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

Coherent forecasting of multiple-decrement life tables: a test using Japanese cause of death data

Planners in public and private institutions would like coherent forecasts of the components of age-specic mortality, such as causes of death. This has been di cult toachieve because the relative values of the forecast components often fail to behave ina way that is coherent with historical experience. In addition, when the group forecasts are combined the result is often incompatible with an all-groups forecast. It hasbeen shown that cause-specic mortality forecasts are pessimistic when compared withall-cause forecasts (Wilmoth, 1995). This paper abandons the conventional approachof using log mortality rates and forecasts the density of deaths in the life table. Sincethese values obey a unit sum constraint for both conventional single-decrement life tables (only one absorbing state) and multiple-decrement tables (more than one absorbingstate), they are intrinsically relative rather than absolute values across decrements aswell as ages. Using the methods of Compositional Data Analysis pioneered by Aitchison(1986), death densities are transformed into the real space so that the full range of multivariate statistics can be applied, then back-transformed to positive values so that theunit sum constraint is honoured. The structure of the best-known, single-decrementmortality-rate forecasting model, devised by Lee and Carter (1992), is expressed incompositional form and the results from the two models are compared. The compositional model is extended to a multiple-decrement form and used to forecast mortalityby cause of death for Japan

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

Shared knowledge

Agents use their knowledge on the history of the economy in orderto choose what is the optimal action to take at any given moment of time,but each individual observes history with some noise. This paper showsthat the amount of information available on the past evolution of theeconomy is an endogenous variable, and that this leads to overconcentrationof the investment, which can be interpreted as underinvestment in research.It presents a model in which agents have to invest at each period in one of$K$ sectors, each of them paying an exogenous return that follows a welldefined stochastic path. At any moment of time each agent receives an unbiasednoisy signal on the payoff of each sector. The signals differ across agents,but all of them have the same variance, which depends on the aggregate investmentin that particular sector (so that if almost everybody invests in it theperceptions of everybody will be very accurate, but if almost nobody doesthe perceptions of everybody will be very noisy). The degree of hetereogeneityacross agents is then an endogenous variable, evolving across time determining,and being determined by, the amount of information disclosed.As long as both the level of social interaction and the underlying precisionof the observations are relatively large agents behave in a very preciseway. This behavior is unmodified for a huge range of informational parameters,and it is characterized by an excessive concentration of the investment ina few sectors. Additionally the model shows that generalized improvements in thequality of the information that each agent gets may lead to a worse outcomefor all the agents due to the overconcentration of the investment that thisproduces.

The impact of the reference price system on the pharmaceutical market: A theoretical approach

This article analyses the impact of the reference pricesystem on the price-setting strategies of thepharmaceutical firms and on the level of generic usage.This model is the first to take explicitly into accountthe impact of the reference price mechanism on the levelof competition between brand-name and generic drugs andnational pharmaceutical spending. We consider aduopolistic model with one firm producing the brand-namedrug, whose patent has already expired, and the otherproducing the corresponding generic version. We work ina partial equilibrium framework where firms set pricessequentially and consumers face heterogeneous switchingcosts.We show that brand producers compensate thedecline of profits by selling greater quantities insteadof charging higher prices, thus fostering pricecompetition in the pharmaceutical market. This result isa consequence of both the assumption of a verticallydifferentiated model and the introduction of thereference price system.

Strategies for an integrated distribution problem

The problems arising in the logistics of commercial distribution are complexand involve several players and decision levels. One important decision isrelated with the design of the routes to distribute the products, in anefficient and inexpensive way.This article explores three different distribution strategies: the firststrategy corresponds to the classical vehicle routing problem; the second isa master route strategy with daily adaptations and the third is a strategythat takes into account the cross-functional planning through amulti-objective model with two objectives. All strategies are analyzed ina multi-period scenario. A metaheuristic based on the Iteratetd Local Search,is used to solve the models related with each strategy. A computationalexperiment is performed to evaluate the three strategies with respect to thetwo objectives. The cross functional planning strategy leads to solutions thatput in practice the coordination between functional areas and better meetbusiness objectives.

Structural changes in the US economy: is there a role for monetary policy?

This paper investigates the contribution of monetary policy to the changes in outputgrowth and inflation dynamics in the US. We identify a policy shock and a policy rule ina time-varying coefficients VAR using robust sign restrictions. The transmission of policyshocks has been relatively stable. The variance of the policy shock has decreased over time,but policy shocks account for a small fraction of the level and of the variations in inflationand output growth volatility and persistence. We find little evidence of a significant increasein the long run response of the interest rate to inflation. A more aggressive inflation policyin the 1970s would have produced large output growth costs.

An economic theory of church strictness

This paper makes several contributions to the growing literatureon the economics of religion. First, we explicitly introduce spatial-location models into the economics of religion. Second, we offer a newexplanation for the observed tendency of state (monopoly) churches tolocate toward the "low-tension" end of the "strictness continuum" (ina one-dimensional product space): This result is obtained through theconjunction of "benevolent preferences" (denominations care about theaggregate utility of members) and asymmetric costs of going to a moreor less strict church than one prefers.We also derive implications regarding the relationship between religiousstrictness and membership. The driving forces of our analysis, religiousmarket interactions and asymmetric costs of membership, high-light newexplanations for some well-established stylized facts. The analysis opensthe way to new empirical tests, aimed at confronting the implications ofour model against more traditional explanations.

Auctions of licences and market structure

This paper studies sequential auctions of licences to operate in amarket where those firms that obtain at least one licence then engage ina symmetric market game. I employ a new refinement of Nash equilibrium,the concept of {\sl Markovian recursively undominated equilibrium}.The unique solution satisfies the following properties: (i) when severalfirms own licences before the auction (incumbents), new entrants buylicences in each stage, and (ii) when there is no more than one incumbent,either the single firm preempts entry altogether or entry occurs inevery stage, depending on the parameter configuration.

Long-range transport of Saharan dust to northern Europe: The 11-16 October 2001 outbreak observed with EARLINET

The spread of mineral particles over southwestern, western, and central Europeresulting from a strong Saharan dust outbreak in October 2001 was observed at10 stations of the European Aerosol Research Lidar Network (EARLINET). For the firsttime, an optically dense desert dust plume over Europe was characterized coherentlywith high vertical resolution on a continental scale. The main layer was located abovethe boundary layer (above 1-km height above sea level (asl)) up to 3–5-km height, andtraces of dust particles reached heights of 7–8 km. The particle optical depth typicallyranged from 0.1 to 0.5 above 1-km height asl at the wavelength of 532 nm, andmaximum values close to 0.8 were found over northern Germany. The lidar observationsare in qualitative agreement with values of optical depth derived from Total OzoneMapping Spectrometer (TOMS) data. Ten-day backward trajectories clearly indicated theSahara as the source region of the particles and revealed that the dust layer observed,e.g., over Belsk, Poland, crossed the EARLINET site Aberystwyth, UK, and southernScandinavia 24–48 hours before. Lidar-derived particle depolarization ratios,backscatter- and extinction-related A ° ngstro¨m exponents, and extinction-to-backscatterratios mainly ranged from 15 to 25%, 0.5 to 0.5, and 40–80 sr, respectively, within thelofted dust plumes. A few atmospheric model calculations are presented showing the dustconcentration over Europe. The simulations were found to be consistent with thenetwork observations.

Local effects and global impact in neurotoxicity and neurodegeneration: The Xi"an International Neurotoxicology Conference

'Neurotoxicity and Neurodegeneration: Local Effect and Global Impact' was the theme of the Xi"an International Neurotoxicology Conference (XINC), held in Xi"an, June 2011. The Conference was a joint event of the 13th Biennial Meeting of the International Neurotoxicology Association (INA-13) and the 11th International Symposium on Neurobehavioral Methods and Effects in Occupational and Environmental Health (NEUREOH-11) of the Scientific Committee on Neurotoxicology and...

Local effects and global impact in neurotoxicity and neurodegeneration: The Xi"an International Neurotoxicology Conference

'Neurotoxicity and Neurodegeneration: Local Effect and Global Impact' was the theme of the Xi"an International Neurotoxicology Conference (XINC), held in Xi"an, June 2011. The Conference was a joint event of the 13th Biennial Meeting of the International Neurotoxicology Association (INA-13) and the 11th International Symposium on Neurobehavioral Methods and Effects in Occupational and Environmental Health (NEUREOH-11) of the Scientific Committee on Neurotoxicology and...

Reproductive morphology in Mediterranean Seirospora giraudyi (Ceramiales, Rhodophyta)

This paper presents a detailed description of the reproductive characters of Mediterranean Seirospora giraudyi based on fresh material collected in the northwestern coast of Spain. Vegetative cells are uninucleate. The plant is monoecious. Spermantangial parent’s cells are clustered on modified dwarf determinate filaments, usually situated on adaxial surfaces of branches. One to four spermatia are formed by elongation and proximal divisions of the spermatangial parent cells. Spermatium with a nucleus situated ina mec. The thallus is procarpic. The four-celled carpogonial branch is initially L-shaped, and it is situated on a periaxial supporting fertile axial cell. The mature carpogonial branch is U-shaped and the supporting cell and second periaxial cell enlarge and divide transversely to reproduce a pair uninicleate auxiliary cell. The nucleus in the ferlilized carpogonium divides twice and the carpogonium cleaves vertically into two cells that, turn, cut off a pair of uninucleate connecting cells that fuse with the auxiliary cells on opposite sides; the diploid nuclei in the connecting cells divide at the site of fusion and one of the nuclei enters the auxiliary cell white the other is extruded. Each auxiliary cell gives to a terminal primary gonimolobe initials. Gonimolobes form lax chains of carposporangia. As the gonimoblasts mature, both lobes of the foot cell which is situated on the supporting cell elongate the upper one secondary connecting with the supporting cell, and the lower one with the fertile axial cell. The gonimoblasts are subtended at maturity by one to several clusters of involucral flaments. Seirospora is currently placed in the tribe Euptiloteae; however the reproductive character of S.giraudyi is dentical to those described for the Cañllithamnieae. Molecular studies are needed to confirm the taxonomic position of S.giraudyi as well as that of the other species placed Seirospora

Local effects and global impact in neurotoxicity and neurodegeneration: The Xi"an International Neurotoxicology Conference

'Neurotoxicity and Neurodegeneration: Local Effect and Global Impact' was the theme of the Xi"an International Neurotoxicology Conference (XINC), held in Xi"an, June 2011. The Conference was a joint event of the 13th Biennial Meeting of the International Neurotoxicology Association (INA-13) and the 11th International Symposium on Neurobehavioral Methods and Effects in Occupational and Environmental Health (NEUREOH-11) of the Scientific Committee on Neurotoxicology and...