High density SNP and DArT-based genetic linkage maps of two closely related oil palm populations

Oil palm (Elaeis guineensis Jacq.) is an outbreeding perennial tree crop with long breeding cycles, typically 12 years. Molecular marker technologies can greatly improve the breeding efficiency of oil palm. This study reports the first use of the DArTseq platform to genotype two closely related self-pollinated oil palm populations, namely AA0768 and AA0769 with 48 and 58 progeny respectively. Genetic maps were constructed using the DArT and SNP markers generated in combination with anchor SSR markers. Both maps consisted of 16 major independent linkage groups (2n = 2× = 32) with 1399 and 1466 mapped markers for the AA0768 and AA0769 populations, respectively, including the morphological trait “shell-thickness” (Sh). The map lengths were 1873.7 and 1720.6 cM with an average marker density of 1.34 and 1.17 cM, respectively. The integrated map was 1803.1 cM long with 2066 mapped markers and average marker density of 0.87 cM. A total of 82% of the DArTseq marker sequence tags identified a single site in the published genome sequence, suggesting preferential targeting of gene-rich regions by DArTseq markers. Map integration of higher density focused around the Sh region identified closely linked markers to the Sh, with D.15322 marker 0.24 cM away from the morphological trait and 5071 bp from the transcriptional start of the published SHELL gene. Identification of the Sh marker demonstrates the robustness of using the DArTseq platform to generate high density genetic maps of oil palm with good genome coverage. Both genetic maps and integrated maps will be useful for quantitative trait loci analysis of important yield traits as well as potentially assisting the anchoring of genetic maps to genomic sequences

Building Spacetime Meshes over Arbitrary Spatial Domains

We present an algorithm to construct meshes suitable for spacetime discontinuous Galerkin finite-element methods. Our method generalizes and improves the `Tent Pitcher' algorithm of Üngör and Sheffer. Given an arbitrary simplicially meshed domain X of any dimension and a time interval [0, T], our algorithm builds a simplicial mesh of the spacetime domain X * [0, T],in constant time per element. Our algorithm avoids the limitations of previous methods by carefully adapting the durations of spacetime elements to the local quality and feature size ofthe underlying space mesh

Building Space-Time Meshes over Arbitrary Spatial Domains

We present an algorithm to construct meshes suitable for space-time discontinuous Galerkin finite-element methods. Our method generalizes and improves the 'Tent Pitcher' algorithm of /lngSr and Sheffer. Given an arbitrary simplicially meshed domain X of any dimension and a time interval [0, T], our algorithm builds a simplicial mesh of the space-time domain X x [0, T], in constant time per element. Our algorithm avoids the limitations of previous methods by carefully adapting the durations of space-time elements to the local quality and feature size of the underlying space mesh

Spacetime Meshing with Adaptive Refinement and Coarsening

We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain# and a target time value T , our method constructs a tetrahedral mesh of the spacetime domain [0, T] in constant running time per tetrahedron in IR using an advancing front method. Elements are added to the evolving mesh in small patches by moving a vertex of the front forward in time. Spacetime discontinuous Galerkin methods allow the numerical solution within each patch to be computed as soon as the patch is created. Our algorithm employs new mechanisms for adaptively coarsening and refining the front in response to a posteriori error estimates returned by the numerical code. A change in the front induces a corresponding refinement or coarsening of future elements in the spacetime mesh. Our algorithm adapts the duration of each element to the local quality, feature size, and degree of refinement of the underlying space mesh. We directly exploit the ability of discontinuous Galerkin methods to accommodate discontinuities in the solution fields across element boundaries