1. Avian brood parasites include species that are host specialists and others that are generalists. The impact of each kind of parasite on the persistence of the host population is studied by means of a population dynamics model. 2. Our model examines conditions for coexistence and invasions in a community of three South American cowbirds, the shiny cowbird Molothrus bonariensis (a generalist parasite), the screaming cowbird M. rufoaxillaris (a specialist parasite), and the bay-winged cowbird Agelaiodes badius (a nonparasite that hosts the other two). 3. Three biologically realistic characteristics not previously included in brood parasitism models are explored and shown to be crucial for the stability of the system. These characteristics are: (i) female parasites take at least a day to produce an egg and cannot store eggs for delayed laying – this is modelled by means of a type II functional response; (ii) parasites often remove or puncture (destroy) host eggs when visiting a nest; and (iii) hosts desert nests when the total clutch (host plus parasite) exceeds some threshold. 4. These characteristics have a direct impact on parasite population renewal and reduce dramatically the stable coexistence conditions. 5. Comparing the stability conditions of the host–specialist system with those of the three-species system shows the impact of the arrival of a generalist parasite on the persistence of the host–specialist system when the three characteristics are present. The stability boundaries are restricted when the generalist is absent and change little for a realistic density of generalist. 6. The study of invasion by a specialist into a host-generalist stable community shows that the parameter region for coexistence and invasion coincide. 7. Comparison of our model against its precursors using field data for the parameters when available, shows that the three-species cowbird model system is stable for empirically realized parameter values, unlike a previous model by May & Robinson (1985; American Naturalist, 126, 475–494) where none of the three characteristics were included.
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