat is a crop system simulation model, consisting of modules that incorporate aspects of soil water, nitrogen (N), crop residues, crop growth and development. Model outputs were compared with detailed measurements of N fertilizer experiments on loamy soils at three locations in southern New South Wales, Australia. The field measurements allowed the routine for remobilization of assimilates stored prior to grain filling in the model to be tested for the first time and simulations showed close agreement with observed data. Analysing system components indicated that with increasing yield, both the observed and simulated absolute amount of remobilization generally increased while the relative contribution to grain yield decreased. The simulated relative contribution of assimilates stored prior to grain filling to grain yield also decreased with increasing availability of water after anthesis. The model, linked to long-term historical weather records was used to analyse yield benefits from assimilates stored prior to grain filling under rainfed conditions at a range of locations in the main wheat growing areas of Australia. Simulation results highlighted that in each of these locations assimilates stored prior to grain filling often contributed a significant proportion to grain yield. The simulated contribution of assimilates stored prior to grain filling to grain yield can amount to several tonnes per hectare, however, it varied substantially from 5–90% of grain yield depending on seasonal rainfall amount and distribution, N supply, crop growth and seasonal water use. High N application often reduced the proportion of water available after anthesis and decreased the relative contribution of remobilization to grain yield as long as grain yields increased, particularly on soils with greater water-holding capacity. Increasing the capacity or potential to accumulate pre-grain filling assimilates for later remobilization by 20% increased yields by a maximum of 12% in moderate seasons with terminal droughts, but had little effect in poor or very good seasons in which factors that affect the amount of carbohydrates stored rather than the storage capacity itself appeared to limit grain yield. These factors were, little growth due to water or N deficit in the weeks prior to and shortly after anthesis (when most of the assimilates accumulate for later remobilization), poor sink demand of grains due to low grain number as a result of little pre-anthesis growth or high photosynthetic rate during grain filling. Increasing the potential storage capacity for remobilization is expected to increase grain yield especially under conditions of terminal drought.     

Additive genetic variance and covariance between relatives in synthetic wheat crosses with variable parental ploidy levels

Cultivated bread wheat (Triticum aestivum L.) is an allohexaploid species resulting from the natural hybridization and chromosome doubling of allotetraploid durum wheat (T. turgidum) and a diploid goatgrass Aegilops tauschii Coss (Ae. tauschii). Synthetic hexaploid wheat (SHW) was developed through the interspecific hybridization of Ae. tauschii and T. turgidum, and then crossed to T. aestivum to produce synthetic hexaploid wheat derivatives (SHWDs). Owing to this founding variability, one may infer that the genetic variances of native wild populations vs improved wheat may vary due to their differential origin and evolutionary history. In this study, we partitioned the additive variance of SHW and SHWD with respect to their breed origin by fitting a hierarchical Bayesian model with heterogeneous covariance structure for breeding values to estimate variance components for each breed category, and segregation variance. Two data sets were used to test the proposed hierarchical Bayesian model, one from a multi-year multi-location field trial of SHWD and the other comprising the two species of SHW. For the SHWD, the Bayesian estimates of additive variances of grain yield from each breed category were similar for T. turgidum and Ae. tauschii, but smaller for T. aestivum. Segregation variances between Ae. tauschii—T. aestivum and T. turgidum—T. aestivum populations explained a sizable proportion of the phenotypic variance. Bayesian additive variance components and the Best Linear Unbiased Predictors (BLUPs) estimated by two well-known software programs were similar for multi-breed origin and for the sum of the breeding values by origin for both data sets. Our results support the suitability of models with heterogeneous additive genetic variances to predict breeding values in wheat crosses with variable ploidy levels.     

Dissecting Maize Productivity: Ideotypes Associated with Grain Yield under Drought Stress and Well-watered Conditions

To increase maize (Zea mays L.) yields in drought‐prone environments and offset predicted maize yield losses under future climates, the development of improved breeding pipelines using a multi‐disciplinary approach is essential. Elucidating key growth processes will provide opportunities to improve drought breeding progress through the identification of key phenotypic traits, ideotypes, and donors. In this study, we tested a large set of tropical and subtropical maize inbreds and single cross hybrids under reproductive stage drought stress and well‐watered conditions. Patterns of biomass production, senescence, and plant water status were measured throughout the crop cycle. Under drought stress, early biomass production prior to anthesis was important for inbred yield, while delayed senescence was important for hybrid yield. Under well‐watered conditions, the ability to maintain a high biomass throughout the growing cycle was crucial for inbred yield, while a stay‐green pattern was important for hybrid yield. While new quantitative phenotyping tools such as spectral reflectance (Normalized Difference Vegetation Index, NDVI) allowed for the characterization of growth and senescence patterns as well as yield, qualitative measurements of canopy senescence were also found to be associated with grain yield.     

Association mapping in an elite maize breeding population

Association mapping (AM) is a powerful approach to dissect the genetic architecture of quantitative traits. The main goal of our study was to empirically compare several statistical methods of AM using data of an elite maize breeding program with respect to QTL detection power and possibility to correct for population stratification. These models were based on the inclusion of cofactors (Model A), cofactors and population effect (Model B), and SNP effects nested within populations (Model C). A total of 930 testcross progenies of an elite maize breeding population were field-evaluated for grain yield and grain moisture in multi-location trials and fingerprinted with 425 SNP markers. For grain yield, population stratification was effectively controlled by Model A. For grain moisture with a high ratio of variance among versus within populations, Model B should be applied in order to avoid potential false positives. Model C revealed large differences among allele substitution effects for trait-associated SNPs across multiple plant breeding populations. This heterogeneous SNP allele substitution effects have a severe impact for genomic selection studies, where SNP effects are often assumed to be independent of the genetic background.     

Effects of age,lactation, and repeated cycles on rhesus monkey copulatory intervals

Young, sexually mature female rhesus monkeys copulate on more days prior to conception than do older females, and this prolonged discrete mating period is associated with an earlier rise in serum estradiol prior to the first ovulation of the breeding season. The influence of repeated ovulatory cycles and the presence of a suckling infant on the copulatory patterns were examined in two separate analyses. Extending previous work, young, nulliparous females copulated on more days at the first ovulation of the breeding season than did older, multiparous females. However, the duration of the copulatory period at the second ovulation of the breeding season was similar and significantly shorter for both age groups. Furthermore, the presence of a suckling infant did not influence the duration of the mating periods in adult, multiparous females. The onset of copulatory behavior for all females was associated with serum estradiol concentrations of approximately 90 pg/ml, indicating that the age and cycle differences in the duration of the copulatory periods are due to the time course of serum estradiol prior to ovulation. A separate, longitudinal analysis of the duration of the mating period associated with the first ovulation of three successive breeding seasons indicated that females copulated on more days during their first ovulatory cycle of their first breeding season. These data indicate that the copulatory interval is longer for females during the first ovulation of the breeding season, and this pattern is accentuated in young, sexually mature animals.     

Detection of two major grain yield QTL in bread wheat (Triticum aestivum L.) under heat, drought and high yield potential environments

A large proportion of the worlds’ wheat growing regions suffers water and/or heat stress at some stage during the crop growth cycle. With few exceptions, there has been no utilisation of managed environments to screen mapping populations under repeatable abiotic stress conditions, such as the facilities developed by the International Wheat and Maize Improvement Centre (CIMMYT). Through careful management of irrigation and sowing date over three consecutive seasons, repeatable heat, drought and high yield potential conditions were imposed on the RAC875/Kukri doubled haploid population to identify genetic loci for grain yield, yield components and key morpho-physiological traits under these conditions. Two of the detected quantitative trait loci (QTL) were located on chromosome 3B and had a large effect on canopy temperature and grain yield, accounting for up to 22?% of the variance for these traits. The locus on chromosome arm 3BL was detected under all three treatments but had its largest effect under the heat stress conditions, with the RAC875 allele increasing grain yield by 131?kg?ha^?1 (or phenotypically, 7?% of treatment average). Only two of the eight yield QTL detected in the current study (including linkage groups 3A, 3D, 4D 5B and 7A) were previously detected in the RAC875/Kukri doubled haploid population; and there were also different yield components driving grain yield. A number of discussion points are raised to understand differences between the Mexican and southern Australian production environments and explain the lack of correlation between the datasets. The two key QTL detected on chromosome 3B in the present study are candidates for further genetic dissection and development of molecular markers.     

Increasing reproducibility,robustness, and generalizability of biomarker selection from meta-analysis using Bayesian methodology

A major limitation of gene expression biomarker studies is that they are not reproducible as they simply do not generalize to larger, real-world, heterogeneous populations. Frequentist multi-cohort gene expression meta-analysis has been frequently used as a solution to this problem to identify biomarkers that are truly differentially expressed. However, the frequentist meta-analysis framework has its limitations–it needs at least 4–5 datasets with hundreds of samples, is prone to confounding from outliers and relies on multiple-hypothesis corrected p-values. To address these shortcomings, we have created a Bayesian meta-analysis framework for the analysis of gene expression data. Using real-world data from three different diseases, we show that the Bayesian method is more robust to outliers, creates more informative estimates of between-study heterogeneity, reduces the number of false positive and false negative biomarkers and selects more generalizable biomarkers with less data. We have compared the Bayesian framework to a previously published frequentist framework and have developed a publicly available R package for use.     

Fundamental differences between the methods of maximum likelihood and maximum posterior probability in phylogenetics

Using a four-taxon example under a simple model of evolution, we show that the methods of maximum likelihood and maximum posterior probability (which is a Bayesian method of inference) may not arrive at the same optimal tree topology. Some patterns that are separately uninformative under the maximum likelihood method are separately informative under the Bayesian method. We also show that this difference has impact on the bootstrap frequencies and the posterior probabilities of topologies, which therefore are not necessarily approximately equal. Efron et al. (Proc. Natl. Acad. Sci. USA 93:13429-13434, 1996) stated that bootstrap frequencies can, under certain circumstances, be interpreted as posterior probabilities. This is true only if one includes a non-informative prior distribution of the possible data patterns, and most often the prior distributions are instead specified in terms of topology and branch lengths. [Bayesian inference; maximum likelihood method; Phylogeny; support.].     

Identification and validation of QTL for grain yield and plant water status under contrasting water treatments in fall-sown spring wheats

Key message

Chromosome regions affecting grain yield, grain yield components and plant water status were identified and validated in fall-sown spring wheats grown under full and limited irrigation.

Abstract

Increases in wheat production are required to feed a growing human population. To understand the genetic basis of grain yield in fall-sown spring wheats, we performed a genome-wide association study (GWAS) including 262 photoperiod-insensitive spring wheat accessions grown under full and limited irrigation treatments. Analysis of molecular variance showed that 4.1% of the total variation in the panel was partitioned among accessions originally developed under fall-sowing or spring-sowing conditions, 11.7% among breeding programs within sowing times and 84.2% among accessions within breeding programs. We first identified QTL for grain yield, yield components and plant water status that were significant in at least three environments in the GWAS, and then selected those that were also significant in at least two environments in a panel of eight biparental mapping populations. We identified and validated 14 QTL for grain yield, 15 for number of spikelets per spike, one for kernel number per spike, 11 for kernel weight and 9 for water status, which were not associated with differences in plant height or heading date. We detected significant correlations among traits and colocated QTL that were consistent with those correlations. Among those, grain yield and plant water status were negatively correlated in all environments, and six QTL for these traits were colocated or tightly linked (<?1 cM). QTL identified and validated in this study provide useful information for the improvement of fall-sown spring wheats under full and limited irrigation.