Landscape heterogeneity indices

Landscape heterogeneity indices: problems of scale and applicability, with particular reference to animal habitat description P. G. CALE 1 and R. J. HOBBS 2 Efforts to quantify landscape heterogeneity have resulted in the production of a large number of indices based on the number and proportions of different types of landscape (usually vegetation) patches. In this paper we question whether these indices provide useful tools with which to examine functional aspects of landscape heterogeneity. In particular, we consider faunal use of the landscape, focussing on the case of birds in vegetation remnants in the Western Australian wheatbelt. We argue that attempting to describe landscape heterogeneity by a single heterogeneity index is inappropriate, because the qualitative differences between patch types and their spatial relationships frequently cannot both be described by a single value. Also, scales of study have to match the scale of the processes in which we are interested, or the scale at which particular organisms perceive their environment. Generalized indices of landscape heterogeneity may therefore have little predictive capacity for detailed process or habitat studies. Key words: Landscape Heterogeneity; Indices; Scale; Functional Heterogeneity; Habitat Description.

INTRODUCTION LANDSCAPE ecology by definition is the study of patchy or heterogeneous landscapes. It aims to describe landscape patterns and relate these patterns to processes (Forman and Godron 1986; Turner 1989). In this respect, landscape ecology conforms with many other areas of ecology which aim to link observed patterns with underlying processes. The ability to link pattern and process depends on firstly being able to characterize the observed patterns, and this endeavour has occupied a central place in recent landscape ecological literature. Weins (1992) estimated that 21.2 per cent of papers in the first five volumes of the journal Landscape Ecology focussed on spatial pattern description. Landscape heterogeneity represents one level in the nested hierarchy which makes up a region's biodiversity (Noss 1989), and its functional significance in this context has been discussed in a nonquantitative way by Hobbie et al. (1993) and Schulze and Gerstberger (1993). Solbrig (1991) concluded that diversity at the landscape level "is not amenable to the same level of objective measurement as diversity at lower levels in the biological hierarchy". However, there is often a tacit assumption that landscape ecologists have the task of quantifying landscape heterogeneity well in hand (e.g., Angelstam 1992; Richardson and Cowling 1993; Stoms and Estes 1993). Landscape heterogeneity is a complex phenomenon involving the size, shape and composition of different landscape units and the spatial (and temporal) relations between them. In fact, Kolasa and Rollo (1991) state that "Intuitively, the

concept of heterogeneity is clear, but as we scrutinize it our initial impression fractures into complexity". This complexity has led many workers to attempt the development of simple measures which can summarize landscape heterogeneity and allow the comparison of different landscapes. A wide array of indices has been developed which describe various aspects of landscape units and which are purported to allow a quantitative assessment of landscape heterogeneity (Forman and Godron 1986; O'Neill et al. 1988; Turner 1989; Musick and Grover 1990; Li et al. 1993). This again mirrors the development of other areas of ecology; for instance, many indices have been developed to quantify species diversity (Magurran 1988). In this paper we discuss the types of indices that have been developed and the uses to which they have been put. We explore the issue of scale, the importance of which has received much attention recently (Addicott et al. 1987; Turner et al. 1989; Weins 1989; Milne 1991; Cullinan and Thomas 1992; Levin 1992). We develop the idea that landscape heterogeneity is, in fact, a multiscale phenomenon which cannot be adequately described by concentrating on one scale exclusively. We suggest that the indices put forward as general descriptors of landscape heterogeneity may in fact have little value in specific contexts (i.e., to examine specific processes), and that it may, in fact, be impossible to produce generalized indices. We illustrate this by reviewing past use of indices and by discussing a particular case in which we have been involved, i.e., the effects of heterogeneity on bird communities in fragmented landscapes.

lUniversity of Western Australia, Zoology Department, Nedlands, Western Australia. Australia 6009. Present address: CSIRO, Division of Wildlife and Ecology, LMB 4, PO Midland, Western Australia, Australia 6056. 2CSIRO, Division of Wildlife and Ecology, LMB 4, PO Midland. Western Australia, Australia 6056. PACIFIC CONSERVATION BIOLOGY Vol. I: 183-93. Surrey Beatty & Sons, Sydney, 1994.

184

PACIFIC CONSERVATION BIOLOGY

REVIEW OF HETEROGENEITY INDICES We set out to examine the range of landscape heterogeneity indices which have been used and compare their usefulness. Magurran (1988) suggests that indices can be assessed inter aiia on whether they can discriminate between different sites and whether they are widely used and understood. We would add that a useful index must be able to provide a description of landscapes that allows predictions of the effects of differences between landscapes or changes in a particular landscape, with respect to particular organisms or processes. Unfortunately, it proved more difficult than we had imagined to carry out this assessment. A wide array of different indices is available, but few studies have used the same indices (or used them in the same way), and in many cases it was difficult to assess exactly how indices were developed or applied since the methodology was not always stated clearly. Since the methodology used is critical to the success of a study it is difficult to assess the value of the indices without knowing how they were used. We see this as a major problem with the way landscape heterogeneity indices have been applied to date. Because of this problem we do not present a comprehensive analysis of all available indices, but rather summarize the situation as we see it and point out the problems we think are inherent in the search for generalized landscape heterogeneity indices. We do not attempt to invent a new index because of the problems we identify and because we do not wish to add to the current clutter. Magurran (1988), in discussing species diversity indices, states "A quick dip into the literature on diversity reveals a bewildering range of indices. Each of these indices seeks to characterize the diversity of a sample or community by a single number. To add yet more confusion an index may be known by more than one name and written in a variety of notations using a range of log bases. The diversity of diversity indices has arisen because, for a number of years, it was standard practice for an author to review existing indices, denounce them as useless, and promptly invent a new index". It appears that little has been learned from the attempts to develop meaningful species diversity indices, and that the same process is happening for landscape heterogeneity indices. Landscape heterogeneity indices have been derived at two levels, considering differences in the heterogeneity of landscape units between landscapes (regional scale) and considering differences in the heterogeneity within a given landscape unit, within landscapes (landscape scale) (Fig. 1). Regional scale Indices developed for use at a regional scale are in their infancy and have been reviewed by Turner (1989). Some of these indices are indicated

in Figure 1, and include various combinations of estimates of numbers of different landscape units present, areas occupied by different landscape units and lengths of landscape unit perimeters. Other approaches consider the underlying patterns of plant species richness and variations in evenness (Scheiner 1992). To date, most studies using these indices have investigated their ability to quantify landscape pattern in space (Krummel et ai. 1987; O'Neill et ai. 1988; Turner and Ruscher 1988; Hoover and Parker 1991; Ripple et ai. 1991) and with time (Romme and Knight 1982). In general the indices have been considered useful if they have indicated differences between landscapes already known to differ substantially (i.e., have provided blinding glimpses of the obvious). We have found few instances of indices providing new insights, allowing extrapolation to other situations, or where the relationship between the index and functional aspects of heterogeneity have been explored. Turner et ai. (1989) investigated the effect of changing the scale at which some of these landscape heterogeneity indices are measured. They showed that changing the grain (spatial resolution) and extent (total area of study) affected measures of diversity, dominance and contagion differently. Diversity was shown to decrease linearly with increasing grain, and changing the extent produced a variable response. Both dominance and contagion measures showed non-linear decreases with increasing grain and non-linear increases with increasing extent. These non-linear responses were caused by sensitivity to the number of landscape units detected, which changed with scale. Furthermore, the spatial configuration of the landscape units influences the rate of change in their number with changing scale. These findings indicate that it is very difficult to compare measures made at different scales, and for some measures the relationship between scale and the measure differs in different landscapes. This makes it difficult to generalize. Landscape scale One set of studies, at the landscape scale, that has used heterogeneity indices are studies into the effects of fragmentation on faunal groups. The majority of these studies have considered bird communities (Kitchener et ai. 1982; Ambuel and Temple 1983; Lynch and Whigham 1984; Freemark and Merriam 1986; Blake and Karr 1987; Loyn 1987). Most of these studies have looked at forest fragments and have considered heterogeneity within these fragments in the form of structural complexity and/or floristic diversity of the vegetation (Table 1). Ambuel and Temple (1983) used a twodimensional ordination of the vegetation, produced by Peet and Loucks (1977), which describes forest composition and predicts succession on the basis of a successional gradient, based on shade

CALE and HOBBS: LANDSCAPE HETEROGENEITY INDICES

185

Regional Scale (L + 1) Richness/Diversity of landform units Contagion of landform units Fractal dimension of landform units

Landscape Scale (L) Plant Formation Richness/Diversity Patch RichnesslDiversity Fractal dimension of patches

Patch Scale (L - 1) Foliage Height Diversity Plant Species RichnesslDiversity

Fig. 1. Different scales at which heterogeneity may be considered, and various indices of heterogeneity that have been applied at

each scale (see Turner 1989 for details of indices). Processes at one level (L) may be affected by heterogeneity at higher (L + 1) or lower (L - 1) levels, as discussed by Allen and Hoekstra (1992).

186


tolerance in tree species, and on an environmental gradient of moisture-nutrient status. The standard deviation of these two gradients was used to represent heterogeneity within woodlots with respect to the factors measured in the gradients. They also calculated the foliage cover in different layers and from this developed two indices of structural diversity, the Foliage Height Diversity which considered the diversity of foliage in different layers and the Foliage Profile Diversity which measured the diversity of vertical profiles in the woodlot. Freemark and Merriam (1986) developed a Habitat Heterogeneity Index (Table 1) which measured the heterogeneity of habitats defined by plant species composition and structure within each forest fragment. To avoid problems of scaledependence this index was standardized by proportioning each class entry by the total for its respective habitat variable in each forest fragment. The index was calculated for each stratum considered and for all strata combined.

Kitchener et ai. (1982) dealt with a completely different level of heterogeneity compared to the other studies that considered forest fragments. They defined different plant formations and associations within their remnants and used measures of the richness of these formations and associations as indices of heterogeneity. In an attempt to consider both the diversity of vegetation types and the structural diversity within these vegetation types they created a matrix of plant life forms and density classes. They then used the number of unique matrix categories present in each remnant as an index of heterogeneity. These studies have provided contradictory conclusions about whether the heterogeneity of vegetation within fragments is an important factor affecting bird species richness. Because these studies have measured this heterogeneity in different ways (Table 1) and at different scales it is very diffiucult to isolate the reason for these contradictions.

Table 1. Studies that have considered the response of bird communities and individual species to habitat heterogeneity indices measured at the landscape scale. Vegetation type Forest

Forest

Mixed

Forest

Forest

Heterogeneity indices 8 structural variables, importance values for dominant tree species and PC1 and PC2 of PCA analysis of 12 structural and floristic variables. The first 4 principal components of a PCA of 9 structural and floristic variables were used to calculate the average Euclidean distances among points within a woodlot. 8 univariate measures of structural and floristic components.

Mixed

Community - not important Individuals - different variables important for c. 70 per cent of species.

HH=

i

±X;jln(X/X)

Not considered.

j~1

where r is total number of classes used to characterize c habitat plots, Xij is an entry for i'h class in jth habitat plot and Xi is the mean for class i. An index of the number of habitats on a patch, including Not considered. eucalypt communities, types of understorey, special features such as rubbish tips, and types of edge. Indices (forest habitat, farmland habitat and water habitat) which include subsets of total habitats. A matrix of canopy density classes and plant life forms was used by considering the number of categories in this matrix in a reserve (No. of LFDs). Also used number of plant formations, plant associations and plant species.

Source Blake and Karr 1987

Community -low correlation with Lynch and Whigham all variables. 1984 Individuals - important for majority of species.

Within census area, used an index of vegetation volume Important in community and in vertically stratified layers. Measured floristics and individual species analyses, but variables differed. structure. Landscape heterogeneity was determined by an index of the proportion of different habitats in 100 m radius concentric circles around census area. Independent variables from these two indices were produced using factor analyses. Community - Area most Succession Gradient, Moisture-Nutrient Gradient, SD of these two gradients, Foliage Height Diversity, important, habitat secondary. Foliage Profile Diversity, 5 principal components of Individuals - Habitat generally PCA analysis, and herb, shrub, sub-canopy and more important than area. canopy cover.

;=1

Forest

Response by community index and individual species

Not considered.

Pearson 1993

Ambuel and Temple 1983

Freemark and Merriam 1986

Loyn 1987

Kitchener et al. 1982


The studies by Ambuel and Temple (1983), Lynch and Whigham (1984), and Blake and Karr (1987) all considered the relationship of heterogeneity indices with the number of species found in fragments and with the abundances of individual species. All found that relative to the area of the fragment, heterogeneity within the fragments had little influence on bird species richness, but was generally more important than area for individual species (Table 1). This contradiction between the community and individual species suggests that the measures of heterogeneity being used do not represent the same thing for all the species considered and that these species differences are confounded within the community-based comparison. We believe that the use of the single values generated by these heterogeneity indices to generalize for a community of species is a fundamental reason for the contradictory conclusions reached by these studies. These species-specific responses to landscape heterogeneity were clearly demonstrated by Pearson (1993), who measured habitat heterogeneity at the site where the census of species was made and in 100 m radius circles encompassing this area. He found that some species' abundances were best described by variables that measured the composition and structure of the vegetation at the census area, while others were best described by variables that measured the proportion of different habitat types at different distances from the census area. All of these studies concentrated on one level, either that of structural complexity of the forest or that of the diversity of different vegetation types within a remnant. Allen and Hoekstra (1992) discuss the problems of examining particular levels in the ecological hierarchy and the interrelationships between them. By concentrating on one level and ignoring those either above or below it, important information is lost, as we will illustrate below. THE EFFECT OF QUALITATIVE DIFFERENCES BETWEEN HABITAT TYPES The above heterogeneity indices generally use some measure of variability in vegetation structure to characterize heterogeneity within vegetation fragments without defining spatiallyexplicit relationships between patches and without considering qualitative differences between patch types. We explore the implications of this using hypothetical examples which illustrate the problems involved in applying indices to assess the importance of heterogeneity to bird communities. If we consider two equal-sized remnants which contain equal areas of two vegetation types in the

187

same configuration, then any heterogeneity index measured at the scale of vegetation types will clearly have the same value for both remnants. However, if the vegetation types in these remnants were different, there would be qualitative differences between these remnants, because of differences in the heterogeneity at the scale of within vegetation types. This heterogeneity is at the level below that measured by landscape heterogeneity measures. The impact of these scale differences can be demonstrated in two examples. MacArthur and MacArthur (1961) and MacArthur (1964) showed that the number of bird species found in a habitat type was positively correlated with the vertical complexity of the vegetation. Though this relationship has not always been substantiated (Willson 1974), it is clear from these studies that vegetation that differs in its vertical complexity differs in the number of bird species that use it. Furthermore, James and Warmer (1982) demonstrated, using rarefaction techniques, that the rate of bird species accumulation with increasing area of different vegetation types differed. They suggested that this was due to differences in the levels of horizontal heterogeneity within vegetation types. The impact of these different rates of species accumulation in different vegetation types will have considerable confounding effects on heterogeneity indices measured at larger scales (Fig. 2). The estimates of species richness for the four remnants in Figure 2 are determined based on the assumption that there are no interactions between the habitats with respect to species accumulation with increasing area. However, work by Bach (1988a,b) on insect herbivores indicate that such interactions do occur. Bach (1988b) showed that the densities of the striped cucumber beetle (Acalymma vittatum) were significantly affected by host plant (cucurbits) patch size and by the type of adjacent patches. She demonstrated that the effect of adjacent patches of tall vegetation (tomato plants) had a direct positive effect on beetle densities, since the tall vegetation acted as a barrier to the movement of individuals out of the patch. The same did not occur when adjacent patches were mowed pasture which was lower than the host plant patch. She also found that the level of these observed effects of different types of adjacent patches were greater on smaller host plant patches. This demonstrates that the spatial configuration of habitat types is also important in determining the functional heterogeneity of a habitat mosaic. THE EFFECT OF THE SPATIAL CONFIGURATION OF HABITAT PATCHES A further problem is the effect that changing remnant area has on the spatial configuration of


188

.... Vegetation ..... Type 1

16 14 ~12 Q)

.E 10

and k is the number of vegetation formations . Vegetation formations were defined predominantly on structural criteria. Patch Diversity (PD) is determined using the Shannon-Wiener index of diversity:

o

a: 8l

.~

8

A1

6

O

Co

where Pi is the proportion that patch i constitutes of the total area of the remnant and k is the number of patches. Patches were defined as discrete areas (greater than 0.5 ha in area) of a given vegetation formation. The Ecotone Index (EI) describes the quantity of ecotone (including remnant perimeter) for a remnant using the formula proposed by Patton (1975) which standardizes the value with respect to area:

(/) 4

2

2

4

6

8

10

12

14

Area

B A

. m

~ 1

'"u

~ 12

c

B

~ C

C.

12

4

i= 1

vegetation Type 2

16

A re a

Fig. 2. The effect of differences in species accumulation with

area of different vegetation types, on the relationship between heterogeneity indices and species number. (a) Species accumulation curves for two hypothetical vegetation types based on the types of curves observed by James and Warmer (1982). (b) Four remnants with the same level of habitat heterogeneity, but differing in relative proportions of the two vegetation types (Remnants A and B have 3/4 of their area represented by vegetation type 1 while in C and D '\14 is represented by vegetation type 2) and in area (Remnants Band D are four times the size of A and C). (c) The estimated number of species occurring on these remnants is determined by extrapolation from the species accumulation curves for the area of each vegetation type in each remnant (e.g., Al represents the number of species expected in 3 area units of vegetation type 1 and A2 represents the number of species expected in 1 area of vegetation type 2. The number of species expected in remnant A is the sum of Al and A2).

habitat patches and their functional significance to the species in question and the inability of generalized heterogeneity indices to measure these changes. This problem will be demonstrated using data from a study on the effects of fragmentation on the bird community of the Kellerberrin area of the Western Australian wheatbelt (Cale 1994). Four landscape heterogeneity indices were considered in this study. Formation Diversity (FD) was determined using the Shannon-Wiener index of diversity: k

FD = 'Ihlogfi i= 1

where h is the proportion that vegetation formation i constitutes of the total area of the remnant

EI

=

P + E 2VA*1T

where P is the perimeter of the remnant, and E is the length of ecotone separating vegetation patches (in metres), and A is the area (in m2 ) of the remnant. The final index VA was the number of vegetation associations that occurred (greater than 0.5 ha in area) in each remnant. A set of hypothetical remnants demonstrates the effect changing area has on the Patch Diversity measure (Fig. 3). All four remnants contain equal proportions of the two vegetation types, but remnants A and B have a higher value of patch diversity because the stippled vegetation type is fragmented into two patches. On the basis of PD, A and B have an identical patch diversity that is higher than that for remnants C and D. However, the functional significance of this increase in diversity depends on the scale at which individual species of bird operate. Three simple scenarios can be considered: Scenario 1: Species operates on a scale of X but Y

In this case neither Patch 1 or 2 is discrete from the main patch of stippled habitat. Thus P D does not reflect a functionally significant difference between any of the remnants.


Patch 2

Remnant A Area = 25 Patch Diversi~ = 0.41

IJ

RemnantC Area = 25 Patch Diversity = 0.3

RemnantB Area = 100 Patch Diversity = 0.41

189

complicated than for the Patch Diversity index. If formation types represent different levels of resources, then the presence of an extra formation type in a remnant represents an increase in the diversity of the resources in that remnant, regardless of how large an area it occupies. However, if the species of interest uses a specific formation type exclusively, then patch size becomes important. For example, if patch 1 and patch 2 of the hypothetical remnants represented a third formation (Fig. 4), and the species of interest required that formation exclusively for some period of its life history, then it would signify an increase in formation diversity only if the patch was of sufficient size to support that species.

Patch 2 Remnant D Area = 100 Patch Diversity = 0.3

Fig. 3. Hypothetical remnants demonstrating the effect of spatial scale on the functional significance of the patch diversity index (see text). Stippled and unstippled areas represent different vegetation formations. The two vegetation formations occur in equal total area in all remnants. Remnants Band D are four times the area of A and C which represents a two-fold increase in linear scale.

Observations of birds in small remnants «20 ha) in the Kellerberrin area suggested that most species use a large proportion of these remnants throughout a single day (Cale, unpub!. data), which would indicate that Scenario 3 is representative of these species. This would suggest that PD is not a good measure of heterogeneity in these cases. However, linear models describing the species richness of birds dependent on remnant vegetation indicate that both PD and £1, which is based on patches, were good descriptors of species richness. However, models using these two indices were not as descriptive nor as robust as models using either FD or VA (Cale 1994). The descriptive ability of PD and £1 was due to the high level of collinearity between all four variables. The effectiveness of PD and £1 descriptors of bird species richness indicates the problem of interpreting the meaning of an independent variable's correlation with the dependent variable, without knowing the scale at which species are operating. The importance of scale to the functional significance of the Formation Diversity index is more

RemnantA Area = 25 Formation Diversity = 0.41 Patch Diversity = 0.41

Remnant B Area = 100 Formation Diversity = 0.41 Patch Diversity = 0.41

[J RemnantC Area = 25 Formation Diversity = 0.3 Patch Diversity = 0.41

RemnantD Area = 100 Formation Diversity = 0.3 Patch Diversity = 0.41

Fig. 4. Hypothetical remnants demonstrating the effect of spatial scale on the functional significance of the formation diversity index (see text). Stippled, unstippled and solid areas represent different vegetation formations. Remnants Band D are four times the area of A and C which represents a two-fold increase in linear scale. The patch configuration within all remnants is proportional to their size.

Bird species frequently require the resources from a number of habitats for their persistence (Saunders and Ingram 1987; Lambeck and Saunders 1993). In these situations the configuration of habitats in relation to the scale of the species' activities would be important. For example, if the species of interest used both the


190

stippled and solid formations throughout its life history then the functional significance of the value of FD for the remnants represented in Figure 4 could be described by three possible scenarios: Scenario 1: Species operates on a scale of X but Y

In this case Patch 1 and 2 are not isolated from the stippled habitat. Thus FD reflects a functionally significant difference between all of the remnants. This means that not only the relative proportions of different vegetation formations need to be considered, but also their configuration within the remnant, relative to the scale of movement of the species. Clearly this will differ for different species of bird due to differences in the scale at which a species operates, as has been discussed by Addicott et al. (1987), Hansen and Urban (1992) and Holling (1992). In other words, the components of a heterogeneity index must be defined by the scale at which the species in question operates, and hence a general index for a group of species could be misleading.

DISCUSSION If we are to achieve the goal of being able to link pattern and process at the landscape scale, we first have to be confident that we can adequately characterize landscape patterns. This characterization is a difficult process because landscapes are often complex and usually involve spatial scales larger than we are used to studying. We have also indicated in this paper that an adequate description of landscape patterns must include not only a description of the number, sizes and configurations of landscape units, but also some characterization of the structure and composition within them. These two sets of landscape components are measured at two different scales. Past study of landscape heterogeneity has tended to focus on one of these scales (i.e., configuration of landscape units within the landscape

or configuration within landscape units), but seldom both together. There is growing concern in the literature that scales of study are often incompatible with the scales at which patterns and/or processes actually operate (Kotliar and Weins 1990; Allen and Hoekstra 1992), and the definition of the ecological context and recognition of cross-scale dependencies are essential if we are to analyse ecological processes in any sensible way. Up until now the correct definition of context has rarely been attempted, and hence many studies purporting to assess the importance of landscape pattern to particular processes have not linked the relevant scale of pattern to the relevant scale of process. The types of indices used to provide an estimate of landscape heterogeneity may be useful in the rather limited context of comparing different landscapes, but the interpretation of such comparisons may be difficult. If one landscape has a higher index than another this mayor may not have any significance when particular processes or functions are considered. The significance of the measured difference in heterogeneity depends on how well measured heterogeneity corresponds to functional heterogeneity (Kolasa and Rollo 1991) (Fig. 5). Functional heterogeneity is process-dependent and hence can only be defined in the context of a particular process. We have illustrated this by considering the case of habitat heterogeneity and bird distributions. As Colwell (1992) has recently commented, "The particulars of the daily lives of real organisms and the scale and patterning of their environments matter profoundly, creating a rich diversity at the level of process". Indices of diversity either can indicate that differences in heterogeneity exist when no actual change in habitat has occurred from the organism's point of view, or can fail to detect important changes in habitat. The principal reason for this is the problem of matching the scale of measurement with the scale at which the organisms perceive the environment. The same problem will prevail when landscape processes are studied - unless we have a good understanding of the scales at which heterogeneity affects various processes, measurements of heterogeneity may be of little value. We have painted a fairly negative picture of the success to date of attempts to develop and use measures of landscape heterogeneity. Some might argue that we have been unnecessarily negative, since the indices available have been used to the apparent satisfaction of the users in some cases. However, if we look at these cases, either the use of heterogeneity indices seems to have added little new insight to the problem under study, or a number of similar studies have come to contradictory conclusions. Indices have either summarized the obvious or confirmed what was already known. We really need to do better than


Heterogeneity

indices

Mathematical problem

Measured

heterogeneity

Structure of landscape

Biological problem

Functional

heterogeneity

Structure of landscape in relation to function

Fig. 5. Heterogeneity indices are an attempt to provide a simple measure of landscape heterogeneity. The ability to derive an adequate index is firstly a mathematical problem, but the next more complicated step is to ensure that the measured heterogeneity actually captures the salient features of heterogeneity that are functionally important.

this if landscape ecology is to become a predictive science which can usefully be applied to conservation issues. This problem is not restricted to landscape ecology. Peters (1991) has recently commented that indices in general "are surrogates for an interesting phenomenon which we cannot measure, and because we cannot measure this phenomenon, the indices do not represent it. This inadequacy may be disguized by statistical sophistication, but it is not remedied. Indices are descriptions, but descriptions are only informative when their elements are applied to make predictions through scientific theories. Many ecological indices ... fail to make this transition and remain irrelevant". Landscape heterogeneity indices in general fail because of this irrelevance, which is in turn partly due to the lack of a sound theoretical basis into which they can be plugged. This lack of a theoretical framework has been commented on by Weins (1992), and various workers have recently started to develop such a framework (e.g., Dunning et at. 1992; Weins et at. 1993).

191

Until this framework is well worked out and formalized, we suggest that care must be taken when trying to apply generalized measures of landscape heterogeneity. The lure of apparently simple indices to measure complex spatial phenomena must be counterbalanced by a recognition that these indices may have little relevance in the context of particular problems. This does not mean that such indices are useless. It does, however, mean that their use has to involve a prior assessment of their behaviour and limitations in the context of specific studies. It also means that such indices should not yet be presented as tools for decision makers who might uncritically use them as aids for management or planning. In this paper we have pointed out a problem but offered no solution. Adequate methods of quantifying landscape heterogeneity have to be developed, and it may be that existing measures can be useful if they are adequately tested and constrained. Because heterogeneity isa complex, multi-scale attribute, care must be taken to ensure that measures used address the correct scale(s) and respond to functionally important changes in heterogeneity. The challenge is to bridge the gap between those developing heterogeneity measures and those wishing to use them in specific contexts. Theory and application need to be developed in tandem if we wish to avoid a mountain of theoretical literature which proves next to useless and a rash of management and planning decisions based on potentially spurious measures. ACKNOWLEDGEMENTS We thank Graham Arnold, Mike Austin, Robert Lambeck and John Wiens for helpful comments on the draft manuscript. REFERENCES Addicott, J. F .. Aho, J. M., Antolin, M. J., Padilla, D. K., Richardson, J. S. and Soluk, D. A., 1987. Ecological neighbourhoods: scaling environmental patterns. Gikas 49: 340-46. Allen, T. F. H. and Hoekstra, T. W., 1992. Toward a Unified Ecology. Columbia University Press, New York. Ambuel, B. and Temple, S. A., 1983. Area-dependant changes in bird communities and vegetation of southern Wisconsin forests. Ecology 64: 1057--068. Angelstam, P., 1992. Conservation of communities - the importance of edges, surroundings and landscapes mosaic structure. Pp. 9---{)9 in Ecological Principles of Nature Conservation - Application in Temperate and Boreal Environments ed by L. Hansson. Elsevier Applied Science, London. Bach, C. E., 1988a. Effects of host plant patch size on herbivore density: Patterns. Ecology 69: 1090-102. Bach, C. E., 1988b. Effects of host plant patch size on herbivore density: Underlying mechanisms. Ecology 69: 1103-117.

192


Blake, J. G. and Karr, J. R., 1987. Breeding birds of isolated woodlots: Area and habitat relationships. Ecology 68: 1724-734. Cale, P. G., 1994. The effects of fragmentation on the bird community of the Kellerberrin district of the Western Australian wheatbelt. M.Sc. Thesis, University of Western Australia, Perth. Colwell, R. K., 1992. Making sense of ecological complexity: a personal and conceptual retrospective. Biotropica 24: 226-32. Cullinan, V. I. and Thomas, J. M., 1992. A comparison of quantitative methods for examining landscape pattern and scale. Landscape Ecol. 7: 211-27. Dunning, J. B., Danielson, B. J. and Pulliam, H. R., 1992. Ecological processes that affect populations in complex landscapes. Gikos 65: 169-75. Forman, R. T. T. and Godron, M., 1986. Landscape Ecology. Wiley and Sons, New York. Freemark, K. E. and Merriam, H. G., 1986. Importance of area and habitat heterogeneity to bird assemblages in temperate forest fragments. Bioi. Conserv. 36: 115-41.

Lynch, J. F. and Whigham, D. F., 1984. Effects of forest fragmentation on breeding bird communities in Maryland, USA. Bioi. Conserv. 28: 287-324. MacArthur, R. H., 1964. Environmental factors affecting bird species diversity. Amer. Natur. 98: 387-97. MacArthur, R. H. and MacArthur, J. W., 1961. On bird species diversity. Ecology 42: 594-98. Magurran, A. E., 1988. Ecological Diversity and its Measurement. Croom Helm, London. Milne, B. T., 1991. Heterogeneity as a multiscale characteristic of landscapes. Pp. 69-84 in Ecological Heterogeneity ed by J. Kolasa and S. T. A. Pickett. Springer-Verlag, New York. Musick, B. H. and Grover, H. D., 1990. Image textural measures as indices of landscape pattern. Pp. 77-104 in Quantative Methods in Landscape Ecology - The Analysis and Interpretation of Landscape Heterogeneity ed by M. G. Turner and R. H. Gardner. Springer-Verlag, New York.

Hansen, A. J. and Urban, D. L., 1992. Avian response to landscape pattern: the role of species' life histories. Landscape Ecol. 7: 163-80.

Noss, R. F., 1989. Indicators for monitoring biodiversity: a hierarchical approach. Conserv. Bioi. 4: 355--64.

Hobbie, S. E., Jensen, D. B. and Chapin, F. S. I., 1993. Resource supply and disturbance as controls over present and future plant diversity. Pp. 385-408 in Biodiversity and Ecosystem Function ed by E.-D. Schulze and H. A. Mooney. Springer-Verlag, Heidelberg.

O'Neill, R. V., Krummel, J. R., Gardner, R. H., Sugihara, G., Jackson, B., De Angelis, D. L., Milne, B. T., Turner, M. G., Zygmunt, B., Christensen, S. W., Dale, V. H. and Graham, R. L., 1988. Indices of landscape pattern. Landscape Ecol. 1: 153--62.

Holling, C. S., 1992. Cross-scale morphology, geometry, and dynamics of ecosystems. Ecol. Monogr. 62: 447-502.

Patton, D. R., 1975. A diversity index for quantifying habitat edge. Wildl. Soc. Bull. 394: 171-73.

Hoover, S. R. and Parker, A. J., 1991. Spatial components of biotic diversity in landscapes of Georgia, USA. Landscape Ecol. 5: 125-36. James, F. C. and Warmer, N. 0., 1982. Relationships between temperate forest bird communities and vegetation structure. Ecology 63: 159-71.

Pearson, S. M., 1993. The spatial extent and relative influence of landscape-level factors on wintering bird populations. Landscape Ecol. 8: 3-18. Peet, R. K. and Loucks, O. L., 1977. A gradient analysis of southern Wisconsin forests. Ecology 58: 485-99.

Kitchener, D. J., Dell, J., Muir, B. G. and Palmer, M., 1982. Birds in Western Australian wheatbelt reserves - implications for conservation. Bioi. Conserv. 22: 127--63.

Peters, R. H., 1991. A Critique for Ecology. Cambridge University Press, Cambridge.

Kolasa, J. and Rollo, C. D., 1991. Introduction: The heterogeneity of heterogeneity: A glossary. Pp. 1-23 in Ecological Heterogeneity ed by J. Kolasa and S. T. A. Pickett. Springer-Verlag, New York.

Richardson, D. M. and Cowling, R. M., 1993. Biodiversity and ecosystem processes: opportunities in Mediterranean-type ecosystems. Trends Ecof. Evo!. 8: 79-80.

Kotliar, B. N. and Weins, J. A., 1990. Multiple scales of patchiness and patch structure: a hierarchial framework for the study of heterogeneity. Gikos 59: 253--60. Krummel, J. R., Gardner, R. H., Sugihara, G., O'Neill, R. V. and Coleman, P. R., 1987. Landscape patterns in a disturbed environment. Gikos 48: 321-24. Lambeck, R. J. and Saunders, D. A., 1993. The role of patchiness in reconstructed wheatbelt landscapes. Pp. 153--61 in Nature Conservation 3: Reconstruction of Fragmented Ecosystems, Global and Regional Perspectives ed by D. A. Saunders, R. J. Hobbs and P. R. Ehrlich. Surrey Beatty & Sons: Chipping Norton. Levin, S. A., 1992. The problem of pattern and scale in ecology. Ecology 73: 1943-967. Li, H., Franklin, J. F., Swanson, F. J. and Speis, T. A., 1993. Developing alternative forest cutting patterns: a simulation approach. Landscape Eco!. 8: 63-75. Loyn, R. H., 1987. Effects of patch area and habitat on bird abundances, species numbers and tree health in fragmented Victorian forests. Pp. 65-77 in Nature Conservation: The Role of Remnants of Native Vegetation ed by D. A. Saunders, G. W. Arnbld, A. A. Burbidge and A. J. M. Hopkins. Surrey Beatty & Sons, Chipping Norton.

Ripple, W. J., Bradshaw, G. A. and Speis, T. A., 1991. Measuring forest landscape patterns in the Cascade Range of Oregon, USA. Bioi. Conserv. 57: 73-88. Romme, W. H. and Knight, D. H., 1982. Landscape diversity: The concept applied to Yellowstone Park. BioScience 32: 664-70. Saunders, D. A. and Ingram, J. A., 1987. Factors affecting survival of breeding populations of Carnaby's cockatoo Calyptorynchus funereus latirostris in remnants of native vegetation. Pp. 249-58 in Nature Conservation: The Role of Remnants of Native Vegetation ed by D. A. Saunders, G. W. Arnold, A. A. Burbidge and A. J. M. Hopkins. Surrey Beatty & Sons, Chipping Norton. Scheiner, S. M., 1992. Measuring pattern diversity. Ecology 73: 1860-867. Schulze, E.-D. and Gerstberger, P., 1993. Functional aspects of landscape diversity: a Bavarian example. Pp. 453--66 in Biodiversity and Ecosystem Function ed by E.-D. Schulze and H. A. Mooney. Springer-Verlag, Heidelberg. Solbrig, O. T. (ed), 1991. From Genes to Ecosystems: a Research Agenda for Biodiversity. Paris, IUBS.

CALE and HOBBS: LANDSCAPE HETEROGENEITY INDICES Stoms, D. M. and Estes, J. E., 1993. A remote sensing research agenda for mapping and monitoring biodiversity. Int. J. Remote Sensing 14: 1839-860. Turner, M. G., 1989. Landscape ecology: The effect of pattern on process. Ann. Rev. Ecol. Syst. 20: 171-97. Turner, M. G., O'Neill, R. V., Gardner, R. H. and Milne, B. T., 1989. Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecol. 3: 153-62. Turner, M. G. and Ruscher, C. L., 1988. Changes in the spatial patterns of land use in Georgia. Landscape Ecol. 1: 241-51.

193

Weins, J. A., 1989. Spatial scaling in ecology. Funct. Ecol. 3: 385-97. Weins, J. A., 1992. What is landscape ecology, really? Landscape Ecol. 7: 149-50. Weins, J. A., Stenseth, N. c., Van Horne, B. and Ims, R. A., 1993. Ecological mechanisms and landscape ecology. Oikos 66: 369-80. Willson, M. F., 1974. Avian community organization and habitat structure. Ecology 55: 1017-029.