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ARTICLE IN PRESS Basic and Applied Ecology ] (]]]]) ]]]—]]] www.elsevier.de/baae Method in macroecology Tim M. Blackburn School of Biosciences, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK KEYWORDS Observation; Natural experiments; Manipulative experiments; Null-hypothesis; Autocorrelation Summary Macroecology is concerned with understanding the abundance and distribution of species at large spatial and temporal scales. Understanding pattern and process in macroecology thus presents a considerable methodological challenge, as the scales of interest are simply too large for the traditional ecological approach of experimental manipulation to be possible or ethical. Here, I summarise the methods that have been most commonly employed to explore macroecological questions, discuss important methodological issues that need to be considered when interpreting macroecological data, and suggest likely future developments in macroecological methodology. & 2004 Elsevier GmbH. All rights reserved. Zusammenfassung Die Makroökologie befasst sich mit dem Verständnis der Abundanz und der Verbreitung der Arten in groXen räumlichen und zeitlichen MaXstäben. Das Verständnis von Mustern und Prozessen in der Makroökologie stellt deshalb eine beträchtliche methodische Herausforderung dar, weil die Skalen von Interesse für die traditionelle ökologische Vorgehensweise der experimentellen Manipulation einfach zu groX sind, als dass sie möglich oder ethisch vertretbar wäre. Hier fasse ich die Methoden zusammen, die am häufigsten zum Einsatz kommen, um makroökologische Fragen zu erforschen, diskutiere wichtige methodische Punkte, die beachtet werden müssen, wenn makroökologische Daten interpretiert werden, und deute auf wahrscheinliche zukünftige Entwicklungen in der makroökologischen Methodik hin. & 2004 Elsevier GmbH. All rights reserved. Introduction The aim of this paper is to present an overview of how macroecology has been done to date. There is nothing unusual about the macroecological ap- proach in the framework of the scientific method (Gaston & Blackburn, 1999), yet the issue of method has been important in the development of macroecology. As will be seen, the discipline depends on techniques different to those used in Tel.: +44-(0)121-414-5893; fax: +44-(0)121-414-5925. E-mail address: [email protected] (T.M. Blackburn). 1439-1791/$ - see front matter & 2004 Elsevier GmbH. All rights reserved. doi:10.1016/j.baae.2004.08.002 ARTICLE IN PRESS 2 the majority of ‘traditional’ ecological studies. In consequence, it has been criticised by those unfamiliar with these alternative methods of asking and answering questions. These criticisms seem to have been prompted less by a genuine disregard for macroecology than by a lack of understanding of the logic underlying the approach. The response of macroecologists has been more clearly to explain this logic (e.g. Brown, 1995, 1999; Gaston & Blackburn, 1999; Maurer, 1999; Gaston & Blackburn, 2000), and there is evidence that the field appears to be gaining wider acceptance as a result (e.g. Brown, 1999; Faaborg, 2001; Marquet, 2001). The paper is divided into three sections. In the first, I summarise the methods that scientists have most commonly employed to explore macroecological questions. Then, I go on to discuss some important issues that these methods require scientists to consider when interpreting macroecological data. This will not be an exhaustive review of such issues, but rather an overview of those I consider to be most significant. More extensive or specific considerations of methodological issues can be found elsewhere (e.g. Diamond, 1986; Maurer, 1994; Brown, 1995; Gotelli & Graves, 1996; Harvey, 1996; McArdle, 1996; Blackburn & Gaston, 1997b, 1998; Gaston & Blackburn, 1999; Maurer, 1999; Gaston & Blackburn, 2000; Blackburn & Gaston, 2002). Finally, I conclude with a few remarks about likely future developments in macroecological methodology. Methodological approaches to macroecology Macroecology is concerned with patterns expressed by ecological systems over extensive spatial and temporal scales, and with the processes that determine these patterns (Brown & Maurer, 1989; Brown, 1995; Gaston & Blackburn, 2000), and thus presents a significant problem: How is it possible to study scientifically the characteristics of an ecological system over such scales? The traditional approach to the study of complex ecological systems has been to attempt to reduce the complexity by isolating and studying fragments of it. This is a standard strategy in science. The workings of simple systems are easier to elucidate than those of complex ones. The implicit aim of such a ‘reductionist’ approach is ultimately to understand the workings of the whole system by piecing together the understanding gained about each constituent part (e.g. Dunbar, 1995). T.M. Blackburn However, there are at least two shortcomings of such an approach. First, it is difficult to put the constituent pieces back together with no idea of the system that is being recreated. For example, study of individual communities may give a clear picture of the forces determining how local abundances are distributed amongst species, but to understand how those communities combine to produce the species-abundance distribution of a region, one needs to know the regional distribution itself. Second, by isolating a fragment of a system, you may be excluding the very influences that are the most important determinants of its character. For example, an important determinant of the number of gall wasp species utilising an individual oak tree is the total number of gall wasp species that utilise that particular oak species (Cornell, 1985). Any attempt to understand the richness of the gall wasp assemblage on a specific tree by considering that tree alone is unlikely to succeed. To understand ecological systems, therefore, it is clear that we need to study the structure and function of such systems in full as well as in part. Sidestepping the issue of complexity by adopting solely a reductionist approach is not an option for macroecologists, as it is the whole that is of interest. There are several consequences of this, but one of the most important is that the option of utilising manipulative experiments is reduced. Macroecological systems are simply too large for most such experiments to be possible (practically or financially) or ethical. This inability to apply experimental manipulations is one reason why the macroecological approach has been criticised (see also Diamond, 1986). However, there are still ways to study pattern and process in large-scale ecological systems. Observation Macroecologists have to date principally relied on observational data to generate and test hypotheses (see references in Gaston & Blackburn, 2000). Indeed, most scientific fields can be viewed as relying principally on such data early in their development, when the field is inevitably largely descriptive and concerned with the establishment of the phenomena which it will eventually try to explain (Wiegert, 1988; Gaston & Blackburn, 1999). In macroecology, the foundation of the field has been laid in the form of studies documenting the existence of particular patterns in the structure of species assemblages at geographical scales (e.g. Fig. 1). The principal of these patterns are the interspecific frequency distributions of abundance, ARTICLE IN PRESS Method in macroecology 3 Natural experiments and experiments in nature 2.25 Log population density 2 1.75 1.5 1.25 1 .75 .5 .25 0 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 Log body mass Figure 1. The relationship between log population density (mean number of individuals per Breeding Bird Survey (Bystrak, 1981) census route) and log body mass (g) for North American bird species. N ¼ 380: From Brown and Maurer (1987). range size and body size, and the relationships between these variables (Cotgreave, 1993; for recent reviews, see Blackburn & Gaston, 1994; Gaston, 1994; Brown, 1995; Brown, Stevens, & Kaufman, 1996; Gaston, 1996a, b; Gaston & Blackburn, 1996; Blackburn & Gaston, 1997a; Gaston, Blackburn, & Lawton, 1997; Gaston & Blackburn, 2000; Holt, Gaston, & He, 2002; Storch & Gaston, 2004). Macroecological patterns, such as Fig. 1, constitute a basic description of facets of the distribution of life across the Earth (Lawton, 1996). However, the primary goal of macroecology is to explain their existence. Unfortunately, observational data generally lack power to distinguish between similar hypotheses for the origin of such patterns (McArdle, 1996). In addition, the large spatial and temporal scales relevant to macroecology mean that it is usually beyond the capabilities of a single scientist, or even group of scientists, to collect all the observational data required to explore any given pattern. Hence, such data sometimes derive from disparate uncoordinated and unplanned sets of observations by multiple observers from different sites over a range of dates. This means that their use must be tempered by caution if spurious and biased conclusions are to be avoided (Gotelli & Graves, 1996; Blackburn & Gaston, 1998, 2002). Nevertheless, with careful attention to their limitations, observational data can be valuable in hypothesis testing (McArdle, 1996), and so inform about process as well as about pattern. Although macroecologists have to date principally relied on observational data, experimental approaches are available. In particular, macroecological studies can draw on conclusions from ‘natural experiments’, and the conceptually similar ‘experiments in nature’ (Diamond, 1986). Natural experiments are changes in systems brought about by natural events, such as earthquakes, volcanic eruptions, or natural colonisations. Experiments in nature are changes in systems brought about as an intentional or accidental product of human activities, such as introductions of alien species, and changes in atmospheric composition. Diamond (1986) also distinguishes between natural snapshot experiments (NSEs), which compare different systems at a point in time, and natural trajectory experiments (NTEs), which compare the same system at different points in time. All these kinds of experiments provide an opportunity to observe and test the consequences of changes in systems that we would not otherwise be able to manipulate for the purpose of testing macroecological theory (Gaston & Blackburn, 1999). They have been a useful source of information on a variety of largescale questions about ecological systems, such as those concerning extinction (e.g. Karr, 1982; Pimm, Jones, & Diamond, 1988; Hinsley, Bellamy, & Newton, 1995; Bellamy, Hinsley, & Newton, 1996; Lomolino, 1996; Manne, Pimm, Diamond, & Reed, 1998; Spiller, Losos, & Schoener, 1998; Duncan & Young, 2000; Terborgh et al., 2001) and invasion (Moulton & Pimm, 1983, 1986; Moulton & Lockwood, 1992; Thornton, 1996; Veltman, Nee, & Crawley, 1996; Duncan, 1997; Blackburn & Duncan, 2001b). Natural experiments and experiments in nature have both advantages and disadvantages in comparison to traditional manipulative experiments. The main disadvantages are that the experimental manipulation is not chosen by the investigator, and control treatments usually are much less precise, if they are possible at all (Diamond, 1986). A consequence of the first problem is that often the question that can be tested is not necessarily exactly the one that the scientist would like to ask. Alternatively, the scientist may be forced to answer a question using a system with which they are less familiar. The lack of adequate controls means that while responses of natural systems to natural or anthropogenic perturbations may be clear, the precise aspect of the perturbation to which they are responding often is not. Natural or anthropogenic ARTICLE IN PRESS 4 effects rarely involve changes in only one aspect of the system. Thus, natural experiments do not have the same power to link pattern to process, as do manipulative experiments. Further, a lack of experimental control means that the response of the system in the absence of the perturbation is often unknown. Typically, statistics quantifying relevant features of the system following the change are compared with the values of those statistics at the start of (for NTEs, or in the absence of, in the case of NSEs) the perturbing event. However, the parameters of all ecological systems tend to vary over time even in the absence of unusual perturbing events, so that robust conclusions may be hard to draw in such cases. For example, Gonzalez (2000) showed that the number of species of micro-arthropods inhabiting moss patches declined following habitat fragmentation, but that changing environmental conditions also caused fluctuations in the species richness observed in control patches. Without the controls, it would have been hard to separate the effects of fragmentation and weather on the communities in the fragmented moss patches. The main advantages of natural experiments and experiments in nature are twofold. First, they are probably the only ways in which experiments can be directly performed at the temporal and spatial scales of concern to macroecologists (Gaston & Blackburn, 1999). Second, they have the advantage that the experimental system is likely to be more realistic than that of any laboratory or field manipulation (Diamond 1986, 2001): the study system is a natural entity. Thus, while it is harder to draw firm conclusions from natural experiments, those conclusions that can be drawn are probably more relevant to natural systems. In contrast, while manipulative experiments can give very precise tests of specific questions, they do so in systems that are generally greatly simplified relative to the ‘real’ world. Such results may lack wider generality. Natural experiments and experiments in nature are not, therefore, simply poor relations of more controlled approaches. Manipulative experiments Although manipulative experiments are impossible to perform on most of the ecological systems that have attracted the attention of macroecologists, they are not entirely precluded, however. They can be used to address macroecological questions in systems where the manipulations are large-scale for the organisms but not for the experimenter, such as laboratory and field-based microcosms (e.g. T.M. Blackburn Cotgreave, Middleton, & Hill, 1993; Naeem, Thompson, Lawler, Lawton, & Woodfin, 1994; Gaston & Warren, 1997; Warren & Gaston, 1997; Gilbert, Gonzalez, & Evans-Freke, 1998; Gonzalez, Lawton, Gilbert, Blackburn, & Evans-Freke, 1998; Fox, McGrady-Steed, & Petchey, 2000). A good example is the study by Gonzalez et al. (1998) of abundance and distribution changes in the fauna of moss microecosystems following fragmentation. Since manipulative experiments offer probably the most powerful way of differentiating between alternate hypotheses, the use of microcosms to elucidate process in macroecology is a potentially valuable tool. However, the wider relevance of this approach is as yet unclear, as the mechanisms structuring communities of organisms amenable to use in microcosms may be different to those for groups such as birds and mammals on which most of our knowledge of macroecological patterns is based (Blackburn & Gaston, 2003a). The issues of scaling between microcosms and geographical landscapes remain to be resolved (Peterson & Parker, 1998). Consequences of the methodological approaches The extent of the reliance of macroecology on observational data and unplanned natural experiments has general consequences for the way in which the data so obtained are subsequently treated and interpreted. The usual lack of control treatments accompanying observations means that thought needs to be given to the relationship that the controls would express were they to exist. This is termed the ‘null hypothesis’. Lack of control treatments also means that analyses frequently have to be more sophisticated to extract useful information. The greater reliance on statistical manipulation of macroecological data means that particular attention has to be paid to how the data might violate the assumptions of the statistics. An important assumption of standard statistics is that each data point contributes an independent piece of information to the analysis. Since many macroecological studies rely on comparisons between species, one way in which the assumption of independence may be violated is because species tend to share characteristics through common evolutionary ancestry, termed ‘phylogenetic autocorrelation’. Another way the assumption may be violated is when the ecological characteristics of locations are compared, because locations closer together in space tend to be more similar. This is termed ‘spatial autocorrelation’. In this section, ARTICLE IN PRESS Method in macroecology I briefly discuss these issues in the context of macroecology. The null hypothesis Lacking controls, observational studies and natural experiments must rely instead on a null hypothesis. This has been defined as one that ‘‘entertain(s) the possibility that nothing has happened, that a process has not occurred, or that change has not been produced by a cause of interest’’ (Strong, 1980). The importance of a good null hypothesis to macroecological studies has been repeatedly emphasised (Gotelli & Graves, 1996; Blackburn & Gaston, 1998; Gaston & Blackburn, 1999, 2000). That an observed pattern is a simple consequence of the null expectation should always be the first hypothesis considered by the macroecologist (Gaston & Blackburn, 2000; see also Maurer & McGill, this issue). The failure to frame an adequate null hypothesis for any particular test may result in the acceptance of a pattern as the result of a biological process, when in fact it is no more than an artefact of a particular methodology, or would be expected in the absence of any biological mechanism. An example of the first problem is provided by the study of the relationship between niche breadth and abundance (reviewed by Gaston, 1994). It has been suggested that abundant species may be common because they can use a wider spectrum of resources (they have a broader niche) than rare species (e.g. Brown, 1984). However, early demonstrations of a positive association between abundance and niche breadth were later called in question when it was noted that we would expect the fewer individuals of the rarer species to be encountered in fewer habitats, and hence appear to have a narrower niche, by chance alone (Burgman, 1989; Gaston, 1994). The positive association may have been little more than a methodological artefact. Indeed, subsequent studies that address the issue of sample size find much weaker evidence for any such relationship (Gaston et al., 1997; Gregory & Gaston, 2000). The importance of considering the possibility that a pattern may be expected in the absence of any biological mechanism is illustrated by study of the relationship between species number and area. Species–area relationships tend to be positive, so that larger areas hold more species, and a variety of biological mechanisms have been suggested as the cause (reviewed by Rosenzweig, 1995). However, the random distribution of individuals across the environment will also tend to result in a 5 positive relationship. Thus, before searching for a biological driver, we need to test whether or not observed positive relationships differ from the null expectation. In fact, they generally do (Rosenzweig, 1995; Storch, Sizling, & Gaston, 2003). This example highlights a further point about the null hypothesis: it is easy to fall into the trap of thinking that it will be that there is no relationship between the variables of interest. In fact, that will often not be the case. Note that Strong’s definition includes the notion that a ‘‘change has not been produced by a cause of interest’’. It follows that null relationships may be non-zero, and in macroecological systems they frequently are (e.g. Blackburn, Harvey, & Pagel, 1990; Wright, 1991; Colwell & Hurtt, 1994; Rosenzweig, 1995; Blackburn & Gaston, 1996; Wright, Patterson, Mikkelson, Cutler, & Atmar, 1998; Colwell & Lees, 2000; Jetz & Rahbek, 2001). Statistical tests The outcome of a well-formulated manipulative experiment would ideally be a situation where the only difference between the control and experimental treatments is in the variable or process under test. Changes in the treatment relative to the control can then be assigned to this difference, and its effect easily assessed using simple statistics (typically, ANOVA: e.g. Underwood, 1997). Although this ideal is rarely achieved in practice in ecology (even simple ecological systems are complicated in comparison to those of most other scientific disciplines), the existence of controls makes the interpretation of data from manipulative experiments much easier than data from observational studies and natural experiments, where a variety of processes could potentially be driving any observed changes. In these latter, the absence of controls can to some degree be compensated for using statistical techniques. However, a greater variety of statistical approaches typically need to be adopted to extract meaningful information from the raw data. Statistics can aid interpretation of macroecological data in at least three ways. First, statistical null models can help identify significant features of macroecological data (Blackburn et al., 1990; Gotelli & Graves, 1996; Gaston & Blackburn, 1999; Colwell & Lees, 2000; Gotelli, 2000). An example was discussed in the previous section, where the comparison of real species–area relationships with those expected from random distributions of individuals confirmed that the real pattern differed from the null expectation. ARTICLE IN PRESS 6 However, given that a variety of processes may potentially generate macroecological patterns (Gaston & Blackburn, 1999), the field may particularly benefit from the application of informationtheoretic approaches to hypothesis testing (Burnham & Anderson, 2001; Johnson & Omland, 2004). This provides an alternative to null hypothesis testing in which, instead of a single model being compared to a null hypothesis, a variety of a priori candidate models can be tested simultaneously and ranked in terms of the support provided for them by the data. Pursuing the example above, a variety of mechanisms have been proposed to generate species–area relationships (including random distribution of individuals, habitat diversity, colonisation-extinction dynamics, neutral biodiversity theory). Testing the predictions of each hypothesis separately against a null hypothesis would tell us whether each was a better predictor of the relationship than expected by chance, but would not tell us which was the best model. The information-theoretic approach, in contrast, would allow the shape of the species–area relationship predicted by the different models to be compared to observed data. The models could then be weighted and ranked in terms of fit to provide a quantitative measure of relative support for each hypothesis (Johnson & Omland, 2004). Second, multivariate techniques can help factor out uncontrolled variation in natural systems (e.g. Mac Nally, 1996; Thomson, Weiblen, Thomson, Alfaro, & Legendre, 1996). For example, Blackburn and Duncan (2001a) included a variable coding for biogeographic region in a multivariate analysis of introduction success in birds, to account for the fact that introduction success varies significantly among regions. Since Blackburn & Duncan were analysing an unplanned (as an experiment) set of species translocated by humans, any significant results found could have been a spurious consequence of uncontrolled differences between regions, rather than being due to the effect of the predictor variables in their analysis. Third, macroecologists can use statistics to simplify complex environmental or biological variation into more manageable summaries of the data (e.g. Preston, 1948; Rapoport, 1982; Williamson & Lawton, 1991; Maurer, 1994; Ruggiero, Lawton, & Blackburn, 1998; Gregory & Gaston, 2000). For example, both Gaston (1994) and Maurer (1994) show how complex variation in the structure of a species’ geographic distribution can be summarised in terms of a fractal dimension that quantifies the degree of range fragmentation (see also Williamson & Lawton, 1991). T.M. Blackburn In many cases the data or questions of interest to macroecologists are difficult to analyse using traditional statistics (Blackburn & Gaston, 1998), presenting a whole extra set of problems. Some studies simply present standard statistical analyses while acknowledging the short-comings of the approach. An example is provided by a study of how the mean (across species) range of depths inhabited by marine fish varies with latitude (Stevens, 1996). However, mean depth ranges calculated at different latitudes are not independent, because neighbouring latitudes share many species in common, and so standard estimates of the significance of statistics calculated for these data are invalid. Thus, while Stevens (1996) presents regression lines and correlation coefficients, he acknowledges that the statistical significance of some of these relationships cannot reliably be assessed. However, in some cases, the lack of suitable statistics to test macroecological ideas has been the spur for theoretical developments to attempt to solve the problem. For example, the idea that polygonal relationships such as that in Fig. 1 are caused by boundary constraints has led to the search for methods to estimate the values of the slopes of such boundaries (Blackburn, Lawton, & Perry, 1992; Thomson et al., 1996; Cade, Terrell, & Schroder, 1999). Phylogenetic autocorrelation An obvious feature of most macroecological patterns is that they comprise observational data on characteristics exhibited by large numbers of ecological ‘particles’, typically species (Brown, 1995, Brown, Gillooly, West, & Savage, 2003). A problem encountered when attempting to identify the processes generating such multi-species patterns is that the characteristics of species are not independent. Phylogenetically related species share characteristics through their common evolutionary ancestry (Felsenstein, 1985). Two closely related species will therefore tend to be more similar to each other in a range of characters than will two species chosen at random from the entire assemblage being compared. This may be termed ‘phylogenetic autocorrelation’. It is a problem because it makes it harder to identify whether associations between variables are causal or due to shared characteristics. For example, Nee, Read, Greenwood, and Harvey (1991) showed that the population size of a British bird species is negatively related to its body mass (Fig. 2). However, they demonstrated that this negative relationship was due to a simple differ- ARTICLE IN PRESS Method in macroecology 7 7 7 A 20 22 8 passerines non-passerines Log population size 6 5 17 4 9 B 24 14 C 30 20 D 35 VALUES OF Y 40 VALUES OF X 3 A 2 B d1 Y X d1 2 4 C d2 6 10 d2 d3 9 13 d3 1 0 .5 D 1 1.5 2 2.5 3 3.5 4 4.5 Log body mass 10 d3 Y VARIABLE COMPARISONS d2 5 Figure 2. The relationship between log population size (number of individuals) and log body mass (g) for British bird species. The equation of the regression line through all species is y ¼ 0:749x þ 5:641: N ¼ 147 species. From Nee et al. (1991). ence between passerines and non-passerines: the former tend to be small-bodied and common, whereas the latter tend to be large-bodied and rare. Within these groups, there was no relationship between population size and body mass. This suggests that a causal relationship between population size and body mass is unlikely, and that the overall negative relationship between them could be a consequence of any characteristic that differs between passerines and non-passerines. One way in which the problem of phylogenetic relatedness can be circumvented, and the ability of observational data for multi-species assemblages to test hypotheses simultaneously improved, is through application of a phylogenetically controlled comparative method (Harvey & Pagel, 1991; Harvey, 1996). A variety of such methods is now available, together with computer programmes for their implementation, which account for the relatedness of species in several different ways (e.g. Purvis & Rambaut, 1995; Agapow & Isaac, 2002). For example, the phylogenetically independent contrast (PIC) method solves the relatedness problem by performing comparisons between characteristics only for related taxa (Fig. 3 and Purvis & Rambaut, 1995). Any differences between the taxa compared must have developed since they last shared a common ancestor. If such comparisons repeatedly find associations between characteristics in related species, that provides much stronger evidence of a causal link between the characteristics than a simple comparison across d1 0 5 10 X VARIABLE COMPARISONS 15 Figure 3. The top box shows the values of two traits, X and Y, for each of four species, A to D. Higher nodes, in this simplified illustration, are calculated as the average value of lower nodes. Species A and B diverged at the higher node, so any differences between them, d1, must have evolved since then. Similarly, the differences between C and D, d2, must have arisen since those lineages split. These two sets of differences are independent. Furthermore, the differences between the higher nodes, d3, makes up a third independent comparison. These three independent comparisons are shown and tabulated in the second box. If the Y-variable comparisons are plotted against the X-variable comparisons, as shown in the third box, we can see whether evolutionary change in the two traits has been correlated. From Purvis & Rambaut (1994). all species. These methods require some hypothesis about the phylogenetic relationships of the taxa compared, but these now exist for many animal and plant groups, even if just in terms of a simple taxonomy. Phylogenetically controlled comparative methods, such as PICs, are now routinely applied in macroecology (e.g. Blackburn, Gates, Lawton, & Greenwood, 1994; Blackburn, Lawton, & Gregory, 1996; Blackburn, Gaston, Quinn, Arnold, & Gregory, 1997; Fa & Purvis, 1997; Jones & Purvis, 1997; Johnson, 1998; Gregory & Gaston, 2000; Poulin, 2004), although some controversy about their utility persists (see e.g. Harvey, Read, & Nee, 1995a, b; Rees, 1995; Westoby, Leishman, & Lord, 1995a–c; Harvey, 1996; Ricklefs & Starck, 1996; Harvey & Rambaut, 2000; Freckleton, Pagel, & Harvey, 2003). ARTICLE IN PRESS 8 Spatial autocorrelation The standard statistical assumption that each data point contributes an independent piece of information to the analysis may also be violated if data points are associated in space, or spatially autocorrelated. Sites close together will share many characteristics through that proximity, such as the presence of certain species, habitats, or climatic conditions, and so not provide independent information about ecological processes. Spatial autocorrelation can seriously bias statistical tests that assume that data are independent (e.g. Legendre, 1993; Carroll & Pearson, 2000; Lennon, 2000). Failure to account for it may result in either Type I or Type II errors, or in misleading estimates of statistical parameters such as correlation coefficients; predictions from the subsequent models may be highly inaccurate as a result. Lennon (2000) further notes that spatial autocorrelation will bias analyses such that highly autocorrelated predictor variables are most frequently identified as significantly related to an autocorrelated response variable, even if the spatial patterns are completely independent. Macroecological studies frequently concern spatially or temporally explicit data, and so necessitate controls for associated autocorrelation (Carroll & Pearson, 2000; Lennon, 2000; Lennon, Koleff, Greenwood, & Gaston, 2001; Brewer & Gaston, 2002; Perry et al., 2002; DinizFilho, Bini, & Hawkins, 2003; Storch, Konvicka, Benes, Martinkova, & Gaston, 2003). Several examples exist in the macroecological literature of statistical solutions to the problem of spatial autocorrelation. For example, Lennon et al. (2001) apply the modified correlation test of Clifford, Richardson, and Hemon (1989) to correct the significance of the Pearson correlation coefficients they calculate between measures of species richness calculated across Britain at two different spatial scales. The correction reduces the degrees of freedom used to calculate significance for each correlation by an amount that reflects the degree of redundancy in the original data (i.e. the fact that sites that are close together effectively provide duplicate information for the analysis). In Lennon et al.’s study, the extent of redundancy meant that the corrected sample size was typically one or two orders of magnitude less than the actual number of raw data points. A different approach was taken by Carroll and Pearson (1998), who explicitly modelled spatial non-independence in relationships between the number of butterfly species and the number of tiger beetle species in grid squares covering North America, to investigate the utility of the latter for predicting the former. T.M. Blackburn They found that the estimated relationship changed substantially when estimates with and without spatial autocorrelation accounted for were compared. This difference would critically affect predictions based on the model (Carroll & Pearson, 1998, 2000). Closing remarks and future directions I think it fair to say that any scientist that has tried to investigate ecological systems at the macroecological scale will at some point in their career have encountered some prejudice from fellow ecologists about this approach. In part, that relates to the methods that macroecologists have had to use, perhaps because some ecologists equate science with manipulative experiments. Yet, methodological approaches other than manipulative experiments are just as scientific, and indeed can produce novel and exciting insights. Our understanding of ecological systems will only benefit from a greater variety of lines of enquiry, and macroecology offers great potential as one such line. However, if the field is to develop and evolve, its future will see changes. I finish by briefly noting four ways in which this evolution may occur in the near future. First, the frequency of manipulative experiments in macroecological studies should increase. The technique is simply too powerful not to use. Although the large scale of study presents significant obstacles, there are ways to circumvent them, as has already been demonstrated by studies exploiting field and laboratory microcosms (see above). Finding new ways to sidestep the problems poses a major challenge for the future, but one that offers great potential benefits. Second, natural experiments and experiments in nature should continue to start and develop, which will provide new and different opportunities to derive insights about large-scale patterns in processes in ecology. Increasing information on introduced species, for example, offers the opportunity to gain insights about the factors determining the limits to species distributions (e.g. Blackburn & Duncan, 2001a). The responses of species to global climate change will be an experiment in nature on a grand scale, one that macroecologists should not fail to exploit (see also Lawton, 2000), albeit one that few would have wished for. Third, the explosive growth in the availability of phylogenetic data will allow a much greater integration of historical information into macroecological studies than currently occurs. Patterns in ARTICLE IN PRESS Method in macroecology the distribution and abundance of species across the planet can be viewed as the end point of processes of evolution spanning many millions of years (these processes also leave their imprint in patterns of macroevolution). Therefore, it makes sense to consider the relationship between evolutionary history and current macroecological patterns. Phylogenies provide a map of that evolution. Finally, I expect the future to bring a general growth in the number of macroecological studies. That growth is already underway (Brown, 1995, 1999; Maurer, 1999; Gaston & Blackburn, 2000; Blackburn & Gaston, 2003b), but wider understanding of macroecology, its aims and its methods, will help not only by encouraging more people to consider large-scale questions and research, but also by reducing the frequency of ill-informed criticism of such studies (hopefully leaving more room for constructive criticism). All of ecology will benefit as a result. Acknowledgements I thank B.A. Maurer and S. Nee for supplying data on which Figs. 1 and 2 were based, Paul Harvey for allowing me to use Fig. 3, David Storch for helpful criticism, and Kevin Gaston both for commenting on this manuscript and for a decade of inspiration on macroecological questions. References Agapow, P. -M., & Isaac, N. J. B. (2002). MacroCAIC: revealing correlates of species richness by comparative analysis. Diversity and Distributions, 8, 41–43. Bellamy, P. E., Hinsley, S. A., & Newton, I. (1996). 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