  We study how manifestations of strong electron-phonon interaction (EPI)
depend on the carrier concentration by solving the two-dimensional Holstein
model for the spin-polarized fermions using an approximation free bold-line
diagrammatic Monte Carlo (BDMC) method. We show that the strong EPI, obviously
present at very small Fermion concentration, is masked by the Fermi blockade
effects and Migdal's theorem to the extent that it manifests itself as moderate
one at large carriers densities. Suppression of strong EPI fingerprints is in
agreement with experimental observations in doped high temperature
superconductors
