  The inclusive production of {\Lambda} hyperons in proton-proton collisions at
$\sqrt{s}$ = 3.18 GeV was measured with HADES at the GSI Helmholtzzentrum f\"ur
Schwerionenforschung in Darmstadt. The experimental data are compared to a
data-based model for individual exclusive {\Lambda} production channels in the
same reaction. The contributions of intermediate resonances such as
{\Sigma}(1385), {\Delta}++ or N* are considered in detail. In particular, the
result of a partial wave analysis is accounted for the abundant pK$^+${\Lambda}
final state. Model and data show a reasonable agreement at mid rapidities,
while a difference is found for larger rapidities. A total {\Lambda} production
cross section in p+p collisions at $\sqrt{s}$ = 3.18 GeV of {\sigma}(pp $\to$
{\Lambda} + X) = 207.3 $\pm$ 1.3 +6.0 -7.3 (stat.) $\pm$ 8.4 (syst.) +0.4 -0.5
(model) {\mu}b is found.
