  In the singularly perturbed limit corresponding to a large diffusivity ratio
between two components in a reaction-diffusion (RD) system, quasi-equilibrium
spot patterns are often admitted, producing a solution that concentrates at a
discrete set of points in the domain. In this paper, we derive and study the
differential algebraic equation (DAE) that characterizes the slow dynamics for
such spot patterns for the Brusselator RD model on the surface of a sphere.
Asymptotic and numerical solutions are presented for the system governing the
spot strengths, and we describe the complex bifurcation structure and
demonstrate the occurrence of imperfection sensitivity due to higher order
effects. Localized spot patterns can undergo a fast time instability and we
derive the conditions for this phenomena, which depend on the spatial
configuration of the spots and the parameters in the system. In the absence of
these instabilities, our numerical solutions of the DAE system for $N = 2$ to
$N = 8$ spots suggest a large basin of attraction to a small set of possible
steady-state configurations. We discuss the connections between our results and
the study of point vortices on the sphere, as well as the problem of
determining a set of elliptic Fekete points, which correspond to globally
minimizing the discrete logarithmic energy for $N$ points on the sphere.
