  We study the impact of different bias and redshift-space models on the halo
power spectrum, quantifying their effect by comparing the fit to a subset of
realizations taken from the WizCOLA suite. These provide simulated power
spectrum measurements between $k_{\rm min}$ = 0.03 h/Mpc and $k_{\rm max}$ =
0.29 h/Mpc, constructed using the comoving Lagrangian acceleration method. For
the bias prescription we include (i) simple linear bias; (ii) the McDonald &
Roy model and (iii) its coevolution variant introduced by Saito et al.; and
(iv) a very general model including all terms up to one-loop and corrections
from advection. For the redshift-space modelling we include the Kaiser formula
with exponential damping and the power spectrum provided by (i) tree-level
perturbation theory and (ii) the Halofit prescription; (iii) one-loop
perturbation theory, also with exponential damping; and (iv) an effective field
theory description, also at one-loop, with damping represented by the EFT
subtractions. We quantify the improvement from each layer of modelling by
measuring the typical improvement in chi-square when fitting to a member of the
simulation suite. We attempt to detect overfitting by testing for compatibility
between the best-fit power spectrum per realization and the best-fit over the
entire WizCOLA suite. For both bias and the redshift-space map we find that
increasingly permissive models yield improvements in chi-square but with
diminishing returns. The most permissive models show modest evidence for
overfitting. Accounting for model complexity using the Bayesian Information
Criterion, we argue that standard perturbation theory up to one-loop, or a
related model such as that of Taruya, Nishimichi & Saito, coupled to the
coevolution bias model, is likely to provide a good compromise for near-future
galaxy surveys operating with comparable $k_{\rm max}$.

Cosmology and Nongalactic Astrophysics