Genomic consequences of mating system evolution in the Pacific coastal dune endemic, Abronia umbellata (Nyctaginaceae)

The advent of next-generation sequencing has significantly reduced the cost of obtaining large-scale genetic resources, opening the door for genomic studies of non-model but ecologically interesting species. The shift in mating system, from outcrossing to selfing, has occurred thousands of times in angiosperms and is accompanied by profound changes in the population genetics and ecology of a species. A large body of work has been devoted to understanding why the shift occurs and the impact of the shift on the genetics of the resulting selfing populations, however, the causes and consequences of the transition to selfing involve a complicated interaction of genetic and demographic factors which are difficult to untangle. Abronia umbellata is a Pacific coastal dune endemic which displays a striking shift in mating system across its geographic range, with large-flowered outcrossing populations south of San Francisco and small-flowered selfing populations to the north. Abronia umbellata is an attractive model system for the study of mating system transitions because the shift appears to be recent and therefore less obscured by post-shift processes, it has a near one-dimensional geographic range which simplifies analysis and interpretation, and demographic data has been collected for many of the populations. In this study, we generated transcriptome-level data for 12 plants including individuals from both subspecies, along with a resequencing study of 48 individuals from populations across the range. The genetic analysis revealed a recent transition to selfing involving a drastic reduction in genetic diversity in the selfing lineage, potentially indicative of a recent population bottleneck and a transition to selfing due to reproductive assurance. Interestingly, the genetic structure of the populations was not coincident with the current subspecies demarcation, and two large-flowered populations were classified with the selfing subspecies, suggesting a potential need for re-evaluation of the current subspecies classification. Our finding of low diversity in selfing populations may also have implications for the conservation value of the threatened selfing subspecies.

Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.