  As a computationally less costly test case for full QCD, we investigate an
SU(3) Yang-Mills theory coupled to a bosonic spinor field. This theory
corresponds to QCD with minus two quark flavors and is known as the bermion
model. Our central object of interest is the step scaling function which
describes the scale evolution of the running coupling in the Schrodinger
functional scheme. We develop a suitable algorithm for the simulation of O(a)
improved bermions and compare its performance with unimproved bermions and full
QCD. We study in detail the lattice artefacts and the continuum extrapolation
of the step scaling function from lattice simulations when improvement is used.
Our results are compared to the unimproved bermion and dynamical fermion cases,
and to renormalized perturbation theory in the continuum limit.
  We also examine the step scaling function with massive quarks in the bermion
model. According to the Appelquist-Carazzone theorem the contributions from
matter fields are expected to vanish for large masses, such that the step
scaling function converges to the pure gauge theory case. If one wants to
connect non-perturbatively different effective theories with different numbers
of active quarks over flavor thresholds, lattice artefacts should be reasonably
small. In order to test the feasibility of such a method, we investigate the
step scaling function and its lattice artefacts for several values of the mass.
