Sensitivity analyses of population projection matrix (PPM) models are often used to identify life-history perturbations that will most influence a population's future dynamics. Sensitivities are linear extrapolations of the relationship between a population's growth rate and perturbations to its demographic parameters. Their effectiveness depends on the validity of the assumption of linearity. Here we assess whether sensitivity analysis is an appropriate tool to investigate the effect of predation by cats on the population growth rates of their avian prey. We assess whether predation by cats leads to non-linear effects on population growth and compare population growth rates predicted by sensitivity analysis with those predicted by a non-linear simulation. For a two-stage, age-classified House Sparrow Passer domesticus PPM slight non-linearity arose when PPM elements were perturbed, but perturbation to the vital rates underlying the matrix elements had a linear impact on population growth rate. We found a similar effect with a slightly larger three-stage, age-classified PPM for a Winter Wren Troglodytes troglodytes population perturbed by cat predation. For some avian species, predation by cats may cause linear or only slightly nonlinear impacts on population growth rates. For these species, sensitivity analysis appears to be a useful conservation tool. However, further work on multiple perturbations to avian prey species with more complicated life histories and higher-dimension PPM models is required.