The Quantitative Incidence Function Model and Persistence of an Endangered Butterfly Metapopulation

The incidence function model is derived from a linear first-order Markov chain of the presence or absence of a species in a habitat patch. The model can be parameterized with "snapshot" presence/absence data from a patch network. Using the estimated parameter values the Markov chain can be iterated in the same or in some other patch network to generate quantitative predictions about transient metapopulation dynamics and the stochastic steady state. We tested the ability of the incidence function model to predict patch occupancy using extensive data on an endangered butterfly, the Glanville fritillary ( Melitaea cinxia ) Parameter values were estimated with data collected from a 50-patch network in 1991. In 1993 we surveyed the entire geographic range of the species in Finland, within an area of 50 × 70 km², with 1502 habitat patches (dry meadows) of which 536 were occupied. Model predictions were generated for the 1502 patches and were compared with the observed pattern of occupancy in 1993. The model predicted patch occupancy well in more than half of the study area, but prediction was poor for one quarter of the area, probably because of regional variation in habitat quality and because metapopulations may have been perturbed away from the steady state. The incidence function model provides a practical tool for making quantitative predictions about metapopulation dynamics of species living in fragmented landscapes.