Combining genetic resources and elite material populations to improve the accuracy of genomic prediction in apple

Genomic selection is an attractive strategy for apple breeding that could reduce the length of breeding cycles. A possible limitation to the practical implementation of this approach lies in the creation of a training set large and diverse enough to ensure accurate predictions. In this study, we investigated the potential of combining two available populations, i.e., genetic resources and elite material, in order to obtain a large training set with a high genetic diversity. We compared the predictive ability of genomic predictions within-population, across-population or when combining both populations, and tested a model accounting for population-specific marker effects in this last case. The obtained predictive abilities were moderate to high according to the studied trait and small increases in predictive ability could be obtained for some traits when the two populations were combined into a unique training set. We also investigated the potential of such a training set to predict hybrids resulting from crosses between the two populations, with a focus on the method to design the training set and the best proportion of each population to optimize predictions. The measured predictive abilities were very similar for all the proportions, except for the extreme cases where only one of the two populations was used in the training set, in which case predictive abilities could be lower than when using both populations. Using an optimization algorithm to choose the genotypes in the training set also led to higher predictive abilities than when the genotypes were chosen at random. Our results provide guidelines to initiate breeding programs that use genomic selection when the implementation of the training set is a limitation

Global attractor and asymptotic dynamics in the Kuramoto model for coupled noisy phase oscillators

We study the dynamics of the large N limit of the Kuramoto model of coupled phase oscillators, subject to white noise. We introduce the notion of shadow inertial manifold and we prove their existence for this model, supporting the fact that the long term dynamics of this model is finite dimensional. Following this, we prove that the global attractor of this model takes one of two forms. When coupling strength is below a critical value, the global attractor is a single equilibrium point corresponding to an incoherent state. Conversely, when coupling strength is beyond this critical value, the global attractor is a two-dimensional disk composed of radial trajectories connecting a saddle equilibrium (the incoherent state) to an invariant closed curve of locally stable equilibria (partially synchronized state). Our analysis hinges, on the one hand, upon sharp existence and uniqueness results and their consequence for the existence of a global attractor, and, on the other hand, on the study of the dynamics in the vicinity of the incoherent and synchronized equilibria. We prove in particular non-linear stability of each synchronized equilibrium, and normal hyperbolicity of the set of such equilibria. We explore mathematically and numerically several properties of the global attractor, in particular we discuss the limit of this attractor as noise intensity decreases to zero.Comment: revised version, 28 pages, 4 figure

Generalized and weighted Strichartz estimates

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schr\"odinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.Comment: Final version, to appear in the Communications on Pure and Applied Analysis. 33 pages. 2 more references adde

Continental mass change from GRACE over 2002-2011 and its impact on sea level

Present-day continental mass variation as observed by space gravimetry reveals secular mass decline and accumulation. Whereas the former contributes to sea-level rise, the latter results in sea-level fall. As such, consideration of mass accumulation (rather than focussing solely on mass loss) is important for reliable overall estimates of sea-level change. Using data from the Gravity Recovery And Climate Experiment satellite mission, we quantify mass-change trends in 19 continental areas that exhibit a dominant signal. The integrated mass change within these regions is representative of the variation over the whole land areas. During the integer 9-year period of May 2002 to April 2011, GIA-adjusted mass gain and mass loss in these areas contributed, on average, to −(0.7 ± 0.4) mm/year of sea-level fall and + (1.8 ± 0.2) mm/year of sea-level rise; the net effect was + (1.1 ± 0.6) mm/year. Ice melting over Greenland, Iceland, Svalbard, the Canadian Arctic archipelago, Antarctica, Alaska and Patagonia was responsible for + (1.4±0.2) mm/year of the total balance. Hence, land-water mass accumulation compensated about 20 % of the impact of ice-melt water influx to the oceans. In order to assess the impact of geocentre motion, we converted geocentre coordinates derived from satellite laser ranging (SLR) to degree-one geopotential coefficients. We found geocentre motion to introduce small biases to mass-change and sea-level change estimates; its overall effect is + (0.1 ± 0.1) mm/year. This value, however, should be taken with care owing to questionable reliability of secular trends in SLR-derived geocentre coordinates

On the supercritical KDV equation with time-oscillating nonlinearity

For the initial value problem (IVP) associated to the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, \begin{equation*} u_{t}+\partial_x^3u+\partial_x(u^{k+1}) =0,\qquad k\geq 5, \end{equation*} numerical evidence [Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R.: Conservative, high-order numerical schemes for the generalized Korteweg–de Vries equation. Philos. Trans. Roy. Soc. London Ser. A 351, 107–164 (1995) ] shows that, there are initial data $\phi\in H^1(\mathbb{R})$ such that the corresponding solution may blow-up in finite time. Also, with the evidence from numerical simulation [Abdullaev F.K., Caputo J.G., Kraenkel R.A., Malomed B.A.: Controlling collapse in Bose–Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A 67, 012605 (2003) and Konotop V.V., Pacciani P.: Collapse of solutions of the nonlinear Schrödinger equation with a time dependent nonlinearity: application to the Bose–Einstein condensates. Phys. Rev. Lett. 94, 240405 (2005) ], it has been claimed that a periodic time dependent coefficient in the nonlinearity would disturb the blow-up solution, either accelerating or delaying it. In this work, we investigate the IVP associated to the gKdV equation \begin{equation*} u_{t}+\partial_x^3u+g(\omega t)\partial_x(u^{k+1}) =0, \end{equation*} where $g$ is a periodic function and $k\geq 5$ is an integer. We prove that, for given initial data $\phi \in H^1(\mathbb{R})$, as $|\omega|\to \infty$, the solution $u_{\omega}$ converges to the solution $U$ of the initial value problem associated to \begin{equation*} U_{t}+\partial_x^3U+m(g)\partial_x(U^{k+1}) =0, \end{equation*} with the same initial data, where $m(g)$ is the average of the periodic function $g$. Moreover, if the solution $U$ is global and satisfies $\|U\|_{L_x^5L_t^{10}}<\infty$, then we prove that the solution $u_{\omega}$ is also global provided $|\omega|$ is sufficiently large.M. P. was partially supported by the Research Center of Mathematics of the University of Minho, Portugal through the FCT Pluriannual Funding Program, and through the project PTDC/MAT/109844/2009, and M. S. was partially supported by FAPESP Brazil

The planform of epeirogeny: vertical motions of Australia during the Cretaceous

Estimates of dynamic motion of Australia since the end of the Jurassic have been made by modeling marine flooding and comparing it with palaeogeographical reconstructions of marine inundation. First, sediment isopachs were back stripped from present-day topography. Dynamic motion was determined by the displacement needed to approximate observed flooding when allowance is made for changes in eustatic sea-level. The reconstructed inundation patterns suggest that during the Cretaceous, Australia remained a relatively stable platform, and flooding in the eastern interior during the Early Cretaceous was primarily the result of the regional tectonic motion. Vertical motion during the Cretaceous was much smaller than the movement since the end of the Cretaceous. Subsidence and marine flooding in the Eromanga and Surat Basins, and the subsequent 500 m of uplift of the eastern portion of the basin, may have been driven by changes in plate dynamics during the Mesozoic. Convergence along the north-east edge of Australia between 200 and 100 Ma coincides with platform sedimentation and subsidence within the Eromanga and Surat Basins. A major shift in the position of subduction at 140 Ma was coeval with the marine incursion into the Eromanga. When subduction ended at 95 Ma, marine inundation of the Eromanga also ended. Subsidence and uplift of the eastern interior is consistent with dynamic models of subduction in which subsidence is generated when the dip angle of the slab decreases and uplift is generated when subduction terminates (i.e. the dynamic load vanishes). Since the end of the Cretaceous, Australia has uniformly subsided by about 250 m with little apparent tilting. This vertical subsidence may have resulted from the northward migration of the continent from a dynamic topography high and geoid low toward lower dynamic topography and a higher geoid.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71983/1/j.1365-2117.1994.tb00076.x.pd

Persistent acceleration in global sea-level rise since the 1960s

Previous studies reconstructed twentieth-century global mean sea level (GMSL) from sparse tide-gauge records to understand whether the recent high rates obtained from satellite altimetry are part of a longer-term acceleration. However, these analyses used techniques that can only accurately capture either the trend or the variability in GMSL, but not both. Here we present an improved hybrid sea-level reconstruction during 1900–2015 that combines previous techniques at time scales where they perform best. We find a persistent acceleration in GMSL since the 1960s and demonstrate that this is largely (~76%) associated with sea-level changes in the Indo-Pacific and South Atlantic. We show that the initiation of the acceleration in the 1960s is tightly linked to an intensification and a basin-scale equatorward shift of Southern Hemispheric westerlies, leading to increased ocean heat uptake, and hence greater rates of GMSL rise, through changes in the circulation of the Southern Ocean

A century of sea level measurements at Newlyn, SW England

The Newlyn Tidal Observatory is the most important sea level station in the UK. It commenced operations in 1915 as part of the Second Geodetic Levelling of England and Wales, and the mean sea level determined from the tide gauge during the first six years (May 1915-April 1921) defined Ordnance Datum Newlyn (ODN) which became the national height datum for the whole of Great Britain. The 100 years of sea level data now available have contributed significantly to many studies in oceanography, geology and climate change. This paper marks the centenary of this important station by reviewing the sea level (and, more recently, detailed land level) measurements and Newlyn’s contributions to UK cartography, geodesy and sea-level science in general. Recommendations are made on how sea and land level measurements at Newlyn might be enhanced in the future