An R 0 theory for source-sink dynamics with application to Dreissena competition

Source-sink dynamics may be ubiquitous in ecology. We developed a theory for source-sink dynamics using spatial extensions of the net reproductive value, R (0), which has been used elsewhere to define fitness, disease eradication, population growth, and invasion risk. R (0) decomposes into biologically meaningful components-lifetime reproductive output, survival, and dispersal-that are widely adaptable and easily interpreted. The theory provides a general quantitative means for relating fundamental niche, biotic interactions, dispersal, and species distributions. We applied the methods to Dreissena and found a resolution to a paradox in invasion biology-competitive coexistence between quagga (Dreissena bugensis) and zebra (D. polymorpha) mussels among lakes despite extensive niche overlap within lakes. Source-sink dynamics within lakes between deepwater and shallow habitats, which favor quagga and zebra mussels, respectively, yield a metacommunity distribution where quagga mussels dominate large lakes and zebra mussels dominate small lakes. The source-sink framework may also be useful in spatial competition theory, habitat conservation, marine protected areas, and ecological responses to climate change.