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3C tiuc i,,acions in demographic parameters in causing the decline or exun4ion of a population. In most cases, however, accurate predic- tion cif extinction probabilities for demirv-dependent agc-structured popu ations requires extensive computer simulation (34). Ede effects. Two Types of edge effects can be distinguished. The first deterioration of habitat quality near an ecological boundary. Thus] after clearing surrounding areas for pastureland, new parches of tropical rain forest quickh• undergo desiccation and vegetational thanes up to hundreds of meters from the boundarv, which makes the coiges unsuitable for manv rain forest species (35). The second ripe of edge effect concerns dispersal of individuals across an ecological boundary into unsuitable regions where they may perish or faJil to reproduce. The rate of dispersal of individuals into unsu0ble areas determines the minimum size of a patch of suitable habitat on which a population an persist, known as the critical catch size (36). Kjo rstead and Slobodkin (37) employed a reaction-diffusion equation to describe population growth and random dispersal of individuals on a patch of suitable habitat surrounded by a region unsut blc for individual survival. They derived a condition for the population to increase when rare, assuming that population growth is de ity-independent at low densities (no Allee effect) and that individual dispersal movements arc randomly oriented (no habitat selection behavior). Their result an be expressed in terms of the variance in dispersal distance per generation, d2, and two conven- tion demographic parameters that apply to individuals within the suitable region (excluding dispersal into unsuitable arras). The intrinsic rate of increase, r, is the exponential rate of population gro per unit time, and the generation time, T, is the average age of mbthcrs of newbom individuals (38), in a population with a stable age distribution. Persistence of a population with a low intrinsic rate of increase per generation (rT << 1) requires the diameter of a circular patch of suitable habitat to be much larger than 41. and defense of a home range (46). Classical demography can be integrated with habitat occupancy by identifying the individual temrony as the spatial unit. Local extinction then corresponds to the death of an individual inhabiting a taritorv, and colonization corresponds to individual dispersal and settlement on a suitable unoccupied territory. For anahmcal tractability, I assumed that patches of habitat, each the size of individual territories, are either suitable or unsuitable for survival and reproduction, and suitable tcrrimries are randomly or evenly distributed in space. Juveniles disperse prior to reproduction and an search a certain number of potential temtories before perishing from predation, starvation, and so on, if they do not find a suitable unoccupied territory. The proportion of a large region composed of suitable territories is denoted as h, and the proportion of suitable territories that are occupied by adult females is p. The dispersal behavior and life history information are contained in a composite parameter, k, called the demographic potential of the population (43), because it gives the equilibrium occupancy (p) in a completely suitable region (p = k when h = 1). Increasing either the number of territories a dispersing individual can search, or the expected number of off- spring produced, increases both the demographic potential of the population and the equilibrium occupancy of suitable habitat. At demographic equilibrium the occupancy of suitable habitat is p=1-(1-k)lhif h>1-k,and p=0if hsl-k(Fig.1). This model demonstrates two important features of populations malntam??loal acnncnon an co onrzanon. First, as the amount o suuta e fi-a-bitat (random or evenly distributed) -in a region Sccrcues, sorocs th-'T ro root of the suitasic habitat that is occupl -ccond, there is an extinction o or minuniulu proportion of suitable habitat in a region necessary for a population to persist. If the proportion of suitable habitat falls below 1 - k, the population will become acting. Extensions of this model show that an Ally effect caused by difficulty in finding a mate, an edge effect due to the finite extent of the region containing suitable habitat, or a Th? critical patch size model has been extended to include AIIec fluctuating environment all increase the extinction threshold (43). effects, survival (and reproduction) of individuals outside the patchX,-' (38), 6oarandom dispersal through behavioral habitat selection, and l quo a.r Q t ?, i { apis ra: c? o ._ movein--nt of the patch caused by climatic change (39). The second CoIIClus'flns ra r tin ic. and ird of these decrease the c iticai patch size, whereas the first The difficulty of incorporating a multiplicity of factors into a and 1 t increase it. Of course, if an area with fixed boundaries has realistic model of octi c ion has prompted conservation biologists to been, blished as a natural preserve containing suitable habitat for suggest numbers for minimum viable population sizes based on some species, long-term climatic trends may induce major evolution- single factors. By whatever criteria, populations with these numbers any anges in the population, or render the entire preserve unsuit- are supposed to have a high probability of persistence for some able 40). This problem is compounded for species that undergo specified period of time-for example, a 95% probability of persis- long- ' tance seasonal migrations and require two or more width, tence for at least 100 wars, or a 99% probability for 1000 vears (47). separ, Lted patches of suitable habitat (41). An c£ecrive population size of 500 has been suggested as sufficient Lm al exrinaion and colonization. ManV species exist in subdivided to maintain genetic variation for adaptation to a changing environ- popu?ations for social reasons or because suitable habitat has a ment (8, 21), but, as explained above, this number is of dubious patch spatial distribution. Fluctuating environments may make validity as a general rule for managing mild populations. To some habitat patches temporarily unsuitable, so that a wideh• illustrate this point, I give two examples of management plans based distributed population persists through a balance between local primarily on population genetics. These plans threaten the existence cx nckion and colonization. For example, some species of plants in of the populations they were designed to protect because basic rropica forests exist only in light gaps left by fallen urea and rely on demographic factors were ignored. Botts examples concern bird rapid growth and c i : dispersal to use a continually shifting species inhabiting mature or old forests that now occur mainly on mosaic of suitable habitat (42). Such localized sporadic disturbances federal lands subject to intensive logging. help maintain species diversity in many natural communities (43). ? The northern spotted owl, Strix caunna occidentalis, is a Critical factors affecting the persistence of a subdivided population mous territorial subspeaesiat inhabits old-growth conifer forests inciu a the number, size, and spatial distribution of patches of in the Pacific Northwest. Pairs maintain home ranges of roughly 1 suitable habitat and dispersal rates bem,cen them (6)_ to 3 square miles of conifer forest more dean about 250 years old Lc%qnS (44) developed a model of a subdivided population below an elevation of about 4000 feet (48). They usually nest in old main ed by local extinction and colonization of suitable habitat hollow trees and require an open understory, characteristic of old- patch . I modified his model to describe habitat use by territorial growth forests, for effective hunting of small mammalian prey that spar (43). Territorial behavior ranges from the mere occupation compose the bulk of their diet. Adults arc long-lived but have low of spa to active maintenance ofint_Er_diidstance or patrolling fecundity, and juveniles experience high mortality (49). Recent 1458 - - SCIENCE, VOL. 2$I