  We study the statistics of dwarf galaxy populations as a function of
environment in the cold dark matter (CDM) and warm dark matter (WDM)
cosmogonies, using hydrodynamical simulations starting from initial conditions
with matched phases but differing power spectra, and evolved with the EAGLE
galaxy formation model. We measure the abundance of dwarf galaxies within 3~Mpc
of DM haloes with a present-day halo mass similar to that of the Milky Way
(MW), and find that the radial distribution of galaxies $M_{*}>10^7$\Msun is
nearly identical for WDM and CDM. However, the cumulative mass function becomes
shallower for WDM at lower masses, yielding 50~per~cent fewer dwarf galaxies of
$M_{*}\gtrsim10^{5}$~\Msun than CDM. The suppression of low-mass halo counts in
WDM relative to CDM increases significantly from high-density regions to
low-density regions for haloes in the region of the half-mode mass,
$M_\rm{hm}$. The luminous fraction in the two models also diverges from the
overdense to the underdense regions for $M>2M_\rm{hm}$, as the increased
collapse delay at small densities pushes the collapse to after the reionization
threshold. However, the stellar mass--halo mass relation of WDM haloes relative
to CDM increases towards lower-density regions. Finally, we conclude that the
suppression of galaxies with $M_{*}\gtrsim10^5$\Msun between WDM and CDM is
independent of density: the suppression of halo counts and the luminous
fraction is balanced by an enhancement in stellar mass--halo mass relation.
