  We upgraded the chemical network from the UMIST Database for Astrochemistry
2006 to include isotopes such as ^{13}C and ^{18}O. This includes all
corresponding isotopologues, their chemical reactions and the properly scaled
reaction rate coefficients. We study the fractionation behavior of
astrochemically relevant species over a wide range of model parameters,
relevant for modelling of photo-dissociation regions (PDRs). We separately
analyze the fractionation of the local abundances, fractionation of the total
column densities, and fractionation visible in the emission line ratios. We
find that strong C^+ fractionation is possible in cool C^+ gas. Optical
thickness as well as excitation effects produce intensity ratios between 40 and
400. The fractionation of CO in PDRs is significantly different from the
diffuse interstellar medium. PDR model results never show a fractionation ratio
of the CO column density larger than the elemental ratio. Isotope-selective
photo-dissociation is always dominated by the isotope-selective chemistry in
dense PDR gas. The fractionation of C, CH, CH^+, and HCO^+ is studied in
detail, showing that the fractionation of C, CH and CH^+ is dominated by the
fractionation of their parental species. The light hydrides chemically derive
from C^+, and, consequently, their fractionation state is coupled to that of
C^+. The fractionation of C is a mixed case depending on whether formation from
CO or HCO^+ dominates. Ratios of the emission lines of [C II], [C I], ^{13}CO,
and H^{13}CO^+ provide individual diagnostics to the fractionation status of
C^+, C, and CO.
