The effects of habitat destruction in finite landscapes: a chain-binomial metapopulation model

We present a stochastic model for metapopulations in landscapes with a fini te but arbitrary number of patches. The model, similar in form to the chain -binomial epidemic models, is an absorbing Markov chain that describes chan ges in the number of occupied patches as a sequence of binomial probabiliti es. It predicts the quasiequilibrium distribution of occupied patches, the expected extinction time (<(<tau>)over bar>), and the probability of persis tence ((l) over bar (x)) to time x as a function of the number N of patches in the landscape and the number S of those patches that are suitable for t he population. For a given value of N, the model shows that: (1) <(<tau>)ov er bar> and (l) over bar (x) are highly sensitive to changes in S and (2) t here is a threshold value of S at which <(<tau>)over bar> declines abruptly from extremely large to very small values. We also describe a statistical method for estimating model parameters from time series data in order to ev aluate metapopulation viability in real landscapes. An example is presented using published data on the Glanville fritillary butterfly, Meltiaea cinxi a, and its specialist parasitoid Cotesia melitaearum. We calculate the expe cted extinction time of M. cinxia as a function of the frequency of parasit e outbreaks, and are able to predict the minimum number of years between ou tbreaks required to ensure long-term persistence of M. cinxia. The chain-bi nomial model provides a simple but powerful method for assessing the effect s of human and natural disturbances on extinction times and persistence pro babilities in finite landscapes.