We present statistically convergent profile likelihood maps obtained via global
fits of a phenomenological Minimal Supersymmetric Standard Model with 15 free parameters
(the MSSM-15), based on over 250M points. We derive constraints on the model
parameters from direct detection limits on dark matter, the Planck relic density measurement
and data from accelerator searches. We provide a detailed analysis of the rich
phenomenology of this model, and determine the SUSY mass spectrum and dark matter
properties that are preferred by current experimental constraints. We evaluate the impact
of the measurement of the anomalous magnetic moment of the muon (g −2) on our results,
and provide an analysis of scenarios in which the lightest neutralino is a subdominant component
of the dark matter. The MSSM-15 parameters are relatively weakly constrained by
current data sets, with the exception of the parameters related to dark matter phenomenology
(M1, M2, µ), which are restricted to the sub-TeV regime, mainly due to the relic density
constraint. The mass of the lightest neutralino is found to be < 1.5 TeV at 99% C.L., but
can extend up to 3 TeV when excluding the g − 2 constraint from the analysis. Low-mass
bino-like neutralinos are strongly favoured, with spin-independent scattering cross-sections
extending to very small values, ∼ 10−20 pb. ATLAS SUSY null searches strongly impact
on this mass range, and thus rule out a region of parameter space that is outside the reach
of any current or future direct detection experiment. The best-fit point obtained after inclusion
of all data corresponds to a squark mass of 2.3 TeV, a gluino mass of 2.1 TeV and a
130 GeV neutralino with a spin-independent cross-section of 2.4×10−10 pb, which is within
the reach of future multi-ton scale direct detection experiments and of the upcoming LHC
run at increased centre-of-mass energy.