On Use of Logarithms to Accommodate Scale

Both lipoprotein-associated phospholipase A(2) (Lp-PLA(2)) activity, a biomarker of inflammation, and concentration of its primary associated lipoprotein, LDL, are correlated with adverse coronary outcomes. We previously reported a quantitative trait locus (QTL) corresponding to HSA2p24.3-p23.2 with pleiotropic effects on Lp-PLA(2) activity and LDL-cholesterol (LDL-C) concentration in baboons fed a basal diet. Here, our goal was to locate pleiotropic QTLs influencing both traits in the same baboons fed a high-cholesterol, high-fat (HCHF) diet, and to assess whether shared genetic effects on these traits differ between diets. We assayed Lp-PLA(2) activity and LDL-C concentration in 683 baboons fed the HCHF diet. We used a bivariate maximum likelihood-based variance components approach in whole-genome linkage screens to locate a QTL [logarithm of odds (LOD) = 3.13, genome-wide P = 0.019] corresponding to HSA19q12-q13.2 with pleiotropic effects on Lp-PLA(2) activity and LDL-C levels in the HCHF diet. We additionally found significant evidence of genetic variance in response to diet for Lp-PLA(2) activity (P = 0.0017) and for LDL-C concentration (P = 0.00001), revealing a contribution of genotype-by-diet interaction to covariation in these two traits. We conclude that the pleiotropic QTLs detected at 2p24.3-p23.2 and 19q12-q13.2 on the basal and HCHF diets, respectively, exert diet-specific effects on covariation in Lp-PLA(2) activity and LDL-C concentration.

The aim of the present study was to assess the effect of sex and to estimate genetic parameters for several traits related to plasma oxidative status in slaughter pigs, i.e., ferric reducing ability of plasma (FRAP), concentrations of α-tocopherol and malondialdehyde (MDA), and glutathione peroxidase (GPx) activity. Blood samples were collected at slaughter from 477 Piétrain × (Landrace × Large White intercross) pigs of 2 performance test stations. Heritabilities (±SE) of plasma oxidative status traits as well as their phenotypic and additive genetic correlations with animal performance traits were estimated with multiple-trait REML animal models using VCE software. Results displayed no significant difference between barrows and gilts for FRAP and α-tocopherol in plasma. However, gilts had a significantly higher concentration of MDA and lower GPx activity compared with barrows. Heritability estimates were high for GPx (0.55 ± 0.05), and medium to low for α-tocopherol (0.30 ± 0.06), FRAP (0.22 ± 0.05), and MDA (0.15 ± 0.04). Estimated additive genetic and phenotypic correlations between these four traits were generally low, except for a negative additive genetic correlation between FRAP and GPx of -0.45 (±0.23). Additive genetic correlations between plasma oxidative status traits and animal performance traits were also generally absent or low with maximum values of ~0.3. Parameter estimates in this study have to be interpreted with caution because of the small size of the dataset. Nevertheless, it may be concluded that there is considerable additive genetic variance for plasma oxidative status traits in slaughter pigs. More research is warranted on the genetic determination of oxidative stress in farm animals and its relevance in breeding programs.

Linkage disequilibrium in two‐stage marker‐assisted selection

In my article (Feingold, 1992a), I examined sex differences in variability of performance on cognitive tests by calculating the ratios of males' variances to females' variances. Thus, variance ratios (VRs) of 1.00 indicated homogeneity of variance, VRs greater than 1.00 indicated greater male variability, and VRs less than 1.00 indicated greater female variability. However, because each test was normed separately by grade and year, multiple male-female comparisons were conducted, yielding a set of VRs for each test. Thus, the VRs needed to be summarized to determine whether there was an overall sex difference in variability on each test. The median of a sample of VRs must be an unbiased estimate of the population VR when the null hypothesis is true (i.e., when there is homogeneity of variance in the population and when all variation among VRs in a sample drawn from that population is attributable to sampling error), because one group will-by chance-be more variable half of the time and the second group will be more variable the other half of the time. Thus, the expected value of a median VR, as of a single VR, is 1.00. However, VRs follow the Fdistribution (indeed, Fratios are variance ratios), which is positively skewed (Snedecor & Cochran, 1967). Therefore, when the null hypothesis is true, the mean (i.e., the arithmetic mean) VR is greater than the unbiased median VR, making the mean an inappropriate measure of central tendency for VRs. (The direction of the bias favors the group-males in my work-that is arbitrarily selected as the numerator of the VR.) A positively skewed distribution of scores (e.g., VRs) can be normalized via an appropriate transformation, such as a log transformation, that spreads out differences among values at the left tail of the distribution (Tukey, 1977). Thus, it is not wrong to calculate the mean of log-transformed VRs. However, because the mean and the median of a normal distribution of scores are the same, the mean logtransformed VR and the median log-transformed VR are comparable. Thus, both measures of central tendency yield essentially the same unbiased average in a sample of log-transformed VRs. Most important, a log transformation is a monotonic transformation-that is, a transformation that does not change the rank order of scores. Therefore, the median (which is a function of rank order) of a sample of logtransformed VRs equals the log-transformed median VR of the same sample. Thus, it is pointless to use a log transformation when VRs are summarized by medians because the outcome is identical whether or not the transformation is used (when the medians are expressed in a common metric). Moreover, because the mean and median are the same when the distribution is normal (and about the same when the distribution is nearly normal), the median log-transformed VR, the mean logtransformed VR, and the median VR are all about the same (when expressed in the same metric). Thus, there are no advantages in using the mean log-transformed VR instead of the median VR when the sole objective is to summarize VRs. Yet, there is one major disadvantage in using the mean log-transformed VR. The magnitude of

Studies on quantitative genetics of foliar resistance to black pod disease in cacao could inadvertently use cocoa swollen shoot virus (CSSV) infected leaves which could bias the results especially in West Africa where the virus is prevalent. However, effects of CSSV on inheritance and heritability of foliar resistance to Phytophthora species is not known. Choice of an efficient breeding method requires an accurate estimation of genetic effects in selection schemes for foliar resistance to Phytophthora species in cacao. The objective of this study was to investigate the effect of CSSV infection on quantitative genetic parameters of foliar resistance to cocoa black pod disease in a population of 36 F1 hybrids developed by mating six cacao genotypes using a diallel method. The generated F1s and their parents were evaluated for foliar resistance to P. palmivora and P. megakarya using a randomized complete block design (RCBD) with three replications. 1A CSSV and Nsaba CSSV strains were used to infect the cacao genotypes using the patch graft method. The parents chosen showed significant variations for scores of leaf discs after inoculation with P. palmivora and P. megakarya. The leaf disc scores of CSSV infected crosses were lower than leaf disc scores of CSSV-free crosses. Genetic component analysis showed that the effects of GCA and SCA was significant for both CSSV-free and CSSV-infected crosses in resistance to P. palmivora and P. megakarya. The significant GCA and SCA for both CSSV-free and CSSV-infected crosses strongly suggest that both additive and non-additive genetic effects play an important role in the determination of inheritance of foliar resistance to Phytophthora species in cacao. There was significant variability in mean squares of GCA and SCA of CSSV-free and CSSV-infected crosses indicating that CSSV infection modifies GCA and SCA of affected plants. Narrow sense heritability was relatively low (0.31) for foliar resistance to P. palmivora and P. megakarya under CSSV-free and 1A CSSV strain infected conditions. However, heritability for foliar resistance to P. palmivora (0.43) and P. megakarya (0.36) was significantly higher under Nsaba CSSV infected condition. The modifications of mean squares of GCA and SCA and narrow sense heritability due to CSSV infection could mislead in choice of breeding methods indicating that attention must be paid to the infection status of plants when conducting quantitative genetics studies using diseased and healthy plants. CSSV status of leaf samples should be known before using them in leaf disc test. Genotypes Pa7/808 and Pound 7 had high negative GCA effects and are promising parents for enhancement of resistance to black pod disease in cacao.

BackgroundPlant height is an important selection target since it is associated with yield potential, stability and particularly with lodging resistance in various environments. Rapid and cost-effective estimation of plant height from airborne devices using a digital surface model can be integrated with academic research and practical wheat breeding programs. A bi-parental wheat population consisting of 198 doubled haploid lines was used for time-series assessments of progress in reaching final plant height and its accuracy was assessed by quantitative genomic analysis. UAV-based data were collected at the booting and mid-grain fill stages from two experimental sites and compared with conventional measurements to identify quantitative trait loci (QTL) underlying plant height.ResultsA significantly high correlation of R2 = 0.96 with a 5.75 cm root mean square error was obtained between UAV-based plant height estimates and ground truth observations at mid-grain fill across both sites. Correlations for UAV and ground-based plant height data were also very high (R2 = 0.84–0.85, and 0.80–0.83) between plant height at the booting and mid-grain fill stages, respectively. Broad sense heritabilities were 0.92 at booting and 0.90–0.91 at mid-grain fill across sites for both data sets. Two major QTL corresponding to Rht-B1 on chromosome 4B and Rht-D1 on chromosome 4D explained 61.3% and 64.5% of the total phenotypic variations for UAV and ground truth data, respectively. Two new and stable QTL on chromosome 6D seemingly associated with accelerated plant growth was identified at the booting stage using UAV-based data. Genomic prediction accuracy for UAV and ground-based data sets was significantly high, ranging from r = 0.47–0.55 using genome-wide and QTL markers for plant height. However, prediction accuracy declined to r = 0.20–0.31 after excluding markers linked to plant height QTL.ConclusionThis study provides a fast way to obtain time-series estimates of plant height in understanding growth dynamics in bread wheat. UAV-enabled phenotyping is an effective, high-throughput and cost-effective approach to understand the genetic basis of plant height in genetic studies and practical breeding.

The estimation of the contribution of an individual quantitative trait locus (QTL) to the variance of a quantitative trait is considered in the framework of an analysis of variance (ANOVA). ANOVA mean squares expectations which are appropriate to the specific case of QTL mapping experiments are derived. These expectations allow the specificities associated with the limited number of genotypes at a given locus to be taken into account. Discrepancies with classical expectations are particularly important for two-class experiments (backcross, recombinant inbred lines, doubled haploid populations) and F2 populations. The result allows us firstly to reconsider the power of experiments (i.e. the probability of detecting a QTL with a given contribution to the variance of the trait). It illustrates that the use of classical formulae for mean squares expectations leads to a strong underestimation of the power of the experiments. Secondly, from the observed mean squares it is possible to estimate directly the variance associated with a locus and the fraction of the total variance associated to this locus (r l (2) ). When compared to other methods, the values estimated using this method are unbiased. Considering unbiased estimators increases in importance when (1) the experimental size is limited; (2) the number of genotypes at the locus of interest is large; and (3) the fraction of the variation associated with this locus is small. Finally, specific mean squares expectations allows us to propose a simple analytical method by which to estimate the confidence interval of r l (2) . This point is particularly important since results indicate that 95% confidence intervals for r l (2) can be rather wide:2-23% for a 10% estimate and 8-34% for a 20% estimate if 100 individuals are considered.

Three populations of navy bean (Phaseolus vulgaris L.), consisting of recombinant inbred lines, were grown at two locations for 2 years and were used to study canning quality. The traits measured included visual appeal (VIS), texture (TXT), and washed drained mass (WDM). Genotype mean squares were significant for all three traits across populations, although location and year mean squares were higher. We found a positive correlation (r = 0.19 to 0.66) between VIS and TXT and a negative correlation (r = -0.26 to -0.66) between VIS and WDM and between TXT and WDM (r = -0.53 to -0.83) in all three populations. Heritability estimates were calculated for VIS, TXT, and WDM, and these values were moderate to high (0.48 to 0.78). Random amplified polymorphic DNA markers associated with quantitative trait loci (QTL) for the same canning quality traits were identified and studied in each population. Marker-QTL associations were established using the general linear models procedure with significance set at P=0.05. Location and population specificity was common among the marker-QTL associations identified. Coefficient of determination (R2) values for groups of markers used in multiple regression analyses ranged from 0.2 to 0.52 for VIS, 0.11 to 0.38 for TXT, and 0.25 to 0.38 for WDM. Markers were identified that were associated with multiple traits and those associations supported correlations between phenotypic traits. MAS would offer no advantage over phenotypic selection for the improvement of negatively associated traits.

BackgroundThis study aimed to present normative reference values of heart rate variability and salivary alpha-amylase in a healthy young male population with a particular focus on their distribution and reproducibility.MethodsThe short-term heart rate variability of 417 young healthy Japanese men was studied. Furthermore, salivary alpha-amylase was measured in 430 men. The average age of the subjects were 21.9 years with standard deviation of 1.6 years. Interindividual variations in heart rate variability indices and salivary alpha-amylase levels were plotted as histograms. Data are presented as the mean, median, standard deviation, coefficient of variation, skewness, kurtosis, and fifth and 95th percentiles of each physiological index.ResultsMean recorded values were heart period 945.85 ms, log-transformed high frequency component 9.84 ln-ms2, log-transformed low frequency component 10.42 ln-ms2, log-transformed low frequency to high frequency ratio 0.58 ln-ratio, standard deviation of beat-to-beat interval 27.17 ms and root mean square of successive difference 37.49 ms. The mean value of raw salivary alpha-amylase was 17.48 U/mL, square root salivary alpha-amylase 3.96 sqrt[U/mL] and log-transformed salivary alpha-amylase 2.65 ln[U/mL]. Log-transformed heart rate variability indices exhibited almost symmetrical distributions; however, time-domain indices of heart rate variability (standard deviation of beat-to-beat interval and root mean square of successive difference) exhibited right-skewed (positive skewness) distributions. A considerable right-skewed distribution was observed for raw salivary alpha-amylase. Logarithmic transformation improved the distribution of salivary alpha-amylase, although square root transformation was insufficient. The day-to-day reproducibility of these indices was assessed using intraclass correlation coefficients. Intraclass correlation coefficients of most heart rate variability and salivary indices were approximately 0.5 to 0.6. Intraclass correlation coefficients of raw salivary markers were approximately 0.6, which was similar to those of heart rate variability; however, log transformation of the salivary markers did not considerably improve their reproducibility. Correlations between sympathetic indicators of heart rate variability and salivary alpha-amylase were not observed.ConclusionBecause the sample population examined in this study involved limited age and gender variations, the present results were independent of these factors and were indicative of pure interindividual variation.

This research was carried out to evaluate the performance of eight Egyptian cotton genotypes and their F1 hybrids under Upper Egypt heat conditions using Line x Tester analysis, during 2016 and 2017 seasons. In addition, to determine the combining ability, heterosis and gene action which control yielding ability and fiber traits. Eight Egyptian cotton genotypes and 15 crosses were evaluated at Shandaweel Agricultural Research Station, Sohag governorate. Analysis of variance indicated that genotypes, parents, crosses and parents vs. crosses were significant or highly significant for all the studied traits, except lint percentage in parents and parents vs. crosses, which were insignificant. The mean squares due to lines or tester (G.C.A.) were significant or highly significant for most of the studied traits. Line x Tester (S.C.A.) main squares was highly significant for most yield traits, while insignificant Line x Tester (S.C.A.) mean squares were found for all fiber quality traits. Regarding mean performance and heterosis, the varieties Giza 90, Giza 95 and Giza 86 were the best parents in yielding ability and gave high yielding crosses under heat conditions, while Giza 45 and Giza 92 were the good parents to produce the best fiber quality crosses. The results of heterosis also showed that seven crosses had positive and highly significant heterosis based on mid-parents in seed and lint cotton yield /plant and number of bolls/plant i.e., (Giza 80 x Giza 90), (Giza 86 x Giza 90), (Giza 86 x Giza 95), (Giza 87 x Giza 90), (Giza 45 x (Giza 90 x Australian)), and (Giza 92 x Giza 90), while the cross (Giza 92 x Giza 95) had better yield and fiber traits. The line Giza 86 was the best combiner for seed and lint cotton yield/plant, number of bolls/plant and seed index, while lines Giza 45 and Giza 92 were the best combiners for fiber fineness, fiber strength and fiber length. The tester Giza 90 was the best combiner for seed cotton yield/plant and lint cotton yield/plant. Four crosses exhibited positive and significant values of specific combining ability (S.C.A.) effects for seed cotton yield/plant, lint cotton yield/plant, lint percentage and number of bolls/plant. The non-additive of genetic variance was larger than additive genetic variance in all yielding ability traits and additive genetic variance was higher than dominance variance for all fiber quality traits. Broad sense heritability (Hb%) was higher than narrow sense heritability (Hn%) for all traits and high heritability estimates in narrow sense were found for all fiber traits.

This paper presents a comparison of three methods of parameter estimation in analysis of linkage between a quantitative trait locus (QTL) and a marker locus: maximum likelihood, mean square for trait cumulative distribution function, and method of moments, employing simulated backcross data. The sensitivity of estimates to violation of assumptions of normality and equal variances were also studied. Some measures of discrepancy between the trait distributions in the QTL groups are considered to evaluate the potential dependence of the resolution capacity of the QTL substitution effect with respect to trait mean value and variance.

Analysis of variance can be used to detect the linkage of segregating quantitative trait loci (QTLs) to molecular markers in outbred populations. Using independent full-sib families and assuming linkage equilibrium, equations to predict the power of detection of a QTL are described. These equations are based on an hierarchical analysis of variance assuming either a completely random model or a mixed model, in which the QTL effect is fixed. A simple prediction of power from the mean squares is used that assumes a random model so that in the mixed-model situation this is an approximation. Simulation is used to illustrate the failure of the random model to predict mean squares and, hence, the power. The mixed model is shown to provide accurate prediction of the mean squares and, using the approximation, of power.

BackgroundRequirements for successful implementation of multivariate animal threshold models including phenotypic and genotypic information are not known yet. Here simulated horse data were used to investigate the properties of multivariate estimators of genetic parameters for categorical, continuous and molecular genetic data in the context of important radiological health traits using mixed linear-threshold animal models via Gibbs sampling. The simulated pedigree comprised 7 generations and 40000 animals per generation. Additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits were simulated, resembling situations encountered in the Warmblood horse. Quantitative trait locus (QTL) effects and genetic marker information were simulated for one of the liabilities. Different scenarios with respect to recombination rate between genetic markers and QTL and polymorphism information content of genetic markers were studied. For each scenario ten replicates were sampled from the simulated population, and within each replicate six different datasets differing in number and distribution of animals with trait records and availability of genetic marker information were generated. (Co)Variance components were estimated using a Bayesian mixed linear-threshold animal model via Gibbs sampling. Residual variances were fixed to zero and a proper prior was used for the genetic covariance matrix.ResultsEffective sample sizes (ESS) and biases of genetic parameters differed significantly between datasets. Bias of heritability estimates was -6% to +6% for the continuous trait, -6% to +10% for the binary traits of moderate heritability, and -21% to +25% for the binary traits of low heritability. Additive genetic correlations were mostly underestimated between the continuous trait and binary traits of low heritability, under- or overestimated between the continuous trait and binary traits of moderate heritability, and overestimated between two binary traits. Use of trait information on two subsequent generations of animals increased ESS and reduced bias of parameter estimates more than mere increase of the number of informative animals from one generation. Consideration of genotype information as a fixed effect in the model resulted in overestimation of polygenic heritability of the QTL trait, but increased accuracy of estimated additive genetic correlations of the QTL trait.ConclusionCombined use of phenotype and genotype information on parents and offspring will help to identify agonistic and antagonistic genetic correlations between traits of interests, facilitating design of effective multiple trait selection schemes.

Fibre length, fibre width, tree height and stem diameter in 25-yr-old Scots pine (Pinus sylvestris L.) were investigated by genetic analysis. The analysis was carried out on nearly 400 trees for all traits simultaneously using multiple-trait, individual tree equations with simultaneous variance estimation. Narrow-sense heritabilities were estimated at about 0.3 for all traits except for stem diameter, which was lower (0.17). Low genetic coefficients of variation for fibre length may be partially explained by the sampling method, which was 5 mm increment boring resulting in fibre fragmentation, but the method served well for heritability and correlation analysis. The additive genetic correlation was strongly negative between fibre length and stem diameter, and strongly positive between fibre width and growth traits. The pair of fibre traits showed mutually strong negative additive-genetic but weak positive environmental correlation. The pair of growth traits showed no genetic but strong positive environmental correlation. Other correlation estimates were minor and uncertain, with the exception of a weak negative environmental correlation between fibre length and stem diameter. An additional approach, where stem diameter was regarded as a covariate, revealed positive environmental correlation between fibre length and tree height and negative environmental correlation between fibre width and tree height.

The effectiveness of five selection methods for genetic improvement of net merit comprising trait 1 of low heritability (h(2) = 0.1) and trait 2 of high heritability (h(2) = 0.4) was examined: (i) two-trait quantitative trait loci (QTL)-assisted selection; (ii) partial QTL-assisted selection based on trait 1; (iii) partial QTL-assisted selection based on trait 2; (iv) QTL-only selection; and (v) conventional selection index without QTL information. These selection methods were compared under 72 scenarios with different combinations of the relative economic weights, the genetic correlations between traits, the ratio of QTL variance to total genetic variance of the trait, and the ratio of genetic variances between traits. The results suggest that the detection of QTL for multiple-trait QTL-assisted selection is more important when the index traits are negatively correlated than when they are positively correlated. In contrast to literature reports that single-trait marker-assisted selection (MAS) is the most efficient for low heritability traits, this study found that the identified QTL of the low heritability trait contributed negligibly to total response in net merit. This is because multiple-trait QTL-assisted selection is designed to maximize total net merit rather than the genetic response of the individual index trait as in the case of single-trait MAS. Therefore, it is not economical to identify the QTL of the low heritability traits for the improvement of total net merit. The efficient, cost-effective selection strategy is to identify the QTL of the moderate or high heritability traits of the QTL-assisted selection index to facilitate total economic returns. Detection of the QTL of the low h(2) traits for the QTL-assisted index selection is justified when the low h(2) traits have high negative genetic correlation with the other index traits and/or when both economic weights and genetic variances of the low h(2) traits are larger as compared to the other index traits of higher h(2). This study deals with theoretical efficiency of QTL-assisted selection, but the same principle applies to SNP-based genomic selection when the proportion of the genetic variance 'explained by the identified QTLs' in this study is replaced by 'explained by SNPs'.