Variability in water and nitrogen availability at plot scale and its effect on Maize (Zea Mays L.) production

p.21-30

Variability in water and nitrogen availability at plot scale and its effect on Maize (Zea Mays L.) production

p.21-30

Chapman Family burial plot, Forest Lawn, Glendale, California

Chapman Family burial plot, Forest Lawn, Glendale, California. "La Carita" statue.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certain assumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur in the proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p. There are many statistical tests being used to check whether empirical marker data obeys the Hardy-Weinberg principle. Among these are the classical xi-square test (with or without continuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combination with Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE) are numerical in nature, requiring the computation of a test statistic and a p-value. There is however, ample space for the use of graphics in HWE tests, in particular for the ternary plot. Nowadays, many genetical studies are using genetical markers known as Single Nucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the counts one typically computes genotype frequencies and allele frequencies. These frequencies satisfy the unit-sum constraint, and their analysis therefore falls within the realm of compositional data analysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotype frequencies can be adequately represented in a ternary plot. Compositions that are in exact HWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected in a statistical test are typically “close" to the parabola, whereas compositions that differ significantly from HWE are “far". By rewriting the statistics used to test for HWE in terms of heterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted in the ternary plot. This way, compositions can be tested for HWE purely on the basis of their position in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphical representations where large numbers of SNPs can be tested for HWE in a single graph. Several examples of graphical tests for HWE (implemented in R software), will be shown, using SNP data from different human populations

Efecto de la violaci??n de la normalidad y esfericidad en el modelo lineal mixto en dise??os split-plot

Resumen tomado de la publicaci??n

Múltiplos y divisores : una aplicación del material Plot.

Proyecto realizado por 6 profesores integrados en el grupo GAUSS y que ejercen su labor docente en diferentes centros públicos y privados-concertados, en los niveles de Primaria y Secundaria de la provincia de Salamanca. Tienen como objetivo: Elaborar una Unidad Didáctica de Matemáticas para la Educación Secundaria Obligatoria con las siguientes características: utilizar como base el material Plot; parte de la experiencia práctica (manipulación) hacia las estructuras conceptuales. La organización del aula será en pequeños grupos de 4-6 miembros. El desarrollo de la experiencia pasó por las siguientes fases: -elaboración de guiones de trabajo; -adquisición de materiales; -experimentación de la unidad en los Centros; -valoración de resultados. Los materiales entregados constan de una guía para el profesor y materiales para el alumno. El trabajo no está publicado..

The EU's Promotion of External Democracy: In search of the plot. CEPS Policy Brief No. 281, 13 September 2012

This policy brief illustrates that both the conceptualisation of democracy and the means to achieve it remain vague, and explains why this is problematic. It points out the risks that stem from a lack of clear understanding about how human rights, governance, civil society and socio-economic development relate to democratisation. It concludes that the EU should reflect on the substance of its external democracy promotion policies and conceptualise the relationship between the different elements of democracy promotion cited above and democratisation. While ongoing reforms of international democracy promotion should continue, a wider debate on substance could help identify what the EU should support in the future. The EU should also establish a reflective external democracy promotion policy where the assessment of actions on democratic development becomes systematic and is institutionalised.

The effect of potato variety mixtures on epidemics of late blight, in relation to plot size and level of resistance

Potatoes of a number of varieties of contrasting levels of resistance were planted in pure or mixed stands in four experiments over 3 years. Three experiments compared the late blight severity and progress in mixtures with that in pure stands. Disease on susceptible or moderately resistant varieties typical of those in commercial use was similar in mixtures and pure stands. In 2 of 3 years, there were slight reductions on cv. Sante, which is moderately susceptible, in mixture with cv. Cara, which is moderately resistant. Cara was unaffected by this mixture. Mixtures of an immune or near-immune partner with Cara or Sante substantially reduced disease on the latter. The effect of the size of plots of individual varieties or mixtures on blight severity was compared in two experiments. Larger plots had a greater area under the disease progress curve, but the average rate of disease progress was greater in smaller plots; this may be because most disease progress took place later, under more favourable conditions, in the smaller plots. In one experiment, two planting densities were used. Density had no effect on disease and did not interact with mixture effects. The overall conclusion is that, while mixtures of potato varieties may be desirable for other reasons, they do not offer any improvement on the average of the disease resistance of the components.

Use of the ratio plot in capture-recapture estimation

Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Recovery based on plot experiments is a poor predictor of landscape-level population impacts of agricultural pesticides

Current European Union regulatory risk assessment allows application of pesticides provided that recovery of nontarget arthropods in-crop occurs within a year. Despite the long-established theory of source-sink dynamics, risk assessment ignores depletion of surrounding populations and typical field trials are restricted to plot-scale experiments. In the present study, the authors used agent-based modeling of 2 contrasting invertebrates, a spider and a beetle, to assess how the area of pesticide application and environmental half-life affect the assessment of recovery at the plot scale and impact the population at the landscape scale. Small-scale plot experiments were simulated for pesticides with different application rates and environmental half-lives. The same pesticides were then evaluated at the landscape scale (10 km × 10 km) assuming continuous year-on-year usage. The authors' results show that recovery time estimated from plot experiments is a poor indicator of long-term population impact at the landscape level and that the spatial scale of pesticide application strongly determines population-level impact. This raises serious doubts as to the utility of plot-recovery experiments in pesticide regulatory risk assessment for population-level protection. Predictions from the model are supported by empirical evidence from a series of studies carried out in the decade starting in 1988. The issues raised then can now be addressed using simulation. Prediction of impacts at landscape scales should be more widely used in assessing the risks posed by environmental stressors.