THE QUANTITATIVE INCIDENCE FUNCTION MODEL AND PERSISTENCE OF AN ENDANGERED BUTTERFLY METAPOPULATION

The incidence function model is derived from a linear first-order Mark ov chain of the presence or absence of a species in a habitat patch. T he model can be parameterized with ''snapshot'' presence/absence data from a patch network. Using the estimated parameter values the Markov chain can be iterated int eh same or in some other patch network to ge nerate quantitative predictions about transient metapopulation dynamic s and the stochastic steady state. We tested the ability of the incide nce function model to predict patch occupancy using extensive data on an endangered butterfly, the Glanville fritillary (Melitaea cinxia). P arameter values were estimated with data collected from a 50-patch net work in 1991. In 1993 we surveyed the entire geographic range of the s pecies in Finland, within an area 50 x 70 km(2), with 1502 habitat pat ches (dry meadows) of which 536 were occupied. Model predictions were generated for the 1502 patches and were compared with the observed pat tern of occupancy in 1993. The model predicted patch occupancy well in more than half of the study area, but prediction was poor for one qua rter of the area, probably because of regional variation in habitat qu ality and because metapopulations may have been perturbed away from th e steady state. The incidence function model provides a practical tool for making quantitative predictions about metapopulation dynamics of species living in fragmented landscapes.