Because the d ij are defined in terms of immigration flux, the MST on the
landscape network identifies the core habitat supporting a metapopulation.
7.4 A Case Study
An example system particularly suited to landscape graphs is the spatial
population structure of the Mexican spotted owl. The Mexican subspecies
of the spotted owl is distributed from Utah and Colorado south to central
Mexico (USDI 1995). In 1993, the subspecies was listed as threatened under
the Endangered Species Act. A graph-theoretic approach was used previously to characterize owl habitat connectivity across four southwestern
states (Utah, Colorado, New Mexico, and Arizona) as part of a federally
mandated conservation plan (Keitt et al. 1995, 1997). The habitat distribution for Mexican spotted owls is highly fragmented in the Southwest
because suitable foraging and nesting sites are largely determined by topographic relief. Because of the arid climate and orographic effects, much
Mexican spotted owl habitat is divided into “sky islands” surrounded by
grasslands and desert. Juvenile spotted owls are known to disperse considerable distances in search of vacant nesting territories. Thus it is highly
likely that dispersal success plays an important role in the genetic, demographic, and metapopulation structure of the Mexican spotted owl. Because
dispersal success depends principally on the time and energy spent searching for suitable sites, the connectivity of suitable habitat patches is a prime
concern when making habitat conservation decisions.
Figure 7.3 shows a map of potential spotted owl habitat in the Southwest
overlayed by the minimum spanning tree of the landscape network. The
forest map was derived from Advanced Very High Resolution Radiometer
(AVHRR) satellite imagery (Evans et al. 1993; Evans and Zhu 1993). I used
mark-recapture data from juvenile owls (USDI 1995) to parameterize the
network. The minimum spanning tree highlights several types of patches.
Large “core” patches have many connections (high “degree” in graphtheory parlance). These patches are almost certainly critical to survival of
the metapopulation. “Bridge” patches have few connections but appear
deep in the tree and sit between larger core patches. By “deep,” I mean the
minimum number of connections that must be crossed to reach a “leaf” of
the tree. Leaf patches occur at the ends of tree branches and have only a
single connection (degree = 1). Depth in the tree is a good proxy for patch
importance. A simple, iterative algorithm for ranking the patches is to
repeatedly remove the lowest quality (or smallest) leaf patch from the tree
until there is only a single patch. Patches are ranked in order as they are
removed. These rankings correspond well to rankings produced by patch
deletion combined with sensitivity measures. Model results (Urban and
7. Network Theory: An Evolving Approach to Landscape Conservation
131
landscape network identifies the core habitat supporting a metapopulation.
7.4 A Case Study
An example system particularly suited to landscape graphs is the spatial
population structure of the Mexican spotted owl. The Mexican subspecies
of the spotted owl is distributed from Utah and Colorado south to central
Mexico (USDI 1995). In 1993, the subspecies was listed as threatened under
the Endangered Species Act. A graph-theoretic approach was used previously to characterize owl habitat connectivity across four southwestern
states (Utah, Colorado, New Mexico, and Arizona) as part of a federally
mandated conservation plan (Keitt et al. 1995, 1997). The habitat distribution for Mexican spotted owls is highly fragmented in the Southwest
because suitable foraging and nesting sites are largely determined by topographic relief. Because of the arid climate and orographic effects, much
Mexican spotted owl habitat is divided into “sky islands” surrounded by
grasslands and desert. Juvenile spotted owls are known to disperse considerable distances in search of vacant nesting territories. Thus it is highly
likely that dispersal success plays an important role in the genetic, demographic, and metapopulation structure of the Mexican spotted owl. Because
dispersal success depends principally on the time and energy spent searching for suitable sites, the connectivity of suitable habitat patches is a prime
concern when making habitat conservation decisions.
Figure 7.3 shows a map of potential spotted owl habitat in the Southwest
overlayed by the minimum spanning tree of the landscape network. The
forest map was derived from Advanced Very High Resolution Radiometer
(AVHRR) satellite imagery (Evans et al. 1993; Evans and Zhu 1993). I used
mark-recapture data from juvenile owls (USDI 1995) to parameterize the
network. The minimum spanning tree highlights several types of patches.
Large “core” patches have many connections (high “degree” in graphtheory parlance). These patches are almost certainly critical to survival of
the metapopulation. “Bridge” patches have few connections but appear
deep in the tree and sit between larger core patches. By “deep,” I mean the
minimum number of connections that must be crossed to reach a “leaf” of
the tree. Leaf patches occur at the ends of tree branches and have only a
single connection (degree = 1). Depth in the tree is a good proxy for patch
importance. A simple, iterative algorithm for ranking the patches is to
repeatedly remove the lowest quality (or smallest) leaf patch from the tree
until there is only a single patch. Patches are ranked in order as they are
removed. These rankings correspond well to rankings produced by patch
deletion combined with sensitivity measures. Model results (Urban and
7. Network Theory: An Evolving Approach to Landscape Conservation
131