Oecologia (2004) 139: 277–287 DOI 10.1007/s00442-004-1499-1

ECOSYSTEM E COLO GY

T. Michael Anderson . Samuel J. McNaughton . Mark E. Ritchie

Scale-dependent relationships between the spatial distribution of a limiting resource and plant species diversity in an African grassland ecosystem Received: 28 July 2003 / Accepted: 6 January 2004 / Published online: 6 March 2004 # Springer-Verlag 2004

Abstract One cornerstone of ecological theory is that nutrient availability limits the number of species that can inhabit a community. However, the relationship between the spatial distribution of limiting nutrients and species diversity is not well established because there is no single scale appropriate for measuring variation in resource distribution. Instead, the correct scale for analyzing resource variation depends on the range of species sizes within the community. To quantify the relationship between nutrient distribution and plant species diversity, we measured NO3- distribution and plant species diversity in 16 paired, modified Whittaker grassland plots in Serengeti National Park, Tanzania. Semivariograms were used to quantify the spatial structure of NO3- from scales of 0.4–26 m. Plant species diversity (Shannon-Weiner diversity index; H ′) was quantified in 1-m2 plots, while plant species richness was measured at multiple spatial scales between 1 and 1,000 m2. Small-scale variation in NO3- (<0.4 m) was positively correlated with 1-m2 H ′, while 1,000-m2 species richness was a log-normal function of average NO3- patch size. Nine of the 16 grassland plots had a fractal (self-similar across scales) NO3- spatial distribution; of the nine fractal plots, five were adjacent to plots that had a non-fractal distribution of NO3-. This finding offered the unique opportunity to test predictions of Ritchie and Olff (1999): when the spatial distribution of limiting resources is fractal, communities should display a left-skewed log-size distribution and a log-normal relationship between net primary production and species richness. These predictions were supported by comparisons of plant size distributions and biomass-richness relationships in paired plots, one with a fractal and one with a non-fractal distribution of NO3-. In addition, fractal plots had greater large-scale richness than paired non-fractal plots (1,0– 1000 m2), but neither species diversity (H ′) nor richness T. M. Anderson (*) . S. J. McNaughton . M. E. Ritchie Biological Research Laboratories, Syracuse University, 130 College Place, Syracuse, NY, 13244, USA e-mail: [email protected] Fax: +1-315-4432012

was significantly different at small scales (1 m2). This result is most likely explained by differences in the scale of resource variation among plots: fractal and non-fractal plots had equivalent NO3- variation at small scales but differed in NO3- variation at large scales (as measured by the fractal dimension). We propose that small-scale variation in NO3- is largely due to the direct effects of plants on soil, while patterns of species richness at large scales is controlled by the patch size and fractal dimension of NO3- in the landscape. This study provides an important empirical step in understanding the relationship between the spatial distribution of resources and patterns of species diversity across multiple spatial scales. Keywords Spatial scale . Fractal geometry . Nitrogen . Serengeti National Park . Soil heterogeneity

Introduction One fascinating aspect of communities is that many seemingly functionally redundant organisms coexist while competing for the same resources (Walker 1992; Lawton and Brown 1993). Community ecology attempts to explain how multi-species communities persist when energy and resources are in short supply. Theories have attempted to explain species coexistence on the basis of limiting similarity among community members (Abrams 1983), tradeoffs among the foraging abilities of competitors (Vincent et al. 1996), temporal variation in resource availability that results in the storage effect (Chesson 1994; Pake and Venable 1996), and other stabilizing effects of intra-specific resource competition (Chesson 2000). Models of species coexistence have commonly incorporated spatial variation in how the relative fitness of species can vary in space (Tilman and Pacala 1993), or how species vary in their ability to colonize vacant patches due to different responses to the environment (Connolly and Roughgarden 1999). The competition-colonization hypothesis suggests that multiple species can coexist in

278

space given sufficient tradeoffs between species’ competitive abilities and colonization abilities (Tilman 1994). In addition, spatial variation in supply rates of limiting resources allows multiple species to coexist as long as sufficient limiting similarity exists among species (Pacala and Tilman 1994). In herbaceous plant communities, while some welldocumented differences in rooting depth (Jumpponen et al. 2002), timing of resource allocation (Hooper and Vitousek 1997), and resource partitioning (McKane et al. 2002) may explain how plant species coexist at small scales, they fail to account for species richness patterns at larger scales. At large scales, species richness patterns have been attributed to habitat heterogeneity or environmental gradients (Whittaker and Niering 1975; Shmida and Wilson 1985; Currie 1991), which fail to account for small-scale species interactions and the acquisition of resources. In fact, one feature of models of species coexistence is that they attempt to explain diversity at either local or regional scales, but not both (Ricklefs and Schluter 1993). In contrast, models that incorporate organism size and resource distributions in space account for patterns of diversity across a range of spatial scales (Wiens 1989; Ritchie and Olff 1999). The relationship between the spatial distribution of limiting resources and patterns of plant diversity is one that has eluded plant ecologists. At small scales, plants extracting nutrients from the same patch may partition the soil profile with different rooting strategies, such as tap versus fibrous root systems, or by employing rapid morphological plasticity in root uptake and growth (Casper and Jackson 1991). But at larger spatial scales that include many individuals extracting nutrients from different patches, how does a landscape with many small nutrient patches differ from one with just a few large ones? One important consideration is that resource variation is scale-dependent; variation at one scale may be significant for a species of one size but meaningless to another. For example, variation in resource concentration within an area of a few square millimeters matters a great deal to microbes but not to a giant sequoia. On the other hand, variation in the distribution of insect larvae across a single leaf is insignificant to an insectivorous bird that has access to the entire surface of many different leaves. A resulting prediction is that species diversity is expected to change with variation in resource distribution in a manner that depends on organism size and resource or habitat requirements (Morse et al. 1985). Although plant ecologists have studied spatial variation of soil resources, most studies have emphasized how plants directly affect the distribution of macronutrients (Jackson and Caldwell 1993a, 1993b; Halverson 1995). Less well understood is how the spatial distribution of resources influences the number and types of species that can coexist, colonize, and persist within a community. A recent theoretical model based on spatial-scaling predicts that when resources are fractal, that is, they are self-similar across scales, species diversity and size distributions should differ from those of habitats that contain resources

that are randomly distributed (Ritchie and Olff 1999). To demonstrate the concept of fractal resources, imagine a checkerboard with dark squares that contain resources and white squares that lack them. Now imagine that the dark resource-containing squares are themselves made up of a spatial pattern exactly like that of the checkerboard; when the pattern of checkerboards within checkerboards extends across multiple spatial scales, the resource distribution is considered fractal. Although oversimplified (fractal resources are rarely evenly distributed as in the checkerboard example), this example highlights an important corollary: species “perceive” resources proportional to their size, so that resource patches (squares) for one species may not even be recognized by another species. The Ritchie and Olff model (1999) makes several falsifiable predictions. 1. When resources are fractal, the size difference between the largest and smallest species should be greater than when resources are random, because the spatial structure of resources across scales allows for a wide gap in body sizes. 2. In a fractal habit, the model predicts greater species packing at larger sizes, and therefore a left-skewed size distribution. This is because small species require small high-quality resource patches, while large species can tolerate large, relatively poor resource patches. Since large species encounter proportionally more resource volume in a fractal landscape than do smaller species, the size ratio (γ) of adjacent species decreases with size, until the largest resource patch provides the upper limit. 3. When resources have a fractal distribution, the model predicts that species richness is a log-normal function of primary production. As productivity increases, maximum patch size increases allowing more large species to coexist, resulting in a rapid increase in species richness. However, as productivity further increases, patches coalesce, eliminating the small patches on which diminutive species specialize. The result is that small species are eliminated at high productivity and species richness declines. 4. Finally, fractal landscapes contain a variety of differentsized habitat patches that allow organisms with different habitat or resource requirements to coexist, in turn increasing the number of species (richness) within a community (Palmer 1992). Species that coexist on a fractal landscape should be spatially distributed in patches as fractal resources occur in patches. Therefore, greater species spatial heterogeneity (β-diversity) is predicted in a fractal compared to a random landscape. To test these predictions, we quantified the spatial distribution of NO3- and plant species diversity at different spatial scales in grassland plant communities of Serengeti National Park (SNP), Tanzania. N is the most common limiting nutrient for terrestrial plant communities (Vitousek and Howarth 1991), including the Serengeti grasslands (McNaughton, unpublished study). Moreover, Serengeti

279

grasslands are characterized by high β-diversity within landscape regions (McNaughton 1983, 1994), suggesting spatial patterning at scales above individual plant competition. One feasible, yet untested, hypothesis is that patterns of plant species diversity observed in SNP are determined by the pattern of spatial variation of N, the ecosystem’s major plant-limiting nutrient. If so, when N has a fractal distribution, plant communities should have greater species richness and β-diversity, and should display a left-skewed size distribution and a log-normal relationship between productivity and species richness.

Materials and methods Site description Fieldwork was conducted in SNP from March to May 2002. The Serengeti-Mara ecosystem (Fig. 1), which includes SNP and the Masai-Mara national reserve to the north, encompasses some 25,000 km2 and is operationally defined by the seasonal movements of wildebeest, the ecosystem’s dominant migratory herbivore. SNP has two characteristic wet seasons driven by the intercontinental convergence zone: the short rains from November to December and the long rains from March to May (Norton-Griffiths et al. 1975), which began shortly after the beginning of our fieldwork. Eight sites, separated by a maximum linear distance of 100 km, were chosen to represent grassland communities that span the Serengeti’s significant rainfall (Norton-Griffiths et al. 1975) and soil fertility gradient (de Wit 1978; Jager 1982). At each of the eight sites, two modified Whittaker plots (MWPs; Stohlgren et al. 1995) Fig. 1 Map of Africa and the location of Serengeti National Park (SNP) in Tanzania (shown in gray). The locations of eight study sites (●) within SNP are labeled with three letter codes. At each site, two modified Whittaker plots (MWP) were established to study plant species diversity and the spatial distribution of NO3- availability. The 1,000-m2 whole plot (K) contains subplots 1–10, A , B , and C (identified by rectangles), which are drawn to scale. The locations of 53 resin bags are shown in the inset at the bottom left-hand corner of the figure

were established not more than 2 km from one another (Fig. 1) in which plant species diversity and nutrient abundance were quantified. Plots were paired at each site to control for variation in soil and rainfall when intra-site comparisons were made. To control for variation in slope and aspect, plots were arbitrarily located in relatively flat grassland. Average rainfall data for the sites were interpolated from >40 years of rain gauge data at ~50 sites across the Serengeti precipitation gradient; rainfall data were collected by the Serengeti Ecological Monitoring Program.

Plant species diversity, size, and biomass MWPs include one 100-m2 (C), two 10-m2 (A, B), and ten 1-m2 (1– 10) subplots nested within a whole plot area (K) of 1,000 m2 (Fig. 1). Percent cover for each species was estimated in all 1-m2 subplots so that vegetation and bare ground summed to 100%. Species richness (total number of species in a sample area) was measured for each plot at four spatial scales: 1 m2 (the average richness value from the ten small plots), 10 m2 (the average richness from A and B), 100 m2 (richness from C), and 1,000 m2 (richness of K). Whole-plot species richness will refer to the total number of species in K, while subplot richness will hereafter refer to average 1m2 species richness from ten subplots. Species diversity was calculated using the Shannon-Weiner diversity index (H ′): H ′= −Σ(pi)×(lnpi), where pi is the proportional abundance of species i, summed for all n species measured and averaged over ten subplots in a MWP. To test predictions of the spatial scaling law model (SSL) of Ritchie and Olff (1999), we collected data on plant sizes and standing biomass within each MWP. A rigorous test of the SSL would include total primary production, roots plus shoots, rather than aboveground standing biomass, as is the case in this study. Standing biomass can be a poor surrogate for primary production

280 when herbivory is severe (McNaughton 1985). However, data were collected prior to the migrating wildebeest reaching any of the sites, so defoliation was sporadic and insignificant during the study. Moreover, studies of root biomass in SNP grasslands suggest that aboveground productivity is representative of productivity belowground (McNaughton et al. 1998). Plant size was measured as the vertical distance from the soil surface to the tallest, fully expanded leaf for four randomly chosen, mature individuals (not seedlings) of each species within the plot. In the rare case that less than four individuals could be located, we measured heights of all individuals located. Standing crop biomass was determined for each MWP by clipping all aboveground biomass in six of the ten 1-m2 subplots. Phytomass was returned to the laboratory, dried at >60°C, weighed on a balance and averaged for each plot.

Nutrient analysis Soil nutrient heterogeneity was studied with in situ ion-exchange resin bags, which have proven successful in measuring nutrient heterogeneity (Gibson 1986; Yavitt and Wright 1996). In each MWP, 53 polyethylene bags, filled with ~25 g cation/anion exchange resin (Fisher scientific), were buried in a nested grid design (Fig. 1). Resin bags were buried to a depth of 10 cm; the great majority of roots in SNP occur in the upper 20 cm of the soil (McNaughton et al. 1998) and samples must be located in the primary extraction zone to appropriately capture nutrient availability. Linear arrays of six resin bags, in which bags were separated by 0.4 m, were buried in six subplots. Subplots A, B, C and K had resin bags at the corners and in the center of each subplot. The resin bags at the plot corners were separated by 53.85 m, the maximum linear distance between samples. Resin bags were buried over a 4day period beginning 15 March 2002 and were exhumed after 30 days. After collection, resin bags were transported to Syracuse University where they were washed with de-ionized water, oven dried at 65°C for 48 h, and extracted with 50 ml of 1 N KCl. Resin and KCl were shaken at 12 h and filtered through Fisher brand P5 Fig. 2 Various functions used to model semivariance (γ) as a function of the lag distance (h). The random model (···) has a slope=0 and demonstrates no spatial structure in the measured variable. The linear model (—) has a constant slope and indicates a continuous gradient in the measured variable. The similar exponential (- -) and spherical (not shown) models have a lag distance over which there is spatial structure in the variable (range parameter; Ao) and no spatial structure beyond it. The nugget variance (Co) measures the amount of variation that exists below the smallest measurement (0.4 m in this study). The structural variance (C) describes the amount of variance explained by the model. The sill (C + Co), is the total amount of variance over the sampled lag distance. Equations for models are shown below the graph

medium porosity slow flow rate filter paper at 24 h. Extracts were analyzed for NH4+ and NO3- with a continuous flow Lachat QuikChem AE auto-analyzer (Milwaukee, Wis.). Seasonal rainfall began just days after bags were buried and continued sporadically throughout the sampling period. While the resin adsorbs both NH4+ and NO3-, Binkley (1984) showed that NH4+ levels measured by resin bags depended on water availability, while NO3- levels depended on actual soil available NO3-. Because of this finding, we focus all subsequent analyses of nutrient spatial patterns on NO3- only.

Geostatistical analyses Semivariograms, plots of semivariance (γ) as a function of lag distance (h), were constructed for the 16 plots using GS+ version 5.1.1 (2001). γ is an autocorrelation statistic defined as: γ (h)=[1/2 N (h)]×Σ(zi−zi+h); where γ (h)= γ for lag distance class h; z i=the measured NO3- value at point i; z i + h =the measured NO3- value at point i + h; and N (h)=the number of sample pairs used to calculate γ for lag class h. Semivariograms were constructed on the natural lognormalized NO3- values with ten lag intervals between 0.4 m, the smallest distance between resin bags, and 26 m, half the distance of the maximum linear distance between bags. The number of sample pairs used to generate lag distance classes varied between 30 at 0.4 m and 206 at 19.3 m. To facilitate comparisons among plots, γ was standardized by dividing by the total variance in the sample, a method that has been used to compare γ among sites (Augustine and Frank 2001). Regressions fit by GS+ conform to one of several models: linear, exponential, and spherical (Fig. 2). Best fit models were those that minimized the residual sum of squares. Linear models have two parameters: a slope and y -intercept, called the nugget variance (Co). The slope measures the degree of the unidirectional change in variation (i.e., gradient) and Co measures the amount of variation that exists at scales below the smallest linear measurement, which is 0.4 m in our study. Linear semivariograms with slopes=0 lack spatial structure with respect to NO3- variation

281

Fig. 3 Unimodal relationship between average precipitation (cm) and the number of plant species in a 1,000-m2 modified Whittaker plot. Precipitation values were interpolated from >40 years of data for ~50 rain gauge locations throughout Serengeti National Park. The equation for the least squares non-linear regression is: y = −224.14+8.2 x−0.06 x2 (F2,13 =3.64, P =0.056)

Fig. 4 Positive correlation between Co, and α-diversity estimated by the average Shannon-Weiner diversity index (H ′) value from ten 1-m2 subplots (ρ15=0.60, P =0.013). Values are for 16 plots at eight sites that span the rainfall gradient within SNP. As the relationship is a correlation the regression line is shown for visual purposes only. For other abbreviations, see Figs. 1 and 2

and are associated with random spatial variation. Exponential and spherical models have four parameters: “nugget variance” (Co), “structural variance” (C), “range” (Ao), and “sill” (Co+ C) (Robertson and Gross 1994). In the exponential and spherical models Co is the same as in the linear model, Co+ C is the total amount of variation in the model, and Ao is the distance over which the variance occurs, and is theoretically equivalent to the average nutrient patch size. The proportion of variance explained by the model is the ratio of the total to the structural variance (C / Co+ C). Resources are considered fractal if their distributions are selfsimilar at different scales (Sugihara and May 1990). The fractal dimension (D) of a resource occurring in a two-dimensional plane varies between 0 and 2; D ≈0 is a single point, D ≈1 indicate highly clustered and self-similar distributions, while D ≈2 more completely fill the plane and are likely indistinguishable from a random distribution (Sugihara and May 1990). D can be obtained from a log-log plot of the γ as a function of lag distance, where the slope (m) is statistically different from zero indicating a fractal dimension and D =2− m /2. The fractal dimension of a NO3- was obtained from the fractal analysis module of GS+.

with small-scale species diversity, measured by average H′ in 1-m2 subplots (Fig. 4; ρ15=0.60, P =0.013). Whole plot species richness was log-normally related to average NO3patch size, estimated by Ao (Fig. 5; R =0.69, F2,10=4.5, P =0.04). According to the log-normal equation between plant species richness and average NO3- patch size, maximum 1,000-m2 plant species richness in Serengeti grasslands should occur when the average NO3- patch size has a diameter of 41.3 m. Nine of 16 sites had a distribution of NO3- that was described well with fractal geometry (Table 1). At five sites, plot pairs consisted of one plot in which NO3- had a fractal distribution across the landscape and one in which the distribution of NO3- was non-fractal. To test predic-

Results Species richness at the whole plot scale displayed a unimodal relationship with rainfall (Fig. 3; F2,13=3.639, P =0.056), but was neither related in a linear nor quadratic way to rainfall at the 1-m2 scale (non-linear, F2,13=1.14, P =0.35; linear, F1,13=0.57, P =0.46). However, at any given site, plots displayed a dramatic variation in species richness despite equivalent rainfall (Table 1); for example, in one site, KCW, plots separated by only a few hundred meters varied in whole plot richness by 40 species. The remainder of this paper is dedicated to explaining the factors correlated with intra-site differences in species richness, and α- and β-diversity. Differences in the spatial patterning of NO3- provide insight into patterns of species richness and diversity among plots. For example, small-scale variation in NO3-, as estimated by the nugget variance Co, was correlated

Fig. 5 The relationship between species richness found in a 1,000m2 modified Whittaker plot and the average patch size of NO3measured within the plot using geostatistics. Average patch size was obtained from Ao estimated from the best fit model of NO3- γ as a function of h. The solid line is fitted with the log-normal equation: y=57.76 e−0.5×{[ln(x/41.25)/1.35]2} (F2,10=4.5, P=0.04). For abbreviations, see Fig. 2

49.9

BRS

71.1

KCW 76.6

KUH 78.0

TOG 67.7

BAL

MSB 89.1

KMS 79.9

53.8

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

E S L E E E E E L E L S S E E E

0.84 0.50 1.05 0.81 0.35 0.44 0.45 0.79 0.96 0.81 1.06 0.31 0.55 0.72 0.74 0.78

1.68 1.71 1.08 1.62 1.17 1.05 1.03 1.58 1.07 1.63 1.06 1.26 1.75 1.44 1.48 1.56

148.86 57.93 NA 105.15 6.51 11.22 14.73 152.01 NA 183.00 NA 18.74 50.51 72.51 111.84 183.00

Nugget (Co ) Sill (Co + C) Range (Ao )

Average rainfall (cm) Plot Model Model parameters

SOT

Site

0.50 0.71 0.03 0.50 0.70 0.58 0.56 0.50 0.10 0.50 0.00 0.75 0.69 0.50 0.50 0.50

0.17 0.11 1.39 0.16 0.33 0.11 2.57 0.03 0.04 0.03 0.17 0.18 0.27 0.03 0.07 0.02

7.7 6.8 10.1 12.8 6.8 7.9 6.5 7.4 13.7 7.6 9.2 10.5 11.4 10.3 13.7 9.3

2

13.0 22.0 14.0 17.5 12.5 13.5 10.0 10.5 24.0 14.0 19.5 21.5 18.5 17.0 18.5 13.5

10 m

2

16 27 20 29 16 22 16 15 38 24 35 39 22 25 44 19

100 m

2

25 58 22 43 25 38 30 24 61 40 54 60 53 46 70 30

1,000 m

Scale-dependent species richness 2

1.42 1.23 1.84 1.84 1.30 1.36 1.25 1.33 1.99 1.43 1.95 1.57 1.83 1.61 2.00 1.64

59.18 72.67 41.47 67.47 57.80 69.96 49.76 53.16 65.80 54.27 45.09 67.38 49.18 47.22 59.87 47.44

NS 1.89 NS 1.94 NS 1.91 1.9 1.94 NS NS NS 1.84 1.9 1.94 1.95 NS

D

α (H ′) β (100-PS)

NS 0.009 NS 0.004 NS 0.005 0.007 0.015 NS NS NS 0.001 0.019 0.006 0.035 NS

P

Fractal dimension

Diversity measures

RSS root sum of squares, H′ Shannon-Weiner diversity index, α α-diversity measured by H′, PS percent similarity, β β-diversity measured by 100-PS, D fractal dimension, P significance of slope parameter from a log-log plot of NO3- semivariance and distance, NS not significant

C / Co+ C RSS 1 m

Table 1 Semivariogram parameter values and species diversity measures from 16 modified Whittaker plots (MWP); plots were paired by sites across the Serengeti National Park (SNP) precipitation gradient (Fig. 1). The eight study sites within SNP are identified by three -letter codes. See text and Fig. 2 for explanations of how semivariogram parameters and species diversity measures were calculated. E Exponential model, S spherical model, L linear model,

282

283

Fig. 6 Species richness as a function of standing crop biomass for plots with a fractal (A) and non-fractal (B) distribution of NO3-. Richness is the average number of species recorded in ten 1-m2 subplots within five fractal or non-fractal plots. Standing crop biomass is the average aboveground phytomass from six subplots within each of five fractal and five non-fractal plots, except in the case of one fractal plot, in which data were collected for only five subplots. The solid lines are log-normal fits to the data with the following equations: fractal, y =13.46 e −0.5×{[ln(x /244.44)/0.76]2} (F2,16 =2.54, P =0.11); non-fractal, y =9.26 e −0.5×{[ln(x /199.77)/1.48]2} (F2,17 =0.79, P =0.47)

tions of SSL, we compared plant size distributions, the phytomass-richness relationship, and species diversity and richness in paired fractal and non-fractal plots that occurred at the same sites (Table 2). Plant size distribuTable 2 Comparisons of diversity and plant size measures between paired MWP with either a fractal or non-fractal distribution of NO3-. Table values are means from five plots paired by site with SEs in parentheses; t -statistics and Pvalues are for paired t-tests with Ho: fractal=non-fractal plots, with df=4. Italics show P
tions were analyzed with log-log plots of plant size versus the next larger plant in a ranked series. Slopes=1 indicate a log-normal size distribution; slopes >1 indicate rightskewed log size distributions; slopes <1 indicate leftskewed log size distributions (Brown 1995). Plant size distributions in fractal plots were significantly left-skewed compared to paired non-fractal plots, indicated by smaller slopes of fractal plots. Likewise, the range of plant sizes, log maximum size–log minimum size (cm), in fractal plots was significantly larger than those of non-fractal plots. As predicted by the SSL, species richness as a function of standing phytomass fit a log-normal distribution better in plots with a fractal (Fig. 6A; F2,16=2.54, P =0.11) than non-fractal (Fig. 6B; F2,17=0.79, P =0.47) distribution of NO3-. At scales of 10–1,000 m2, fractal plots had higher species richness than non-fractal plots, but small-scale measures of plant species diversity, including average 1m2 richness and H ′, were not different between fractal and non-fractal plots. Accordingly, small-scale variation in NO3-, as estimated by Co, did not differ between fractal and non-fractal plots (t4=1.78, P =0.15). This result is in agreement with the previously described correlation between 1-m2 species diversity and Co. However, βdiversity, measured as 100-percent similarity, was significantly higher in fractal than non-fractal plots (Table 2), indicating that species were more clustered in fractal plots compared to non-fractal plots. Differences between fractal and non-fractal plots were not related to mean differences in soil properties, as no consistent differences between any component of soil texture existed between plots (%sand, t4=0.7, P =0.70; %silt, t4=0.12, P =0.91; %clay, t4=0.65, P =0.55).

Discussion The unimodal relationship identified between species richness and average annual precipitation in our 16 grassland plots is typical for vascular plant communities measured at this scale (Mittelbach et al. 2001). A more intriguing characteristic of this relationship, however, is the amount of variance in species richness and diversity that exists between grasslands of equivalent rainfall; differences in the spatial patterning of limiting nutrients may offer an explanation. Our results demonstrate a strong

Variable

Fractal plots (n =5)

Non-fractal plots (n =5)

Slope of log-log plant size regression Range of log plant sizes (cm) 1,000-m2 Richness 100-m2 Richness 10-m2 Richness 1-m2 Richness α (H′) β (100−PS)

0.89 (0.04) 1.38 (0.06) 53.8 (5.85) 32.2 (4.04) 18.6 (1.54) 10.32 (1.34) 1.6 (0.14) 67.47 (2.13)

0.95 0.94 31.2 21.2 14.5 8.62 1.63 50.2

(0.03) (0.07) (5.84) (3.54) (1.27) (0.6) (0.12) (3.52)

t4

2.81 3.63 3.62 2.97 2.93 1.94 0.25 6.0

P

0.048 0.022 0.022 0.041 0.043 0.125 0.816 0.004

284

link between the spatial distribution of nutrients and plant species diversity and richness up to scales of 1,000 m2. Moreover, the form of the relationship between species diversity and nutrient distribution is scale specific; at scales ~0.4 m, species diversity and nutrient heterogeneity are linearly related, while at scales >0.4 m species richness and nutrient patch size are log-normally related. Since these results are largely correlational, assigning causation to our findings is not possible. Indeed, the necessary next step in this line of research is to experimentally determine to what extent the spatial distribution of resources influences plant distribution, versus the extent to which plant distribution determines the spatial distribution of limiting nutrients. With that said, however, the fact that all aspects of our study support the predictions of the SSL (Table 2) suggests that over at least the range of spatial scales sampled here, underlying patterns of resource distributions interact with organism body size to influence the way species coexist within communities. Scale-dependent relationships are common in ecology (Schneider 2001), and often arise because different processes operate at the different scales (Shmida and Wilson 1985; Crawley and Harral 2001; Dixon et al. 2002). Scale-dependent processes may be responsible for the different patterns observed in our study and may resolve the seemingly inconsistent conclusion that plant communities simultaneously determine and are determined by nutrient availability. For example, at the scale of a single plant, plant roots create zones of depletion in the soil immediately surrounding the rhizosphere (Casper and Jackson 1997) and respond to proximate nutrient rich patches by increased uptake (Jackson et al. 1990) and root proliferation (Gross et al. 1993; Fransen et al. 1999). Shrubs (Halverson et al. 1995; Schlesinger et al. 1996) and grasses (Burke 1989; Jackson and Caldwell 1993a, 1993b) in relatively dry climates act as “islands of fertility” by increasing organic matter, N mineralization, and many trace elements in the immediate soil surrounding their roots. Different plant functional types can have contrasting effects on soil; woody vegetation creates greater soil heterogeneity in moisture and available N than does herbaceous vegetation (Kleb and Wilson 1997). Moreover, within functional types, plant effects on soil can be species-specific (Wedin and Tilman 1990; Groffman et al. 1996; Van Der Krift and Berendse 2001). Mechanisms for plant effects on soil and the microbial community are varied, but include differences in the quality of decaying roots and litter inputs (Hobbie 1992), root exudates (Hamilton and Frank 2001), root morphology (Casper and Jackson 1991), and nutrient requirements (Tilman 1982, 1988). Therefore, at the scale of single plants, there is substantial evidence that plants influence, and even determine, nutrient distributions. We believe direct plant effects provide an explanation for the observed correlation between species and small-scale NO3- variation in our study. On the other hand, at scales greater than that of an individual plant, the spatial heterogeneity of resource

distributions can affect emergent properties of plant communities such as primary production and vegetation cover. Plant cover alters microclimatic conditions in ways that can further influence nutrient availability (Ball et al. 2002). It is well known that the experimental alteration of nutrient availability in a sward changes plant species composition and richness (Tilman 1984; Barnes et al. 1987; Gough et al. 2000). Likewise, where gradients of underlying parent material create differences in soil nutrient availability, plant communities often reflect these changes in their composition and abundances (Hutchinson et al. 1999; Rosales et al. 2001; Seastedt and Vaccaro 2001). Landscape characteristics, such as catena position, influence nutrient cycling and therefore the suite and level of available nutrients for plants (Schimel et al. 1985; Burke 1989; Fisk et al. 1998; Burke et al. 1999). Additionally, herbivory by largebodied ungulates creates heterogeneous nutrient distribution at local scales because of excretion (Augustine and Frank 1999), feeding (Adler 2001), and death (Towne 2000), and regionally because of seasonal movements (McNaughton 1990). Robertson et al. (1988) showed that N patches occurred at a scale commensurate with variation in plant community composition in a Michigan old field and was correlated with, at least to some degree, surface topography, which they argued could influence the way plant community succession developed. Therefore, at scales larger than individual plants, nutrient distributions exert strong controls on plant species diversity and community composition. Robertson et al. (1988) suggested that: “Whether spatial complexity affects or mainly reflects plant community structure is not known”. We believe a resolution to this query lies in scale-dependent relationships betweens plants and limiting nutrients. At small scales, on the order of the diameter of a plant’s rooting zone, variation in soil resources is largely a function of plant effects on soil via the previously cited mechanisms. At larger scales, soil nutrient heterogeneity, created by landscape-level processes such as topography, soil parent material, and the effects of large herbivores, controls the number and types of species that occupy plant communities. Our explanation is an extension of previous scale-dependent theories of species diversity (Shmida and Wilson 1985), and is testable with experimental methods. The high variability of average NO3- patch sizes in our plots, from ~7–183 m, was consistent with the variability in the Ao from other systems. Studies from southern Michigan, report Ao values for NO3- and N processes that vary from ~2 to >100 m. For example, soil NO3- values were spatially autocorrelated up to ~18 m in a nature reserve in southeastern Michigan (Robertson et al. 1988). Ao varied from ~2 to >16 across a series of three successional fields at Kellogg Biological Field (KBS) in southwest Michigan (Gross et al. 1995). In a cultivated field at KBS, Robertson et al. (1997) reports a value of Ao=90 m for NO3-. In addition, nitrification and N mineralization rates in two KBS fields displayed Ao values of ~10 m in fields undisturbed for >30 years, and 100 m in

285

recently cultivated fields (Robertson et al. 1993). This last study suggests that disturbance history might contribute to the variability of NO3- patch size at our sites. Disturbances, such as fire and flooding, are associated with variation in plant community composition in Serengeti grasslands (McNaughton 1983), offering further support that disturbance may contribute to large-scale nutrient heterogeneity. Regardless of the process that generates variation in the patch size of limiting nutrients, we believe the log-normal relationship between Ao and species richness is mechanistically similar to the observed relationship between productivity and richness. As average nutrient patch size increases, larger and a greater number of species can coexist within the multiple patches in the landscape. However, as Ao becomes large, resources coalesce to create large homogeneous patches with little or no heterogeneity to allow coexistence of species with different resource requirements. Until experimental tests are conducted, we cannot rule out the possibility that NO3patches of 41.3 m and associated high plant species richness, as observed in our study, are a result of some other factor, such as animal-derived disturbance. Grasslands that are geographically isolated can display striking functional similarities. For example, grasslands of SNP and those of Yellowstone National Park (YNP), Wyoming, are redundant with respect to many aspects of ecosystem function and determinants of community composition (Frank et al. 1998). In grassland plant communities of YNP, greater small-scale variation in total soil N and N-mineralization potential was associated with higher small-scale species diversity and richness (Augustine and Frank 2001), as was the case in our study. However, in YNP, the higher fine-grain variability was a result of ungulate grazing in plots versus paired plots where migratory ungulates were excluded for >30 years. Grazed sites displayed linear semivariograms, indicating homogeneous patches did not occur throughout their sample plot. We have yet to see whether the linear patterns in our data set are associated with grazing or not; however, given the ubiquitous nature of grazing in the Serengeti (McNaughton 1985) this seems unlikely. The YNP study focused on spatial variation in nutrients at much smaller scales than the present study (2 m compared to 26 m), and whether more extensive sampling would produce similar patterns is not known. The most compelling result from this study is the strong support for the SSL model, which explains organism coexistence as a function of the spatial distribution of limiting resources (Ritchie and Olff 1999). Landscape heterogeneity has been linked to plant species diversity at the scale of several hectares (Harner and Harper 1976; Burnett et al. 1998) to the scale of regions or watersheds (Nichols et al. 1998); in all cases species diversity increases with landscape heterogeneity. However, the SSL model goes beyond the simple direct relationship between heterogeneity and species diversity, and makes specific predictions about the nature of species distributions when the spatial distribution of limiting resources is

controlling biodiversity. For example, the SSL model predicts left-skewed unimodal size distributions and a right-skewed unimodal relationship between production and species richness when resource distributions follow spatial scaling laws. A comprehensive review study demonstrates that many, but not all, communities have a unimodal relationship between production and species richness (Mittelbach et al. 2001). The underlying mechanism is that larger organisms can tolerate lower concentrations of limiting nutrients but require larger resource patches. In fractal landscapes, larger resourcepoor patches occupy proportionally more total volume than the small resources-rich patches required by small species. Two results follow: (1) greater species packing at large sizes [a decreasing body size ratio (γ) with increasing organism size] until a point where the largest species are limited by maximum patch size, and (2) a rapid increase in richness with production and then a slow decrease because larger resource patches exclude smaller species that require small resource-rich patches. Both predictions were verified by our comparisons of fractal and nonfractal plots (Table 2; Fig. 6). Perhaps the various relationships between richness and net primary production observed in nature (e.g., Mittlebach et al. 2001) can be explained by differences in the spatial patterns of limiting resources. Computer simulations have demonstrated complex interactions between the fractal dimension (D) of a resource, environmental variability, and species coexistence (Palmer 1992). Predictions that follow from the results of Palmer (1992) are greater microsite and landscape species richness and lower β-diversity as a function of increased D. We found greater α- and βdiversity in sites with fractal resource distributions, but our sample size (n =9) does not allow empirical tests of the influence of D on measures of diversity. Future and more extensive analyses could improve on this rather crude comparison between fractal and non-fractal plots by increasing the sample size to allow for an empirical comparison among grassland swards with different D. It is not clear whether the results of this study are mutually exclusive to those of other models, because many models have not been developed beyond the scale of local interactions. However, it is clear that spatial structure is just one of the many factors that contribute to the maintenance of species diversity. Coexistence is a complex balance between factors that reduce fitness differences between species and those that increase intraspecific competition resulting in a negative-feedback from densitydependant mechanisms (Chesson 2000). Models that incorporate the spatial distribution of resources or habitat and organism body size have both features; small species experience greater intraspecific competition while larger species experience reduced fitness differences among competitors. This study demonstrates that by including variation in the spatial distribution of resources and habitat in models of coexistence, considerable progress can be made towards understanding the mechanisms that generate and maintain species diversity.

286 Acknowledgements Special thanks to E. M. Peter for help in the field and M. M. McNaughton for help in the laboratory. D. E. O’Connell, L. L. Wolf, and B. Schmedicke improved the manuscripts with editorial comments. Thanks to M. Coughenour for providing a field vehicle and the Serengeti Monitoring Program for providing rainfall data. This research was funded by NSF grant DEB-9903845 to S. J. McNaughton and an NSF doctoral fellowship to T. M. Anderson.

References Abrams PA (1983) The theory of limiting similarity. Annu Rev Ecol Syst 14:359–376 Adler PB, Raff DA, Lauenroth WK (2001) The effect of grazing on the spatial heterogeneity of vegetation. Oecologia 128:465–479 Augustine DJ, Frank DA (2001) Effects of migratory grazers on spatial heterogeneity of soil nitrogen properties in a grassland ecosystem. Ecology 82:3149–3162 Ball MC, Egerton JJG, Lutze JL, Gutschick VP, Cunningham RB (2002) Mechanisms of competition: thermal inhibition of tree seedling growth by grass. Oecologia 133:120–130 Barnes GR, Bransby DI, Tainton NM (1987) Fertilization of southern tall grassveld of Natal: effects on botanical composition and utilization under grazing. J Grassl Soc S Afr 4:63–67 Binkley D (1984) Ion exchange resin bags: factors affecting estimates of nitrogen availability. Soil Sci Soc Am J 48:1181–1184 Brown JH (1995) Macroecology. The University of Chicago Press, Chicago, Ill. Burke IC (1989) Control of nitrogen mineralization in a sagebrush steppe landscape. Ecology 70:1115–1126 Burke IC, Lauenroth WK, Riggle R, Brannen P, Madigan B, Beard S (1999) Spatial variability of soil properties in the shortgrass steppe: the relative importance of topography, grazing, microsite, and plant species in controlling spatial patterns. Ecosystems 2:422–438 Burnett MR, August PV, Brown JH Jr, Killingbeck KT (1998) The influence of geomorphological heterogeneity on biodiversity. I. A patch-scale perspective. Biol Conserv 12:363–370 Casper BB, Jackson RB (1997) Plant competition underground. Annu Rev Ecol Syst 28:545–570 Chesson P (1994) Multispecies competition in variable environments. Theor Popul Biol 45:227–276 Chesson P (2000) Mechanisms of maintenance of species diversity. Annu Rev Ecol Syst 31:343–366 Connolly SR, Roughgarden J (1999) Theory of marine communities: competition, predation, and recruitment-dependent interaction strength. Ecol Monogr 69:277–296 Crawley MJ, Harral JE (2001) Scale dependence in plant biodiversity. Science 291:864–868 Currie DJ (1991) Energy and large-scale patterns of animal and plant species richness. Am Nat 137:27–49 Dixon MD, Turner MG, Jin C (2002) Riparian tree seedling distribution on Wisconsin river sandbars: controls at different scales. Ecol Monogr 72:465–485 Fisk MC, Schmidt SK, Seastedt TR (1998) Topographic patterns of above- and belowground production and nitrogen cycling in alpine tundra. Ecology 79:2253–2266 Frank DA, McNaughton SJ, Tracy BF (1998) The ecology of the earth’s grazing ecosystems. Bioscience 48:513–521 Fransen B, Blijjenberg J, de Kroon H (1999) Root morphological and physiological plasticity of perennial grass species and the exploitation of spatial and temporal heterogeneous nutrient patches. Plant Soil 211:179–189 Gibson DJ (1986) Spatial and temporal heterogeneity in soil nutrient supply measured using in situ ion-exchange resin bags. Plant Soil 96:445–450 Gough L, Osenberg CW, Gross KL, Collins SL (2000) Fertilization effects on species density and primary productivity in herbaceous plant communities. Oikos 89:428–439

Groffman PM, Eagan P, Sullivan WM, and Lemunyon JL (1996) Grass species and soil type effects on microbial biomass and activity. Plant Soil 183:61–67 Gross KL, Peters A, Pregitzer KS (1993) Fine root growth and demographic responses to nutrient patches in four old-field species. Oecologia 95:61–64 Gross KL, Pregitzer KS, Burton AJ (1995) Spatial variation in nitrogen availability in three successional plant communities. J Ecol 83:357–367 Halverson JJ, Smith JL, Bolton Jr H, Rossie RE (1995) Evaluating shrub-associated spatial patterns of soil properties in a shrubsteppe ecosystem using multiple-variable geostatistics. Soil Sci Soc Am J 59:1476–1487 Hamilton EW III, Frank DA (2001) Can plants stimulate soil microbes and their own nutrient supply? Evidence from a grazing tolerant grass. Ecology 82:2397–2402 Harner RF, Harper KT (1976) The role of area, heterogeneity, and favorability in plant species diversity of pinyon-juniper ecosystems. Ecology 57:1254–1263 Hobbie SE (1992) Effects of plant species on nutrient cycling. Trends Ecol Evol 7:336–339 Hooper DU, Vitousek PM (1997) The effect of plant composition and diversity on ecosystem processes. Science 277:1302–1305 Hutchinson TF, Boerner RE, Iverson LR, Sutherland S, Kennedy Sutherland E (1999) Landscape patterns of understory composition and richness across a moisture and nitrogen mineralization gradient in Ohio (U.S.A.) Quercus forests. Plant Ecol 144:177–189 Jackson RB, Caldwell MM (1993a) Geostatistical patterns of soil heterogeneity around individual perennial plants. J Ecol 81:682–692 Jackson RB, Caldwell MM (1993b) The scale of nutrient heterogeneity around individual plants and its quantification with geostatistics. Ecology 74:612–614 Jackson RB, Manwaring JH, Caldwell CC (1990) Rapid physiological adjustment of roots to localized soil enrichment. Nature 344:58–60 Jager Tj (1982) Soils of the Serengeti woodlands, Tanzania. Agricultural research reports no. 912. Pudoc, Wageningen, pp 1–239 Jumpponen A, Hoegberg P, Huss-Danell K, Mulder CP (2002) Interspecific and spatial differences in nitrogen uptake in monocultures and two-species mixtures in north European grasslands. Funct Ecol 16:454–461 Kleb HR, Wilson SD (1997) Vegetation effects on soil resource heterogeneity in prairie and forest soils. Am Nat 150:283–298 Lawton JH, Brown VK (1993) Redundancy in ecosysytems. In: Schulze E-D, Mooney HA (eds) Biodiversity and ecosystem function. Springer, Berlin Heidelberg New York, pp 255–270 McKane RB, Johnson LC, Shaver GR, Nadelhoffer KJ, Rastetter EB, Fry B, Giblin AE, Kielland K, Kwiatkowski BL, Laundre JA, Murray G (2002) Resource-based niches provide a basis for plant species diversity and dominance in arctic tundra. Nature 412:68–71 McNaughton SJ (1983) Serengeti grassland ecology: the role of composite environmental factors and contingency in community organization. Ecol Monogr 53:291–320 McNaughton SJ (1985) Ecology of a grazing ecosystem: the Serengeti. Ecol Monogr 55:259–294 McNaughton SJ (1990) Mineral nutrition and seasonal movements of African migratory ungulates. Nature 345:613–615 McNaughton SJ (1994) Conservation goals and the configuration of biodiversity. In: Forey PL, Humphries CJ, Vane-Wright RI (eds) Systematics and conservation evaluation, volume no. 50. Clarendon Press, Oxford, pp 41–62 McNaughton SJ, Banyikwa FF, McNaughton MM (1998) Root biomass and productivity in a grazing ecosystem: the Serengeti. Ecology 79:587–592 Mittelbach GG, Steiner CF, Scheiner SM, Gross KL, Reynolds HL, Waide RB, Willig MR, Dodson SI, Gough L (2001) What is the observed relationship between species richness and productivity? Ecology 82:2381–2396

287 Morse DR, Lawton JH, Dodson MM, Williamson MH (1985) Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature 314:731–732 Nichols WF, Killingbeck KT, August PV (1998) The influence of geomorphological heterogeneity on biodiversity. II. A landscape perspective. Conserv Biol 12:371–379 Norton-Griffiths M, Herlocker D, Pennycuick L (1975) The patterns of rainfall in the Serengeti ecosystem, Tanzania. East Afr Wildl J 13:347–374 Pacala SW, Tilman D (1994) Limiting similarity in mechanistic and spatial models of plant competition in heterogeneous environments. Am Nat 143:222–257 Pake CE, Venable DL (1996) Seed banks in desert annuals: implications for persistence and coexistence in variable environments. Ecology 77:1427–1435 Palmer MW (1992) The coexistence of species in fractal landscapes. Am Nat 139:375–397 Ricklefs RE, Schluter D (1993) Species diversity in ecological communities: historical and geographical perspectives. University of Chicago Press, Chicago, Ill. Ritchie ME, Olff H (1999) Spatial scaling laws yield a synthetic theory of biodiversity. Nature 400:557–560 Robertson GP, Gross KL (1994) Assessing the heterogeneity of belowground resources: quantifying pattern and scale. In: Caldwell MM, Pearcy RW (eds) Exploitation of environmental heterogeneity by plants. Academic Press, San Diego, Calif., pp 237–253 Robertson GP, Huston MA, Evans FC, Tiedje JM (1988) Spatial variability in a successional plant community: patterns of nitrogen availability. Ecology 69:1517–1524 Robertson GP, Crum JR, Ellis BG (1993) The spatial variability of soil resources following long-term disturbance. Oecologia 96:451–456 Robertson GP, Klingensmith KM, Klug MJ, Paul EA, Crum JR, Ellis BG (1997) Soil resources, microbial activity, and primary production across an agricultural ecosystem. Ecol Appl 7:158– 170 Rosales J, Petts G, Knabb-Vispo C (2001) Ecological gradients within riparian forests of the lower Caura River, Venezuela. Plant Ecol 152:101–118 Schimel D, Stillwell MA, Woodmansee RG (1985) Biogeochemistry of C, N, and P in a soil catena of the shortgrass steppe. Ecology 66:276–282 Schlesinger WH, Raikes JA, Hartley AE, Cross AF (1996) On the spatial pattern of soil nutrients in desert ecosystems. Ecology 77:364–374 Schneider DC (2001) The rise of scale in ecology. Bioscience 51:545–553

Seastedt TR, Vaccaro L (2001) Plant species richness, productivity, and nitrogen and phosphorus limitations across a snowpack gradient in alpine tundra, Colorado, USA. Arct Antarct Alp Res 33:100–106 Shmida A, Wilson MV (1985) Biological determinants of species diversity. J Biogeogr 12:1–20 Stohlgren TJ, Falkner MB, Schell LD (1995) A modified-Whittaker nested vegetation sampling method. Vegetatio 117:113–121 Sugihara G, May RM (1990) Applications of fractals in ecology. Trends Ecol Evol 5:79–86 Tilman D (1982) Resource competition and community structure. (Monographs in population biology, vol 17) Princeton University Press, Princeton, N.J., pp 1–296 Tilman D (1984) Plant dominance along an experimental nutrient gradient. Ecology 65:1445–1453 Tilman D (1988) Plant strategies and the dynamics and structure of plant communities. (Monographs in population biology, vol 26) Princeton University Press, Princeton, N.J., pp 1–359 Tilman D (1994) Competition and biodiversity in spatially structured habitats. Ecology 75:2–16 Tilman D, Pacala S (1993) The maintenance of species richness in plant communities. In: Ricklefs RE, Schluter D (eds) Species diversity in ecological communities: historical and geographical perspectives. University of Chicago Press, Chicago, Ill., pp 13–25 Towne EG (2000) Prairie vegetation and soil nutrient responses to ungulate carcasses. Oecologia 122:232–239 Van Der Krift TAJ, Berendse F (2001) The effect of plant species on soil nitrogen mineralization. J Ecol 89:555–561 Vincent TLS, Scheel D, Brown JS, Vincent TL (1996) Trade-offs and coexistence in consumer resource models: Its all depends on what and where you eat. Am Nat 148:1039–1058 Vitousek PM, Howarth RW (1991) Nitrogen limitation on land and sea: how can it occur? Biogeochemistry 13:87–115 Walker BH (1992) Biodiversity and ecological redundancy. Conserv Biol 6:18–23 Wedin DA, Tilman D (1990) Species effects on nitrogen cycling: a test with perennial grasses. Oecologia 84:433–441 Whittaker RH, Niering WA (1975) Vegetation of the Santa Catalina Mountains, Arizona. V. Biomass, production and diversity along an elevational gradient. Ecology 56:771–790 Wiens JA (1989) Spatial scaling in ecology. Funct Ecol 3:385–397 Wit HA de (1978) Soils and grassland types of the Serengeti plain (Tanzania). Dissertation. University of Wageningen, Wageningen Yavitt JB, Wright SJ (1996) Temporal patterns of soil nutrients in a Panamanian moist forest revealed by ion-exchange resin and experimental irrigation. Plant Soil 183:117–129