  A theorem of Tate asserts that, for an elliptic surface E/X defined over a
number field k, and a section P of E, there exists a divisor D on X such that
the canonical height of the specialization of P to the fibre above t differs
from the height of t relative to D by at most a bounded amount.
  We prove the analogous statement for a one-parameter family of polynomial
dynamical systems. Moreover, we compare, at each place of k, the local
canonical height with the local contribution to the height relative to D, and
show that the difference is analytic near the support of D, a result which is
analogous to results of Silverman in the elliptic surface context.
