Running head: Fine-scale species-area relationships
CONNECTING FINE- AND BROAD-SCALE PATTERNS OF SPECIES DIVERSITY: SPECIES-AREA
RELATIONSHIPS OF SOUTHEASTERN U.S. FLORA
Jason D. Fridley1,2, Robert K. Peet1,3, Thomas Wentworth4, and Peter S. White1,3
1
Department of Biology
CB 3280, Coker Hall
University of North Carolina
Chapel Hill, NC 27599-3280 USA
2
(919) 962-6934 (phone)
(919) 962-6930 (fax)
fridley@unc.edu
3
Curriculum in Ecology
CB 3275, Miller Hall
University of North Carolina
Chapel Hill, NC 27599-3275 USA
4
Department of Botany
CB 7612, Gardner Hall
North Carolina State University
Raleigh, NC 27695-7612 USA
DRAFT 11/10/03
NEED TO ADD SPECIFICS TO ACKNOWLEDGEMENTS
FRIDLEY ET AL.
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Abstract
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Investigations of fine-scale (1000 m2 and below) species-area curves have been traditionally
3
decoupled from those of broader-scale diversity studies, but there has never been an extensive
4
empirical analysis of fine-scale species-area curves using consistent survey protocol over a large
5
region. We re-examined fine-scale species-area relationships using the extensive database of the
6
Carolina Vegetation Survey (NC, SC, and GA, USA), including 1369 plots with values of
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vascular plant richness at each of 6 areas regularly spaced on a log-10 scale, from 0.01 to 1000
8
m2. Contrary to prevailing theory, our data closely and consistently fit an Arrhenius (power law)
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species-area model, echoing broader-scale patterns and suggesting that local species
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accumulation patterns are controlled in part by those that control diversity at larger scales.
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Species accumulation rate (Z) values fell within a narrow range (0.2-0.4) despite a 30-fold range
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in 1000 m2 richness. When regional- and global-scale richness estimates were added to our
13
results a Preston-type triphasic curve emerged. We suggest that 1) fine-scale species-area
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relationships are remarkably consistent and indicate narrow constraints on local community
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structure, and 2) full-scale species-area curves reveal scale dependencies in diversity data that are
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not accounted for by current species-area theory.
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Key words: nested species-area curve, Arrhenius, Gleason, Carolina Vegetation Survey, North
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Carolina, South Carolina, scale, Z value, species diversity
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FRIDLEY ET AL.
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Introduction
The sensitivity of patterns and processes to scale is of great interest in ecology and has
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many implications for how studies are extrapolated across space and time (Levin 1992, Crawley
4
and Harral 2001). One of the oldest and most fundamental aspects of spatial dependence is the
5
relationship between species richness and area, which has important consequences for
6
conservation biology and ecology (May 1994, Tilman and Lehman 1997). Since their inception,
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species-area curves have been the basis of debates over scale-extrapolation (Gleason 1922,
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Arrhenius 1923), the fitting of statistical models to ecological data (Kilburn 1966, Connor and
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McCoy 1979, He and Legendre 1996), and the relevancy of “fine-scale” (ca. 1000 m2 and below)
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ecological studies to larger-scale phenomena (Williams 1964, Rosenzweig 1995, Williamson et
11
al. 2001, Williamson 2003). In particular, there has been much contention and confusion over
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the relevance of species-area relationships constructed from fine-scale data to larger-scale
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biodiversity patterns (Arrhenius 1921, 1923, Gleason 1922, 1925, Rosenzweig 1995, Williamson
14
et al. 2001). For example, it has often been argued that fine-scale species-area curves are
15
fundamentally different from larger-scale curves because they are better fit by a “Gleason”
16
(exponential) model rather than the otherwise-universal “Arrhenius” or power law model
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(Gleason 1922, 1925, Hopkins 1955, Whittaker 1972, van der Maarel 1988, Stohlgren et al.
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1995). By extension, the processes that determine fine-scale patterns are thought to be largely
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decoupled from those at larger scales (Rosenzweig 1995), making it difficult to extrapolate
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results based on fine-scale studies—the scales at which most detailed studies of communities are
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performed—to landscape, regional, or global processes controlling biodiversity.
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Consideration of fine-scale species-area relationships is of fundamental importance to the
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study of local communities. Fine-scale species-area relationships should reflect the inherent
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spatial structure of plant communities and their comparison may help identify causal factors of
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FRIDLEY ET AL.
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local diversity in different systems. The rate that species accumulate with area in nested samples
2
in community surveys has long been regarded as an important characterization of fine-scale
3
community structure (Arrhenius 1921, Gleason 1925, Williams 1964, Whittaker 1975).
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Although several studies have examined this rate—often called Z value (Rosenzweig 1995)—in
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meta-analyses of different studies conducted at different scales (reviews in Williams 1964,
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Williamson 1988, Rosenzweig 1995), few if any studies have systematically examined variation
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in Z values across whole regions with many independent samples of consistent survey protocol.
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Indeed, although the availability of large plot databases is increasing, there are very few with
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nested multi-scalar measurements of species richness in a form appropriate for evaluating true
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nested species-area curves (cf. Stohlgren et al. 1995, Kalkhan and Stohlgren 2000). As a result,
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there has yet to be a detailed investigation of fine-scale species-area curves using extensive
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empirical data, including whether they fit Gleason or Arrhenius models, how species
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accumulation rates vary systematically across whole regions, or how fine-scale richness data fit
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within the context of larger-scale species-area relationships.
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A dataset particularly appropriate for addressing the nature of fine-scale species-area
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curves across a large geographic region is the vegetation plot database of the Carolina Vegetation
17
Survey (CVS). Begun in 1988, the current CVS database of ca. 1400 0.1 ha plots is both
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extensive, covering coastal to mountain habitats across the Southeast U.S., and intensive,
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including a consistent protocol of 6 fully nested, multi-scalar richness values for each plot from
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the scale of individual plants (0.01 m2) to 1000 m2. We used richness data from 1369 plots of
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the Carolina Vegetation Survey to address the functional form and variation of fine-scale
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species-area curves. We specifically examined 1) the appropriate functional form for fine-scale
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species-area curves (exponential versus power models), 2) the distribution of species
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accumulation rate with area in fine-scale data (Z values) across the Southeast, and 3) how rates
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FRIDLEY ET AL.
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of species accumulation at fine scales compare to rates of species accumulation at larger scales,
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from quadrats within the Southeast to county, state, national, and global values of plant richness.
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Methods
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Study area and field methods
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We used 0.1 ha vegetation plots from the Carolina Vegetation Survey (archived by the
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North Carolina Botanical Garden, Chapel Hill, NC, USA) that span North and South Carolina
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and Georgia (USA), from coastal dune vegetation to the mountains of the southern Blue Ridge
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(see Figure A1 of digital appendix). The 1369 plots chosen were generally collected as regional
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projects, with particular concentrations in southern Blue Ridge montane forests (ca. 550 plots)
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and coastal plain upland pine savannas (ca. 450 plots). Within a project the landscape was
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typically subdivided by dominant vegetation types and plots were evenly distributed across
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types. A full listing of plot locations and richness data is given in the digital supplement.
14
All plots were surveyed with the CVS protocol described in Peet et al. (1998). Plots used
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in this study were sampled between 1988 and 2000. Within each plot rooted vascular plant
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richness was estimated for 6 nested areas regularly spaced on a log-10 scale, from 0.01 to 1000
17
m2 (Figure 1). Replicate richness values for areas less than 1000 m2 within each plot were
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averaged (see below). Vascular plant nomenclature was standardized to follow Kartesz (1999).
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Analysis
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For each of 1369 plots we calculated the mean richness per log-10 area, using 8 values at
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scales of 0.01, 0.1, 1, and 10 m2, 4 at 100 m2, and 1 at 1000 m2. The highest average 0.01 m2
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richness value we report for a plot is 10.5 species; the maximum richness for an individual 0.01
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m2 subplot was 15 species. Because logarithms are undefined at zero we excluded quadrats with
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no individuals from the analysis (see Williams 1996 for a description of the small biases
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FRIDLEY ET AL.
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introduced by excluding zeros). We evaluated the fit of richness data to “Gleason” semilog (S =
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Z log A + log c) and “Arrhenius” log-log (log S = Z log A + log c) models using two approaches:
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1) for each model, evaluation of the goodness-of-fit of the original data to a curve fit to these
4
data by simple linear regression with richness values averaged across all 1369 plots; and 2)
5
comparison of the distributions of coefficient of determination (R2) for the two models when fit
6
separately to the original data from each of the 1369 plots. Because nested species-area curves
7
do not reach an asymptote (Williamson et al. 2000), we did not attempt to use asymptotic models
8
appropriate for other forms of species-area data (He and Legendre 1996, Tjorve 2003).
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We placed our fine-scale area-richness data into the context of a larger species-area curve
10
by increasing spatial extent from the Carolinas to a global estimate of vascular plant richness
11
(250,000 species). We included floristic richness data from the 146 counties of North and South
12
Carolina from the USDA Plants database (USDA, NRCS 2002) and state and contiguous U.S.
13
richness data from Kartesz (1999). All native and introduced taxa were included at all scales.
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Results
Plant species richness data averaged by nested quadrat sizes of areas from 0.01 to 1000
17
m2 for 1369 plots across the Southeast U.S. closely fit a power (Arrhenius) function (Figure 2B).
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These same data provided a poorer fit to a semi-log (Gleason) linear function (Figure 2A). With
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untransformed richness (Gleason model), there was marked heteroscedasticity in richness among
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quadrat sizes (Figure 2A); variances appeared to be homogeneous when described by the
21
Arrhenius model. Additional evaluation of the goodness-of-fit of Arrhenius and Gleason models
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fitted individually by plot to generate R2 distributions of 1369 values for each model suggest that
23
a power function provides a consistently better fit to fine-scale richness data (Figure 3; t = 95.5,
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FRIDLEY ET AL.
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P < 0.0001, df = 2736). Together, these results demonstrate the superiority of the Arrhenius
2
model as a two-parameter function of fine-scale species-area curves for areas up to 1000 m2.
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Given the power function [log S = Z log A + log c] as an appropriate characterization of
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the fine-scale species-area curve, an assessment of the rate of species accumulation (Z) as area
5
increases from 0.01 to 1000 m2 determined individually by plot reveals an approximately normal
6
distribution with a mean of 0.315 (Figure 4). Minimum and maximum Z values are 0.125 and
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0.450; 95% of these Z values are between 0.214 and 0.417, and half are within 0.284 and 0.352.
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This relatively narrow range of species accumulation rates is found despite the fact that 0.01 m2
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richness values vary 10-fold from 1 to 10.5 and that of 1000 m2 from 30-fold from 6 to 179.
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When means of richness values for each quadrat size from 0.01 to 1000 m2 among our
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1369 plots are put within the context of larger-scale richness values from county to global areas,
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a triphasic curve emerges in log-log space (Figure 5). Extrapolation of the fine-scale species-
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area relationship to the world land area gives a global richness estimate of the same order of
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magnitude (ca. 182,000 species) as the approximate known value of 250,000 species, but areas
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above 1000 m2 have richness values below this line. At some area between 104 and 108 m2, the
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rate of species accumulation begins to steadily accelerate to reach the global richness value.
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Discussion
At the spatial scales at which communities are most often surveyed and manipulated
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(1000 m2 and below), the accumulation of species richness with area closely follows an
21
“Arrhenius” power law (Arrhenius 1921, 1923), the same general model that applies to species-
22
area curves at the much broader scales of landscapes and geographic regions (Williams 1964,
23
Rosenzweig 1995). The significance of model consistency between neighborhood and regional
24
scales is that local investigations of species interactions and community structure can be more
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FRIDLEY ET AL.
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formally tied to patterns that occur at much larger scales. Because the power function is thought
2
to be more representative of self-similarity in ecological phenomena with changes in scale, as
3
habitat diversity is often perceived (Gleason 1925, van der Maarel 1988, Rosenzweig 1995), the
4
fit of the power function to fine-scale data leaves open the possibility that species richness at
5
small scales is controlled at least in part by the same processes that control richness at larger
6
scales. However, because rates of species accumulation at fine scales are consistently higher
7
than those at intermediate scales (Figure 5; Preston 1960, Williams 1964, Williamson 1988,
8
Rosenzweig 1995), there is still an important difference between the distribution of diversity at
9
fine and intermediate spatial scales. In particular, fine-scale richness should be fundamentally
10
constrained by the density of individuals in small quadrats, what Preston (1960) referred to as
11
“sampling error” (not errors resulting from varied survey effort at different scales). Although the
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influence of this sampling error can be estimated with a variety of rarefaction techniques if
13
individual density data are available for each scale (Preston 1960, Gotelli and Colwell 2001),
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estimating individual density for organisms of indeterminate growth is notoriously difficult and
15
in many cases impossible (e.g., clonal forest herbs). Separation of “sampling” and “habitat”
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processes in the control of fine-scale species-area curves of plant communities remains a critical
17
issue for further research.
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Much previous work on fine-scale species-area curves has argued for the superiority of
19
the “Gleason” exponential model, which is likely the result of insufficient data and the desire to
20
extrapolate the fine-scale relationship to larger scales without recognizing the triphasic nature of
21
full-scale species-area curves in log-log space. Most previous empirical studies used datasets of
22
few plots (Gleason 1925, Shmida and Whittaker 1981), few quadrat sizes (He and Legendre
23
1996), or non-nested richness data (Rosenzweig 1995, Stohlgren et al. 1995). Over a small range
24
of scales the relative goodness-of-fit of power and exponential functions is difficult to determine,
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FRIDLEY ET AL.
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particularly with few data points (He and Legendre 1996, McGill 2003). Gleason (1922, 1925)
2
introduced and defended the exponential curve primarily on the basis of its more reasonable
3
approximation of richness at much larger scales than the plant neighborhood. Although our data
4
suggest that the global vascular plant richness value is well predicted by fine-scale species-area
5
data (cf. Crawley and Harral 2001), those of intermediate scales are over-predicted by fine-scale
6
power curves. Significantly, this is not a result of the power function being a poor fit to fine-
7
scale data, but rather that log-log species-area curves are triphasic, with slower accumulation
8
rates in intermediate areas. In his comprehensive treatment of species-area curves, Rosenzweig
9
(1995) dismissed the usefulness of fine-scale species area relations as a result of several of the
10
above concerns. Following Preston (1960), we assert that the different rates of species
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accumulation at fine scales compared to intermediate scales is an important consideration in
12
scaling up from local to regional studies, but the consistency of fine-scale curves and their
13
agreement with a power law attests to their significance as a tool for analyzing diversity patterns.
14
Rates of species accumulation with area in log-log space, often referred to as Z values,
15
range in the literature over nearly all possible values from 0 to 1, with lower values typical of
16
intraprovincial curves and higher values typical of species-area relationships that span biotic
17
provinces (Williams 1964, Rosenzweig 1995, Williamson 2003). For fine-scale data, Z values
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should be constrained by the maximum levels of richness in relatively small quadrats. For our
19
data, a maximum possible accumulation rate can be estimated by noting the mimimum 0.01 m2
20
richness value (1) and maximum 1000 m2 value (179), giving a Z value of around 0.45, which
21
was in fact the maximum Z value in our data. A minimum Z value boundary is theoretically 0
22
from a 1000 m2 monoculture; we obtained a minimum accumulation rate of around 0.12.
23
However, the majority of our Z values are far from these boundary conditions: half were between
24
0.28 and 0.35. Preliminary evidence suggests these Z values are typical for multi-scale floristic
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FRIDLEY ET AL.
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studies of at the scales of 1000 m2 and below (Shmida and Wilson 1985; OK tallgrass prairie,
2
M.W. Palmer, personal communication; LA longleaf savanna, P.A. Keddy, personal
3
communication; cf. Crawley and Harral 2001, Williamson 2003). This consistency hints at some
4
statistical or biological constraint over the spatial distribution of species richness at small scales
5
that deserves further study.
6
Of the relatively few existing species-area curves that include nested data from the scale
7
of individuals to that of national or global richness for a taxon, nearly all are conspicuously
8
triphasic, with relatively fast initial and final rates of species accumulation and an intermediate
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region of relatively slow accumulation (Preston 1960, Williams 1964, Shmida and Wilson 1985,
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Hubbell 2001, but see Crawley and Harral 2001). The ubiquity of the three phases of full-length
11
species-area curves suggests that this should be the standard species-area model (Hubbell 2001,
12
Williamson et al. 2001, Williamson 2003), replacing the two-phase intra- vs. inter-provincial
13
model suggested by Rosenzweig (1995). Shmida and Wilson (1985), Rosenzweig (1995), and
14
Hubbell (2001), among others, have suggested that the upturn in the species-area curve
15
approximates the scale at which large barriers to the dispersal of entire biotas lead to over-
16
enrichment of species richness from the production of “ecological equivalents” in isolated
17
provinces. We note that the area at which this upturn occurs in plots nested from within NC and
18
SC occurs at a much smaller scale than what most researchers would call a biotic province—
19
likely well before the county level (Figure 5). This may indicate limits to the dispersal of plant
20
taxa that are smaller than previously recognized, and we suggest more detailed studies of this
21
point of upturn in full-range species-area curves from other regions.
22
Our results highlight the usefulness of fine-scale species-area curves and should revive
23
attempts to formally reconnect biodiversity patterns at the smallest scales to that of the globe
24
(Preston 1960). We see future research needs in documenting the relationship between fine-scale
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FRIDLEY ET AL.
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and regional/global diversity species-area curves from both temperate (e.g., Stohlgren et al.
2
1995, Crawley and Harral 2001) and tropical (e.g., Williamson 2003) regions. Of particular
3
importance is identifying the principal biological or statistical constraints on species
4
accumulation rates at different spatial scales, including the influence of “sampling”-type density
5
constraints on richness at various scales. Although it is increasingly clear that patterns of
6
biodiversity are scale-dependent (Reed et al. 1993, Palmer and White 1994, Crawley and Harral
7
2001), the processes that govern this scale-dependence remain elusive, and mechanistic
8
investigations at small scales may prove crucial to interpreting larger-scale patterns.
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Acknowledgements
We gratefully acknowledge the more than 600 individuals who have participated in
12
collection of vegetation data in the Carolina Vegetation Survey archive. We particularly thank
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A. Weakley, M. Shafale, __. Members of the UNC Plant Ecology Laboratory and especially J.
14
Gramling, D. Vandermast, T. Jobe, A. Senft, M. McKnight, and J. Kaplan provided valuable
15
suggestions at all stages of this work. Plot collection was made possible through challenge cost-
16
share grants from the United States Forest Service. Data compilation and analysis was supported
17
by NSF grants DBI-9905838 & DBI-0213794 to RKP. JDF was supported by the National Parks
18
Ecological Research Fellowship program, a partnership between the National Park Service, the
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Ecological Society of America, and the National Park Foundation and funded through a generous
20
grant from the Andrew W. Mellon Foundation.
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Figure Legends
Figure 1. Vegetation plot design of the Carolina Vegetation Survey (Peet et al. 1998).
3
Tenth-hectare plots of 20 x 50 m (above) include 10 “modules” of 10 x 10 m, the inner four of
4
which are sampled intensively (below) in opposite corners (indicated as bold squares above) of
5
nested square quadrats sized 0.01 to 10 m2.
6
Figure 2. Species richness at 6 log-transformed nested areas for 1369 vegetation plots of
7
the Carolina Vegetation Survey, presented as (A) Gleason and (B) Arrhenius curves. Solid lines
8
connect mean values (+/- s.d.). Dashed lines are linear least-squares regressions and represent
9
predicted values from (A) Gleason and (B) Arrhenius models.
10
Figure 3. Histograms of the coefficient of determination (R2) for Gleason and Arrhenius
11
models fit to species-area curves for 1369 CVS vegetation plots. Each R2 value is the result of a
12
linear least-squares fit of 6 values (1 plot) to Gleason or Arrhenius models.
13
Figure 4. Histogram of log-log species accumulation rate (Z value) of 1369 vegetation
14
plots as sample area increases from 0.01 to 1000 m2. Bin size is 0.01. Dashed line is mean Z
15
value of 0.315; solid lines are 95% confidence intervals of the mean, [0.214, 0.417].
16
Figure 5. Log-log species-area curve of vascular plant richness from fine scales to global
17
land area, starting from within the Carolinas, USA. Lowest 6 values are mean richness values
18
from 1369 0.1 ha vegetation plots of the Carolina Vegetation Survey, with solid line as the mean
19
species accumulation rate for these scales. Richness data (means +/- 95% CI) for the 146
20
counties of NC and SC are from USDA, NRCS (2002). State and contiguous U.S. richness data
21
are from Kartesz (1999); global richness is an estimate of 250,000 species.
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FRIDLEY ET AL.
Figure 1
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FRIDLEY ET AL.
Figure 2
Species Richness
80
A
60
40
20
0
-2
-1
0
1
2
2
3
2
3
Log10 Species Richness
Log10 Area (m )
2.0
B
1.5
1.0
0.5
0.0
-2
-1
0
1
2
Log10 Area (m )
17
FRIDLEY ET AL.
Figure 3
400
Frequency
300
Arrhenius (power) fit
200
Gleason (exponential) fit
100
0
0.7
0.8
0.9
1.0
2
Coefficient of determination (R )
18
FRIDLEY ET AL.
Figure 4
120
100
Count
80
60
40
20
0
0.1
0.2
0.3
0.4
0.5
Accumulation rate (Z)
19
FRIDLEY ET AL.
Figure 5
4
cont. US
NC + SC
3
z = 0.315
2
Counties, NC & SC
0.1 ha
1
Log10 Species Richness
5
World land (- ice)
CVS quadrats
-2
0
2
4
6
8
10
12
14
Log10 Area (m2)
20
FRIDLEY ET AL.
Digital appendix and supplement
Digital appendix: Figure of plot locations
Figure A1. Locations of 1369 0.1 ha vegetation plots of the Carolina Vegetation Survey, from
NC, SC, and GA (USA), within the context of Type III Ecoregions (U.S. EPA. 2002.
Level III Ecoregions of the United States, August 2002 revision. National Health and
Environmental Effects Research Laboratory. Corvallis, OR, USA).
D1
FRIDLEY ET AL.
Digital supplement: Multi-scalar richness data for 1369 CVS vegetation plots (NC, SC, GA)
[to be available as a text file in the following format]
PlotID
State
County
0.01 m2 richness
0.1 m2 richness
1 m2 richness
10 m2 richness
100 m2 richness
1000 m2 richness
Z value
log C value
D2