  We study Lefschetz pencils on symplectic four-manifolds via the associated
spheres in the moduli spaces of curves, and in particular their intersections
with certain natural divisors. An invariant defined from such intersection
numbers can distinguish manifolds with torsion first Chern class. We prove that
pencils of large degree always give spheres which behave `homologically' like
rational curves; contrastingly, we give the first constructive example of a
symplectic non-holomorphic Lefschetz pencil. We also prove that only finitely
many values of signature or Euler characteristic are realised by manifolds
admitting Lefschetz pencils of genus two curves.
