  We calculate perturbatively the normalized spatial skewness, $S_3$, and full
three-point correlation function (3PCF), $\zeta$, induced by gravitational
instability of Gaussian primordial fluctuations for a biased tracer-mass
distribution in flat and open cold-dark-matter (CDM) models. We take into
account the dependence on the shape and evolution of the CDM power spectrum,
and allow the bias to be nonlinear and/or evolving in time, using an extension
of Fry's (1996) bias-evolution model. We derive a scale-dependent,
leading-order correction to the standard perturbative expression for $S_3$ in
the case of nonlinear biasing, as defined for the unsmoothed galaxy and
dark-matter fields, and find that this correction becomes large when probing
positive effective power-spectrum indices. This term implies that the inferred
nonlinear-bias parameter, as usually defined in terms of the smoothed density
fields, might depend on the chosen smoothing scale. In general, we find that
the dependence of $S_3$ on the biasing scheme can substantially outweigh that
on the adopted cosmology. We demonstrate that the normalized 3PCF, $Q$, is an
ill-behaved quantity, and instead investigate $Q_V$, the variance-normalized
3PCF. The configuration dependence of $Q_V$ shows similarly strong
sensitivities to the bias scheme as $S_3$, but also exhibits significant
dependence on the form of the CDM power spectrum. Though the degeneracy of
$S_3$ with respect to the cosmological parameters and constant linear- and
nonlinear-bias parameters can be broken by the full configuration dependence of
$Q_V$, neither statistic can distinguish well between evolving and non-evolving
bias scenarios. We show that this can be resolved, in principle, by considering
the redshift dependence of $\zeta$.
