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Very little attention has been given in the literature to the interesting question of how to handle relatedness in finite populations. The main problem is that a finite population is never really ieat equilibriuml. in that it represents just one realization of an infinite assemblage of possible allelic distributions. A recent paper of Rousset and Billiard (manu- script) provides coefficients which, if used in inclusive fitness models under conditions of weak selection, give us a measure of average allele frequency change where the average is taken over all such realizations. Their coefficients are expressed in terms of identity in state, and an alternative formulation (Taylor and Day, manuscript) in terms of coefficients of consanguinity permits the calculation of relatedness in simple cases from pedigree analysis. Here we implement these calculations in a finite asexual haploid population with either a deme structure or a one-dimensional stepping-stone structure and verify our results with numerical simulations in small populations. Our simulations al- low us to investigate the dependence of relatedness on allele frequency, and our results here agree qualitatively with those obtained by Rousset and Billiard. Finally, we examine a model of altruism in a deme-structured population to verify numerically that our relatedness coefficients provide a correct measure of allele frequency change.

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Journal of Radioanalytical and Nuclear Chemistry
Authors: E. Hoppe, A. Seifert, C. Aalseth, A. Day, O. Farmer, T. Hossbach, J. McIntyre, H. Miley, J. Smart, and G. Warren

Abstract  

Spectrometers for the lowest-level radiometric measurements require materials of extreme radiopurity. Measurements of rare nuclear decays, e.g., neutrinoless double-beta decay, can require construction and shielding materials with bulk radiopurity reaching one micro-Becquerel per kilogram or less. When such extreme material purity is achieved, surface contamination, particularly solid daughters in the natural radon decay chains, can become the limiting background. High-purity copper is an important material for ultra-low-background spectrometers and thus is the focus of this work. A method for removing surface contamination at very low levels without attacking the bulk material is described. An assay method using a low-background proportional counter made of the material under examination is employed, and the preliminary result of achievable surface contamination levels is presented.

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Abstract  

The search for neutrinoless double beta decay in 76Ge has driven the need for ultra-low background Ge detectors shielded by electroformed copper of ultra-high radiopurity (<0.1 μBq/kg). Although electrodeposition processes are almost sophisticated enough to produce copper of this purity, to date there are no methods sensitive enough to assay it. Inductively coupled plasma mass spectrometry (ICP/MS) can detect thorium and uranium at femtogram levels, however, this assay is hindered by high copper concentrations in the sample. Electrodeposition of copper samples removes copper from the solution while selectively concentrating thorium and uranium contaminants to be assayed by ICP/MS. Spiking 232Th and 238U into the plating bath simulates low purity copper and allows for the calculation of the electrochemical rejection rate of thorium and uranium in the electroplating system. This rejection value will help to model plating bath chemistry.

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