### Defining the strength of edge effects

- Top of page
- Summary
- Introduction
- Defining the strength of edge effects
- A statistical approach to quantifying the strength of edge effects
- A case study of edge-effect magnitude and extent calculations
- Discussion
- Implications and applications of the logistic and unimodal models
- Acknowledgements
- References

Edge effects can be thought of in terms of a continuum from strong to weak effects, but this continuum is actually a composite of two interrelated factors that are seldom separated: the magnitude or amplitude of the effect, and the scale or spatial extent over which the effect occurs (Chen *et al*. 1995; Cancino 2005; Harper *et al*. 2005). For example, a strong edge effect may be considered by some authors to be one that penetrates a large distance into a particular habitat type, whereas a weak edge effect does not. In contrast, a large magnitude response that occurs across a very short distance may also be considered by other authors to be a strong effect. For instance, differences in air temperature across forest–grassland edges are frequently large (Chen *et al*. 1995) but occur over very short spatial scales of just 10–20 m (Cadenasso, Traynor & Pickett 1997).

We contend that a simplistic continuum of strong to weak edge effects is insufficient to describe the full complexity of biotic and abiotic responses to edges that have been described in the empirical literature (Murcia 1995; Lidicker 1999; Cadenasso *et al*. 2003; Ries *et al*. 2004). Instead, we argue that a more precise approach is to describe edge effects in terms of two discrete categories of effect strength, which we term the magnitude and extent of edge effects (after Chen *et al*. 1995; Cancino 2005; Harper *et al*. 2005; Hylander 2005). We define the magnitude of an edge effect as the difference between the maximum and minimum values of a response variable that is measured from the interior of the patch to the interior of the matrix habitat. In contrast, the extent of an edge effect is the distance over which that change in the response variable can be detected, and has previously been referred to as the edge-effect penetration distance (Laurance & Yensen 1991) and the depth of edge influence (Ries *et al*. 2004).

#### the magnitude of edge effects

Having made the distinction between the magnitude and extent of edge effects, it becomes somewhat easier to compare and contrast the results of separate studies in the diverse edge-effects literature (Murcia 1995; Ries & Sisk 2004; Ries *et al*. 2004; Ewers & Didham 2006). The magnitude of change in many variables across habitat boundaries has been well documented (Cadenasso, Traynor & Pickett 1997; Harper *et al*. 2005). A simple comparison of magnitudes will allow quick and effective tests of hypotheses about the role of the matrix in mediating edge effects, and the degree of consistency with which the matrix exerts that control. However, it should be noted that such estimates will be critically dependent on the researcher's definition of habitat and matrix ‘interior’. In many cases, the interior is an arbitrarily defined distance from the edge (often the far end of a sample transect) rather than an ecologically or statistically defined point. Moreover, in small habitat patches there may be no interior habitat (Laurance & Yensen 1991; Tscharntke *et al*. 2002). An obvious definition of habitat interior is habitat that is unaffected by edge effects, and we advocate using the statistical approach described below for determining the distance from the edge at which this definition is met.

#### problems in quantifying the extent of edge effects

In contrast to the relative ease with which the magnitude of edge effects can be compared across studies, the comparison of edge extent remains problematic for two reasons. The first is that most edge-effect studies investigate only the penetration of a response variable from the edge into the interior of the focal patch, without explicit consideration of the adjacent matrix habitat response (Ries *et al*. 2004). The notable exceptions to this criticism are studies of landscape boundaries that explicitly consider fluxes of materials or organisms across habitat boundaries (Wiens, Crawford & Gosz 1985; Hayward, Henry & Ruggiero 1999).

Given the widespread recognition of the role played by the surrounding landscape matrix in mediating ecological processes within habitat fragments (Fagan, Cantrell & Cosner 1999), it is surprising that the measurement of parameters in the matrix is so frequently left out of the design of edge-effect studies. Furthermore, theoretical models of edge effects all consistently predict edge effects to occur on both sides of the habitat boundary (Lidicker 1999; Cadenasso *et al*. 2003; Ries & Sisk 2004; Ries *et al*. 2004). For studies that do measure variables on just one side of the edge, it is only possible to estimate the edge-effect penetration distance into the focal patch. While this is one facet of the extent of edge effects (and usually the one of greatest conservation concern), it does not represent the full response dynamics and can rarely be extrapolated to matrix responses because edge effects are typically asymmetrical across habitat boundaries (Cadenasso, Traynor & Pickett 1997; Figs 1 and 2). In some cases, sampling up to the patch edge and no further is ecologically justifiable; for example, it is meaningless to record tree mortality or forest canopy insect diversity within a grassland matrix. However, the failure to account for edge effects that do legitimately extend into the matrix can lead to spurious conclusions; for example, tree mortality within a patch may be caused by changes in parameters within the surrounding landscape matrix such as wind speed (Laurance *et al*. 1998, 2002), so those parameters should be measured across the edge.

The second problem with measuring the extent of edge effects is that there is no widely accepted statistical method for quantifying the spatial scale of edge responses. Some authors have suggested comparing parameter values to an arbitrary proportion of the value obtained in the habitat interior (Chen, Franklin & Spies 1992; Brand & George 2001; Hylander 2005) and at other times a subjective, visual inspection of graphs has been used (Chen *et al*. 1995). One more rigorous approach has been to compare parameter values near edges to the range of variation in that parameter that occurs in the habitat interior (Laurance *et al*. 1998; Didham & Lawton 1999; Harper & MacDonald 2001). However, this method depends entirely on the definition of interior habitat. Because many edge effects occur over large spatial scales in the order of hundreds of metres (Laurance *et al*. 2002), it is likely that the edge gradient investigated in many studies is not adequate to provide a robust, interior-habitat control site. For the numerous studies conducted in small remnant patches, the entire patch may be affected by proximity to habitat boundaries (Laurance & Yensen 1991; Tscharntke *et al*. 2002). In these cases, even if responses are compared to a control site located in the centre of the habitat, the edge-effect penetration distance will almost certainly be underestimated.

Most recently, Toms & Lesperance (2003) and Cancino (2005) have advocated the use of piecewise, or breakpoint, regression to determine the location of ecological thresholds such as edge-effect zones. However, this approach explicitly aims to identify discrete (compartmentalized) changes in response rates across boundaries, when in fact the rate of change in most response functions is continuous. Moreover, complex edge responses that are measured from the patch out into the matrix require additional breakpoints to be added (Cadenasso, Traynor & Pickett 1997). This technique does have the flexibility required to describe the complex, non-linear responses across habitat boundaries that are theoretically predicted and empirically demonstrated (Lidicker 1999; Ries *et al*. 2004). However, we argue that it is more parsimonious to model response curves with a single, continuous function than to force a set of multiple, disjointed responses on the data. Below, we present a form of the general logistic model that is able to do this, and illustrate how to use the model to delineate both the magnitude and extent of ecological changes across habitat boundaries.

### A case study of edge-effect magnitude and extent calculations

- Top of page
- Summary
- Introduction
- Defining the strength of edge effects
- A statistical approach to quantifying the strength of edge effects
- A case study of edge-effect magnitude and extent calculations
- Discussion
- Implications and applications of the logistic and unimodal models
- Acknowledgements
- References

We illustrate the use of these models with data from the Hope River Forest Fragmentation Project, investigating the effects of habitat fragmentation on invertebrate communities in the Southern Alps of New Zealand (Ewers, Didham & Ranson 2002). A total of 233 flight intercept traps was placed at up to 11 distances from forest edges into forest interiors (*D* = 0, −2, −4, −8, −16, −32, −64, −128, −256, −512 and −1024 m) and at the same series of distances out from these forest edges into the adjacent grassland matrix (*D* = +2, +4, +8, +16, +32, +64, +128, +256, +512, +1024 m). Edge gradients were established at the edges of 15 forest fragments spanning nine orders of magnitude in size (0·01–1 060 408 ha). In fragments with a minimum diameter of less than 2 km, larger edge distances were sequentially dropped from edge gradients, resulting in consequent variation in sample size from near-edge distances (*D* = ±4 m, *n*= 15 fragments) to far-from-edge distances (*D* = ±1024 m, *n*= 3 fragments). Two control sites were selected to quantify the degree of variability in invertebrate abundance in interior habitat: (i) deep continuous forest at least 2 km from the nearest edge and (ii) deep continuous matrix at least 2 km from the nearest forest remnant. In the deep forest control (coded as *D* = −2048 m) and deep matrix (*D* = +2048 m) control sites, the full complement of 21 traps was established from −1024 to +1024 m around an arbitrarily defined zero point.

Invertebrates were collected over a 10-week period in the antipodean summer (December 2000–February 2001). All invertebrates were sorted to Order and counted. We present data for just the Coleoptera (*n* = 35 461), Diptera (*n* = 24 671), Orthoptera (*n* = 6499) and Hemiptera (*n* = 15 589), as these groups exhibited four common categories of edge response (Fig. 1a–d). The Coleoptera is primarily a forest taxon at this site, with highest abundance in the forest and a decline in abundance across the habitat boundary into the pasture matrix. The reverse trend is seen in the Orthoptera, which also has a very rapid edge response, whereas the Diptera fit the criterion for an edge specialist taxon, with a unimodal peak in abundance near the forest edge. The Hemiptera are similar to the Orthoptera in that they are most abundant in the matrix, but the scale of our sampling design was evidently not large enough to encompass the full response of this taxon to forest edge (Fig. 1).

Invertebrate abundance was standardized to number of individuals captured per m^{2} of trap surface area per day, and log_{10} transformed to meet assumptions of normality. Edge distances were log_{2} transformed and forest sites were manually coded with negative values. We fitted all models described above (equations 1–5), calculated AIC weights for each model and for each taxon, then selected the model with the highest weight as being the best model (Table 1a). The edge-effect magnitudes and extents and edge-effect penetration distances were determined from the fitted curves (Fig. 1) and are presented in Table 2a.

Table 1. Comparison of model fits to observed data for five theoretical models describing edge effects. Models are compared for the abundance of four ordinal taxa (a) and for four other common types of ecological data (b): abundance of a single species (*Xylophilus* sp.; Coleoptera: Aderidae), a measure of community diversity, a microclimatic gradient and a measure of habitat variability. Tree size variability was modelled twice, once including all sites and once omitting sites with no trees (*D* = +16 m). *K* is the number of parameters estimated for each model, *r*^{2} is the model coefficient of determination, AIC refers to the Akaike information criterion and *W* is the Akaike weight, representing the probability that a particular model gives the best fit to the data for the five models tested. Note that *r*^{2} cannot be assessed for mean-only models Model (*K*) | Mean-only (1) | Linear (2) | Power (2) | Logistic (4) | Unimodal (5) |
---|

Response variable | *r*^{2} | AIC | *W* | *r*^{2} | AIC | *W* | *r*^{2} | AIC | *W* | *r*^{2} | AIC | *W* | *r*^{2} | AIC | *W* |
---|

(a) Ordinal responses to habitat boundaries |

Coleoptera | NA | −409 | 0·000 | 0·34 | −534 | 0·001 | 0·37 | −490 | 0·000 | 0·49 | −549 | 0·999 | 0·38 | −504 | 0·000 |

Diptera | NA | −565 | 0·000 | 0·03 | −597 | 0·001 | 0·00 | −563 | 0·000 | 0·04 | −588 | 0·000 | 0·13 | −611 | 0·999 |

Orthoptera | NA | −322 | 0·000 | 0·12 | −361 | 0·025 | 0·10 | −342 | 0·000 | 0·18 | −367 | 0·602 | 0·17 | −365 | 0·374 |

Hemiptera | NA | −437 | 0·000 | 0·09 | −500 | 0·832 | 0·09 | −470 | 0·000 | 0·09 | −496 | 0·168 | 0·04 | −479 | 0·000 |

(b) Other responses to habitat boundaries |

Species-level abundance | NA | −268 | 0·000 | 0·06 | −277 | 0·000 | 0·02 | −272 | 0·000 | 0·16 | −294 | 0·000 | 0·27 | −322 | 1·000 |

Shannon diversity | NA | −524 | 0·000 | 0·14 | −551 | 0·000 | 0·11 | −548 | 0·000 | 0·31 | −589 | 0·091 | 0·32 | −589 | 0·909 |

Light differential | NA | −183 | 0·000 | 0·56 | −522 | 0·000 | 0·60 | −535 | 0·000 | 0·69 | −623 | 1·000 | 0·69 | −582 | 0·000 |

Tree size variability |

All values of *D* | NA | −496 | 0·000 | 0·52 | −632 | 0·000 | 0·41 | −613 | 0·000 | 0·64 | −706 | 1·000 | 0·64 | −683 | 0·000 |

*D* +16 m | NA | −559 | 0·000 | 0·50 | −690 | 0·000 | 0·36 | −659 | 0·000 | 0·54 | −706 | 0·917 | 0·54 | −701 | 0·082 |

Table 2. Estimation of edge-effect penetration distances, edge-effect extent and edge-effect magnitude. Values in parentheses are bootstrapped 95% CI, with ∞ indicating a value greater than the scale over which response functions were recorded (−1024 to +1024 m). The calculations are made for the abundance of four ordinal taxa (a) and for four other common types of ecological data (b), as described in Table 1. Values could not be calculated for Hemiptera as this response variable was best described by a linear model, which gives no information on edge-effect extent or magnitude. Responses to edge are portrayed graphically in Figs 1a–d and 2. Forest edge-effect penetration distance is defined as the point at which invertebrate abundance ceased to be different to forest interior abundance (Forest), and matrix edge-effect penetration distance is where abundance ceased to be different from matrix interior abundance (Matrix), calculated from the second derivative of the fitted model. The extent of edge effects is the difference between the forest and matrix penetration distances Response | Model | Penetration distance (m) | Strength of edge effect |
---|

Forest | Matrix | Extent (m) | Magnitude |
---|

(a) Ordinal responses to habitat boundaries |

Coleoptera abundance | Logistic | −79 (∞, −10) | 1 (−5, 5) | 80 (7, ∞) | 0·67 (0·47, 1·62) |

Diptera abundance | Unimodal | −175 (∞, −36) | 40 (23, 267) | 215 (40, ∞) | 0·24 (0·11, 0·28) |

Orthoptera abundance | Logistic | −2 (−9, 1) | 1 (−2, 7) | 3 (2, 10) | 0·37 (0·25, 0·53) |

Hemiptera abundance | Linear | NA | NA | NA | NA |

(b) Other responses to habitat boundaries |

Species-level abundance | Unimodal | −385 (∞, −191) | 2 (1, 5) | 387 (193, ∞) | 0·65 (0·44, 0·68) |

Shannon diversity | Logistic | 2 (−1, 5) | 16 (6, 45) | 14 (3, 35) | 0·37 (0·28, 0·45) |

Light differential | Logistic | −1 (−2, 2) | 7 (4, 15) | 8 (3, 10) | 0·68 (0·59, 0·79) |

Tree size variability |

All values of *D* | Logistic | −6 (−12, −3) | −1 (−2, 2) | 5 (3, 8) | 0·47 (0·40, 0·55) |

*D* +16 m | Logistic | −6 (−13, −3) | −1 (−2, 2) | 5 (2, 10) | 0·46 (0·38, 0·58) |

We were able to determine the magnitude and extent of edge effects for three of the four taxa, but not for the Hemiptera, whose edge response was best described by a linear model (Fig. 1d). No taxa were best described by either the mean-only hypothesis or the power model. The Coleoptera and Diptera models exhibited an asymmetrical edge effect across the habitat boundary, whereas the Orthoptera model was less obviously skewed, but in all three cases it was clear that the overall edge-effect extent was dominated by greater extent values into the forest habitat than into the adjacent matrix habitat. There were obvious differences in the strength of edge effects for the four taxa across the habitat boundary, with Coleoptera having the largest effect magnitude and Diptera the largest effect extent, whereas the Orthoptera had a much smaller effect magnitude over a very short extent.

Confidence intervals around our estimates of edge-effect penetration distance were wide, reflecting high variability in the data and two unforeseen limitations of our sampling design. First, there was lower sampling effort (and hence greater SE) at large edge distances, resulting in the width of the CI increasing with the extent of the edge effect. In taxa with medium to large edge extents (*c.* > 80 m), this elevated variability caused the CI to exceed the scale of our investigation, so that the upper bounds of the edge extent estimates could not be accurately defined (Table 1). Secondly, the CI were always highly skewed because of the log_{2}-based sampling design. We had designed this sampling regime with the *a priori* expectation that the greatest change in community composition would occur near the forest edge, and hence it was best to increase the spatial resolution of sampling near the edge. Distance to edge was linearized prior to analysis (−1024 to +1024 with intervals of 2^{D′}and transformed to *D*′ = −10 to +10 with intervals of 1). This meant that a CI of width 2 and centred at the habitat boundary would back-transform to give a CI of 2 m, whereas the same CI centred at 256 m (2^{8}) would back-transform to be 384 m wide. Thus, the positive correlation between edge extent and CI width does not reflect a failure of the statistical approach but is rather an unexpected outcome of the experimental design.

To demonstrate further the widespread applicability of the logistic approach, we applied it to four different categories of data, also collected in the Hope River Forest Fragmentation Project (Fig. 2, Tables 1b and 2b). As above, the curves were fitted to the transformed data points. In Fig. 2a, we investigated the abundance response to distance to edge for the species *Xylophilus* sp. (Coleoptera: Aderidae). Changes in community diversity across edges were represented with the Shannon diversity index (diversity was assessed from species-level data, not the ordinal data used above; Fig. 2b). It would be equally possible to use a community composition metric such as an ordination score. Interestingly, this model showed that the edge effect does not necessarily occur across a habitat boundary but may instead lie completely to one side of the edge. These data indicate that forest-like diversity extends into the matrix for a short distance, resulting in an environment that is structurally grassland but, in terms of beetle community composition, is more similar to forest. The logistic model also adequately described microclimatic variation across edges, such as changes in light intensity (Fig. 2c). Finally, we applied our approach to variability in tree diameter measured at breast height, both including and excluding all matrix sites beyond a distance of 16 m from the analysis (no trees were encountered at sites with *D* > +16 m; Fig. 2d). It is encouraging that the inclusion or exclusion of these ‘no-data’ samples made little difference to the values of magnitude and extent of edge effects (Table 2b), highlighting the robust nature of this statistical approach to uneven and asymmetrical sampling across edges.

Across all models, there was a non-significant positive correlation between effect magnitude and extent (*r* = 0·128, d.f. = 5, *P* > 0·05; test excluded the Hemiptera and the second tree diameter model fitted without sites with *D* > +16 m). This indicates that the two components of edge effects that we advocate here do provide quantitatively different information about the nature of edge effects.

### Discussion

- Top of page
- Summary
- Introduction
- Defining the strength of edge effects
- A statistical approach to quantifying the strength of edge effects
- A case study of edge-effect magnitude and extent calculations
- Discussion
- Implications and applications of the logistic and unimodal models
- Acknowledgements
- References

We recognize and applaud the growing interest in processes operating across patch–matrix boundaries (Baker, French & Whelan 2002), but statistical methods for delineating the spatial scale of edge effects have undoubtedly lagged behind the development of edge-effect theory and empirical data collection. The widespread use of logarithmic and exponential equations to describe edge responses (Laurance *et al*. 1998; Didham & Lawton 1999; Brand & George 2001; Hylander 2005) have limited applicability, in that they can only be used to describe edge responses on one or other side of the edge and cannot be extended across the full ecotone from one habitat interior to the next. Such a persistent focus on ‘half’ of the edge gradient at best allows the detection of edge-effect penetration distances into one of the two habitats that abut the edge (albeit with recourse to an arbitrarily determined value); it cannot provide rigorous estimates of the overall extent of the edge effect. Furthermore, these approaches have provided no method for estimating the uncertainty around estimates of the edge-effect penetration distance. This in turn inhibits the comparative analysis and synthesis of edge-effect patterns across studies of varying taxa inhabiting different habitat types at multiple locations.

Other, more flexible, methods, such as piecewise regression, are able to describe edge effects across ecotones (Cadenasso, Traynor & Pickett 1997) and it is possible to use this approach to derive CI around the estimates of edge-effect magnitude and extent (after Toms & Lesperance 2003). However, this approach typically divides a continuous response function into multiple, linear responses, which ignores the fact that many responses are both curvilinear and continuous. As such, it makes intuitive sense to use continuous and flexible response curves such as the logistic and unimodal models.

Although not presented in this paper, it is also possible in these models to partial out the effects of additional (co)variables that are frequently of interest to researchers investigating edge effects (e.g. fragment area and isolation, and habitat and landscape characteristics). However, this relatively straight-forward approach has the limitation that interactions between edge effects and covariates cannot be tested for. A more complex approach would be to construct a set of nested models to evaluate the non-linear edge effect equations in concert with additional parameters for the other variables (for a detailed description of testing multiple variables with a non-linear model of edge effects, see Mancke & Gavin 2000).

#### practical constraints on the application of logistic models

There are two potential constraints on the practical application of this approach. First, the logistic and unimodal models require the estimation of four and five parameters, respectively. To achieve this, it is essential that the data include numerous samples from numerous distances away from the edge. Secondly, in order to use the logistic and unimodal models to quantify accurately edge-effect extent and magnitude it is essential that the sampling design encompass as comprehensive a range of potential distances from edge as possible in the landscape, from the patch interior right through to the matrix interior habitat. If either of these conditions is not met, it will still be possible to fit a continuous response function but the accuracy and validity of the resulting parameter values may be compromised. In particular, the researcher may conclude that one of the more basic mean-only, linear or exponential models (which give no useful information about edge-effect extent and magnitude) fits the data, when in fact the more complex logistic or unimodal may have been the correct model had a full range of distances been sampled. This could be a particular problem for studies of edge effects in small habitat patches, partly because the patch is simply too small to accommodate many sampling distances and partly because small patches are unlikely to contain any interior habitat.

For studies measuring microclimatic gradients or sampling small taxa such as invertebrates in large habitat patches, the sampling constraints described above should not present a serious obstacle. However, for larger-bodied taxa or taxa that use space at broader scales, such as birds and mammals, these sampling issues will not be trivial. This is because the definition of small vs. large patches that we have loosely applied here is a context-specific variable that will vary depending on both the taxa being studied and the habitat–matrix system in which the study is being conducted. What is a large patch for an invertebrate may be a medium-sized patch for a bird and a very small patch indeed for a large mammal (Wiens 1989).

One possible means of circumventing these sampling issues is to focus sampling effort on one or a handful of patches, i.e. to trade-off the number of replicate patch boundaries sampled in favour of more intensive sampling of a handful of patch boundaries. Although the fitting of the logistic and unimodal models would obviously benefit from having replicate edge gradients, it is more important, at least in the context of providing a robust quantification of edge effects, to have data that encompass the full extent of the edge effect than it is to have replicate data over just a small portion of the edge extent. In the latter case, the models cannot accurately describe edge-effect magnitude and extent.

Finally, although the full application of our method relies upon sampling a response variable on both sides of the boundary, this may seem nonsensical or trivial in some cases, such as the measurement of tree density on both sides of a forest–grassland boundary. However, as we showed in our example of tree diameter variability, the inclusion or exclusion of zeros makes little difference to the overall estimates of edge-effect magnitude and extent using our statistical approach (Table 2), as long as the non-sampled values can safely be assumed to equal zero. This is because the parameter estimate for the minimum bound on the logistic model should approximate zero, whether the actual zeros are included in the data or not. In cases where a response variable is not measured on one side of the edge, but cannot safely be assumed to equal zero in that habitat, then the logistic models should be applied with caution.

### Implications and applications of the logistic and unimodal models

- Top of page
- Summary
- Introduction
- Defining the strength of edge effects
- A statistical approach to quantifying the strength of edge effects
- A case study of edge-effect magnitude and extent calculations
- Discussion
- Implications and applications of the logistic and unimodal models
- Acknowledgements
- References

Parameters in the logistic and unimodal models allow the two main components of edge-effect strength, magnitude and extent, to be described in a biologically meaningful, as well as rigorous and objective, manner. The effect extent can be further partitioned to examine edge-effect magnitude and extent in both the focal habitat and in the matrix habitat separately, with parameters calculated for both sides of the edge (Table 2). Thus it is possible to compare directly the relative strength of influence that the matrix has on the patch habitat and vice versa. This is important for understanding the differential and, as in our examples, asymmetrical effects of patch boundaries on two abutting ecosystems. It also paves the way for quantitative assessment of variation in edge-effect extent that is mediated by different matrix habitat types. For instance, if a matrix habitat of one type can buffer the impact of edge effects relative to another matrix type (e.g. a forest fragment surrounded by plantation forest vs. pastoral or arable crops), then we would expect to find a significant reduction in edge-effect extent on the forest side of the boundary.

In combination with the objective comparison among alternative models with AIC, our approach can be used to assess quantitatively whether any given habitat patch contains viable core habitat for the particular species or habitat characteristic of interest. This technique also provides a rigorous method for parameterizing models that attempt to predict spatial patterns of edge-affected habitat (Zheng & Chen 2000). Identifying and maintaining core habitat is a central concern to conservation managers because many species are less abundant (Brand & George 2001), have reduced reproductive fitness (Flaspohler, Temple & Rosenfield 2001) or suffer increased competition or predation (Fagan, Cantrell & Cosner 1999; Flaspohler, Temple & Rosenfield 2001) near habitat boundaries, such that core area can be a better predictor of total population size than the total area of a fragment (Temple 1986).

In conclusion, we believe that the ability to apply logistic models to the study of edge effects in a wide range of response variables, across both sides of habitat boundaries, provides a powerful method for delineating the magnitude and extent of edge impact. At the same time, the logistic models provide an essential management tool for rigorous comparison of spatial variation in the strength of edge effects across landscapes, as well as temporal variation in the strength of edge effects following land-use change or habitat restoration.