Power of the joint segregation analysis method for testing mixed major-gene and polygene inheritance models of quantitative traits

Understanding the genetic architecture of quantitative traits can greatly assist the design of strategies for their manipulation in plant-breeding programs. For a number of traits, genetic variation can be the result of segregation of a few major genes and many polygenes (minor genes). The joint segregation analysis (JSA) is a maximum-likelihood approach for fitting segregation models through the simultaneous use of phenotypic information from multiple generations. Our objective in this paper was to use computer simulation to quantify the power of the JSA method for testing the mixed-inheritance model for quantitative traits when it was applied to the six basic generations: both parents (P-1 and P-2), F-1, F-2, and both backcross generations (B-1 and B-2) derived from crossing the F-1 to each parent. A total of 1968 genetic model-experiment scenarios were considered in the simulation study to quantify the power of the method. Factors that interacted to influence the power of the JSA method to correctly detect genetic models were: (1) whether there were one or two major genes in combination with polygenes, (2) the heritability of the major genes and polygenes, (3) the level of dispersion of the major genes and polygenes between the two parents, and (4) the number of individuals examined in each generation (population size). The greatest levels of power were observed for the genetic models defined with simple inheritance; e.g., the power was greater than 90% for the one major gene model, regardless of the population size and major-gene heritability. Lower levels of power were observed for the genetic models with complex inheritance (major genes and polygenes), low heritability, small population sizes and a large dispersion of favourable genes among the two parents; e.g., the power was less than 5% for the two major-gene model with a heritability value of 0.3 and population sizes of 100 individuals. The JSA methodology was then applied to a previously studied sorghum data-set to investigate the genetic control of the putative drought resistance-trait osmotic adjustment in three crosses. The previous study concluded that there were two major genes segregating for osmotic adjustment in the three crosses. Application of the JSA method resulted in a change in the proposed genetic model. The presence of the two major genes was confirmed with the addition of an unspecified number of polygenes.

Teleportation with the entangled states of a beam splitter

We present a teleportation protocol based upon the entanglement produced from Fock states incident onto a beam splitter of arbitrary transmissivity. The teleportation fidelity is analyzed, its trends being explained from consideration of a beam splitter's input-output characteristics.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model within the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.

A model of factors affecting an information system's change in state

Management are keen to maximize the life span of an information system because of the high cost, organizational disruption, and risk of failure associated with the re-development or replacement of an information system. This research investigates the effects that various factors have on an information system's life span by understanding how the factors affect an information system's stability. The research builds on a previously developed two-stage model of information system change whereby an information system is either in a stable state of evolution in which the information system's functionality is evolving, or in a state of revolution, in which the information system is being replaced because it is not providing the functionality expected by its users. A case study surveyed a number of systems within one organization. The aim was to test whether a relationship existed between the base value of the volatility index (a measure of the stability of an information system) and certain system characteristics. Data relating to some 3000 user change requests covering 40 systems over a 10-year period were obtained. The following factors were hypothesized to have significant associations with the base value of the volatility index: language level (generation of language of construction), system size, system age, and the timing of changes applied to a system. Significant associations were found in the hypothesized directions except that the timing of user changes was not associated with any change in the value of the volatility index. Copyright (C) 2002 John Wiley Sons, Ltd.

Body size and latitudinal gradients in regional diversity of New World birds

Axe latitudinal gradients in regional diversity random or biased with respect to body size? Using data for the New World avifauna, I show that the slope of the increase in regional species richness from the Arctic to the equator is not independent of body size. The increase is steepest among small and medium-sized species, and shallowest among the largest species. This is reflected in latitudinal variation in the shape of frequency distributions of body sizes in regional subsets of the New World avifauna. Because species are added disproportionately in small and medium size classes towards low latitudes, distributions become less widely spread along the body size axis than expected from the number of species. These patterns suggest an interaction between the effects of latitude and body size on species richness, implying that mechanisms which vary with both latitude and body size may be important determinants of high tropical diversity in New World birds.

Molecular clocks in reptiles: Life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between bode size and substitution rate for many Molecular data sets. Both the generality and the cause of the negative bode size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles. lizards. snakes, crocodile, and tuatara. Although this Study was limited by the number of comparisons for which both sequence and lite-history data were available, the results, suggest that a negative bode size trend in rate of molecular evloution may be a general feature of reptile molecular evolution. consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.

Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state rho(ss) of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of rho(ss) as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy chi of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy chi increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of chi for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).

The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.