The origin of the high hole density in In$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$N:Mg

InGaN is the nitride of choice for applications requiring high hole density and emission tunability. The increased hole density with In incorporation may be explained by several different mechanisms; however, our electron paramagnetic resonance (EPR) studies reveal a surprising feature: the number of Mg-related acceptors decreases with increasing hole density. In$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$N films, with x between 0.02 and 0.11 and thickness between 0.25 and 0.44 $\mu$m, were grown p-type by doping with Mg to a concentration of 2-3 $\times$ 10$^{19}$ cm$^{-3}$. Hall measurements reveal the expected hole density increase from 5-30x10$^{17}$ cm$^{-3}$ with increasing In mole fraction. However, unlike GaN:Mg where the EPR Mg signal tracks the hole density, the EPR intensity of the Mg-related signal in InGaN is found to decrease as the hole density increases. Together, compensating defects and a lowering of the acceptor level may explain the decrease in EPR intensity and the increase in hole density observed as the In mole fraction is increased.