239 Ecology, 81(1), 2000, pp. 239–251  2000 by the Ecological Society of America ESTIMATING THE PARAMETERS OF SURVIVAL AND MIGRATION OF INDIVIDUALS IN METAPOPULATIONS ILKKA HANSKI, 1,3 JUHA ALHO, 2 AND ATTE MOILANEN 1 1 Department of Ecology and Systematics, Division of Population Biology, P.O. Box 17, FIN-00014 University of Helsinki, Finland 2 Department of Statistics, University of Joensuu, P.O. Box 111, FIN-80101 Joensuu, Finland Abstract. Ecologists working with metapopulations are interested in the rate of mi- gration among several local populations, mortality during migration, and the scaling of migration rate with habitat patch area and isolation. We describe a model of individual capture histories obtained from multisite mark–release–recapture studies, which allows one to measure these parameters using maximum likelihood estimation. The model yields sep- arate estimates of mortality within habitat patches and mortality during migration, on the assumption that only the latter is affected by the isolation of the source population. The model is suitable for studies involving 10 or more populations, with differences in habitat patch areas and isolation, and in which several hundred individuals have been marked and recaptured. We apply the model to a metapopulation of the butterfly Melitaea diamina with 14 local populations, 557 marked individuals, and 1301 recaptures. Immigration and em- igration scaled as patch area to power 0.2. Roughly half of the daily losses of individuals from habitat patches of 1 ha in area were due to emigration, 1% of daily migration distances were 1 km, and 16% of all deaths were estimated to have occurred during migration. Programs are available to calculate the parameter estimates, their confidence intervals, and goodness-of-fit tests. Key words: habitat patch area and isolation effects; mark–release–recapture; Melitaea diamina; maximum likelihood estimates; metapopulation dynamics; migration, butterfly; migration mortality; reproduction by resident vs. migrant individuals; survival, estimation. INTRODUCTION Population biologists are increasingly concerned with the spatial structure of populations and its con- sequences for the behavior of individuals and for the ecology, genetics and evolution of populations. In high- ly fragmented landscapes, species occur as assem- blages of local populations, called metapopulations, of- ten with a high rate of population extinction and rees- tablishment (Hastings and Harrison 1994, Hanski and Gilpin 1997). In metapopulations, migration of indi- viduals among habitat patches is a key process, not only because migration is necessary for gene flow and colonization of empty habitat, but also because migra- tion may affect the dynamics of local populations (Pul- liam 1988, Stacey et al. 1997, Kuussaari et al. 1998) and entire metapopulations (Gyllenberg and Hanski 1992, Hanski et al. 1995). The evolution of migration rate is a major topic in evolutionary ecology (Hamilton and May 1977, Levin et al. 1984, Venable and Brown 1988, Johnson and Gaines 1990, Olivieri and Gouyon 1997). The evolutionary stable migration rate strongly depends on the most obvious cost of migration, mor- tality during migration (Comins et al. 1980, Olivieri and Gouyon 1997), which however is very hard to mea- Manuscript received 1 June 1998; accepted 5 January 1999. 3 E-mail: ilkka.hanski@helsinki.fi sure empirically (Johnson and Gaines 1990, Ims and Yoccoz 1997). Migration rate, in the sense of rate of spread, has been studied with diffusion models for invading pop- ulations (Hengeveld 1989, Okubo and Levin 1989, An- dow et al. 1990) and for sets of marked individuals released at some particular site(s) (Dobzhansky and Wright 1943, Kareiva 1983, Matsuda and Akamine 1994). Migration in the sense of gene flow has been inferred from population genetic data (Wright 1969), but this indirect approach, based on the strong as- sumptions of demographic and genetic equilibria (Slat- kin 1995), is unlikely to be helpful in behavioral and population ecology (Ims and Yoccoz 1997). In popu- lation ecology, the important parameters of migration include the per capita emigration rate, the rate and pat- tern of migratory movements, and mortality during mi- gration, which together determine the expected flow of individuals between any two local populations. It has turned out to be difficult to obtain reliable information on these parameters (Turchin et al. 1991, Stenseth and Lidicker 1992, Ims and Yoccoz 1997). One possible approach to the study of migration in metapopulations is to extend the current methods of modeling individual survival probabilities with mark– release–recapture (MRR) data in single populations (Lebreton et al. 1992, 1993, Ims and Yoccoz 1997, and references therein) to several populations (Arnason