  We develop a statistical model describing the dynamics of magnetic islands in
very large current layers that develop in space plasma. Two parameters
characterize the island distribution: the flux contained in the island and the
area it encloses. We derive an integro-differential evolution equation for this
distribution function, based on rules that govern the small-scale generation of
secondary islands, the rates of island growth, and island merging. Our
numerical solutions of this equation produce island distributions relevant to
the magnetosphere and corona. We also derive and analytically solve a
differential equation for large islands that explicitly shows the role merging
plays in island growth.
