Establishment of a core collection of Cynodon based on morphological data

In a field plot study conducted in Danzhou, Hainan province, China, a total of 537 wild Cynodon accessions from 22 countries and classified into 11 groups according to taxonomy and origin, were characterized in terms of 11 phenotypic traits in order to construct a core collection. For this, the optimal strategy was developed by screening within the following method levels: (i) 7 sampling proportions (5, 10, 15, 20, 25, 30 and 35%); (ii) 3 sampling methods (preferential sampling, deviation sampling and random sampling); (iii) 5 clustering methods [single linkage, completed linkage, median linkage, unweighted pair-group average (UPGMA) and Ward’s method]; (iv) 3 genetic distances (Euclidean distance, Mahalanobis distance and principal component distance); and (v) 3 sampling proportions within groups (simple, logarithmic and square root proportions). Mean difference percentage, variance difference percentage, coincidence rate of range and variation coefficient changing rate were the criteria adopted for evaluating how well the core collection represented the original collection. The correlation between the original and core collections was determined for comparison. The core collections were validated with the sample distribution diagram of the main components. Results showed that the optimal sampling method for constructing a Cynodon core collection was preferential sampling, the optimal sampling proportion being 20%. The optimal sampling proportion within groups was the square root proportion, the optimal genetic distance was Mahalanobis distance and the optimal clustering method was UPGMA. The proposed core collection of Cynodon is composed of 108 accessions; it was constructed following the optimal sampling strategy identified and retained the original collection´s phenotypic diversity, phenotypic trait correlations and phenotypic group structure. Thus, this collection could be considered a representative sample of the entire resource.

Dynamics of a long chain in turbulent flows: impact of vortices

We show and explain how a long bead–spring chain, immersed in a homogeneous isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of three-dimensional (3D) turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In the 3D case on the contrary, the chain is extended even in vortical regions, which suggests that the chain follows axially stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly flexible, inextensible chain also shows preferential sampling in three dimensions, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in two dimensions is considerably reduced. In three dimensions, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

Log-log linearity of the asymptotic distribution - a valid indicator of multi-fractality?

<p>The asymptotic shape of the marginal frequency distribution of geochemical variables has been proposed as indicator of multi-fractality. Transition into a certain statistical regime as inferred from the distribution function may be considered as criterion to delineate geochemical anomalies, including mineral resources or pollutants such as radioactive fallout or geogenic radon.</p><p>The argument is that asymptotic linearity in log-log scale, log(F(z)) = a - b log(z) as z→∞, b>0 a constant, indicates multi-fractality.</p><p>We discuss this with respect to two issues:</p><p>(1) What are the consequences of estimating the slope b for non-ergodic, in particular non-representative and preferential sampling schemes, as often the case in geochemical or pollution surveys?</p><p>(2) Frequently in geochemistry, multiplicative cascades are considered valid generators of multifractal fields, corroborated by observed f(α) functions and variograms (Matèrn or power, for low lags). This generator leads to marginally asymptotically (high cascade orders) log-normal distributions, which in log-log scale are asymptotically (high z) parabolic, not linear.</p><p>Theoretical aspects are addressed as well as examples given.</p>