  The excitation functions of $K^+$ and $K^-$ mesons in heavy ion collisions
are studied within a statistical model assuming chemical and thermal
equilibrium with exact strangeness conservation. At low incident energies the
associate production of kaons, i.e. the production of a K+ together with a
hyperon and the production of a K- together with a K+, implies specific
features: different threshold energies and different dependences of K+ and K-
yields on baryon number density. It is shown that the experimentally observed
equality of the $K^+$ and $K^-$ rates at energies $\sqrt{s} - \sqrt{s_{th}}
\leq 0$ is due to a crossing of the two excitation functions. Furthermore, the
independence of the $K^+$ to $K^-$ ratio on the number of participating
nucleons observed at 1 and 10 $A\cdot$GeV is consistent with this model.
