Accounting for variability in the detection and use of markers for simple and complex traits

There are many sources of variability in gene–phenotype associations. During the measurement of genotype and phenotype and during selection, researchers must deal with experimental error in trials; gene-gene interaction (epistasis) for sub-traits and observed traits; trait-trait interaction (pleiotropy) and gene- or genotype-by-environment interaction. These effects can be structured in a framework that allows simulation of the entire gene-environment ‘landscape’. Studies of these landscapes have been published by others. Here we aim to explain with simple examples some of the types of insights that can be made. A current challenge for breeders working with simple marker–phenotype associations is to design selection strategies that can rapidly create new combinations of multiple marker-based traits. For a real-world example in wheat, we have used simulation to show how gene enrichment during early generations (selection of homozygotes and heterozygotes with desirable alleles) can greatly reduce resource requirements when combining 9 genes into one genotype through marker-assisted selection. Another wheat example compares phenotypic and QTL-based selection for coleoptile length where the QTL also had a pleiotropic association with plant height. These simulations show the relative negative effects of either low heritability, or less than complete detection of QTL associated with traits. Finally, we revisit a marker-assisted selection (MAS) example whereby a QTL study is undertaken on a population for a complex trait, and then those QTL are used in selection. This process is subject to all sources of error described above. If the trait is complex, then interactions among sub-traits; between sub-traits and the environment; or between the chromosomal locations of controlling genes, create an extremely ‘rugged’ selection landscape that slows breeding progress. In this situation, a detailed understanding of some of these interactions is required if MAS is to be able to exceed the progress of conventional breedin

Dusty Starbursts and the Growth of Cosmic Structure

Dusty starbursts were more numerous around z~1 than today and appear to be responsible for the majority of cosmic star formation over the Hubble time. We suggest that they represent a common phase within galaxies in general which is triggered by the growth of cosmic structure. We discuss the origin of the luminosity of luminous infrared galaxies at z~1. Are these galaxies dominated by star formation or nuclear activity ? What is triggering their strong activity ? Is it triggered by external interactions or did it happen naturally within isolated galaxies ? We present HST-ACS high resolution optical images of luminous infrared galaxies at z~0.7 showing the evolution of the morphology of these galaxies as a function of infrared luminosity, or star formation rate, and discuss the effect of the environment on their activity.Comment: 4 pages, 2 figures, to appear in Proceeding of the "Multi-Wavelength Cosmology" Conference held in Mykonos, Greece, June 2003, ed.M. Plionis (Kluwer

Nonlinear and linear timescales near kinetic scales in solar wind turbulence

The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the solar wind these two types of timescales may be directly compared using standard Kolmogorov-style analysis and observational data. The estimated local (in scale) nonlinear magnetohydrodynamic cascade times, evaluated as relevant kinetic scales are approached, remain slower than the cyclotron period, but comparable to or faster than the typical timescales of instabilities, anisotropic waves, and wave damping. The variation with length scale of the turbulence timescales is supported by observations and simulations. On this basis the use of linear theory—which assumes constant parameters to calculate the associated kinetic rates—may be questioned. It is suggested that the product of proton gyrofrequency and nonlinear time at the ion gyroscales provides a simple measure of turbulence influence on proton kinetic behavior

The global build-up to intrinsic ELM bursts and comparison with pellet triggered ELMs seen in JET

We focus on JET plasmas in which ELMs are triggered by pellets in the presence of ELMs which occur naturally. We perform direct time domain analysis of signals from fast radial field coils and toroidal full flux azimuthal loops. These toroidally integrating signals provide simultaneous high time resolution measurements of global plasma dynamics and its coupling to the control system. We examine the time dynamics of these signals in plasmas where pellet injection is used to trigger ELMs in the presence of naturally occurring ELMs. Pellets whose size and speed are intended to provide maximum local perturbation for ELM triggering are launched at pre-programmed times, without correlation to the occurrence times of intrinsic ELMs. Pellet rates were sufficiently low to prevent sustained changes of the underlying plasma conditions and natural ELM behaviour. We find a global signature of the build-up to natural ELMs in the temporal analytic phase of both the full flux loops and fast radial field coil signals. Before a natural ELM, the signal phases align to the same value on a ∼2–5ms timescale. This global build up to a natural ELM occurs whilst the amplitude of the full flux loop and fast radial field coil signals are at their background value: it precedes the response seen in these signals to the onset of ELMing. In contrast these signals do not clearly phase align before the ELM for ELMs which are the first to occur following pellet injection. This provides a direct test that can distinguish when an ELM is triggered by a pellet as opposed to occurring naturally. It further supports the idea [1–4] of a global build up phase that precedes natural ELMs; pellets can trigger ELMs even when the signal phase is at a value when a natural ELM is unlikely to occurEURATOM 633053ONR NICOP N62909-15-1-N14

Recurrence plot statistics and the effect of embedding

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley (Chaos 8 [1998] 861-871) who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear

Global Dynamical Network of the Spatially Correlated Pc2 Wave Response for the 2015 St. Patrick's Day Storm

We show the global dynamics of spatial correlation of Pc2 wave activity can track the evolution of the 2015 St. Patrick's Day geomagnetic storm for an 8 hr time window around onset. The global spatially coherent response is tracked by forming a dynamical network from 1 s data using the full set of 100+ ground-based magnetometer stations collated by SuperMAG and Intermagnet. The pattern of spatial coherence is captured by network parameters which in turn track the evolution of the storm. At onset interplanetary magnetic field (IMF) Bz > 0 and Pc2 power increases, we find a global response with stations correlated over both local and global distances. Following onset, whilst Bz > 0, the network response is confined to the day-side. When IMF Bz < 0, there is a strong local response at high latitudes, consistent with the onset of polar cap convection driven by day-side reconnection. The spatially coherent response as revealed by the network grows and is maximal when auroral (SuperMAG electrojet) and ring current (SuperMAG ring current) 1 min resolution geomagnetic indices peak, consistent with an active electrojet and ring-current. Throughout the storm there is a coherent response both in stations located along lines of constant geomagnetic longitude, between hemispheres, and across magnetic local time. The network does not simply track average Pc2 wave power, it is characterized by network parameters which track the storm evolution. This is the first study to parameterize global Pc2 wave correlation and offers the possibility of statistical studies across multiple events and comparison with, and validation of, space weather models

Football goal distributions and extremal statistics

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored are too heavy-tailed to be fitted over their entire ranges by Poisson or negative binomial distributions which would be expected for uncorrelated processes. Log-normal distributions cannot include zero scores and here we find that the PDFs are consistent with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71–2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics

Testing the SOC hypothesis for the magnetosphere

As noted by Chang, the hypothesis of Self-Organised Criticality provides a theoretical framework in which the low dimensionality seen in magnetospheric indices can be combined with the scaling seen in their power spectra and the recently-observed plasma bursty bulk flows. As such, it has considerable appeal, describing the aspects of the magnetospheric fuelling:storage:release cycle which are generic to slowly-driven, interaction-dominated, thresholded systems rather than unique to the magnetosphere. In consequence, several recent numerical "sandpile" algorithms have been used with a view to comparison with magnetospheric observables. However, demonstration of SOC in the magnetosphere will require further work in the definition of a set of observable properties which are the unique "fingerprint" of SOC. This is because, for example, a scale-free power spectrum admits several possible explanations other than SOC. A more subtle problem is important for both simulations and data analysis when dealing with multiscale and hence broadband phenomena such as SOC. This is that finite length systems such as the magnetosphere or magnetotail will by definition give information over a small range of orders of magnitude, and so scaling will tend to be narrowband. Here we develop a simple framework in which previous descriptions of magnetospheric dynamics can be described and contrasted. We then review existing observations which are indicative of SOC, and ask if they are sufficient to demonstrate it unambiguously, and if not, what new observations need to be made?Comment: 29 pages, 0 figures. Based on invited talk at Spring American Geophysical Union Meeting, 1999. Journal of Atmospheric and Solar Terrestrial Physics, in pres

Random walk through fractal environments

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is less than 2, there is though always a finite rate of unaffected escape. Random walks through fractal sets with D less or equal 2 can thus be considered as defective Levy walks. The distribution of jump increments for D > 2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk-increments. It is shown that the particles undergo anomalous, enhanced diffusion for D_F < 2, the diffusion is dominated by the finite escape rate. Diffusion for D_F > 2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality (SOC) models give rise to enhanced diffusion. The analytical results are illustrated by Monte-Carlo simulations.Comment: 22 pages, 16 figures; in press at Phys. Rev. E, 200