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Keywords:

  • Abundance–occupancy relationship;
  • causal mechanisms;
  • macroecology;
  • pattern and process;
  • species range;
  • statistical artefacts

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

Aim  To investigate the influence of choice of the measure of mean abundance on the abundance–occupancy relationship, and to examine the implications for identifying causal mechanisms.

Innovation  Simulations were performed to generate stochastic abundance–occupancy data sets covering a wide range of scenarios representative of empirical abundance–occupancy data. Two common measures of mean abundance were used: local mean abundance (mean abundance calculated using only data from occupied sites) and global mean abundance (mean abundance calculated using all sites or samples). I found that the choice of mean abundance measure had a strong effect on the correlation between abundance and occupancy. Local mean abundance was associated with a high proportion of negative correlations (mean percentage of negative correlations across 24 simulations = 44.39), while global mean abundance was strongly associated with positive correlations (mean percentage of negative correlations across 24 simulations = 0.02).

Main conclusions  The choice of abundance measure influences the correlation between abundance and occupancy. Negative correlations between local mean abundance and occupancy are an inherent and unavoidable consequence of using this measure of abundance. Efforts to identify causal mechanisms that give rise to the abundance–occupancy relationship have attempted to explain occasional negative correlations when the expectation was for positive correlations. This study shows that negative correlations arise from the choice of mean abundance measure and that this artefact confounds efforts to identify ecological causal mechanisms.


INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

Macroecology examines relationships between attributes of ecological systems measured at large spatial and temporal scales and attempts to infer the processes that give rise to them (Brown, 1995; Gaston & Blackburn, 2000; Blackburn & Gaston, 2004). Pairwise relationships between four key attributes – body mass, species richness, abundance and spatial distribution – have dominated the macroecological literature (Brown, 1995; Gaston & Blackburn, 2000; Blackburn, 2004; Blackburn & Gaston, 2004). The relationship between abundance and spatial distribution (i.e. some index of the amount of space occupied by a species) has received particularly intense scrutiny, with the conceptual foundation for the study of the relationship laid down by Ricklefs (1972), Hanski (1982), Bock & Ricklefs (1983) and Brown (1984, 1995). The motivation for these studies was to link abundance within resource patches (often referred to as ‘local abundance’) with the distribution or availability of resources.

Local abundance is defined as the mean number of individuals in a set of samples computed by excluding zero-count samples (Hanski, 1982; Bock & Ricklefs, 1983; Brown, 1984; Lacy & Bock, 1986; Brown, 1995). I will use the term ‘local mean abundance’ (LMA) to distinguish this measure from ‘global mean abundance’ (GMA) which is the mean abundance computed using all samples. Similar distinctions between methods for computing mean abundance were introduced by Elton (1932).

In the earliest exploration of the relationship by Hanski (1982), the chosen measure of spatial distribution was the proportion of samples or habitat patches occupied by a species; this is usually referred to as ‘occupancy’. Other researchers correlated abundance measures with the number of occupied sites (Bock & Ricklefs, 1983; Brown, 1984; Lacy & Bock, 1986; Brown, 1995), but this is directly proportional to occupancy for a set of samples and therefore does not alter correlation coefficients (Zar, 1999). Although many other measures of abundance and spatial distribution have been used (Gaston, 1996; Quinn et al., 1996; Gaston et al., 2000; Blackburn et al., 2006; Wilson, 2008), the early use of LMA and occupancy has led to the adoption of the generic term ‘abundance–occupancy relationship’ (Gaston et al., 2000).

Bock & Ricklefs (1983), Brown (1984, 1995) and Hanski (1982) concluded, largely on the basis of limited empirical evidence, that the relationship between LMA and occupancy within a given data set should result in a positive correlation. Hanski (1982), for example, postulated as a law of nature that species with the highest local abundance also occupied the largest number of sites. However, subsequent studies have revealed that zero and negative correlations do occur (Gaston & Lawton, 1990; Gaston, 1996; Gaston et al., 1997, 2000; Blackburn et al., 2006; Wilson, 2008), and their presence has led to the search for explanatory processes that generate mostly positive but occasionally zero and negative correlations. The search for explanatory processes has included the development of mathematical models of metapopulation dynamics (Gyllenberg & Hanski, 1992; Hanski & Gyllenberg, 1997; Holt et al., 1997; Freckleton et al., 2006), and conceptual models invoking evolutionary scenarios (Symonds & Johnson, 2006) or the action of ecological and biogeographical constraints on distribution (Gregory & Gaston, 2000).

LMA and GMA values for a given species are related to occupancy (Pennington, 1983; Wright, 1991). Let the total number of samples in a data set, N, be composed of two parts, the number of samples in which one or more individuals were present (NP, the occupied samples), and the number of samples from which individuals were absent (NA, the zero-count or unoccupied samples; equals 1 –NP). Occupancy (ω) is then computed as the proportion of samples with a count greater than zero:

  • image

Occupancy may be interpreted as the probability that a randomly selected sample is occupied, and can therefore range from 0 to 1, inclusive.

Local mean abundance (LMA) is the mean computed using only counts (x) from occupied samples. In statistical terminology, LMA (mL) is a statistic computed using left-censored, conditioned or zero-truncated data. That is,

  • image

Global mean abundance (GMA) is the unbiased estimate of the mean or expected value of the statistical population from which a set of samples was drawn (Freund, 1972). GMA (mG) is computed using the standard formula from elementary statistics, namely,

  • image

The two mean abundances are related via occupancy:

  • image(1)

Since 0 < ω≤ 1, it follows that mLmG always. A further artefact of using mL is that the minimum attainable value for this measure is not zero. Since local mean abundance is measured as individuals per occupied sample, then the minimum value for LMA is 1, which occurs when only one individual is detected in only one sample within a sample set.

Equation 1 defines a hyperbolic function, and the relationship between mG and mL is therefore nonlinear and occupancy dependent. On an abundance–occupancy plot, low-occupancy species will be shifted to the right more than higher-occupancy species when LMA is used, and the shift at very low occupancy (e.g. a very rare species in a large set of samples) may be of several orders of magnitude (Fig. 1). It is therefore possible for a scatter of points on an abundance–occupancy plot with a positive correlation between GMA and occupancy to be transformed into a negative one between LMA and occupancy.

image

Figure 1. Representation of the occupancy-dependent bias caused when local mean abundance is used in abundance–occupancy plots. Open circles represent the same value of global mean abundance (mG= 0.5 individuals/sample) at a range of occupancy values from 0.1 to 1.0. Closed squares are the corresponding local mean abundance, mL, values computed using equation 1. The dotted curve is the locus of mL values for the fixed mG value used in this example.

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The statistical attributes of LMA were considered by Aitchison (1955) and Pennington (1983), and the implications of LMA for modelling the abundance–occupancy relationship was examined by Wright (1991), and mentioned by Hartley (1998). In light of the preliminary assessment that LMA transforms the relationship between abundance and occupancy, I sought to answer the following questions using simulations: What is the influence of the transformation between GMA and LMA on the correlation of each with occupancy? Does the use of LMA explain the observation of occasional negative correlations between LMA and occupancy in empirical data?

METHODS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

The impact of LMA on abundance–occupancy plots

Equation 1 indicates that an abundance–occupancy plot made using GMA can be transformed into one using LMA by a simple rescaling, and that this rescaling is nonlinear and inversely proportional to the occupancy value associated with each data point. To investigate the overall impact of this effect, I implemented a simulation model using the discrete distribution technique to compute occupancy values for a set of randomly generated mean abundance values. For any discrete probability mass function, the value created by one minus the probability that a randomly drawn sample contains zero individuals is the probability that a sample contains at least one individual. As noted earlier, this is the occupancy of a species and, by using a range of discrete distributions, an ensemble of points in an abundance–occupancy scatterplot can be generated with all the properties of an abundance–occupancy plot based on real data. In particular, the method generates data covering the full range of spatial patterns from complete spatial randomness (i.e. Poisson distribution of counts in samples) to highly clumped or aggregated distributions (e.g. negative binomial, Neyman Type A, etc.). Each generated occupancy value corresponding to a mean abundance value simulates an abundance–occupancy data pair for a species. I generated a sample of 10 species from each of the three abundance–occupancy models, Poisson, negative binomial and Neyman Type A, giving a simulated abundance–occupancy plot for 30 species. These sample sizes were found in preliminary trials to produce simulated abundance–occupancy plots covering a realistic spread of abundance and occupancy values.

I used the model to examine the relationship under three scenarios. The first allowed global mean abundance to be selected randomly between 0.001 and 5 individuals per sample, giving a simulated data set covering a wide range of occupancy levels obtained from large data sets (e.g. Gaston et al., 2006). The second scenario restricted mean abundance to a range of 0.001 to 1 individuals per sample, therefore constraining the maximum attainable occupancy to approximately 0.6. This modelled the situation where only rare or low-abundance/low-occupancy species are considered in a study (e.g. Gregory & Gaston, 2000). The third scenario restricted mean abundance to range between 1 and 5 individuals per sample. This represents data for which only high-abundance and therefore high-occupancy species are studied (e.g. Gregory & Gaston, 2000). All models were implemented in R (R Development Core Team, 2007) and the source code is given in Appendices S1 and S2 in Supporting Information.

Sampling properties of abundance–occupancy correlations

The functional analysis presented above indicates that LMA can produce negative correlations with occupancy, but it is not clear how frequently this occurs and, more generally, what form the frequency distribution of correlation coefficients takes. The probability density function for the Pearson correlation coefficient has been the subject of extensive study, including situations where there are departures from the fundamental assumption of a normal distribution for the two variables. However, the outcome is mathematically complex, often contradictory and subject to intense on-going debate (Johnson et al., 1994). There is far less known about the sampling properties of Spearman's rank correlation coefficient, particularly when the two variables are drawn from very different marginal statistical distributions. In the case of abundance–occupancy scatterplots, a preliminary assessment of marginal distributions for large ensembles of species consistently showed that occupancy is represented by a beta distribution and GMA by a gamma distribution.

Given these difficulties, I investigated the statistical properties of Spearman's correlation between abundance and occupancy through an extension of the simulation model used above to investigate the impact of LMA on abundance–occupancy plots. The same number of samples (representing species) was generated for each of the three distributions. For each distribution, a random value of GMA was first generated as a uniform random number between a lower and an upper mean abundance. A corresponding value of occupancy was computed using the appropriate abundance–occupancy relationship. Using the computed value for occupancy, GMA was transformed into LMA using equation 1. Two Spearman's correlation coefficients were computed for each run: one between GMA and occupancy and one between LMA and occupancy.

The number of species (i.e. sample size) was varied from nine (three samples from each of three distributions) to 30 (10 samples from each distribution) to assess the impact of the number of species on the frequency distribution of the abundance–occupancy correlation. To assess the potential impact of restricting GMA, and correspondingly restricting the range of occupancy values, three sets of limits were placed on GMA for each number of species. The first constrained the lower GMA value to 1.5 and the upper limit to 5, thus generating data restricted to high occupancy values and representing studies that focus on ‘common’ species. The second used limits of 0.001 and 5 giving a wide range of occupancy values and generated abundance–occupancy data similar to large empirical datasets where species are included without restriction. Finally, a low-occupancy (‘rare’ species) set of limits was used (0.001 to 1.5). For each pairing of number of species and occupancy range, 5000 runs were made.

RESULTS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

Impact of LMA on abundance–occupancy plots

Output from this simple model (Fig. 2) shows the diffusive effect of the nonlinear occupancy-dependent rescaling of GMA. The correlation coefficients for GMA under wide and both restricted ranges of occupancy (Fig. 2a,c,e) were positive, but the corresponding results for LMA changed from positive to negative (Fig. 2b,d,f). These results indicate that the shift in sign and strength of correlations in a small number of empirical examples provided by Wilson (2008) has a mechanistic basis.

image

Figure 2. Impact of the nonlinear occupancy-dependent rescaling of global mean abundance (GMA; mean abundance using all samples) into local mean abundance (LMA; mean abundance using only occupied samples). The dashed curve represents the limiting condition for samples taken from a population distribution completely at random across the sampling domain. (a) GMA data for samples covering a range of mean abundances restricted to high values and therefore high levels of occupancy. (b) Corresponding LMA data showing the cloud of points skewed towards a negative correlation. (c) GMA data for a wide range of mean abundance and corresponding occupancy values. (d) LMA data are dispersed but less likely to give a negative correlation. (e) GMA data for data restricted to low mean abundance and occupancy values. (f) LMA data skewed more at lower occupancy values inducing a negative correlation.

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These results suggest that negative correlations between LMA and occupancy may arise as a natural consequence of using LMA, and indicate that correlations between GMA and occupancy will be stronger than the corresponding correlations based on LMA because LMA diffuses the cloud of points on the abundance–occupancy plot. My results imply that it is not necessary to search for biological processes that may give rise to diversity in the sign and strength of the correlation between LMA and occupancy.

Sampling properties of abundance–occupancy correlations

The results, summarized in Table 1, support the previous functional analysis and reveal important sample size effects. Typical results for 30 species from a single run of the model are presented in Fig. 3. The frequency distribution of correlation coefficients between GMA and occupancy was distinctly left-skewed, and negative correlations did not occur for either the wide-occupancy range (Fig. 3c) or the low-occupancy range simulations (Fig. 3e). For simulations with the number of species below 15, occasional negative correlations did appear for the GMA data, but the rate was never more than 1% and occurred only for data restricted to high occupancies. Above 15 species, the number of negative correlations for GMA was constant at zero. There is thus a small sample size effect impacting on GMA correlations.

Table 1.  Summary results for simulation investigating the impact of sample size (i.e. number of species) and restrictions on the range of occupancy values in a given data set.
Number of speciesOccupancy rangeGMALMA
Number of negative correlationsPercentageNumber of negative correlationsPercentage
  1. GMA, global mean abundance; LMA, local mean abundance.

 9High220.4409882.0
 9Wide00.03476.9
 9Low00.0219643.9
12High30.1425385.1
12Wide00.01913.8
12Low00.0225245.0
15High00.0436487.3
15Wide00.01152.3
15Low00.0210642.1
18High00.0451290.2
18Wide00.0751.5
18Low00.0213342.7
21High00.0460792.1
21Wide00.0360.7
21Low00.0202340.5
24High00.0466293.2
24Wide00.0230.5
24Low00.0199739.9
27High00.0470494.1
27Wide00.0100.2
27Low00.0193138.6
30High00.0474594.9
30Wide00.070.1
30Low00.0189337.9
image

Figure 3. Illustrative results of the sampling distribution simulation model. These data are taken from a simulation with 30 randomly generated species points replicated 5000 times. (a) Frequency distribution for global mean abundance (GMA)-based correlations when occupancy is restricted to a high band of values. (b) Corresponding frequency distribution for local mean abundance (LMA) data showing a number of negative correlations and a distinctly different shape the distribution. (c) GMA correlations with occupancy unrestricted. (d) Corresponding distribution for LMA data. (e) GMA results for occupancy restricted to a low range of values (i.e. for ‘rare’ species). (f) LMA results for low occupancy range showing a shift in the distribution (median approaching 0) and a consequent rise the proportion of negative correlations.

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As predicted, the correlation between LMA and occupancy was often negative, with the frequency of negative correlations rising to about 95% for the high-occupancy frequency distribution (Table 1, Fig. 3b,d, f). The shape of the LMA frequency distribution was approximately symmetrical. In contrast to the GMA results, negative correlations made up to 45% of the results for low-occupancy data for LMA correlations for all species numbers between 9 and 30. Wide-occupancy range data for LMA correlations included up to 7% negative correlations across the range of species numbers with a general trend to a low frequency of negative correlations as the number of species increased.

These results show that the statistical population from which samples are drawn for empirical correlations between LMA and occupancy are very different from the expectation of a positive correlation that was raised in early studies of the relationship (Hanski, 1982; Bock & Ricklefs, 1983; Brown, 1984; Lacy & Bock, 1986; Brown, 1995). More recently, researchers have assumed a positive correlation to be the canonical form of the relationship (Gaston et al., 1997, 2000; Blackburn et al., 2006; Leger & Forister, 2009; Lovett-Doust et al., 2009; Webb et al., 2009; Zuckerberg et al., 2009).

DISCUSSION

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

LMA represents a nonlinear, occupancy-dependent rescaling of GMA (Pennington, 1983; Wright, 1991). Although Wright (1991) highlighted important aspects of the relationship between the two abundance measures from a macroecological perspective, there has not been a thorough appraisal of the impact of LMA on the abundance–occupancy relationship. My results clearly show that zero and negative correlations between LMA and occupancy are always possible in survey data. Further, the probability of a negative correlation increases as the maximum occupancy within a set of samples decreases. For example, if only rare species are examined, the probability of a negative correlation increases to approximately 0.5. Zero and negative correlations may occur when GMA is used, but are extremely rare events only occurring with probabilities of the order of 0.001 when sample size (e.g. number of species in an inter-specific abundance–occupancy relationship) is small.

The results I have obtained here help clarify the nature of the abundance–occupancy distribution when mean abundance and occupancy are used as the indices of abundance and spatial distribution, respectively. This is the form in which the abundance–occupancy relationship was first described, but many subsequent studies have used other measures for abundance and spatial distribution. Even though there often is a positive correlation between most alternative measures of spatial distribution and occupancy (Gaston, 1991; Gaston, 1994; Quinn et al., 1996), a recent meta-analysis (Wilson, 2008) has shown that these other measures have an impact on the sign of the correlation. A study of the impact that various combinations of measure have on the sampling distribution of correlations between abundance and other measures of distribution may prove to be a fruitful area of further study.

There is long-standing recognition that mean abundance (or its counterpart, mean density) conditioned or truncated in some way may be a meaningful measure of abundance (Elton, 1932; Pennington, 1983; Rudran et al., 1996; Gaston et al., 1999a). However, there does not appear to have been a similar long-standing recognition in ecology that correlating a transformed and truncated variable (e.g. LMA) to an unconditioned variable (e.g. occupancy) may introduce statistical artefacts, even though Brett (2004) highlighted the statistical implications of correlations of the form X/Y correlated with Y. The introduction of statistical artefacts into the correlation between LMA and occupancy appears analogous to the instability in linear relationships when data collected with differing extents and grains are compared (Wiens, 1989; Schneider, 1994, 1998) and different arrangements of regional aggregations (the change of support or modifiable area unit problem, MAUP) used in geographical analyses (Openshaw & Taylor, 1979; Cressie, 1996). Recognition of the possible impact that LMA may have on the relationship between measures of abundance and distribution is, however, beginning to emerge in macroecology (e.g. Pautasso & Weisberg, 2008).

The correlation between LMA and occupancy (represented by the number of occupied sites) was first used by Bock & Ricklefs (1983), and later justified and expanded in scope by Lacy & Bock (1986) to avoid a statistical artefact that they thought was created by using GMA. Their reasoning was as follows. (1) Assume that species are most abundant in the centre of their ranges and decline in abundance towards limits of their range (but see Blackburn et al., 1999; Sagarin & Gaines, 2002; Sagarin et al., 2006). (2) It follows that those species with range limits falling within a study region will have low mean abundance and occur in fewer samples than species whose ranges do not end within the region. (3) This could result in a positive correlation between abundance and occupancy ‘where no such relationship actually existed’ (Bock & Ricklefs, 1983, p.295). Subsequently, Brown (1984, 1995), Gaston and co-authors (e.g. Gaston et al., 1997, 1999b, 2000) and others (e.g. Soininen & Heino, 2005; Leger & Forister, 2009) have continued to use LMA because of its assumed ability to correct for perceived artefactual positive correlations caused, in their view, by inclusion of zero-count or empty samples.

Using LMA does not solve this problem, because sampling the spatial pattern of each species in a region by standardized methods will typically give a positive correlation between GMA and occupancy. The only exceptions occur when sample sizes are small, for example when restricted to a narrow range of abundance values. Fundamental principles from spatial point pattern analysis indicate that this relationship is expected to hold without regard to the position of range boundaries relative to the boundaries of a study region, and without regard to variation in the intensity of the spatial pattern of any species (P.D.W., unpublished). That is, a positive correlation between GMA and occupancy is an inherent property of any sufficiently large ensemble of sampled spatial patterns collated into an abundance–occupancy plot, and not a sampling artefact as suggested by Bock & Ricklefs (1983), Lacy & Bock (1986) and others. Regarding the inclination of some ecologists to discard or avoid zero-count samples, it was noted by Diggle (2003, p.32) that this practice is founded ‘in the mistaken belief that an empty quadrat contains no information’. The impact of this discarded information is clearly apparent when we try to relate LMA to occupancy.

An important aspect of sampling biological populations is the impact of imperfect detection of organisms leading to an underestimate of occupied sites and consequent errors in estimates of mean abundance (Royle et al., 2005; MacKenzie et al., 2006). The impact of so-called zero-inflated data has received some consideration with respect to identifying valid models linking abundance and occupancy (e.g. Wenger & Freeman, 2008; Sileshi et al., 2009). However, it can be shown that zero-inflated data will still be affected by the rescaling of abundance between GMA and LMA when correlated with occupancy. This is because underdetection increases LMA, decreases apparent occupancy and therefore increases the impact of the hyperbolic rescaling of GMA into LMA represented in Fig. 1.

My results may have broad implications for the study of macroecological relationships. Macroecology seeks to infer causal mechanisms from relationships observed at large spatial and temporal scales (Brown, 1995; Gaston & Blackburn, 2000). Although it is necessary to first document and classify observed patterns before making causal inferences (Underwood et al., 2000), and even though there are occasional successes (Diniz-Filho, 2006; Chapman et al., 2009), it has in general proved difficult to make the link between pattern and process in ecology (Cale et al., 1989; Lepš, 1990; McArdle et al., 1997; Tyre et al., 2001). I suggest that efforts to select amongst competing explanatory or causal mechanisms for the abundance–occupancy relationship (e.g. Gaston et al., 1997, 2000; Krüger & McGavin, 2000; Heino, 2005; Päivinen et al., 2005; Blackburn et al., 2006; Webb et al., 2009; Zuckerberg et al., 2009) have been confounded by the presence of a statistical artefact when using LMA to describe spatial patterns.

The present study lends weight to Wright's (1991) view that simple correlations between abundance and occupancy are of limited explanatory value in macroecology, and provide an instance of the general findings of Brett (2004) regarding spurious correlations or statistical artefacts in ecological relationships. The results I have presented suggest that greater care is required to avoid confounding influences of statistical artefacts in the study and application of macroecological relationships.

ACKNOWLEDGEMENTS

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

A substantial portion of this work was completed in partial fulfilment of a PhD degree undertaken at Macquarie University under the supervision of Andy Beattie and Brendan Wintle (University of Melbourne). The author was supported by a post-graduate award while a PhD candidate. Various early versions of this work were reviewed by Jim Nichols, Nicholas Gotelli and anonymous referees leading to substantial improvements.

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

BIOSKETCH

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information

Peter Wilson has worked in the development and implementation of conservation policy and the coordination of large-scale biodiversity surveys, and has extensive experience in computer programming and database development for the management and analysis of biodiversity data. His current research focus is on species distribution modelling under climate change.

Editor: José Alexandre F. Diniz-Filho

Supporting Information

  1. Top of page
  2. ABSTRACT
  3. INTRODUCTION
  4. METHODS
  5. RESULTS
  6. DISCUSSION
  7. ACKNOWLEDGEMENTS
  8. REFERENCES
  9. BIOSKETCH
  10. Supporting Information
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GEB_569_sm_Appendix_S1.doc40KSupporting info item
GEB_569_sm_Appendix_S2.doc45KSupporting info item

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