Paternal origins and migratory episodes of domestic sheep.

The domestication and subsequent global dispersal of livestock are crucial events in human history, but the migratory episodes during the history of livestock remain poorly documented [1-3]. Here, we first developed a set of 493 novel ovine SNPs of the male-specific region of Y chromosome (MSY) by genome mapping. We then conducted a comprehensive genomic analysis of Y chromosome, mitochondrial DNA, and whole-genome sequence variations in a large number of 595 rams representing 118 domestic populations across the world. We detected four different paternal lineages of domestic sheep and resolved, at the global level, their paternal origins and differentiation. In Northern European breeds, several of which have retained primitive traits (e.g., a small body size and short or thin tails), and fat-tailed sheep, we found an overrepresentation of MSY lineages y-HC and y-HB, respectively. Using an approximate Bayesian computation approach, we reconstruct the demographic expansions associated with the segregation of primitive and fat-tailed phenotypes. These results together with archaeological evidence and historical data suggested the first expansion of early domestic hair sheep and the later expansion of fat-tailed sheep occurred ∼11,800-9,000 years BP and ∼5,300-1,700 years BP, respectively. These findings provide important insights into the history of migration and pastoralism of sheep across the Old World, which was associated with different breeding goals during the Neolithic agricultural revolution

Sensitivity of modeled tracer motion in tidal areas to numerics and to non-Hamiltonian perturbations

This study focuses on the motion of passive tracers induced by the joint action of tidal and residual currents in shallow seas with an irregular bottom topography. Interest in this problem has rapidly increased in recent years, because of the detection of large-scale pollution of marine waters by plastics. Early simplified models considered advection of tracers by a two-dimensional depth-averaged velocity field that is solenoidal, thereby resulting in a system that is Hamiltonian and nonintegrable. Here, two new aspects are considered. First, the sensitivity of solutions to three different numerical schemes is investigated. To quantify the behavior of orbits, both the largest Lyapunov exponent and the K-coefficient of the zero-one test for chaos were calculated. It turns out that a new scheme, which extends a known symplectic scheme to systems that also contain non-Hamiltonian terms, performs best. The second aspect concerns the fact that a depth-averaged velocity field is actually divergent, thereby rendering the model of tracer motion to be non-Hamiltonian. It is demonstrated that the divergent velocity components, no matter how small, cause the appearance of attractors in the system and thus they have a strong impact on the fate of tracers. Interpretation of the numerical results is given by deriving and analyzing approximate analytical solutions of the system