  For ion transport in network glasses, it is a great challenge to predict
conductivities specifically based on structural properties. To this end it is
necessary to gain an understanding of the energy landscape where the thermally
activated hopping motion of the ions takes place. For alkali borophosphate
glasses, a statistical mechanical approach was suggested to predict essential
characteristics of the distribution of energies at the residence sites of the
mobile alkali ions. The corresponding distribution of site energies was derived
from the chemical units forming the glassy network. A hopping model based on
the site energy landscape allowed to model the change of conductivity
activation energies with the borate to phosphate mixing ratio. Here we refine
and extend this general approach to cope with minimal local activation barriers
and to calculate dc-conductivities without the need of performing extensive
Monte-Carlo simulations. This calculation relies on the mapping of the
many-body ion dynamics onto a network of local conductances derived from the
elementary jump rates of the mobile ions. Application of the theoretical
modelling to three series of alkali borophosphate glasses with the compositions
$0.33$Li$_2$O$-0.67$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$],
$0.35$Na$_2$O$-0.65$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$] and
$0.4$Na$_2$O$-0.6$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$] shows good agreement
with experimental data.
