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A method is given for design of experiments to detect associations (linkage disequilibrium) in a random population between a marker and a quantitative trait locus (QTL), or gene, with a given strength of evidence, as defined by the Bayes factor. Using a version of the Bayes factor that can be linked to the value of an F -statistic with an existing deterministic power calculation makes it possible to rapidly evaluate a comprehensive range of scenarios, demonstrating the feasibility, or otherwise, of detecting genes of small effect. The Bayes factor is advocated for use in determining optimal strategies for selecting candidate genes for further testing or applications. The prospects for fine-scale mapping of QTL are reevaluated in this framework. We show that large sample sizes are needed to detect small-effect genes with a respectablesized Bayes factor, and to have good power to detect a QTL allele at low frequency it is necessary to have a marker with similar allele frequency near the gene.T HE advent of dense maps of single-nucleotide polydesign. Then we discuss measures of statistical evidence or criteria for "detecting" associations. We argue that morphisms (SNPs) covering the genome with 300,000 or more markers offers new opportunities to find and there are problems with commonly used P-values as a measure of evidence and advocate the Bayes factor (see, identify genes, by testing for population-level associations e.g., Spiegelhalter and Smith 1982) as a replacement between the SNP and disease or other trait of interest.measure. Further information including relationships Associations occur because of linkage disequilibrium between Bayes factors, posterior probabilities, type I error between the marker and trait. "Linkage disequilibrium rates, P-values, power, and false discovery rates as evi-(LD) mapping" aims to detect and locate genes relative dence for gene effects is given in appendix b. Then, we to a map of existing genetic markers. Location informareview and correct the deterministic power calculation tion is obtained because the distance between the gene from Luo (1998) (with technical details in appendix and a marker on a chromosome is one factor influenca) and the classical approach to power of experiments ing the closeness of association between the gene and and then introduce a generic Bayes factor (Spiegelhalmarker. In a population, recombinations affecting the ter and Smith 1982) for comparing linear models, in association between a gene and marker may occur over the absence of prior information. This is linked to the many generations. This potentially gives a much finer classical power calculation, to give designs with a given resolution than pedigrees used for quantitative trait loci probability to detect an effect with a given Bayes factor. (QTL) mapping. Finer resolution comes at a cost, howResults are presented for sample sizes ranging from ever. More genotyping is needed per individual and as 600 to 4800 and Bayes factors ranging from 1 ⁄20 to 20 and we shall show, larger sample s...

Light has been found to increase the proportion of tracheary elements differentiating in callus cultures derived from xylem-parenchyma of Pinus radiata D. Don grown on an induction medium containing activated charcoal but no phytohormones. The differentiation rate increased from 20% when callus was grown in darkness to 45% when callus was grown with a 16 h or 24 h photoperiod. When callus was grown with a 16 h photoperiod, tracheary elements were observed 2 days after transfer of callus to the induction medium, as compared to 5 days when callus was cultured in darkness. The differentiation rate was also influenced by the concentration of activated charcoal added to the induction medium, the optimum concentration being 5 g l )1 . Exclusion of activated charcoal from the induction medium decreased the differentiation rate to 2%. The activities of the lignin-related enzymes L-phenylalanine ammonia lyase and cinnamyl alcohol dehydrogenase were significantly higher in cell cultures grown with a 16 h photoperiod as compared to when grown in darkness. The results show that light had a stimulating effect on tracheary element differentiation and the activities of lignin-related enzymes in P. radiata callus cultures. The new growth conditions markedly improve this cell culture system and make it particularly useful for functional gene testing and cell-wall analysis of in vitro grown tracheary elements of coniferous gymnosperms.

Sensory research on kiwifruit has shown that specific sugars and acids, and volatile flavor compounds have causative effects on “sweet” and “acid” aroma and flavor attributes. New Zealand consumers (n = 162) assessed the perceived flavor intensity and acceptability of three volatile flavor compounds (ethyl butanoate, E‐2‐hexenal and hexanal) at varying levels in a model base solution. Increasing levels of ethyl butanoate positively affected all the acceptability attributes (“overall liking,”“liking of aroma,”“liking of flavor”) as well as increased the perceived intensity of “kiwifruit aroma” and “kiwifruit flavor.” Increasing levels of E‐2‐hexenal negatively affected all the acceptability attributes but increased the perceived intensity of “kiwifruit aroma” and “acid flavor.” An increase in hexanal increased perceived intensity of “kiwifruit aroma.” Ethyl butanoate and E‐2‐hexenel at the levels tested had the most prominent effects on consumer perceived intensity and acceptability of the “kiwifruit flavor.”

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In this chapter we describe a novel Bayesian approach to designing GWAS studies with the goal of ensuring robust detection of effects of genomic loci associated with trait variation.The goal of GWAS is to detect loci associated with variation in traits of interest. Finding which of 500,000-1,000,000 loci has a practically significant effect is a difficult statistical problem, like finding a needle in a haystack. We address this problem by designing experiments to detect effects with a given Bayes factor, where the Bayes factor is chosen sufficiently large to overcome the low prior odds for genomic associations. Methods are given for various possible data structures including random population samples, case-control designs, transmission disequilibrium tests, sib-based transmission disequilibrium tests, and other family-based designs including designs for plants with clonal replication. We also consider the problem of eliciting prior information from experts, which is necessary to quantify prior odds for loci. We advocate a "subjective" Bayesian approach, where the prior distribution is considered as a mathematical representation of our prior knowledge, while also giving generic formulae that allow conservative computations based on low prior information, e.g., equivalent to the information in a single sample point. Examples using R and the R packages ldDesign are given throughout.

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