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Keywords:

  • ecotones;
  • edge effect;
  • edge-effect penetration distance;
  • extent;
  • habitat fragmentation;
  • logistic model;
  • magnitude;
  • patch boundary;
  • scale;
  • unimodal model

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. References
  • 1
    Ecological boundaries are a dominant feature of human-modified landscapes and have been the subject of numerous empirical studies. Robust statistical methods for determining the strength of edge effects are a vital requirement for the effective management of species that are negatively affected by habitat boundaries in heavily fragmented landscapes, but development of such methods has been slow.
  • 2
    We define edge effects as being composed of two complementary, and statistically definable, components: magnitude (the degree of difference in response values between patch and matrix interiors) and extent (the distance over which the difference in response values can be detected).
  • 3
    We present a statistical approach to rigorously delineate edge-effect magnitude and extent. Our approach adapts a form of the general logistic model to describe continuous response functions for any biotic or abiotic variable across ecological boundaries from the landscape matrix into focal patch habitats. The model describes sigmoid and unimodal response functions that have been both theoretically predicted and empirically demonstrated. We use the second derivatives of the functions as an objective means to calculate the magnitude and extent of edge effects, and present a bootstrap technique for calculating confidence intervals around these values.
  • 4
    Synthesis and applications. Our results show clearly that edge-effect magnitude and extent are not necessarily correlated, and therefore provide quantitatively different, and complementary, information about the strength of edge effects. Both effect magnitude and extent can be easily used for cross-study comparisons, either by directly comparing the absolute values of response variables in the patch and matrix, or by converting those values to a percentage change. Furthermore, this method provides a management tool for more accurately predicting the presence, spatial location and utilization of core habitat by species in fragmented landscapes.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. References

Edges, ecotones or ecological boundaries by any other name have had profound effects on the dynamics of species and communities in human-modified landscapes (Yahner 1988; Sisk & Battin 2002; Ries et al. 2004). Boundaries between habitat patches are typically accompanied by a transition in the diversity and structural complexity of plant communities (Fraver 1994; Laurance et al. 2002; Harper et al. 2005), resulting from the complex interplay of direct human disturbance and indirect changes in a wide range of biotic and abiotic processes (Chen, Franklin & Spies 1995; Murcia 1995). Edges also alter species’ interactions (Fagan, Cantrell & Cosner 1999), the trophic structure of communities (Laurance et al. 2002), the movement of individuals through landscapes (Wiens 1992) and resource flows between habitats (Wiens, Crawford & Gosz 1985; Wiens 1992; Huxel & McCann 1998), thereby modifying ecological processes and dynamics at a wide range of spatial and temporal scales (Wiens 1992; Ries et al. 2004).

From a conservation viewpoint, edges can be the focal sites for the invasion of exotic species (Fraver 1994) and reduction in population densities of habitat-interior specialists (Temple 1986). At the same time, edges are frequently associated with elevated densities of predators (Sisk & Battin 2002) that invade from the surrounding matrix habitat and may concentrate their foraging along habitat boundaries (Askins 1995). Yet despite widespread recognition of the importance of habitat boundaries in ecology and conservation, and the vast literature covering the subject, there have been relatively few attempts to define statistically the scale at which edge effects operate across ecological boundaries (Chen, Franklin & Spies 1992, 1995; Cadenasso, Traynor & Pickett 1997; Laurance et al. 1998; Didham & Lawton 1999; Brand & George 2001; Harper & MacDonald 2001; Toms & Lesperance 2003; Cancino 2005). We have defined a conceptual framework for measuring the strength of edge effects that is complementary to current theoretical models, and developed a statistical approach to quantify objectively the degree of variation in response variables across edges.

Defining the strength of edge effects

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. 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.

image

Figure 1. Calculation of the magnitude and extent of edge effects for four invertebrate taxa. Transformed taxon abundance (mean ± 1 SE) is plotted against distance to edge for (a) Coleoptera, (b) Diptera, (c) Orthoptera and (d) Hemiptera. The general logistic curve (equation 4) was fitted to the Coleoptera and Orthoptera (a, c), the unimodal logistic curve (equation 5) was fitted to the Diptera (b) and a linear model (equation 2) fitted to the Hemiptera (d). The first derivatives of the fitted curves are plotted in (e–h), and the second derivatives in (i–l). The extent of the edge effect is the distance between the local maxima and minima (a, c) or between the two local maxima (b), which are shown by vertical arrows in (i–k). Negative edge distances are inside the forest and positive distances are in the matrix. Open circles are the mean ± 1 SE calculated from traps in the habitat interior controls, and are presented for comparison but were not used in model fitting.

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image

Figure 2. Application of logistic edge response models to different types of data. (a) Species-level data showing the abundance of Xylophilus sp. (Coleoptera: Aderidae). (b) Community-level data, showing changes in Shannon diversity index values across the edge. (c) Microclimate data, showing the proportion of incident solar radiation intercepted by light sensors at 0·5 m height. (d) Habitat structure data, showing the coefficient of variation (CV) of tree diameter measured at breast height. Vertical arrows show edge-effect penetration distances, and the extent of the edge effect is the distance between the two arrows. Negative edge distances are inside the forest, and positive distances are in the matrix. Open circles are the mean ± 1 SE calculated from traps in the habitat interior controls, and are presented for comparison but were not used in model fitting.

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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 statistical approach to quantifying the strength of edge effects

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. References

statistical models to describe biotic or abiotic responses to habitat boundaries

Response functions across habitat boundaries can be adequately described by a set of five statistical models that vary in complexity. First, and most simple, is the hypothesis of no discernible edge effect, which is calculated simply as the mean of the response variable η and is described by the formula:

  • image( eqn 1)

where ɛ is an error term. Secondly, response functions may take the form of a simple linear gradient of the form:

  • image( eqn 2)

where β0 and β1 are constants and D is the distance to edge. Also commonly fitted is the power model:

  • image( eqn 3)

The power model has a clear advantage over the linear model in that it predicts the value of η will asymptote on one side of the edge. However, widely accepted theoretical models indicate there should be an asymptote on both sides of the habitat boundary (Lidicker 1999; Cadenasso et al. 2003; Ries & Sisk 2004; Ries et al. 2004). These theoretical models describe a sigmoid increase (or decrease) in a variable across an edge (Fig. 1a,c) that can be described by a form of the general logistic model:

  • image( eqn 4)

where β2 and β3 are additional constants. This model is similar to that presented by Mancke & Gavin (2000), although they were analysing the effect of multiple edges on a response variable rather than a single edge as we analyse here. The logistic model can be modified to describe unimodal peaks in a response function with respect to distance from edge, by including an additional constant and a D2 term (Fig. 1b), giving the formula:

  • image( eqn 5)

It should be noted here that these two forms of the logistic model are not dependent on using binary data, nor do they have a binomial error distribution. The fitted curves are bounded by minimum and maximum values; however, these values are empirically derived from the data, rather than set a priori to zero and one, respectively.

To compare the relative fits of the five different models in an unbiased manner, we used Akaike weights [calculated from Akaike information criterion (AIC) values], which give the probability that a particular model is the best fit to the data from the set of models that are evaluated.

determining edge-effect magnitude and extent

One clear shortcoming of the commonly employed linear and power models (equations 2 and 3, respectively) is that they cannot be used to rigorously quantify either effect magnitude or extent, because they do not give an asymptotic value of the response variable η for both the habitat patch interior and the matrix interior (see the discussion above). The power model, which asymptotes on one side of the edge, gives half of the required information, but previous attempts to use this asymptote as a reference point against which to determine edge extent have been arbitrary, rather than statistical. For instance, some authors have stated that an edge effect extends from the edge to the point at which the predicted value of η is equal to 90% of the asymptote (Brand & George 2001; Hylander 2005). Chen, Franklin & Spies (1992) used the same approach, but chose 67% as the critical value instead. In none of these studies is there any justification given for selecting the particular critical percentage employed.

In contrast, the logistic and unimodal models (equations 4 and 5, respectively) present clear opportunities for rigorous delineation of both edge-effect magnitude and extent. For equation 4, the magnitude of the effect across the edge is the absolute value of the numerator of the equation, or | β1–β0 |, which corresponds to the difference between the maximum and minimum values of the response variable. In the case of equation 5, the magnitude is also the difference between the maximum and minimum points on the curve. The minimum value is the smallest of the two parameters β1 and β0, and the maximum can be found by solving equation 5 for η when D takes the value at the central inflection point on the first derivative of the curve (equation 7; Fig. 1f). For cross-study comparative purposes, these values could easily be converted to a percentage change that would reflect the proportional increase or decrease in the response variable across the boundary.

The extent of edge effects can be delineated from the first and second derivatives of the fitted models. For the logistic equation 4, the first derivative is given by the formula:

  • image( eqn 6)

Graphs of the first derivative against distance to edge reveal either a local maximum or local minimum, depending on whether the response variable has a higher value in the habitat patch or in the matrix (Fig. 1e,g). This maximum or minimum is the distance to edge at which the rate of change in the response variable is greatest across the edge. In other words, this point is where the per metre change in η is most rapid, and can be used to represent the midpoint of the edge effect. For the unimodal equation 5, with the first derivative described by the equation:

  • image( eqn 7)

the midpoint occurs where the slope of η changes from positive to negative, i.e. where the first derivative is equal to zero (Fig. 1f).

To determine the extent of the edge zone, we calculated the second derivatives of the logistic and unimodal models (equations 4 and 5, respectively), which are:

  • image( eqn 8)

and

  • image( eqn 9)

respectively, and have, inline image, inline image and inline image. Solving equation 8 for the local maxima and minima gives the distances to which edge effects penetrate into the focal habitat patch and into the matrix (Fig. 1i,k). In the case of equation 9, the edge-effect penetration distances are obtained from the two local maxima (Fig. 1j). We define the extent of the edge effect as the distance between the two (patch and matrix) edge-effect penetration distances (Fig. 1i–k). This approach to defining the start and end points of an edge effect is similar in principle to that used by Walker et al. (2003) to define ecotonal vegetation boundaries. Similarly, Schmitz (2004) used second derivatives to determine thresholds in ecosystem properties that varied with respect to a gradient of abundance of a dominant plant. The two points represent the edge distances at which the rate of the edge effect changes most rapidly, and provide a sound estimate for the start and end point of an edge effect. The strong advantage of this approach is that it is not determined by reference to an arbitrarily chosen value.

calculating confidence intervals

We derived confidence intervals (CI) for our measures of edge extent and magnitude from the bootstrap technique of non-parametric resampling of the errors (Davison & Hinkley 1997; Toms & Lesperance 2003), which maintains the underlying error structure of the raw data (Shao & Tu 1995; Toms & Lesperance 2003). In this method a bootstrapped sample is created by randomly sampling the residuals from the fitted model and adding them to the fitted values. The model is then refitted to the bootstrapped sample, and edge extent and magnitude recalculated. The process is repeated 1000 times and a 95% CI is given by the 2·5th and 97·5th percentiles of the bootstrapped estimates (Toms & Lesperance 2003).

A case study of edge-effect magnitude and extent calculations

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. 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 m2 of trap surface area per day, and log10 transformed to meet assumptions of normality. Edge distances were log2 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, r2 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 r2 cannot be assessed for mean-only models
Model (K)Mean-only (1)Linear (2)Power (2)Logistic (4)Unimodal (5)
Response variabler2AICWr2AICWr2AICWr2AICWr2AICW
(a) Ordinal responses to habitat boundaries
ColeopteraNA−4090·0000·34−5340·0010·37−4900·0000·49−5490·9990·38−5040·000
DipteraNA−5650·0000·03−5970·0010·00−5630·0000·04−5880·0000·13−6110·999
OrthopteraNA−3220·0000·12−3610·0250·10−3420·0000·18−3670·6020·17−3650·374
HemipteraNA−4370·0000·09−5000·8320·09−4700·0000·09−4960·1680·04−4790·000
(b) Other responses to habitat boundaries
Species-level abundanceNA−2680·0000·06−2770·0000·02−2720·0000·16−2940·0000·27−3221·000
Shannon diversityNA−5240·0000·14−5510·0000·11−5480·0000·31−5890·0910·32−5890·909
Light differentialNA−1830·0000·56−5220·0000·60−5350·0000·69−6231·0000·69−5820·000
Tree size variability
All values of DNA−4960·0000·52−6320·0000·41−6130·0000·64−7061·0000·64−6830·000
D  +16 mNA−5590·0000·50−6900·0000·36−6590·0000·54−7060·9170·54−7010·082
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
ResponseModelPenetration distance (m)Strength of edge effect
ForestMatrixExtent (m)Magnitude
(a) Ordinal responses to habitat boundaries
Coleoptera abundanceLogistic −79 (∞, −10)  1 (−5, 5) 80 (7, ∞)0·67 (0·47, 1·62)
Diptera abundanceUnimodal−175 (∞, −36) 40 (23, 267)215 (40, ∞)0·24 (0·11, 0·28)
Orthoptera abundanceLogistic  −2 (−9, 1) 1 (−2, 7)  3 (2, 10)0·37 (0·25, 0·53)
Hemiptera abundanceLinearNANANANA
(b) Other responses to habitat boundaries
Species-level abundanceUnimodal−385 (∞, −191)  2 (1, 5)387 (193, ∞)0·65 (0·44, 0·68)
Shannon diversityLogistic     2 (−1, 5) 16 (6, 45) 14 (3, 35)0·37 (0·28, 0·45)
Light differentialLogistic      −1 (−2, 2) 7 (4, 15)  8 (3, 10)0·68 (0·59, 0·79)
Tree size variability
All values of DLogistic  −6 (−12, −3)−1 (−2, 2)  5 (3, 8)0·47 (0·40, 0·55)
D  +16 mLogistic  −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 log2-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 2D′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 (28) 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

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. 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

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. 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.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. References

We thank Mary Cadenasso, Bill Fagan, Laura Fagan, Bill Laurance, Susan Laurance and Leslie Ries for providing helpful discussion and comments on an early draft of this manuscript, and Greg Hayward and two anonymous refereees for their constructive reviews. Funding for the Hope River Forest Fragmentation Project was provided by the University of Canterbury, the Brian Mason Scientific and Technical Trust and the Todd Foundation. Support during the writing of this manuscript was provided by the Smithsonian Tropical Research Institute.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Defining the strength of edge effects
  5. A statistical approach to quantifying the strength of edge effects
  6. A case study of edge-effect magnitude and extent calculations
  7. Discussion
  8. Implications and applications of the logistic and unimodal models
  9. Acknowledgements
  10. References
  • Askins, R.A. (1995) Hostile landscapes and the decline of migratory songbirds. Science, 267, 19561957.
  • Baker, J., French, K. & Whelan, R.J. (2002) The edge effect and ecotonal species: bird communities across a natural edge in southeastern Australia. Ecology, 83, 30483059.
  • Brand, L.A. & George, T.L. (2001) Response of passerine birds to forest edge in coast redwood forest fragments. Auk, 118, 678686.
  • Cadenasso, M.L., Pickett, S.T.A., Weathers, K.C. & Jones, C.G. (2003) A framework for a theory of ecological boundaries. Bioscience, 53, 750758.
  • Cadenasso, M.L., Traynor, M.M. & Pickett, S.T.A. (1997) Functional location of forest edges: gradients of multiple physical factors. Canadian Journal of Forest Research, 27, 774782.
  • Cancino, J. (2005) Modelling the edge effect in even-aged Monterey pine (Pinus radiata D. Don) stands. Forest Ecology and Management, 210, 159172.
  • Chen, J., Franklin, J.F. & Spies, T.A. (1992) Vegetation responses to edge environments in old-growth Douglas-fir forests. Ecological Applications, 2, 387396.
  • Chen, J., Franklin, J.F. & Spies, T.A. (1995) Growing-season microclimatic gradients from clearcut edges into old-growth Douglas-fir forests. Ecological Applications, 5, 7486.
  • Davison, A. & Hinkley, D. (1997) Bootstrap Methods and their Application. Cambridge University Press, New York, NY.
  • Didham, R.K. & Lawton, J.H. (1999) Edge structure determines the magnitude of changes in microclimate and vegetation structure in tropical forest fragments. Biotropica, 31, 1730.
  • Ewers, R.M. & Didham, R.K. (in press) Confounding factors in the detection of species responses to habitat fragmentation. Biological Reviews, 81, 117142.
  • Ewers, R.M., Didham, R.K. & Ranson, L.H. (2002) The Hope River forest fragmentation project. Weta: Bulletin of the Entomological Society of New Zealand, 24, 2534.
  • Fagan, W.F., Cantrell, R.S. & Cosner, C. (1999) How habitat edges change species interactions. American Naturalist, 153, 165182.
  • Flaspohler, D.J., Temple, S.S. & Rosenfield, R.N. (2001) Species-specific edge effects on nest success and breeding bird density in a forested landscape. Ecological Applications, 11, 3246.
  • Fraver, S. (1994) Vegetation responses along edge-to-interior gradients in the mixed hardwood forests of the Roanoke River basin, North Carolina. Conservation Biology, 8, 822832.
  • Harper, K.A. & MacDonald, S.E. (2001) Structure and composition of riparian boreal forest: new methods for analyzing edge influence. Ecoogy, 82, 649659.
  • Harper, K.A., MacDonald, S.E., Burton, P.J., Chen, J., Brosofske, K.D., Saunders, S.C., Euskirchen, E.S., Roberts, D., Jaiteh, M.S. & Esseen, P.-A. (2005) Edge influence on forest structure and composition in fragmented landscapes. Conservation Biology, 19, 768782.
  • Hayward, G.D., Henry, S.H. & Ruggiero, L.F. (1999) Response of red-backed voles to recent patch cutting in subalpine forest. Conservation Biology, 13, 168176.
  • Huxel, G.R. & McCann, K.S. (1998) Food web stability: the influence of trophic flows across habitats. American Naturalist, 152, 460469.
  • Hylander, K. (2005) Aspect modifies the magnitude of edge effects on bryophyte growth in boreal forests. Journal of Applied Ecology, 42, 518525.
  • Laurance, W.F. & Yensen, E. (1991) Predicting the impacts of edge effects in fragmented habitats. Biological Conservation, 55, 7792.
  • Laurance, W.F., Ferreira, L.V., Rankin-de Merona, J.M. & Laurance, S.G. (1998) Rain forest fragmentation and the dynamics of Amazonian tree communities. Ecology, 79, 20322040.
  • Laurance, W.F., Lovejoy, T.E., Vasconcelos, H.L., Bruna, E.M., Didham, R.K., Stouffer, P.C., Gascon, C., Bierregaard, R.O., Laurance, S.G. & Sampaio, E. (2002) Ecosystem decay of Amazonian forest fragments: a 22-year investigation. Conservation Biology, 16, 605618.
  • Lidicker, W.Z.J. (1999) Responses of mammals to habitat edges: an overview. Landscape Ecology, 14, 333343.
  • Mancke, R.G. & Gavin, T.A. (2000) Breeding bird density in woodlots: effects of depth and buildings at the edges. Ecological Applications, 10, 598611.
  • Murcia, C. (1995) Edge effects in fragmented forests: implications for conservation. Trends in Ecology and Evolution, 10, 5862.
  • Ries, L. & Sisk, T.D. (2004) A predictive model of edge effects. Ecology, 85, 29172926.
  • Ries, L., Fletcher, R.J.J., Battin, J. & Sisk, T.D. (2004) Ecological responses to habitat edges: mechanisms, models and variability explained. Annual Review of Ecology, Evolution and Systematics, 35, 491522.
  • Schmitz, O.J. (2004) Perturbation and Abrubt shift in Trophic Control of Biodiversity and Productivity. Ecology Letters, 7, 403409.
  • Shao, J. & Tu, D. (1995) The Jackknife and Bootstrap. Springer-Verlag, New York, NY.
  • Sisk, T.D. & Battin, J. (2002) Habitat edges and avian ecology: geographic patterns and insights for western landscapes. Studies in Avian Biology, 25, 3048.
  • Temple, S.A. (1986) Predicting impacts of habitat fragmentation on forest birds: a comparison of two models. Modelling Habitat Relationships of Terrestrial Vertebrates (eds J.Verner & M.L.Morrison), pp. 301304. University of Wisconsin Press, Madison, WI.
  • Toms, J.D. & Lesperance, M.L. (2003) Piecewise regression: a tool for identifying ecological thresholds. Ecology, 84, 20342041.
  • Tscharntke, T., Steffan-Dewenter, I., Kruess, A. & Thies, C. (2002) Contribution of small habitat fragments to conservation of insect communities of grassland–cropland landscapes. Ecological Applications, 12, 354363.
  • Walker, S., Bastow, W.J., Steel, J.B., Rapson, G.L., Smith, B., King, W.M. & Cottam, Y.H. (2003) Properties of ecotones: evidence from five ecotones objectively determined from a coastal vegetation gradient. Journal of Vegetation Science, 14, 579590.
  • Wiens, J.A. (1989) Spatial scaling in ecology. Functional Ecology, 3, 385397.
  • Wiens, J.A. (1992) Ecological flows across landscape boundaries: a conceptual overview. Landscape Boundaries: Consequences for Biotic Diversity and Ecological Flows (eds A.J.Hansen & F.Di Castri), pp. 217235. Springer-Verlag, New York, NY.
  • Wiens, J.A., Crawford, C.S. & Gosz, J.R. (1985) Boundary dynamics: a conceptual framework for studying landscape ecosystems. Oikos, 45, 421427.
  • Yahner, R.H. (1988) Changes in wildlife communities near edges. Conservation Biology, 2, 333339.
  • Zheng, D. & Chen, J. (2000) Edge effects in fragmented landscapes: a generic model for delineating area of edge influences (D-AEI). Ecological Modelling, 132, 175190.