  We deduce an analogue of the Bogomolov conjecture for non-degenerate
subvarieties in fibered products of families of elliptic curves from the
author's recent theorem on equidistribution in families of abelian varieties.
This generalizes results of DeMarco and Mavraki and improves certain results of
Manin-Mumford type proven by Masser and Zannier to results of Bogomolov type,
yielding the first results of this type for subvarieties of relative dimension
$>1$ in families of abelian varieties with trivial trace.
