  We study the organization of topological defects in a system of nematogens
confined to the two-dimensional sphere (S^2). We first perform Monte Carlo
simulations of a fluid system of hard rods (spherocylinders) living in the
tangent plane of S^2. The sphere is adiabatically compressed until we reach a
jammed nematic state with maximum packing density. The nematic state exhibits
four +1/2 disclinations arrayed on a great circle rather than at the vertices
of a regular tetrahedron. This arises from the high elastic anisotropy of the
system in which splay (K_1) is far softer than bending (K_3). We also introduce
and study a lattice nematic model on S^2 with tunable elastic constants and map
out the preferred defect locations as a function of elastic anisotropy. We
establish the existence of a one-parameter family of degenerate ground states
in the extreme splay-dominated limit K_1/K_3 -> 0. Thus the global defect
geometry is controllable by tuning the relative splay to bend modulus.
