Population density and plant availability interplay to shape browsing intensity by roe deer in a deciduous forest

•The functional response relating browsing intensity to plant availability was strongly non-linear and density-dependent.•When plant availability was low, browsing increased with plant availability with an increasing rate with roe deer density.•When plant availability was above 12.5% browsing intensity increased with both plant availability and roe deer density in an additive way.•Forest susceptibility to browsing increases with increasing competition for food, especially when plant availability is low.•Considering functional responses improves the accuracy of management tools when monitoring the herbivore-plant system.