  This paper studies groups of symplectomorphisms of ruled surfaces for
symplectic forms with varying cohomology class. This class is characterized by
the ratio R of the size of the base to that of the fiber. By considering
appropriate spaces of almost complex structures, we investigate how the
topological type of these groups changes as R increases. If the base is a
sphere, this changes precisely when R passes an integer, and for general bases
it stabilizes as R goes to infinity. Our results extend and make more precise
some of the conclusions of Abreu--McDuff concerning the rational homotopy type
of these groups for rational ruled surfaces.
