  We analyze the consequences of models of structure formation for higher-order
($n$-point) galaxy correlation functions in the mildly non-linear regime.
Several variations of the standard $\Omega=1$ cold dark matter model with
scale-invariant primordial perturbations have recently been introduced to
obtain more power on large scales, 20 h$^{-1}$ Mpc, e.g., low-matter-density
(non-zero cosmological constant) models, `tilted' primordial spectra, and
scenarios with a mixture of cold and hot dark matter. They also include models
with an effective scale-dependent bias, such as the cooperative galaxy
formation scenario of Bower, etal. (1993). We show that higher-order galaxy
correlation functions can provide a useful test of such models and can
discriminate between models with true large-scale power in the density field
and those where the galaxy power arises from scale-dependent bias: a bias with
rapid scale-dependence leads to a dramatic decrease of the hierarchical
amplitudes at large scales. Current observational constraints on the
three-point amplitudes $Q_3$ and $S_3$ can place limits on the bias
parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that
scale-dependent bias is responsible for the extra power observed on large
scales.
