  Thanks to the detections of more than 3000 exoplanets these last 20 years,
statistical studies have already highlighted some properties in the
distribution of the planet parameters. Nevertheless, few studies have yet
investigated the planet populations from short to large separations around the
same star since this requires the use of different detection techniques that
usually target different types of stars. We wish to develop a tool that
combines direct and indirect methods so as to correctly investigate the giant
planet populations at all separations. We developed the MESS2 code, a Monte
Carlo simulation code combining radial velocity and direct imaging data
obtained at different epochs for a given star to estimate the detection
probability of giant planets spanning a wide range of physical separations. It
is based on the generation of synthetic planet populations. We apply MESS2 on a
young M1-type, the nearby star AUMic observed with HARPS and NACO/ESO. We show
that giant planet detection limits are significantly improved at intermediate
separations (~20au in the case of AUMic). We show that the traditional approach
of analysing independently the RV and DI detection limits systematically
overestimates the planet detection limits and hence planet occurrence rates.
The use of MESS2 allows to obtain correct planet occurrence rates in
statistical studies, making use of multi-epoch DI data and/or RV measurements.
We also show that MESS2 can optimise the schedule of future DI observations.
