  We present a statistical analysis of the first 300 stars observed by the
Gemini Planet Imager Exoplanet Survey (GPIES). This subsample includes six
detected planets and three brown dwarfs; from these detections and our contrast
curves we infer the underlying distributions of substellar companions with
respect to their mass, semi-major axis, and host stellar mass. We uncover a
strong correlation between planet occurrence rate and host star mass, with
stars M $>$ 1.5 $M_\odot$ more likely to host planets with masses between 2-13
M$_{\rm Jup}$ and semi-major axes of 3-100 au at 99.92% confidence. We fit a
double power-law model in planet mass (m) and semi-major axis (a) for planet
populations around high-mass stars (M $>$ 1.5M$_\odot$) of the form $\frac{d^2
N}{dm da} \propto m^\alpha a^\beta$, finding $\alpha$ = -2.4 $\pm$ 0.8 and
$\beta$ = -2.0 $\pm$ 0.5, and an integrated occurrence rate of $9^{+5}_{-4}$%
between 5-13 M$_{\rm Jup}$ and 10-100 au. A significantly lower occurrence rate
is obtained for brown dwarfs around all stars, with 0.8$^{+0.8}_{-0.5}$% of
stars hosting a brown dwarf companion between 13-80 M$_{\rm Jup}$ and 10-100
au. Brown dwarfs also appear to be distributed differently in mass and
semi-major axis compared to giant planets; whereas giant planets follow a
bottom-heavy mass distribution and favor smaller semi-major axes, brown dwarfs
exhibit just the opposite behaviors. Comparing to studies of short-period giant
planets from the RV method, our results are consistent with a peak in
occurrence of giant planets between ~1-10 au. We discuss how these trends,
including the preference of giant planets for high-mass host stars, point to
formation of giant planets by core/pebble accretion, and formation of brown
dwarfs by gravitational instability.
