  We study a predator-prey model with Holling type I functional response, an
alternative food source for the predator, and multiple Allee effects on the
prey. We show that the model has at most two equilibrium points in the first
quadrant, one is always a saddle point while the other can be a repeller or an
attractor. Moreover, there is always a stable equilibrium point that
corresponds to the persistence of the predator population and the extinction of
the prey population. Additionally, we show that when the parameters are varied
the model displays a wide range of different bifurcations, such as saddle-node
bifurcations, Hopf bifurcations, Bogadonov-Takens bifurcations and homoclinic
bifurcations. We use numerical simulations to illustrate the impact changing
the predation rate, or the non-fertile prey population, and the proportion of
alternative food source have on the basins of attraction of the stable
equilibrium point in the first quadrant (when it exists). In particular, we
also show that the basin of attraction of the stable positive equilibrium point
in the first quadrant is bigger when we reduce the depensation in the model.
