  We deduce an analogue of the Bogomolov conjecture for non-degenerate
subvarieties in fibered products of elliptic families 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.
