Predicting the impacts of edge effects in fragmented habitats

Biological Conservation 55 (1991) 77-92

Predicting the Impacts of Edge Effects in Fragmented Habitats William E Laurance* Museum of Vertebrate Zoology, University of California, Berkeley, California 94720, USA

& Eric Yensen Museum of Natural History, The College of Idaho, Caldwell, Idaho 83605, USA (Received 2 February 1989; revised version received 11 September 1989; accepted 10 April 1990)

ABSTRACT We propose a protocol for assessing the ecological impacts of edge effects in fragments of natural habitat surrounded by induced (artificial) edges. The protocol involves three steps: (1) identification of focal taxa of particular conservation or management interest, (2) measurement of an 'edge function' that describes the response of these taxa to induced edges, and (3) use of a 'Core-Area Model' to extrapolate edge function parameters to existing or novel situations. The Core-Area Model accurately estimates the total area of pristine habitat contained within fragments. Moreover, it can be used to predict the amount of unaltered habitat preserved within any hypothetical fragment, such as a planned park or nature reserve, regardless of its size or shape. The model is simple, requiring two edge function parameters and the area and perimeter length of the fragment. Model simulations revealed that for any edge-sensitive species and habitat type there exists a critical range of fragment sizes in which the impacts of edge effects increase almost exponentially. This critical size range cannot be predicted without empirical measurement of the edge function. * Present address: Centre for Rainforest Studies, Yungaburra, Queensland 4872, Australia. 77 Biol. Conserv.0006-3207/90/$03.50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

78

William F. Lauranee, Erie Yensen

INTRODUCTION A common feature of habitat fragmentation is a sharp increase in the amount of induced habitat edge. Consequently, plant and animal populations in fragmented habitats are not only reduced and subdivided, they are increasingly exposed to ecological changes associated with induced edges (Wilcove et al., 1986). Edge effects in fragments are remarkably diverse. They include proliferation of shade-intolerant vegetation along fragment margins (Ranney et al., 1981; Lovejoy et al., 1986) as well as changes in microclimate and light regimes that affect seedling germination and survival (Levenson, 1981; Ranney et al., 1981; Ng, 1983; Laurance, 1989). Forest interiors often are bombarded by a 'seed rain' of weedy propagules (Janzen, 1983) and by animals originating from outside habitats (Lovejoy et al., 1986; Buechner, 1987; Laurance, 1987). Increased wind-shear forces near edges can cause elevated rates of treefalls and tree mortality that alter forest structure and composition (Levenson, 1981; Lovejoy et al., 1986; Laurance, 1989). Abundant generalist predators, competitors or brood parasites in the vicinity of edges often impact forest-interior birds (Gates & Gysel, 1978; Whitcomb et al., 1981; Ambuel & Temple, 1983; Wilcove, 1985; Andren & Angelstam, 1988) and mammals (Sievert & Keith, 1985; Laurance, in press). Edge effects are especially powerful forces when fragments are small or irregularly shaped (Forman & Godron, 1986), or when the gradient between natural and modified habitats is steep (Thomas et al., 1979; Ranney et al., 1981; Angelstam, 1986). They provide one obvious example in which true islands provide only poor analogs of habitat fragments (Janzen, 1983; Buechner, 1987; Stamps et al., 1987). Edge effect phenomena are not addressed by island biogeography theory (MacArthur & Wilson, 1967), which assumes that biotas in habitat isolates are structured primarily by the opposing forces of colonization and extinction. Efforts to incorporate edge effects into conservation and management planning have followed one of two distinct paths. On the one hand are qualitative, multidisciplinary models that utilize spatial analysis techniques for park or reserve management (Schonewald-Cox & Bayless, 1986). These techniques require detailed knowledge of the distribution of landscapes and habitats, as well as computer expertise and intensive time input. On the other hand is the emerging field of landscape ecology, which attempts to determine local effects of size, shape, proximity, degree of connectedness, and spatial arrangement of fragments (Forman & Godron, 1986). Wildlife managers have been applying landscape design principles for several decades, often by manipulating habitat edges (Leopold, 1932; Thomas et al., 1979). Unlike island biogeography theory, landscape ecology places emphasis on

Edge effects in fragmented habitats

79

the shape as well as size of fragments. There is general agreement, for example, that the perimeter length to area (p/a) ratio of fragments accurately incorporates both size and shape variation (Forman & Godron, 1986; Schonewald-Cox & Bayless, 1986; Buechner, 1987; Stamps et al., 1987). Beyond this, however, few models have been devised to assess the role of fragment shape. Patton (1975) developed a simple 'diversity index' that described the deviation of fragment shapes from circularity. Game (1980) used this index to assess possible effects of different reserve shapes on the rate of between-reserve movements by animals. Working independently, field biologists have amassed considerable descriptive data on edge effects in fragments, often by sampling along edgeinterior transects situated perpendicular to fragment margins (Gates & Gysel, 1978; Ranney et al., 1981; Brittingham & Temple, 1983; Andren & Angelstam, 1988). A frequent goal has been to measure the distance that edge effects penetrate into fragments. Results have varied widely. In different habitats and for different taxa, edge effects may penetrate from 15 m (Ranney et al., 1981) to 5 km (Janzen, 1986). In an insightful study, Temple (1986) used an edge effect penetration distance of 100 m to measure the 'core areas' of 49 fragments in Wisconsin, USA, for 16 species of forest-interior birds. In all 16 cases, fragment core areas were a better predictor of bird abundance than total fragment area. However, there currently are no quantitative models available to incorporate empirical data on edge effects with landscape features of fragments. Consequently, we devised a 'Core-Area Model' that is mathematically simple and, provided its assumptions are approximated, surprisingly precise in predicting core areas of fragments. It is useful for exploring reserve design options, for assessing effects of fragment size and shape on interior species, and it has a number of applications in management contexts. We present the model as part of a general protocol for assessing ecological impacts of edge effects in fragmented habitats.

EDGE FUNCTIONS An edge function is a mathematical description of the penetration-distance (d) of a specific edge effect into the external regions of fragments. For the purpose of the Core-Area Model, it is always measured in meters. In general, d is defined as the perpendicular distance inside the fragment at which the edge effect becomes ameliorated, although d may be defined operationally, especially in management contexts. Values for d are determined by sampling the edge effect phenomenon along several edge-interior transects (e.g. Ranney et al., 1981; Andren & Angelstam, 1988). Because of natural

80

William F. Laurance, Eric Yensen

heterogeneity in habitats and edges, each transect will yield a different d value. Data from all transects are then pooled to yield the edge function. When d values are normally distributed, the edge function is defined as the mean and 95% confidence interval (d__ 2 SE) of values from the transects. When d values are non-normal (see below), the median value and upper and lower deciles are used. Whenever possible, transects should be stratified across several fragments (e.g. four fragments with four transects per fragment). Each fragment should be large enough to contain some unaltered habitat at its core. Otherwise, d may not be detectable (e.g. Yahner & Wright, 1985; Ratti & Reese, 1986). For parametric data, the precision of the Core-Area Model depends on the size of the 95% confidence intervals (//__ 2 SE). Because the standard errors generally will become smaller with increased sample sizes, increasing the number of edge-interior transects will increase precision of the model. For parametric data, variance estimates produced from initial sampling may be useful for predicting adequate sample size, given the level of precision defined by the experimenter (Sokal & Rohlf, 1981).

MODEL DEVELOPMENT For the purpose of developing the Core-Area Model, we assumed that dwas constant (no habitat heterogeneity; hence, d = d). We devised five geometric figures of increasing complexity as habitat fragment analogs (Fig. 1), designed to emulate a range of natural fragment shapes (Myers, 1984: 183; Laurance, 1989). Formulae that provide the percentage core area and perimeter length of each shape (for any given d value and total area) are shown in Table 1. We used the shape index (SI) of Patton (1975), adapted for metric units, to describe the deviation of each fragment from circularity (a perfectly circular fragment will have an S I value of 1.0, whereas all other shapes have higher values--Fig. 1). To derive S l w e require (1) total area of the fragment (TA) in hectares and (2) perimeter length of the fragment (P) in meters: P S I = 200[(nTA)O.5]

(1)

Using a computer spreadsheet package (Lotus 1-2-3), we set the total area of all five fragments at 10 000 ha, then examined the rate at which the core area of each fragment declined as dincreased. The declines were nearly linear (R 2 > 0"99) for each shape (Fig. 2). Thus, for any given area, as edge effects penetrated further, the core areas decreased at a constant, shape-specific

Edge effects in fragmented habitats

CIRCLE

81

2:1 R E C T A N G L E

SI =1.0

=s SI = 1.20 4:t RECTANGLE

sl

1 4S

S1=1.41 lO:l RECTANGLE

sl

I lOs

S1=1.96 FERNLEAF

__1

I SI = 3.04

Fig. I. Five geometric figures used as habitat fragment analogs. The shape index (SI) indicates the degree of deviation from circularity. As shown, all fragments have identical perimeter length to area ratios.

rate. For example, a fragment of 10000 ha might lose 3.55 ha for every 1-m increase in d. These relationships remained linear, or very nearly so, until the core area declined to some m i n i m u m value ( < 5 0 % of TA). Can the rate at which core areas decline be predicted? As shown in Fig. 3, the answer is 'yes'. There is a perfect linear relationship between this rate and the fragment shape index. Not surprisingly, fragments having irregular shapes (higher SI values) accrue edge effects more rapidly than do more circular fragments. However, the rate at which a fragment loses core area depends not only on its shape but also upon its total area. Large fragments lose more hectares as d increases because, in an absolute sense, they have a longer exposed edge than small fragments. To create a formula that is applicable to fragments of any size, we need to know how much the shape-specific rate of core-area loss

William F. Laurance, Eric Yensen

82

TABLE 1 Geometric Formulae" used Empirically to Derive the Perimeter Length (P) and Percentage Core Area (%CA) of Five Simulated Habitat Fragments, for any given Total Area (TA) and Edge Effect Penetration-distance (d)

Shape

TA

P

Circle

nr 2

2rcr

2:1 rectangle

2s 2

6s

4:1 r e c t a n g l e

4s 2

10s

10:1 rectangle

10S 2

22s

Fernleaf

27s 2

56s

%CA ( x 100) 2d

d2

r

r2

3d

2d 2

S

S2

5d

d2

2s

s2

lld

2d 2

5s

5s 2

56d

(20 - 4•)d 2

27s

27s 2

" r, radius length; s, side length (Fig. 1).

(ha m - 1 SI unit - 1) increases as fragment area increases. Using 10 000 ha as a baseline size, we discovered by experimentation that this relationship was entirely predictable. The slope for 10000ha fragments is 3.55 ha m - l S I unit- 1, whereas the slope for any other area may be found by multiplying the constant 3.55 by (TA/IO000) °'5. Thus, the core area of any fragment (in hectares) is predicted by Core Area = TA -Affected Area (AA) where

AA

= {(3"55)(d)(S1)[(TA/lO

000)°'5]}

(2)

We tested the predictions of formula (2) against empirically determined core-area values for 100 simulated habitat islands (using the five shapes in Fig. 1 and many combinations of total areas and d values). As shown in Fig. 4, this formula always underestimated the core area, by a small amount (< 10%) when the edge effect altered only a small portion of the fragment (core area >75% of TA) but by much more (up to 70% error) when the core area was very small. These errors were particularly acute for more circular fragments. Why is this model not perfect? The reason has to do with some peculiar properties of different shapes. In particular, the relationship between the

Edge effects in fragmented habitats

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800

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d

Fig. 2. As edge effects penetrate further into fragments (d increases), each fragment loses pristine core area at a nearly constant (linear) rate. This rate depends on both the shape and area of the fragment. 80-

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215

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Fragment Shape Index Fig. 3. There is perfect concordance between the fragment shape index (SI) and the rate at which fragments initially lose pristine core area as d increases (ha m - t). For fragments of any given size, irregularly shaped fragments lose more hectares as d increases than do morecircular fragments. 7O

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Fig. 4.

Formula (2) underestimates core areas, especially for more-circular fragments when the core area becomes small. See text for discussion.

84

William F. Laurance, Eric Yensen

core area and d (Fig. 2) becomes curvilinear for m o r e circular fragments when the core area becomes small, but stays nearly linear for irregular shapes. These nonlinearities can cause substantial underestimates o f core areas for fragments with S I values o f 1"5 or less. To correct this error the affected area (AA) value derived by formula (2) is adjusted d o w n w a r d with the following formula: AAad j = A A x

{0.265(AA/TA)~l 1 -- \ (Sl)i. 5 elI

(3)

W h e n subtracted from total area, AAad j yields the adjusted core area. This adjustment effectively minimizes any shape-induced errors. The n u m e r a t o r variable ( A A / T A ) increases the correction term as the core area becomes smaller, whereas the exponential d e n o m i n a t o r term [(S/) t s ] compensates for shape-specific differences in the d-core area relationship. The constant in the n u m e r a t o r (0"265) was fitted by least-squares regression analysis. When we compared the adjusted predictions from formula (3) with empirically determined values for the I00 simulated fragments, we found that the average error was only 0-48% and that no prediction erred by more than 3.8% (Fig. 5). The adjustment had reduced the average and m a x i m u m errors o f formula (2) by 92% and 94%, respectively. Even for the most troublesome shapes (perfect circles) under the most difficult conditions (core area < 10% o f TA), the model was > 9 6 % accurate. Moreover, most realistic fragments have a shape index value o f > 1.5 (Laurance, 1989), for which the model is usually > 99% accurate. I00 od

< r~"' 80 o° z

60

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ACTUAL PERCENT CORE AREA

Fig. 5. The Core-Area Model is precise. Data shown are actual (empirically derived) vs predicted percentage core area values for 100 simulated fragments of widely varying shapes and areas. The model was > 96% accurate under all conditions and > 99% accurate for 'realistic' fragment shapes (Shape Index > 1.5).

Edge effects in fragmented habitats

85

ASSESSING N A T U R A L H E T E R O G E N E I T Y IN E D G E E F F E C T S To derive the Core-Area Model we assumed that d was constant. However, individual d values from different transects will vary because of natural variation in habitats and edges. This is the reason for deriving the edge function (d+_ 2 SE, or its nonparametric equivalent), which provides both an average value and confidence limits for d. To assess natural heterogeneity we simply apply the Core-Area Model three times: once using the mean (or median) value for d, and once each using the upper and lower 95% confidence limits (or upper and lower deciles). At present, however, there are few data on natural variability of edge effects (Ranney et al., 1981). Consequently, we measured soil temperatures along transects perpendicular to induced edges of forest clearcuts. Soil temperature is an important ecological parameter that influences seed germination, root growth, soil nitrification rates, and the absorption and transportation of water and ions by plants (Buckman & Brady, 1969; Jeffrey, 1987). Because insulating vegetation is removed, clearcutting of forests should cause an increase in local soil temperature in summer. In August 1989, we measured temperatures in and around a 17-8-ha, three-year-old clearcut at 1585 m elevation in Adams Co., Idaho (Bear Creek, 13 km N, 26 km E New Meadows). The habitat was mixed coniferous forest, dominated by Pseudotsuga menziesii, Abies grand& A. concolor, Pinus ponderosa, P. contorta, Picea engelmannii, and Larix occidentalis. The clearcut had only sparse, patchy grasses and forbs (30-50 cm height), with scattered logs and debris. The soil was a deep ( > 2 m), basalt-derived loam with some rocks. The clearcut was on a NW (320 °) exposure on 20-30 ° slopes. Twenty-four randomly selected transects were established on four different exposures in the clearcut (NE [45°], seven transects; SE [ 130°], four transects; SW [225°], six transects; NW [315°], seven transects). Forest edges were clearly defined by bulldozer damage, forming a sharp boundary (delimited within <0-5m) between the clearcut and undamaged forest vegetation. Soil temperatures were measured at 50-52cm depth at 1-m intervals along the transects, using carefully calibrated Rheotemp soil thermometers. The value for d on each transect was defined as the minimum distance inside the forest at which typical forest-interior temperatures (8.7510-0°C) were detected. Temperatures in the clearcut ranged from 12-515-5°C. Different exposures tended to yield different d values. On average, edge effects penetrated furthest on the NE exposure ( d = 13.3 m), and were lowest on the SW exposure ( d = 4-5 m). The other exposures had intermediate mean values (NW, d = 7.0 m; SE, aT= 8.25 m). When all 24 transects were pooled,

William F. Laurance, Eric Yensen

86 28

~

24

~

20

....

2

4

6

8

1

12

d

m)

14

16

18

20

22

Fig. 6. Distribution of d values describing elevated soil temperatures near induced habitat edges resulting from a forest clearcut. Data were derived from 24 edge-interior transects at Bear Creek, Adams Co., Idaho, in August 1989. In this instance, d values were significantly non-normal (p < 0.001).

data were strongly unimodal (aT= 8-4 m) but skewed to the right (Fig. 6). The only obvious outlier (d= 19m) was from a narrow (40-m wide) forest peninsula that apparently was influenced by two edges. Because these data deviated significantly from normality (p<0.001, Kolmogorov-Smirnov test), we used the median and upper and lower deciles to derive our edge function (median = 7.5m, lower decile = 4m, upper decile = 13 m). We then applied the Core-Area Model. For a 50-ha fragment with a realistic S I value of 2.20, for example, the core area is predicted to be 45.9 ha, with a lower and upper limit of 42.9-47.8 ha.

SYNOPSIS OF THE CORE-AREA M O D E L (1) Determine d values in meters by sampling the edge effect along several edge-interior transects (the more transects and fragments the better). (2) Use the d values to derive the edge function. (3) Apply formula (1) to derive the fragment shape index. (4) Apply formulae (2) and (3) three times, alternately using d - 2 SE, d, and aT+ 2 SE in formulae (or, for non-normal data, the median and upper and lower deciles).

C R E A T I N G PREDICTIVE MODELS The Core-Area Model has an especially powerful application: generating general models for entire communities. Once the edge function parameters

Edge effects in .fragmented habitats

87

are k n o w n , it is a s i m p l e m a t t e r to e x t r a p o l a t e the results to f r a g m e n t s o f a n y size o r shape. T h i s c a n be u s e d to test the efficacy o f v a r i o u s reserve design o p t i o n s , o r to g e n e r a t e apriori p r e d i c t i o n s o f the c o r e a r e a o f a n y specific fragment. W e used a n a r b i t r a r y e d g e f u n c t i o n (118"5-I-15.5 m) to c r e a t e a g e n e r a l p r e d i c t i v e m o d e l f o r s o m e h y p o t h e t i c a l c o m m u n i t y . W e p r e d i c t e d the c o r e a r e a s o f f r a g m e n t s w i t h t w o s h a p e s (SI = 1.5, S I = 2.5) o v e r a wide r a n g e o f t o t a l a r e a s (Fig. 7). N o t e t h a t c o r e a r e a s declined s h a r p l y as f r a g m e n t s b e c a m e smaller, b u t t h a t the r a t e also d e p e n d e d o n f r a g m e n t shape. B e l o w 500

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500

TOTAL FRAGMENT AREA ( h a ) (b)

Fig. 7. A Core-Area Model for a hypothetical community. An arbitrary edge function (2_+ SE = I 18'5 -I- 15'5 m) was used to predict core areas for two fragment shapes (SI = 1-5 and 2'5) over a range of total areas. Curves for each shape are predicted mean values (solid lines with circles) and 95% confidence limits (dashed lines). In Fig. 7(a), core areas are expressed in hectares. In Fig. 7(b), the same data are expressed as a percentage of total fragment area. Percentage core areas of fragments decline sharply below some critical size range.

88

William F. Laurance, Eric Yensen

some crucial size range, the impacts of edge effects increase almost exponentially. The curves undoubtedly will vary for different habitats and taxa, and they cannot be predicted without knowledge of the edge function.

DISCUSSION The Core-Area Model emphasizes (1) quantification of edge effect phenomena and (2) extrapolation of these data to existing as well as hypothetical situations. For example, based on measurements of edgeinduced changes in forest structure and floristics, Laurance (1989) argued that isolated rainforest reserves in tropical Queensland, Australia, should exceed 20(0)0000 ha (depending on reserve shape) to ensure that unaltered core areas would comprise > 50% of the reserve's total area. This was a hypothetical prediction of the Core-Area Model, not an empirical result, because the largest fragment Laurance (1989) surveyed was only 590 ha. The Core-Area Model provides an alternative to traditional island models for the study of fragment biotas. When abundances of interior species are correlated more strongly with the core area of fragments than with total area, edge effects probably are a powerful structuring force for those taxa (Temple, 1986). A number of putatively 'area-related' extinctions cited in earlier studies of fragment biotas may actually be related to boundary processes (Schonewald-Cox & Bayless, 1986). The confusion between area- and boundary-related extinctions arises because edge and area effects both become increasingly important in small fragments (Temple, 1986; Wilcove et aL, 1986). In addition to area, however, fragment shapes are an important determinant of edge effects. Consequently, researchers should employ at least three metrics when attempting to explain abundances of species in fragments. (1) Interior species that are sensitive to edges should be most strongly and positively correlated with core areas (Temple, 1986). (2) Other taxa that depend on primary habitat but are not sensitive to edges should be positively correlated with total areas. (3) Edge species, especially those with small home ranges, should be positively correlated with the total length of fragment edges (Leopold, 1932; Gotfryd & Hansell, 1986). Additional landscape predictors describing the isolation (Lomolino, 1984, 1986) and spatial arrangement of fragments (Forman & Godron, 1986), as well as permeability of edges and location of dispersal sinks or source pools (Buechner, 1987; Stamps et aL, 1987), also may help explain abundances of species in fragments. How are core areas related to fragment perimeter length to area (p/a) ratios employed in earlier studies (Forman & Godron, 1986; SchonewaldCox & Bayless, 1986; Buechner, 1987; Stamps et al., 1987)? The p/a ratio is an index of percentage core area. It is approximately linearly correlated with

Edge effects in fragmented habitats

89

percentage core area, with the slope of the relationship depending on the value of d. However, this relationship becomes increasingly non-linear for more circular shapes, and ceases to exist altogether when core areas have disappeared in small fragments (Laurance, 1989). Thus, under some conditions, p/a ratios are imprecise measures of vulnerability of fragments to edge effects. For example, by adjusting their areas, the circle and fernleaf(Fig. 1) can be given identical p/a ratios. Because their p/a ratios are the same, both shapes should have nearly identical percentages of core area under all circumstances. However, as edge effects penetrate further (as d increases relative to fragment area), the core area of the fernleaf disappears, while the circle's core area still comprises 22% of its total area (Laurance, 1989). In other words, p/a ratios can yield errors of > 2 0 % when used to compare different shapes. Moreover, because the core area is an areal measure rather than a ratio, it can be used to assess m i n i m u m core area requirements of interior species. Of course, the Core-Area Model requires empirical measurement of an edge function, whereas p/a ratios can be generated without these data. However, data yielded by edge functions are direly needed for reserve design and management. In the design of buffer zones, for example, there are few guidelines on penetration or variability of edge effects associated with reserve boundaries (Schonewald-Cox & Bayless, 1986). Core areas decline sharply when fragments fall below some critical size threshold (Fig. 7). Because this curvilinear relationship lacks an inflection point, no single 'optimum size' can be identified to maximize the core area of fragments while simultaneously minimizing their total area. Instead, some operational criterion must be used (e.g. ensuring core areas exceed 1000 ha, or comprise > 50% of total area) when determining minimum reserve sizes. For the conservation of interior species, many of which are vulnerable to habitat modification, the core-area approach yields a different set of guidelines than island paradigms. In addition to being as large as possible, reserves should be continuous (no holes in the interior) and circular in shape (Diamond, 1975; Temple, 1986). This is a profoundly different goal than simply maximizing total area, because most existing reserves, even the largest ones, have angular edges and irregular shapes (Schonewald-Cox & Bayless, 1986) that translate into much smaller core areas. For example, to maximize core areas of existing reserves, managers could add land or restore outside habitat to increase the reserve's circularity. Nonetheless, for certain taxa or management contexts, circular reserves may not be o p t i m u m (Game, 1980). Gotfryd & Hansell (1986), for example, advocated irregularly shaped fragments to maximize abundances of forest-edge birds in urban habitat islands in Toronto, Canada. The Core-Area Model is not applicable to all edge-related phenomena. It will be of limited utility for assessing h u m a n impacts in reserves, unless these

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effects occur along boundaries in a quantifiable fashion. It also may be inappropriate when boundaries or forest interiors exhibit striking heterogeneity. In these circumstances, qualitative, multidisciplinary models that categorize different types of edges and consider both human and natural impacts may be most appropriate (Schonewald-Cox & Bayless, 1986). The Core-Area Model is appropriate for comparative landscape studies at the regional or sub-regional level, when fragments have similar types of edges. Caution should be used when extrapolating results of the model between different regions because, even if primary habitats are similar, significant ecological differences may arise. For example, the total percentage of modified habitat in a region can influence populations of generalist predators, that in turn impact wildlife in fragments (Angelstam, 1986). Likewise, different modified habitats surrounding fragments (e.g. farmland vs secondary regrowth) can lead to different edge effects (Janzen, 1983; Buechner, 1987). Variation in the age of induced edges may or may not be important. Recent edges usually create a sharp gradient that may be more damaging than older edges, but available evidence suggests that these effects equilibrate quickly (Ranney et aL, 1981). However, the only crucial assumption of the Core-Area Model is that the penetration-distance of an edge effect (d), while being variable, should be unimodal. Our data on forest soil temperatures clearly were unimodal, suggesting that this assumption is reasonable. Although the model is most precise when d values are normally distributed, predictions based on the median value and deciles can be generated under any circumstance. In an era in which critical conservation and management decisions must be made on a daily basis, certainly this is better than having no information at all. A C K N O W L E D G E M ENTS We thank C. M. Schonewald-Cox, D. D. Murphy, W.Z. Lidicker Jr, N. C. Stenseth, T. Sisk, E H. J. Crome, R.H. Barrett, N.K. Johnson, and two anonymous reviewers for helpful comments. This research was partially supported by grants to W.F.L. from the US National Science Foundation (DEB-8601089), Wildlife Conservation International, World Wildlife Fund--US, World Wildlife Fund--Australia, M. A. Ingram Trust, Museum of Vertebrate Zoology, and Sigma Xi. REFERENCES Ambuei, B. & Temple, S. A. (1983).Area-dependentchanges in the bird communities and vegetation of southern Wisconsin forests. Ecology, 64, 178-86.

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