Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certainassumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur inthe 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 theHardy-Weinberg principle. Among these are the classical xi-square test (with or withoutcontinuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combinationwith 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 ternaryplot. Nowadays, many genetical studies are using genetical markers known as SingleNucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the countsone typically computes genotype frequencies and allele frequencies. These frequencies satisfythe unit-sum constraint, and their analysis therefore falls within the realm of compositional dataanalysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotypefrequencies can be adequately represented in a ternary plot. Compositions that are in exactHWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected ina statistical test are typically “close" to the parabola, whereas compositions that differsignificantly from HWE are “far". By rewriting the statistics used to test for HWE in terms ofheterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted inthe ternary plot. This way, compositions can be tested for HWE purely on the basis of theirposition in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphicalrepresentations where large numbers of SNPs can be tested for HWE in a single graph. Severalexamples of graphical tests for HWE (implemented in R software), will be shown, using SNPdata from different human populations

Right-left digit ratio (2D:4D) and maximal oxygen uptake.

A low digit ratio (2D:4D) and low 2D:4D in the right compared with the left hand (right-left 2D:4D) are thought to be determined by high in utero concentrations of testosterone, and are related to "masculine" traits such as aggression and performance in sports like running and rugby. Low right-left 2D:4D is also related to sensitivity to testosterone as measured by the number of cytosine-adenine-guanine triplet repeats in exon 1 of the androgen receptor gene. Here we show that low right-left 2D:4D is associated with high maximal oxygen uptake (VO2(max)), high velocity at VO2(max), and high maximum lactate concentration in a sample of teenage boys. We suggest that low right-left 2D:4D is linked to performance in some sports because it is a proxy of high sensitivity to prenatal and maybe also circulating testosterone and high VO2(max).

Acute oxygen sensing in heme oxygenase-2 null mice.

Hemeoxygenase-2 (HO-2) is an antioxidant enzyme that can modulate recombinant maxi-K(+) channels and has been proposed to be the acute O(2) sensor in the carotid body (CB). We have tested the physiological contribution of this enzyme to O(2) sensing using HO-2 null mice. HO-2 deficiency leads to a CB phenotype characterized by organ growth and alteration in the expression of stress-dependent genes, including the maxi-K(+) channel alpha-subunit. However, sensitivity to hypoxia of CB is remarkably similar in HO-2 null animals and their control littermates. Moreover, the response to hypoxia in mouse and rat CB cells was maintained after blockade of maxi-K(+) channels with iberiotoxin. Hypoxia responsiveness of the adrenal medulla (AM) (another acutely responding O(2)-sensitive organ) was also unaltered by HO-2 deficiency. Our data suggest that redox disregulation resulting from HO-2 deficiency affects maxi-K(+) channel gene expression but it does not alter the intrinsic O(2) sensitivity of CB or AM cells. Therefore, HO-2 is not a universally used acute O(2) sensor.

Mechanisms of hydrogen peroxide-induced vasoconstriction in the isolated perfused rat kidney.

The vasoconstrictor effect of hydrogen peroxide (H(2)O(2)) on isolated perfused rat kidney was investigated. H(2)O(2) induced vasoconstriction in the isolated rat kidney in a concentration-dependent manner. The vasoconstrictor effects of H(2)O(2) were completely inhibited by 1200 U/ml catalase. Endothelium-removal potentiated the renal response to H(2)O(2). The H(2)O(2) dose-response curve was not significantly modified by administration of the NO inhibitor L-NAME (10(-4) mol/l), whereas it was increased by the non-specific inhibitor of K+-channels, tetraethylammonium (3.10(-3) mol/l). Separately, removal of extracellular Ca(2+), administration of a mixture of calcium desensitizing agents (nitroprusside, papaverine, and diazoxide), and administration of a protein kinase C (PKC) inhibitor (chelerythrine, 10(-5) mol/l) each significantly attenuated the vasoconstrictor response to H(2)O(2), which was virtually suppressed when they were performed together. The pressor response to H(2)O(2) was not affected by: dimethyl sulfoxide (7.10(-5) mol/l) plus mannitol (3.10(-5) mol/l); intracellular Ca(2+) chelation using BAPTA (10(-5) mol/l); calcium store depletion after repeated doses of phenylephrine (10(-5) g/g kidney); or the presence of indomethacin (10(-5) mol/l), ODYA (2.10(-6) mol/l) or genistein (10(-5) mol/l). We conclude that the vasoconstrictor response to H(2)O(2) in the rat renal vasculature comprises the following components: 1) extracellular calcium influx, 2) activation of PKC, and 3) stimulation of pathways leading to sensitization of contractile elements to calcium. Moreover, a reduced pressor responsiveness to H(2)O(2) in female kidneys was observed.

Effects of dopamine on total oxygen consumption and oxygen delivery in healthy men.

The effect of acute intravenous dopamine (DA) administration at three sequential (but randomized) infusion rates was studied in eight young male volunteers. DA was infused at 2.5, 5, and 10 micrograms.kg-1.min-1. O2 consumption (VO2) and CO2 production (VCO2) were measured continuously by means of a computerized indirect calorimeter (blood system). In response to the 5- and 10-micrograms.kg-1.min-1 DA infusion rates, a significant increase (P less than 0.01) in VO2 corresponding to a 6% (range, 3-10) and 15% (range, 12-23) increase, respectively, of preinfusion values was observed. In contrast, at the low dose (2.5 micrograms.kg-1.min-1), DA induced no significant change in VO2. Cardiac output (Qc) increased significantly after the three DA administration rates [19% (range, 0-42), 34% (range, 17-71), and 25% (range, -3 to +47)] for the doses 2.5, 5, and 10 micrograms.-kg-1.min-1, respectively. The increase in O2 delivery (QO2) outweighed VO2 at all administration rates despite the relative drop in QO2 at the maximal DA administration rate. These results indicate that in humans DA improves net O2 supply to tissues proportionally more than it increases VO2 at all doses used in the present study.

Constraints on the upper Permian to upper Triassic marine carbon isotope curve : case studies from the Tethys

Secular variations of the seawater carbon isotopic composition provide evidence for paleoceanographic and paleoclimatic changes and may serve for chemiostratigraphic correlations. The present study aimed to improve the current knowledge on the Upper Permian and Triassic segment of the Phanerozoic marine carbon isotope curve, whose Triassic part was poorly constrained by previous studies. Profiles of inorganic carbon isotopes are provided for sections from Himalaya (Salt Range, Kashmir, Spiti and Nepal), Oman and North Dobrogea (Romania) on the basis of whole-rock carbonate analysis. The data acquired, together with a literature compilation confirmed that most of the Upper Permian is characterized by high δ13C values (averaging +40/00) but failed to detect a positive excursion as suggested by recent compilations. In the light of these observations, the large drop in δ13C values associated with the end-Permian mass extinction appears to be driven by a sudden transfer of previously stocked 13C depleted carbon, rather than by the overturn of a Late Permian stratified ocean. The Triassic data-set outlines significant secular variations. The best documented is a carbon isotope positive excursion just across the Lower-Middle Triassic boundary, globally developed since it was detected in various paleogeographic settings. It is interpreted to reflect variations in surface ocean chemistry, possibly related to increased primary productivity, at times when the biotic recovery after the end-Permian mass-extinction began to accelerate significantly and when a sharp rise in seawater δ34S values occurred globally. Strontium isotope data obtained from well preserved biogenic phosphates allow a refinement of the Middle Triassic segment of the seawater strontium isotope curve and show a major inflexion point of the seawater strontium isotope curve also near the Lower Triassic - Middle Triassic boundary. These facts suggest that the transition from the Early to the Middle Triassic was a time of revolutionary global change which represented an important step in the evolution of Mesozoic marine environments. A tentative carbon isotope curve for the Upper Permian to Upper Triassic time interval is proposed. Its major features are: ? high but constant δ13C values during the Late Permian ? a sharp drop in δ13C values in the latest Permian ? subsequent recovery of δ13C values ? a short-lived positive excursion across the Early-Middle Triassic boundary ? a gradual rise in δ13C values starting in the Late Ladinian or in the Early Carnian It is foreseen that these fluctuations of the carbon isotope curve may serve as chronostratigraphic markers and further assist in the correlation of Permian and Triassic carbonate deposits.

Evaluation of the quantity of Fe3+ in spinels for obtaining the oxygen fugacities in xenoliths.

The analysis by electron microprobe allows the evaluation of the quantity of Fe3+ ih spinels with considerable errors. The use of a correction equation which is based on a the calibration of analyses with an electron microprobe in relation to those carried out with Mossbauer spectroscopy gives more precise evaluations of Fe3+. In fact, it allows a calculation of the oxygen fugacity in peridotitic xenoliths. The obtained results show that peridotites of the French Central Massif crystallised under oxygen fugacities which were higher than those of the Moroccan Anti-Atlas.

Modelling the cardiovascular system for automatic interpretation of the blood pressure curve

A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. A sensitivity analysis is first carried out to determine which are the most important model parameters to characterise the blood pressure signal. A four stage process is then described which accurately determines all parameter values. This process is applied to data from three patients and good agreement is shown in all cases.

Modelling changes in stable isotope compositions of minerals during net transfer reactions in a contact aureole: Wollastonite growth at the northern Hunter Mountain Batholith (Death Valley National Park, USA)

One of the world's largest wollastonite deposits was formed at the contact of the northern Hunter Mountain Batholith (California, USA) in Paleozoic sediments. Wollastonite occurs as zones of variable thickness surrounding layers or nodules of quartzite in limestones. A minimum formation temperature of 650 degrees C is estimated from isolated periclase-bearing lenses in that area. Contact metamorphism of siliceous carbonates has produced mineral assemblages that are consistent with heterogeneous, and partly limited infiltration of water-rich fluids, compatible with O-18/O-16 and C-13/C-12 isotopic patterns recorded in carbonates. Oxygen isotope compositions of wollastonites in the study area may also not require infiltration of large quantities of externally-derived fluids that were out of equilibrium with the rocks. 8180 values of wollastonite are high (14.8 parts per thousand to 25.0 parts per thousand; median: 19.7 parts per thousand) and close to those of the host limestone (19.7 parts per thousand to 28 parts per thousand; median: 24.9 parts per thousand) and quartz (18.0 parts per thousand. to 29.1 parts per thousand; median: 22.6 parts per thousand). Isotopic disequilibrium exists at quartz/wollastonite and wollastonite/calcite boundaries. Therefore, classical batch/Rayleigh fractionation models based on reactant and product equilibrium are not applicable to the wollastonite rims. An approach that relies on local instantaneous mass balance for the reactants, based on the wollastonite-forming reaction is suggested as an alternative way to model wollastonite reaction rims. This model reproduces many of the measured delta O-18 values of wollastonite reaction rims of the current study to within +/- 1 parts per thousand, even though the wollastonite compositions vary by almost 10 parts per thousand. (C) 2011 Elsevier B.V. All rights reserved.

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Social capital and the equilibrium number of entrepreneurs

Social capital is viewed either as a proprietary asset that serves private interests, including those of entrepreneurs, or as a collective asset that supports trust-based transactions saving on transaction costs both in markets and within the boundaries of firms, and benefiting society as a whole. This paper explains the relative specialization between entrepreneurs and market-governed exchanges as a result of the interaction between social capital that lowers transaction costs, and the scale economies of ability in managerial jobs (Lucas 1978). The main hypothesis formulated in the paper is that higher social capital will benefit the hierarchy relatively more than the market as a governance mechanism, and therefore in economies with higher social capital, the equilibrium number of entrepreneurs will be lower and their average span of control larger than in economies with lower social capital. The empirical evidence, with data from the Spanish Autonomous Communities, is consistent with this prediction.