Incomplete block designs with blocks of two plots

Various workers have shown that considerable economies in experimentation can be achieved by the use of identical twins, halves of leaves and halves of plants. The basic statistical principle enabling these economies is that of incomplete block designs. These make possible the comparison of treatments within pairs of identical twins, pairs of half-leaves or whatever grouping is used, so that experimental error arises only because of differences between individuals within the pairs. Extensive use of these natural groupings is possible only when the possible incomplete block designs have been enumerated. The purpose of this bulletin is to present what is essentially a complete array of incomplete block designs with blocks of two plots. The balanced incomplete block design requires (n-1) replications, where n is the number of treatments. Any design using a lesser number of replications must necessarily be unbalanced. Designs are presented which require (n-2), (n-3), ... , three replications, whenever such is possible, for any number of treatments between 6 and 12. These designs have been extracted from a pool of designs formed by (a) the class of partially balanced incomplete block designs with two classes of associates and (b) the class of circulant designs. The design chosen to cover each situation is the design which has the highest efficiency factor among all the designs in the pool applicable to the given situation. The tabulation of material necessary for the analysis of the respective designs is made to facilitate computations. The computations are exemplified by the inclusion of a worked example covering both the intrablock and interblock analysis

Significance of soil organic phosphorus to plant growth

The first indication that soils contain organic phosphorus was obtained in 1844 by Mulder (20), in experiments wherein he could not obtain phosphorus-free preparations of certain soil organic matter fractions. Since the time of Mulder, a number of investigations have dealt specifically with the problem of soil organic phosphorus, and it is now generally recognized that a portion of the soil phosphorus occurs in organic forms. The distribution of organic phosphorus in different soil types and groups has been investigated in only a preliminary way, but it has become apparent that the quantities of organic phosphorus are correlated with the quantities of soil organic matter. In Iowa and other North Central states, there are extensive areas of soils that contain relatively large quantities of both substances

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

<p>Abstract</p> <p>Background</p> <p>Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).</p> <p>Results</p> <p>In this paper, we further explore the differences and links between the F_∞and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞model. A new way of linking the Cockerham and F_∞model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞models are applied.</p> <p>Conclusion</p> <p>The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞model can then be calculated by translating formulas derived for the Cockerham models.</p

Joint phenotypes, evolutionary conflict and the fundamental theorem of natural selection

Multiple organisms can sometimes affect a common phenotype. For example, the portion of a leaf eaten by an insect is a joint phenotype of the plant and insect and the amount of food obtained by an offspring can be a joint trait with its mother. Here, I describe the evolution of joint phenotypes in quantitative genetic terms. A joint phenotype for multiple species evolves as the sum of additive genetic variances in each species, weighted by the selection on each species. Selective conflict between the interactants occurs when selection takes opposite signs on the joint phenotype. The mean fitness of a population changes not just through its own genetic variance but also through the genetic variance for its fitness that resides in other species, an update of Fisher\u27s fundamental theorem of natural selection. Some similar results, using inclusive fitness, apply to within-species interactions. The models provide a framework for understanding evolutionary conflicts at all levels

Enhanced insulin signalling ameliorates C9orf72 hexanucleotide repeat expansion toxicity in Drosophila

G4C2 repeat expansions within the C9orf72 gene are the most common genetic cause of amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD). The repeats undergo repeat-associated non-ATG translation to generate toxic dipeptide repeat proteins. Here, we show that insulin/Igf signalling is reduced in fly models of C9orf72 repeat expansion using RNA-sequencing of adult brain. We further demonstrate that activation of insulin/Igf signalling can mitigate multiple neurodegenerative phenotypes in flies expressing either expanded G4C2 repeats or the toxic dipeptide repeat protein poly-GR. Levels of poly-GR are reduced when components of the insulin/Igf signalling pathway are genetically activated in the diseased flies, suggesting a mechanism of rescue. Modulating insulin signalling in mammalian cells also lowers poly-GR levels. Remarkably, systemic injection of insulin improves the survival of flies expressing G4C2 repeats. Overall, our data suggest that modulation of insulin/Igf signalling could be an effective therapeutic approach against C9orf72 ALS/FTD

Presymptomatic risk assessment for chronic non-communicable diseases

The prevalence of common chronic non-communicable diseases (CNCDs) far overshadows the prevalence of both monogenic and infectious diseases combined. All CNCDs, also called complex genetic diseases, have a heritable genetic component that can be used for pre-symptomatic risk assessment. Common single nucleotide polymorphisms (SNPs) that tag risk haplotypes across the genome currently account for a non-trivial portion of the germ-line genetic risk and we will likely continue to identify the remaining missing heritability in the form of rare variants, copy number variants and epigenetic modifications. Here, we describe a novel measure for calculating the lifetime risk of a disease, called the genetic composite index (GCI), and demonstrate its predictive value as a clinical classifier. The GCI only considers summary statistics of the effects of genetic variation and hence does not require the results of large-scale studies simultaneously assessing multiple risk factors. Combining GCI scores with environmental risk information provides an additional tool for clinical decision-making. The GCI can be populated with heritable risk information of any type, and thus represents a framework for CNCD pre-symptomatic risk assessment that can be populated as additional risk information is identified through next-generation technologies.Comment: Plos ONE paper. Previous version was withdrawn to be updated by the journal's pdf versio

Different strategies for recovering metals from CARON process residue

http://dx.doi.org/10.1016/j.jhazmat.2011.03.048The capacity of Acidithiobacillus thiooxidans DMS 11478 to recover the heavy metals contained in the residue obtained from the CARON process has been evaluated. Different bioreactor configurations were studied: a two-stage batch system and two semi-continuous systems (stirred-tank reactor leaching and column leaching). In the two-stage system, 46.8% Co, 36.0% Mg, 26.3% Mn and 22.3% Ni were solubilised after 6 h of contact between the residue and the bacteria-free bioacid. The results obtained with the stirred-tank reactor and the column were similar: 50% of the Mg and Co and 40% of the Mn and Ni were solubilised after thirty one days. The operation in the column reactor allowed the solid–liquid ratio to be increased and the pH to be kept at low values (<1.0). Recirculation of the leachate in the column had a positive effect on metal removal; at sixty five days (optimum time) the solubilisation levels were as follows: 86% Co, 83% Mg, 72% Mn and Ni, 62% Fe and 23% Cr. The results corroborate the feasibility of the systems studied for the leaching of metals from CARON process residue and these methodologies can be considered viable for the recovery of valuable metals

The use of measured genotype information in the analysis of quantitative phenotypes in man.

We have begun a measured genotype approach to the genetic analysis of lipid and lipoprotein variability. This approach enables one to simultaneously estimate the frequencies and effects of alleles at specific loci along with the residual polygenetic variance component. In this study we consider the contribution of three common alleles at the locus coding for apolipoprotein E to interindividual variation of total cholesterol, betalipoprotein, and triglyceride levels. A sample of 102 nuclear families consisting of 434 individuals was studied. The frequencies of the ε2, ε3, and ε4 alleles in this sample are 0·137,0·740, and 0·123, respectively. In separate analyses of cholesterol and betalipoprotein levels, a complete model that includes the effects of the six apo E genotypes, unmeasured polygenes, and individual specific environmental effects fits these data significantly better than a reduced model that does not include the effects of the apo E polymorphism or a reduced model that does not include the effects of polygenes. On the average the ε2 allele lowers total cholesterol and betalipoprotein levels by 0·425 mmol/l and 0·811 units, respectively. The ε4 allele is associated with an average increase of these phenotypes by 0·255 mmol/l and 0·628 units, respectively. Simultaneous estimates of the interindividual variability of total cholesterol levels attributable to the apo E polymorphism and to residual polygenic effects are 8% and 56%, respectively. For betalipoprotein levels, we simultaneously estimate these values to be 7% and 42%, respectively. A reduced model including the effects of polygenes but not the effects of the apo E polymorphism fitted the triglyceride data as well as the complete model. The estimate of the fraction of interindividual variability associated with polygenetic effects was 26.5%. We review our present understanding of the genetic architecture underlying variability of cholesterol levels in the population at large and infer that the majority of the genetic variability may be accounted for by polymorphic gene loci with moderate effects on cholesterol levels.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65212/1/j.1469-1809.1987.tb00874.x.pd

How To Perform Meaningful Estimates of Genetic Effects

Although the genotype-phenotype map plays a central role both in Quantitative and Evolutionary Genetics, the formalization of a completely general and satisfactory model of genetic effects, particularly accounting for epistasis, remains a theoretical challenge. Here, we use a two-locus genetic system in simulated populations with epistasis to show the convenience of using a recently developed model, NOIA, to perform estimates of genetic effects and the decomposition of the genetic variance that are orthogonal even under deviations from the Hardy-Weinberg proportions. We develop the theory for how to use this model in interval mapping of quantitative trait loci using Halley-Knott regressions, and we analyze a real data set to illustrate the advantage of using this approach in practice. In this example, we show that departures from the Hardy-Weinberg proportions that are expected by sampling alone substantially alter the orthogonal estimates of genetic effects when other statistical models, like F2 or G2A, are used instead of NOIA. Finally, for the first time from real data, we provide estimates of functional genetic effects as sets of effects of natural allele substitutions in a particular genotype, which enriches the debate on the interpretation of genetic effects as implemented both in functional and in statistical models. We also discuss further implementations leading to a completely general genotype-phenotype map