Pedodiversity-area relationships for islands

Ecological Modelling 182 (2005) 257–269

Pedodiversity-area relationships for islands J.J. Ibáñez a,∗ , J. Caniego b , F. San José b , C. Carrera a a

Centro de Ciencias Medioambientales, Consejo Superior de Investigaciones Cient´ıficas, Madrid, Spain b Department of de Matemática Aplicada a la Ing. Agronómica, E.T.S.I. Agrónomos, Universidad Politécnica de Madrid, Madrid, Spain

Abstract Our objectives were examine whether the pedotaxa-abundance distributions conform to abundance distribution models and how pedorichness-area data fit diversity-area models considered by ecologists. The study area selected was the Aegean Islands. Standard statistical methods were used to gauge the abundance distribution models (Smirnov–Kolmogorov test of goodness of fit) and pedorichness-area models (linear regression, log–log or semi-log). The Smirnov–Kolmogorov test of goodness of fit indicated that the logseries and the broken stick distribution models should be rejected, whereas the geometric and lognormal models were not rejected (P < 5%) Pedorichness-area relationships conform to a power law whose exponent is close to 0.25, as ecological literature predicts. No significant difference was observed between the abundance distribution models and the diversity-area relationships followed by biodiversity and pedodiversity data in similar situations. © 2004 Elsevier B.V. All rights reserved. Keywords: Size-area laws for islands; Bio- and pedotaxa-area relationships; Abundance distribution models; Power laws; Aegean Islands

1. Introduction For Huston (1994), “The concept of diversity has two primary components, and two unavoidable value judgments. The primary components are statistical properties that are common to any mixture of different objects, whether the objects are balls of different colors, segments of DNA that code for different proteins, species or higher taxonomic levels, or soil types or habitat patches on a landscape. Each of these groups of items has two fundamental properties: (1) the number of different types of objects (e.g., species, soil types) in the mixture or sample; and (2) the ∗ Corresponding author. Tel.: +34-91-745-25-00; fax: +34-91-564-08-00. E-mail addresses: [email protected] (J.J. Ib´añez), [email protected] (J. Caniego), [email protected] (F. San Jos´e).

relative number or amount of each different type of object. The value judgments are (1) whether the selected classes are different enough to be considered separate types of objects; and (2) whether the objects in a particular class are similar enough to be considered the same type. On these distinctions hang the quantification of biological diversity”. Measuring biodiversity has recently become a growth industry (Williams and Humphries, 1996). However, notions such as geodiversity and pedodiversity are as suitable as biodiversity. Geodiversity (e.g. geological structures, landforms, fossils and so on . . . ) has not been measured to the same degree, even though it is important to assess geodiversity for interpretation of the geological history of the Earth, past and present climates and landscapes, and the origin and evolution of life. Earth scientists have only recently become involved with these problems. International and national forums are now being organized, such

0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2004.04.005

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as, The European Association for the Conservation of Geological Heritage (www.sgu.se/hotell/progeo). Several approaches have been applied to preserve the geological heritage (e.g. natural parks, legislation, environmental impact, geoparks), but quantitative methods have rarely been used. Several aspects of geodiversity (e.g. geomorphic diversity and lithodiversity) should be quantified when estimating a territory’s ecological value. These aspects refer to non-renewable natural resources with profound qualitative and quantitative repercussions on the architecture of landscapes and ecosystems (Ibáñez et al., 1990, 1995a,b, 2003). This may be one of the ways to quantify the complexity of abiotic landscape structures in different areas and environments (Ibáñez et al., 1998a,b). The quantitative study of pedodiversity is just beginning (Ibáñez et al., 1990, 1994, 1995a, 1998a; Ibáñez and De Alba, 2000; McBratney, 1992; Saldaña and Ibánez, 2004; Phillips, 2001). Several approaches to pedodiversity analysis have been proposed (Ibáñez et al., 1990, 1995a, 1998b; McBratney, 1995). These are: taxonomic pedodiversity (i.e. diversity of soil classes), functional pedodiversity (i.e. soil behaviour under different uses), genetic pedodiversity (i.e. diversity of genetic horizons) and diversity of soil properties. Some pedologists have discussed the value of these methods (e.g. Yaalon, 1998; Wilding and Nordt, 1998; Phillips, 1999; McBratney et al., 2000; Ibáñez and De Alba, 1999, 2000). Ibáñez and De Alba (2000) and Phillips (2001) have shown that pedotaxa-area relationships could be fitted to a power law. This paper is not concerned with a mechanical application and transposition of certain methodologies and mathematical techniques from biological diversity, but with the discussion of their suitability and the implications of their use in pedodiversity problems. We use the taxonomic classification of soils in the same way as the taxonomic classification of biotic components of ecosystems is handled in biodiversity analysis. We do not count objects belonging to the same taxonomic group, but evaluate the extension of each pedotaxa in the area of study (e.g. Magurran, 1988). From an abstract point of view, this approach is a coherent one. However it does not suggest an uncritical exchange of conclusions between entities of such disparate nature as the biotic and abiotic components in an ecosystem.

2. Preliminaries on diversity analysis There are three different ways of measuring diversity (Magurran, 1988): • Indices of richness: number of categories (e.g. biological species, communities, pedotaxa, soilscapes, etc.) known to occur in a defined sampling area. • Indices based on proportional abundance of categories: not only the number but also their relative abundance (in our case, the relative area occupied by each pedotaxon) is taken into account. • Parameters and models describing the distribution of abundance of categories: these provide the most complete description. This paper deals with the third type, pedotaxa-abundance distribution models and the related topic of richness-area interrelationships. 2.1. Abundance distribution models The most popular abundance distribution models in ecology (May, 1975; Magurran, 1988; Tokeshi, 1993; and the references therein) are summarized below. 2.1.1. Geometric series model This model (Motomura, 1932) is based on the assumption that one entity (which represents the limiting factor or the niche common to all the taxa in ecological studies) is subdivided recursively following a fixed rule for a given fraction k. If the entity is likened to the unit segment, the first fragment is k, the next one is a fraction k of what remains, then it measures k(1–k), the third k(1–k)2 to give the geometric series k, k(1–k), K(1–k)2 , k(1–k)3 , k(1–k)4 . It is assumed that the abundance of each taxon is proportional to the fractions in this series. For a community of NT individuals, NT Ck k(1 − k)i−1 is the size of the ith most abundant taxon (the ranked-abundance list), where Ck
is a constant to ensure that Ni = NT . The value of  −1 Ck is 1 − (1 − k)ST , ST being the total number of taxa. Following May (1975), the statistical distribution of taxa sizes is given by a hyperbolic distribution with a constant whose value is computed by assuming that the integral of the density function over the values of sizes is one. If f (N) is the density function, then, for

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(1 − k)ST −1 ≤ N ≤ k, 1 1 f(N) = . (1 − ST )log(1 − k) N

where ST is the total number of taxa. When γ = 1, it is called the canonical lognormal distribution. (1)

2.1.2. Broken-stick model In this model (MacArthur, 1957), the unit segment is broken once and at random, among the number of observed taxa: for ST taxa, ST − 1 points are located randomly in the unit interval so that the predicted sizes are proportional to those of the subintervals obtained. As before, the abundance distribution may be computed. In this case, the density function is a negative exponential with parameter ST (0 < N < ∞) f(N) = ST exp(−ST N).

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(2)

2.1.3. Lognormal model This is a mixture of the preceding models. It has both recursivity and randomization. The segment of unit length is broken at a randomly chosen point into two parts. One part is chosen randomly and independently of its length, and it is broken again into two parts by choosing one of its points at random. One of the three resulting parts is chosen randomly and independently of its length, and it is also broken into two parts by choosing one of its points at random, and so on. The lengths of all the parts follow a lognormal distribution (Kolmogorov, 1941). In ecology, this has the following interpretation: if we assume that species in a multispecies community have divided up some limiting resource among themselves in this manner, and that the abundance of each taxon is proportional to its share of the resource, then the taxa-abundance distribution is lognormal. This fragmentation process has been applied previously to model soil aggregate and particle-size distributions (e.g. Hatch, 1933; Kolmogorov, 1941). The density function is   −(logN − µy )2 1 f(N) = √ , (3) exp 2σy2 2πσy2 where µy and σ y are the mean and standard deviation, respectively, of the random variable y = log N. The parameter γ is also used to characterize this distribution. Following May (1975) it holds that σy log 2 , (4) γ= 2 log ST − log(2πσy2 )

2.1.4. Logseries model If the mechanism of the geometric series model stems from the fact that the taxa arrive at successive uniform time intervals and occupy a fraction k of the remaining niche before the arrival of the next taxon, then the randomization of the time intervals leads to a logseries distribution (Boswell and Patil, 1971). According to the logseries distribution, the frequency of species with N individuals is fN =

αXN , N

(5)

for N = 1, 2, . . . , where α > 0 and 0 < X < 1 are constants. It is, therefore, a discrete distribution. For the continuous models S(N) = ST f(N), where S(N) represents the number of taxonomic groups (species, soil types, etc.), ST is the total number of taxonomic groups and f is the corresponding density function of the considered model. However, for the logseries model (the discrete model) S(N) = fN . The broken-stick model is a statistically realistic expression of an intrinsically uniform distribution. At the opposite extreme, the geometric and logseries models are the statistical expressions of extremely uneven distributions. The lognormal model is in most respects “intermediate” between the broken-stick model on the one hand, and the geometric and logseries models on the other. 2.2. Theory of island biogeography The theory of island biogeography (MacArthur, 1960, 1965; MacArthur and Wilson, 1963, 1967) has been for decades the keystone in conservation biology. Since its publication, many ecologists have used archipelagos as natural laboratories to investigate the mechanisms that generate biodiversity patterns and to test diversity estimation techniques. However, there are currently other lines of reasoning. One of them focuses on habitat heterogeneity (Williamson, 1981). The theory of island biogeography rests on the assumption that the number of species residing in a habitat is the result of an equilibrium between immigration and extinction, whereas habitat heterogeneity argues that the number of species reflects the range

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of habitats included in the area. One of the goals of MacArthur and Wilson’s theory is an explanation of the dependence of species richness upon such factors as area and the proximity and magnitude of sources of immigrants. Two predictions of the “Theory of Island Biogeography”, among others, are: (i) the most widespread abundance distribution patterns of species assemblages into island communities (as well as on the mainland) is the canonical lognormal distribution (e.g. MacArthur and Wilson, 1967; May, 1975), and (ii) the species’ number increase with area according to a power law (e.g. MacArthur and Wilson, 1967; May, 1975). If early studies provided empirical evidence for the theory, it is also true that it has been subjected to a number of criticisms and/or possible modifications (e.g. May, 1975; Gilbert, 1980; Rosenzweig, 1995, 1998, 1999; Lomolino, 2000; Lomolino and Weiser, 2001). May (1975, 1981) observed that the lognormal pattern (which does not require Preston’s canonical hypothesis (Preston, 1962a,b)), which is often associated with undisturbed equilibrium communities, tends to be replaced by geometric or logseries patterns as a result of environmental impact. The same is true with small samples belonging to larger assemblages. In spite of this debate, an impressive body of field data has been accumulated to support the validity of the equations of the theory (e.g. O’Neill, 2000; Lomolino, 2000). 2.3. Richness-area curves In ecology, the relationship between the number of species S and the area A (e.g. of an island or analogous habitat of patchy spatial occurrence), may be described by two kinds of models: those that can be approximated by a linear relation between log S and log A, i.e. log S = p log A + q where p and q are constants (Arrhenius, 1921, 1923; Preston, 1962a,b; MacArthur and Wilson, 1967; May, 1975), and those which approximate to a linear relation between S and log A, i.e. S = a log A+b, where a and b are constants (Gleason, 1922; Fisher et al., 1943; Williams, 1947, 1964). We emphasize that the first relation is a power function with exponent p and prefactor eq (S = eq Ap ) and the second is simply a logarithmic function of S in terms of A or alternatively an exponential function of

A in terms of S. The former will be called the power model and the latter the logarithmic model. Each of the above abundance distribution models implies one of these relations assuming that the total number of individuals is proportional to the area A (May, 1975). Each model of abundance distribution is then related to a model of richness-area curve. The lognormal and the broken-stick models yield power curves. For the lognormal model the exponent p is related to parameter γ by the expression (May, 1975) γ for γ ≥ 1, p= 4 (6) 1 p= for γ < 1. (1 + γ)2 The smallest exponent p = 1/4 is obtained for γ = 1, that is to say, for the canonical lognormal model. For the broken-stick model p = 1/2. The geometric and logseries models (very common in small samples of a given population, as well as disturbed communities) yield logarithmic expressions for the richness-area curves. It holds (May, 1975) that −1 log(1 − k) a=α a=

for the geometric model, and

(7)

for the logseries model.

The view that the canonical lognormal model and the power function for species-area relationships are the most widely applicable has become almost universally accepted (see Connor and McCoy, 1979; Sugihara, 1981). However, for small samples, data usually fit simultaneously to both models of richnessarea curves and geometric distributions (e.g. Taylor, 1978; May, 1975; Coleman et al., 1982; Tokeshi, 1993). It should be stressed that a fit to a power or a logarithmic function of the species-area data does not necessarily imply that the assemblage has an underlying lognormal or logseries pattern of species abundance; there is as yet no proof of one-to-one correspondence in this matter (Connor and McCoy, 1979). Some experts even question whether the effect of area, per se, as a factor affecting species richness, is of biological significance (e.g. Usher, 1991; Durrett and Levin, 1996). For Tokeshi (1993), mechanisms leading to richness-area curves are at best obscure. In any case, those mechanisms must include: (i) habitat heterogeneity—

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a larger area encompasses more diverse microhabitats which support more species; (ii) susceptibility to extinction—a larger area allows a larger population size, leading to a reduced chance of local extinction; and (iii) susceptibility to immigration—a larger area receives more immigrants from source pools. Although Connor and McCoy (1979) propose “passive sampling” (i.e. larger areas collecting more species as a purely sampling process) as a mechanism devoid of biological process, for Tokeshi (1993) this argument cannot be logically established as being separate from the processes of immigration and extinction. Tokeshi claims that the species-area relationship derived of such passive sampling should not be used as a null mode for testing biological interactions. Much interest has been focused on the value of p, the slope of the ln S versus ln A regression line. For islands (mainland data, in general, give smaller P-values than data from islands; e.g. see Rosenzweig, 1995, 1998, 1999), since the exact relationship between ln S and ln A is not a linear one, when the canonical lognormal distribution is assumed, fitting a linear regression to theoretical expectations leads to a slight overestimation (e.g. P = 0.262 in Preston (1962b), and P = 0.263 in MacArthur and Wilson (1967)) compared to the asymptotically exact value of 0.25 (May,

261

1975). Observed values often fall in the range 0.2–0.4 (Preston, 1962b; MacArthur and Wilson, 1963; May, 1975; McGuinness, 1984), which led Connor and McCoy (1979) to suggest mathematical artifacts as a reason, which in turn was disputed by Sugihara (1981). May observed that Preston’s argument yields a power law relation in the limit of large S if the canonical lognormal distribution is replaced by more general lognormal distributions, provided γ is constant among the islands under consideration and falls in the range 0.6–1.70. It is arguable whether much biological insight can be gained from the postulated tight clustering of data points around the theoretical ln S versus ln A regression line expected from the lognormal canonical hypothesis (γ = 1) with an exponent close to 0.25. We have tried to test that the mechanism (i) hypothesized by Tokeshi is the major cause of the richness-area curves by analazing pedotaxa data.

3. Case study: the Aegean Islands The Aegean Islands, in the eastern Mediterranean, form an archipelago of around two thousand isles (Fig. 1). The CORINE database (see below) includes

Fig. 1. Map of the study area: Mediterranean basin and detail of Aegean Sea.

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Table 1 Plate Segments and environments Environmental influence

Litho spheric material Topography Volcanism Seismic activity Pedodiversity (potential)

Plate segments Tensional margin

Plate centre

Compressional magin

Basaltic Steep with plateaux Active non-explosive Localized Low

Granite Gentle None None-weak Medium–low

Mixed Steep Explosive Strong regional High

After Paton et al., 1995; modified by Ib´añez et al., 1997.

682 of them. The archipelago is a mixture of landbridge (or continental) and true oceanic islands (with intense volcanism) (Bridges, 1990). They have a great lithological diversity. The Hellenic Arc and the Ionian Islands have the largest concentration of deep, intermediate and shallow earthquakes (Ud´ıas, 1985). Volcanism and seismicity seem frequently correlated in space and time (Economou, 1988). For Paton et al. (1995), from a global point of view, the primary factors controlling the distribution of soil are lithospheric materials and topography, both determined by plate tectonics. Any continental lithospheric plate consists of three segments, a tensional margin, a plate center and a compressional margin. The factors determining soil formation within each of these segments are very different (Table 1). The Mediterranean basin is a compresional margin plate segment (Paton et al., 1995). It has a complex physiography with a wide range of lithological materials. Seismic events cause frequent landslides and erosion. Therefore, the region has a high geomorphological, pedological and biological diversity (Ibáñez et al., 1997), but the soils are for the same reasons shallow and immature. Ibáñez et al. (1998a) have shown how, at a global level, the pedodiversity of Mediterranean pedomes is the greatest, while Ibáñez et al. (1995b) pointed out that, pedodiversity in the Mediterranean European countries is greater than in any other biogeographic region of Europe. They also have the most eroded landscapes, rich in Lithosols and Regosols (CEC, 1985).

4. Methods We used the 1:1,000,000 EU Soil Map (CEC, 1985), digitized by Platou et al. (1989) and incorporated into the CORINE database of the European Union (Briggs and Martin, 1988). In order to estimate the proportion of each pedotaxon in each mapping unit, the FAO standard rules (FAO, 1978) were applied. The percentages were converted into estimated areas by multiplying them by the area of each of the islands studied. The above mentioned digitized map was available in vectorial format. All GIS operations performed in order to obtain raw data were carried out with Arc/Info software. The resulting soil database was stored in Excel format. Standard techniques in mathematical ecology were used to determine whether the data conforms to the abundance distribution and richness-area models tested in the ecological literature. Estimates of pedodiversity were obtained from a small scale map (1:1,000,000). Thus, the results obtained can only be considered as rough estimates. However, at present, there is no published data for the whole of the Aegean Archipelago more accurate than what we have used here. All soil classifications are substantially limited in their ability to describe the great structural and genetic variability of soils. For example, only 23 soil types appear in this analysis (CEC, 1985). In some instances, neighboring islands are assigned to the same unit legend, despite very disparate sizes. Usually the larger islands have all pedotaxa described in the map legend, but the smaller ones contain fewer pedotaxa. Nevertheless, the aforementioned limitations are also present in other coarse data sets

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and should not be prevent analysis of the available data (Wilding and Nordt, 1998).

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Table 3 Estimated values of the parameters of the distribution models and Kolmogorov–Smirnoff significance test P-values Distribution model

5. Results and discussion 5.1. Results Of the 682 islands studied, 170 of them exceed 1 km2 in area (Table 2). Their size-frequency distribution fits to a Pareto distribution (power law) with, as is reported in the literature (Korvin, 1992; Turcotte, 1992), an exponent of −0.50 (R2 = 0.971). Table 2 Distribution of island sizes A

N

A

N

1 2 3 4 5 6 7 8 10 15 16 20 22 25 28 32 33 34 35 36 38 40 41 43 48 50 53 58 63 64 66 73 74

682 170 131 101 99 90 82 80 72 68 62 61 60 59 57 56 55 54 53 52 51 50 48 46 45 44 43 42 41 40 39 38 37

76 85 86 95 96 97 99 108 111 121 151 178 195 209 255 278 290 301 373 379 402 428 475 477 592 781 803 842 1063 1389 3654 8300

36 35 33 32 30 29 28 27 26 25 23 22 21 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

A is the area of islands (km2 ) and N is the number of islands with area greater than A.

Geometric

Book Stick

Lognormal

Logseries

Distance P-value

0.097 0.982

0.300 0.032

0.098 0.980

0.392 0.002

Parameters

k = 0.23 ST = 23

ST = 23

µy = 2.440 σ y = 0.612

α = 2.5 X = 0.999

Distance means the maximum vertical distance between model and observed curves. Standard errors of parameters µy and σ y , are 0.151 and 0.075, respectively, for lognormal model.

Fig. 2 is a plot of the ranked-abundance list of the 23 soil types distinguished in the CORINE soil database and shows that the areal extent of these soil types forms a characteristic “hollow curve” (Willis and Yule, 1922), which is typical of the abundance distribution of species in biodiversity inventories and suggests an underlying similarity with biological entities. Fig. 3 shows the observed cumulative distribution function (cdf) of the distribution of areas (km2 ) of each soil taxon in the archipelago. Also shown are the fitted cdf curves for the four models defined previously. Table 3 shows the parameter(s) of each model and the corresponding P-value obtained with the Smirnov–Kolmogorov test of goodness of fit (Conover, 1980). At a significance level of 5%, the Smirnov–Kolmogorov test rejects the broken-stick and the logseries models, and at a 1% it rejects the logseries model. However, the test does not indicate whether the lognormal or the geometric models fit the data best. Richness-area relationships were fitted to the power (Fig. 4) and logarithmic (Fig. 5) models. To accomplish this we plotted area on intervals determined by the powers of 2 so that they are gathered in a similar manner as with the “octaves”, using the conventional terminology (Preston, 1962a, 1962b). The estimated parameters are 0.255 for the power model and 2.200 for the logarithmic model. The coefficients of determination were very similar in both cases (R2 = 0.932 for the power model and 0.944 for the logarithmic model). The exponent of the power model (0.255) is in accord with that proposed for richness-area relationships in the ecological literature and supported by

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Area

5000 4000 3000 2000 1000

Re

Gc

Oe

Bh

I+RO

Vc

U

Lo

Bd

E

I

To

Lv

Id

Bk

Bc

Be

Jc

RO

Ie

Rc

Lc

Ic

0

Pedotaxa Fig. 2. Plot of ranked-abundance list (area in km2 ) of pedotaxa distinguished in the CORINE soil database. In order of increasing development they are: Rock outcrops (RO); Undifferentiated mixture of Lithosols and surface rocks (I + RO); Calcaric Lithosols (Ic); Eutric Lithosols (Ie); Dystric Lithosols (Id); Undifferentiated Lithosols mainly associated with volcanic rocks (I); Calcaric Regosols (Rc); Eutric Regosols (Re); Rendzinas (E); Rankers (U); Eutric Cambisols (Be); Chromic Cambisols (Bc); Dystric Cambisols (Bd); Calcic Cambisols (Bk); Humic Cambisols (Bh); Ochric Andosols (To); Calcaric Fluvisols (Jc); Calcaric Gleysols (Gc); Eutric Histosols (Oe); Chromic Vertisols (Vc); Orthic Luvisols (Lo); Vertic Luvisols (Lv); Chromic Luvisols (Lc).

much empirical data (e.g. May, 1975; Rosenzweig, 1995). In order to corroborate this result we repeated the same analysis using the Johnson and Simberloff (1974) data for British islands. Similar results were obtained (0.251 and 0.20 as the exponents of power model and, 0.923 and 0.726 as the coefficients of determination for the pedotaxa-area and biotaxa-area relationships, respectively). We have the estimated parameters of both abundance distribution models (Table 3) and richness-area relation models. However, as pointed out previously, assuming that the extent of each taxonomic group grows linearly in area allows the relationship between these parameters to be established (Eqs. (1) and (2)). In this case, these relationships do not hold for any model, suggesting that this assumption should be reexamined. As a preliminary conclusion, no significant difference can be detected between the abundance distribution models for island biodiversity and pedodiversity in similar situations. Both seem to follow similar patterns, notwithstanding the very disparate nature of the two datasets.

5.2. Discussion The major limitations for the application of abundance distribution models in Ecology and Pedology are (Ibáñez et al., 2001): (i) the methodological anarchy existing when organizing and adjusting raw data sets for the different models proposed; (ii) the enormous disparity and notable deficiencies in sampling designs, which make comparing results and detecting regularities difficult; (iii) the fact that different authors use different tests for the distribution models proposed; (iv) variation in the fits of the tested models according to the sampling time duration, the theories in vogue and the dominant criteria on authority; (v) the difficulty in detecting which models conform best to the data; (vi) the lack of criteria for delimiting space and time sampling intervals; (vii) the existence of other possible distribution models that conform to the data sets better than those tested up to now; (viii) the abundance distribution models to which the data conform may change with sampling intensity, observation time or area, and that those data correspond to entities whose space de-

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265

Fig. 3. Cumulative distribution function of pedotaxa areas and the distribution functions of the four models. A—area (km2 ) and N—number of pedotaxa with area less than A.

limitation is inherently ambiguous (see also Tokeshi, 1993). As we have seen, pedodiversity-area relationships and biodiversity-area relationships appear to be simi-

lar. Our results suggest that the biological assumptions underlying the theory of island biogeography could not be the cause of the generalized value of 0.25 for the exponent of the power law model. In other words,

Fig. 4. Regression line plot for the power model of log S (richness) vs. log A (area).

Fig. 5. Regression line plot for the logarithmic model of S (richness) vs. log A (area).

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contrary to the most popular opinion in ecology, the power law model for island geography does not appear to be an exclusive property of spatial distribution of the species. Habitat heterogeneity and area per se could be better candidates to explain this law (see Ibáñez et al., 2004 in this issue). In fact, if we consider pedotaxa as a component of habitat heterogeneity, the spatial distribution of habitats could be the driving force for biodiversity-area relationships. Alternatively, both perspectives could be manifestations of a more general trend of nature, independent of the objects analyzed, whether they are biological or non-biological. Gaston (1996) and other ecologists claim that topographic diversity (only elevation has traditionally been analyzed) and possibly other geomorphic features influence biodiversity. Some authors report a strong correlation between topography and taxonomic diversity (e.g. Rosenzweig, 1995; Gaston and Williams, 1996). However, area and elevation are not independent variables, though they have traditionally been analyzed as such in ecological literature (e.g. Johnson and Simberloff, 1974). For this reason, discrepancies in the biodiversity literature about the influence of area on biodiversity probably reflect the presence of other features, but not necessarily topographic diversity, of the earth surface systems which act more or less simultaneously (Ibáñez et al., 1990, 1994; Gaston and Williams, 1996). In other words, increasing area can support more species because of increases in both habitat heterogeneity (such as pedodiversity) and relief diversity (Ibáñez et al., 1994, 1999; Gaston, 1996). However, contrary to the opinion of most ecologists (Rosenzweig, 1995; among others), measuring area is not a trivial matter. This is probably a fractal problem (Frontier, 1987; Ibáñez et al., 1994, 1999, 2003; Gaston, 1996), so that, as relief increases, the area increases as well (Mandelbrot, 1983; Gaston and Williams, 1996). Such problems are difficult to solve satisfactorily, and most studies treat the earth as if it were flat, ignoring the nested digital elevation models which are currently available in many areas (Ibáñez et al., 1999). MacArthur (1964) suspected that the slope of richness-area curves measures the “horizontal” diversity of habitats. There are a few precedents in the literature on relationships among biodiversity, abiotic diversity and area. Let us review the most relevant ones.

Williamson (1981) found an almost perfect linear relationship between the logarithm of the number of geological types and the logarithm of the mapped area (a power law) using a geological map. He concluded that “Should this pattern of environmental variation be found to be common, then at least some species-area variation found in plants could be ascribed reasonably directly to the environment in which they are growing, while that of animals might be ascribed either to the environment, or to the plants, or to both” Cody (1983) observed that bird diversity on islands in the Gulf of California increased in a stepwise fashion as island area increased. He suggested this phenomenon was controlled by the geomorphology of drainage basins: larger islands can support higher-order stream channels and therefore, a greater range of riparian habitats than smaller islands (see also Ibáñez et al. (1990, 1994) for a detailed treatment of pedodiversity-drainage basins relationships). Johnson and Simberloff (1974) observed in the British Isles that the number of island soil types is the best predictor of the island species number. They suggest that soils may be an index of habitat heterogeneity. How might pedodiversity-area relationships affect the species-area relationship? Is it possible that the power laws between biodiversity or pedodiversity and area can be extrapolated to other abiotic natural resources such as the geomorphic and lithologic ones? The size-frequency distribution of islands is known to follow a power law (Korvin, 1992; Turcotte, 1992). According to Bak et al. (1997), this distribution may be a result of the chaotic and fractal nature of plate tectonics dynamics. In addition, Hastings and Sugihara (1993) and others have demonstrated the chaotic nature and fractal features of ecological systems. Could these phenomena explain species-area and pedotaxaarea relationships? How are they interrelated?

6. Conclusions Abundance distribution models are statistical tools which ecologists have applied for decades to analyze the intrinsic regularities of ecological entities. We applied some of these techniques in the sphere of pedology with the purpose of detecting similarities and differences between both natural resources, biological and non-biological. We have explored the state

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of the art in ecology, and then applied different abundance distribution models to a specific pedological example: the Aegean archipelago. The regularities detected in the pedological entities tested (pedotaxa) are surprisingly similar to those in ecological studies. The Smirnov–Kolmogorov test of goodness of fit indicated that the logseries and the broken stick distribution models should be rejected, whereas the geometric and lognormal models were not rejected (P < 5%); this may indicate that the underlying fragmentation scheme is slightly uneven. The parameter obtained for the lognormal model differed from that of the canonical lognormal, in spite of what is dictated by the most widespread theories (as biodiversity research now begins to recognize). Pedorichness-area relationships conformed to a power law whose exponent was close to 0.25, as the ecological literature predicts. Soils, as they reflect the influence of numerous environmental factors may be the best single predictor of habitat heterogeneity accounts for (a significant portion of) the variance in biotaxa richness explained by richness-area relationships. Therefore, our results suggest that richness-area relationships for soils should be examined for patterns and structures similar to biological richness-area relationships. Since results in ecology are usually interpreted in biological terms, our analysis may be relevant in at least three different domains: (i) determining reasons for the similarities and differences between biotic and soil resources; (ii) whether some aspects of the ecological theory should be modified; and (iii) implications for environmental management and assessment. The first point leads us to discern between regularities (theories) of a low level (biological, pedological) and regularities of a high level (e.g. those applicable to whole of earth surface systems, both biotic and abiotic). At the low level both the biological and pedological theories are incommensurate; at the high level they could be analyzed simultaneously, using the available tools in the so-called sciences of complexity (there are signs indicating that both have non-linear dynamics with similar patterns of space and time selforganization). The second and third points seem to have obvious responses, with potentially profound implications for the future of pedology. The comparative analysis of biologic and pedologic datasets could serve to corrob-

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