Domesticated species are impacted in unintended ways during domestication and breeding. Changes in the nature and intensity of selection impart genetic drift, reduce diversity, and increase the frequency of deleterious alleles. Such outcomes constrain our ability to expand the cultivation of crops into environments that differ from those under which domestication occurred. We address this need in chickpea, an important pulse legume, by harnessing the diversity of wild crop relatives. We document an extreme domestication-related genetic bottleneck and decipher the genetic history of wild populations. We provide evidence of ancestral adaptations for seed coat color crypsis, estimate the impact of environment on genetic structure and trait values, and demonstrate variation between wild and cultivated accessions for agronomic properties. A resource of genotyped, association mapping progeny functionally links the wild and cultivated gene pools and is an essential resource chickpea for improvement, while our methods inform collection of other wild crop progenitor species.

To date, only the implicit (Crank-Nicholson) integration method has ben used for numerical integration of the Schrodinger equation for collision processes. The standard explicit methods are known to be unstable and a high price is paid for the implicit method due to the inversion of the large matrices involved. Furthermore, the method is prohibitive in more than two dimensions due to restrictions on memory and large computation times, An explicit method (i.e., a method which doesn't require the solution of simultaneous equations) is presented, and is shown to be stable in n dimensions to the same order of accuracy as the implicit method with the unitarity being secured to two orders higher accuracy than that for the wave function. 2794

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