Nested versus non-nested characterization of vegetation ...



Date: Sun, 22 Feb 2004 22:46:31 -0500

From: Tom Wentworth

To: Dane Kuppinger , Lee Anne Jacobs ,

Kristin Taverna , Tom Wentworth ,

Jason Fridley , Brooke Wheeler ,

Brooke Wheeler , Jack Weiss ,

Robert Peet , Peter White

Subject: updated Stohlgren MS

Parts/Attachments:

1 Shown 38 lines Text

2 83 KB Application

3 Shown 13 lines Text

----------------------------------------

Hi folks,

Here's an updated Stohlgren MS, incorporating many suggestions that emerged

at our last meeting in November. I have more directly addressed concerns

with both the Whittaker (Shmida 1984) and modified-Whittaker (Stohlgren et

al. 1995) methods. I've also mentioned that we did some work with the

arithmetic-Arrhenius model. And I've done a lot of editing.

As a footnote to my enhanced discussion of the Stohlgren et al. (1995)

approach, I have refrained from critiquing what many of us considered to be

a rather strange approach in that paper to evaluating species-area

data. Indeed, in carefully re-reading their paper, I found myself even

more confused about how they actually handled their data. I became so

dissatisfied with my understanding of this paper that I have written to Tom

Stohlgren requesting clarification. It will be interesting to see what (if

anything) I get back from Tom! I'll let you know.

Another thing I've done in this version is to back away from much

discussion of spatial autocorrelation. We really don't address it

specifically in our work, and I'm hesitant to make this topic more

prominent unless we have something definitive to say about it. If any of

you have thoughts about how we could elevate the discussion of spatial

autocorrelation, please let me know.

Finally, this draft still reflects the empirical results in hand at the

time we created the ESA poster. However, I have proposed that we explore

more fully Jack Weiss's idea (advanced at our meeting in November) that we

dissect accuracy and precision components associated with deviations of

predicted from observed 400m2 richness. Jack had also discussed further

exploration of spatial autocorrelation and pseudoreplication issues in our

analyses, but any discussion of these issues will have to await such

further exploration, hopefully fairly soon.

I would certainly welcome comments on this draft, but it might be best to

wait until a subset of the Stohlgren co-authors have had a chance to

discuss some of the issues raised in the preceding paragraph. This might

result in some substantial modification of our results and discussion sections.

Nested versus non-nested characterization of vegetation composition and species richness at multiple spatial scales

DRAFT: February 22, 2003

Thomas R. Wentworth1

Peter S. White2,3

Brooke E. Wheeler3

Kristin Taverna3

Dane Kuppinger3

Lee Anne Jacobs2

Jason D. Fridley2

Jack Weiss3

Robert K. Peet2,3

1Department of Botany

Campus Box 7612

North Carolina State University

Raleigh, NC 26795-7612 USA

2Department of Biology

CB#3280, Coker Hall

University of North Carolina

Chapel Hill, NC 27599-3280 USA

3Curriculum in Ecology

CB#3275, Miller Hall

University of North Carolina

Chapel Hill, NC 27599-3275 USA

Abstract

The importance of characterizing vegetation composition and species richness at multiple spatial scales is increasingly recognized by ecologists, but there is no consensus as to whether variation with scale is best characterized by subplots arranged in a design that is nested or non-nested. We examined how well these fundamentally different designs allow characterization of change in species richness with change in grain of observation. From a conceptual perspective, we find that the nested design offers a means to interpret underlying spatial patterns of richness that the non-nested design does not. In particular, the nested design is more appropriate if the goal is to assess changes in species composition with changing grain size of observation, because the non-nested design confounds the influence of grain with that of extent. From an empirical perspective, we evaluated nested and non-nested designs for characterizing species richness at multiple scales (species-accumulation curves) for vascular plants, using data collected by the Carolina Vegetation Survey in 873 0.04 ha plots. We compared goodness-of-fit of exponential (Gleason) and power-function (Arrhenius) models for species-accumulation curves. Using both models, we also determined which inventory design allowed more effective extrapolation of the species-accumulation relationship to the 0.04 ha scale. The Arrhenius model provided the best fit for both sampling designs. With the Arrhenius model, subplot data collected using the nested design better predicted richness at the 0.04 ha scale than did data collected using the non-nested design, which resulted in consistent over-prediction. The latter finding was consistent with our hypothesis that data collected using a non-nested design are prone to over-predict richness in larger areas within which they are nested. We conclude that the nested design is equivalent or superior to the non-nested design for most applications and should be the standard method for multi-scale inventories.

Key words: Arrhenius model, Gleason model, nested sampling design, non-nested sampling design, spatial extent, spatial scale, species richness, species-area curves, species-accumulation curves.

Introduction

Assessment of number of species per unit area is a common objective for terrestrial plant ecologists concerned with inventory and conservation of natural resources. Among community properties, species richness is of particular interest because it is the outcome of numerous density dependent and independent processes (Huston 1979, Grace 1999) and because it contributes to community structure and function (Loreau et al. 2001). Because processes relating to species richness are scale-dependent (Huston 1994, Rosenzweig 1995, Fridley 2001, Chase and Liebold 2002), it is essential that patterns of species richness be quantified at a variety of spatial scales. In particular, determination of richness at multiple spatial scales has three benefits: (1) as research questions and objectives evolve, analyses are possible at a variety of spatial scales; (2) the pattern of increase in species richness may be the attribute of greatest interest, not the richness at any particular scale (Gleason 1925, Williams 1964, Rosenzweig 1995); and (3) species richness data spanning multiple spatial scales facilitate both interpolation of richness for comparison with studies at varied scales and extrapolation of the species-area relationship to larger scales.

Implementing an inventory protocol at multiple spatial scales involves many choices, including the spatial arrangement and relative sizes of subplots and how such subplots are analyzed to make inferences about the underlying spatial structure of the vegetation. A design choice of particular importance is whether variation of species richness with increasing scale is best characterized by subplots arranged in a design that is nested or non-nested. In a nested design, each subplot inventoried is fully enclosed within the next larger subplot; in a non-nested design subplots of different sizes are inventoried independently of one another (although they are not truly independent, because non-nested subplots are typically nested within a larger plot). There is no consensus as to the circumstances under which nested versus non-nested multi-scale sampling designs should be preferred. Recently, Stohlgren et al. (1995) and Barnett and Stohlgren (2003) have promoted a non-nested design, using a “modified-Whittaker” 0.1 ha plot. Their primary objections to Whittaker’s previous use of a nested design (Shmida 1984) were the lack of consistent subplot shape (length-to-width ratio), the use of a single replicate of nested subplots in the center of a larger 0.1 ha plot, and the spatial autocorrelation inherent in all nested designs. Researchers of the Carolina Vegetation Survey (Peet et al. 1998) have advocated use of a nested design, also using 0.1 ha plots. However, the Carolina Vegetation Survey method alters Whittaker’s nested design (Shmida 1984) by maintaining a consistent subplot shape (square) and deploying multiple nested-subplot replicates within the larger 0.1 ha plot. Rosenzweig (1995, p. 10), following the pioneering work of Gleason (1925), also recommended use of contiguous, nested subplots because data from non-nested or “scattered” subplots result in species-area curves that climb “too fast” and exhibit “too much curvature.” Given the influence of Stohlgren and colleagues’ non-nested modified-Whittaker design, and prevailing counter-arguments favoring the nested approach, there are pressing needs for (1) an analysis of the conceptual merits and advantages of both designs and (2) an empirical evaluation of the effectiveness of nested versus non-nested inventory designs in characterizing species richness patterns. In this paper, we first address conceptual and practical issues associated with selection of inventory design, and we then undertake an empirical evaluation of nested and non-nested designs.

Conceptual and Practical Issues

Researchers should consider the implications of several conceptual issues before selecting a particular inventory design. In this section, we present seven such issues that have been identified by previous workers or that have arisen during inventories conducted by the Carolina Vegetation Survey. (1) The non-nested design is thought to be more desirable from a statistical perspective because richness values derived from non-nested subplots of different scales (grain sizes) are more statistically independent; richness values derived from nested subplots are spatially autocorrelated (Stohlgren et al. 1995). (2) However, the nested design is generally more appropriate if the goal is to assess change in species richness with changing grain size of observation, because it minimizes the confounding of grain and extent. The non-nested design, in contrast, confounds the influence of grain with that of extent, making the search for mechanisms controlling richness difficult. (3) Only subplots established using a nested design allow for a meaningful way to obtain well-defined “replicate” sets of fine-scale species-area relationships within a larger area. (4) Use of the nested design constrains the species-area relationships to a monotonic form. Undesirable “reversals” of this relationship are possible when a non-nested design is employed. (5) Extrapolation of the relationships discovered in small-scale data to larger scales is inherently a “nested” approach, so a nested design is preferred because it maintains a consistent approach to data collection. (6) The non-nested design is superior when the goal is to find as many species as possible within a specific subsample of a larger area, i.e., when the largest extent is not itself sampled as the largest grain size. If the goal is to inventory all species in a larger area (i.e., the largest extent equals the largest grain), neither design presents a clear advantage, and indeed sampling at multiple spatial scales is unnecessary. (7) Use of a nested design is logistically simpler and more time-efficient. Setup of a series of nested subplots requires less time than setup of a series of independent non-nested subplots spanning the same range of scales; if plots are to be permanently marked, a nested design requires fewer permanent subplot markers than does a non-nested design.

Empirical Issues

Because of continued interest in protocols for species inventory at multiple spatial scales, we compared nested and non-nested approaches using data available from the Carolina Vegetation Inventory (Peet et al. 1998). Like Stohlgren et al. (1995), we also used model goodness-of-fit to discriminate between nested and non-nested approaches. However, we evaluated two popular models, while Stohlgren et al. (1995) evaluated only one. We also compared species-area relationships developed from nested data with those developed from non-nested data to determine which design allows for more accurate prediction of richness at a larger scale within the scope of a particular community. We chose accuracy of extrapolation as a benchmark for comparing nested and non-nested designs because this approach was adopted by Stohlgren et al. (1995) in their comparison of inventory designs. Because extrapolation is a curve-fitting activity, we also conducted our comparisons using two popular models. We hypothesized that data collected using a non-nested design would over-predict richness in larger areas within which they are inherently nested.

Methods

Model-fitting

Model-fitting has a long history in the study of species-area relationships, extending back to seminal work by Arrhenius (1921) and Gleason (1922). While many possible models exist, data from relatively small areas (defined for our purposes as those < 0.1 ha) seem best fit by either exponential (S = zlog(A) + c) or power-function (S = cAz) models (He and Legendre 1996), referred to in this paper as Gleason and Arrhenius models, respectively. In both models, S is the number of species, A is the area examined, and c and z are constants. The parameters of the Gleason model may be estimated using simple linear regression. As noted by Rosenzweig (1995), most authors transform the Arrhenius model to its linear form, log(S) = zlog(A) + log(c) and estimate its parameters using linear regression. In preliminary analyses, we found some advantages to the use of a non-linear model for fitting the power function to multi-scale richness data. However, we chose the approach of linear regression for estimating parameters of both the Gleason and Arrhenius models; in so doing we kept the number of parameters consistent and conformed to the most widespread usage.

Species-area versus species-accumulation curves

Non-nested subplot designs add an additional level of complexity by allowing two different ways to tally species with increasing area. The first, a species-area curve (SPARC), simply charts the number of species found at each increasingly larger area. The second, a species-accumulation curve (SPACC), charts the cumulative number of different species encountered as larger areas are inventoried. For nested designs, SPARCs and SPACCs are identical; however, for non-nested designs, SPARCs and SPACCs may differ. Individual SPARCs developed from nested data always increase monotonically, while individual SPARCs developed from non-nested data may not be monotonically increasing functions. SPARCs developed by averaging both nested and non-nested sets of multi-scale data collected from within the same larger area are expected to be identical; efforts to compare them would thus be uninteresting. However, because SPACCs developed from nested and non-nested data collected from within the same larger area may differ, this paper focuses exclusively on comparison of species-area relationships described by SPACCs.

Data structure

A total of 873 0.1 ha plots with nonzero richness values at each of four spatial scales were available from the Carolina Vegetation Survey data set, covering a wide range of communities and environmental conditions across the Carolinas (USA). [TRW: Jason suggested that we might want to use a subset of the plot-location figure he presented in the FS-SPARC paper – any thoughts on this? Also, should we elaborate on the nature of our data set? We might comment on the specific range of communities sampled and the range of 0.1 ha richness encountered.] The data were collected following the protocol of Peet et al. (1998; Figure 1). Within each plot, four contiguous 10x10m modules with a total area of 400m2 were used to generate species richness data for this study. Subplot data came from the 0.1, 1, 10, and 100m2 scales (subplot data from the 0.01 m2 scale were also available but not used in this investigation because of the large number of zero-richness values encountered at that scale). These data represent the number of vascular plant species rooted within a subplot (cf. Williamson 2003). The four 10x10m modules were nested within larger 1000m2 plots, but we focused on the contiguous block of 10x10m modules, with a combined area of 400m2. By confining our study to this 400 m2 block, both plot and subplots had the same square shape, eliminating any confounding of plot/subplot size and shape.

Four separate sets of nested richness data were generated for each plot using values collected within each of the four 10x10m modules. Four separate sets of non-nested richness data were also generated; each set started with a value for the smallest scale drawn from one of the four modules and then accumulated values for increasingly larger scales from the remaining modules in a counter-clockwise fashion through the block of four modules, such that no value at a given scale was selected more than once. Each set of richness data was used to generate an individual SPACC, resulting in four nested replicate and four non-nested replicate SPACCs in a given plot. In modeling SPACCs from nested data, the values for the independent variable (cumulative area) were 0.1, 1, 10, and 100 m2. However, SPACCs from non-nested data accumulated area at a slightly greater rate, so the corresponding values for cumulative area were adjusted to be 0.1, 1.1, 11.1, and 111.1 m2.

Curve-fitting

Gleason and Arrhenius models were fit to each of the four nested and four non-nested sets of richness data in each plot using simple linear regression. Figures 2a-b illustrate our curve-fitting procedure for nested data from one plot representing median richness in our data set. The model results were extrapolated to predict species richness at the 400m2 scale for each of four nested and non-nested replicates in each plot, and deviations of the predicted values from the actual 400m2 richness were calculated. In the scatter plots of predicted versus observed richness values, the result from each set of richness data in a plot is individually depicted (resulting in 873 x 4 = 3492 points per scatter plot) for data from both non-nested and nested designs (a and b, respectively, in Figures 3-4).

Rank-sum tests

Within each plot, we obtained 8 extrapolated estimates of 400 m2 richness, 4 from nested data and 4 from non-nested data. To determine the extent to which deviations of these estimates from the observed 400m2 richness differed for the two inventory designs, we devised a rank-sum test. The absolute deviations of the 400m2 richness predictions from the actual 400m2 richness values for the eight replicates (4 nested and 4 non-nested) were ranked within each of the 873 plots (lowest deviation=1, highest=8). For each plot, the four ranks for the nested data were summed; the four ranks for the non-nested data were also summed, yielding 873 rank sums for both nested and non-nested sampling designs (minimum rank-sum = 10, maximum rank-sum = 26). The frequency distributions of rank sums for each sampling design were compared with a null distribution for the rank sums to determine which sampling design better predicted 400m2 richness under each model (c in Figures 3-4). The null distribution is the distribution obtained if nested and non-nested replicates are equally (in)accurate in estimating richness. If so, then the assignment of ranks to the two kinds of replicates should be independent of their classification. In particular, the ranks of the nested (or non-nested) data sets for each plot will be a random sample (without replacement) of size 4 from the set of numbers 1, 2, 3, 4, 5, 6, 7, 8, assuming no ties. The rank sums of all such samples were computed. The frequency distribution of these sums yields the null distribution of no difference against which the rank-sums from the two inventory designs could be compared.

Results

When species-accumulation data were collected using the non-nested inventory design, the Arrhenius model provided a slightly better average fit (R2 = 0.957) than did the Gleason model (R2 = 0.939) (Table 1). However, the non-nested data used with the Arrhenius model consistently over-predicted 400m2 richness, yielding the highest averages for both absolute and actual deviations of predicted from observed values of any design-model combination (Figure 4b, Table 1). Non-nested predictions of 400m2 richness improved with the Gleason model, however, but with a shift to consistent under-prediction (Figure 3b, Table 1). When species-accumulation data were collected using the nested inventory design, the Arrhenius model also provided a better average fit (R2 = 0.963) than did the Gleason model (R2 = 0.916) (Table 1). With the Arrhenius model, the nested data tended to slightly over-predict 400m2 richness (Figure 4a, Table 1); with the Gleason model, the nested data substantially under-predicted 400m2 richness, and both absolute and actual deviations of predicted from observed values increased (Figure 3a, Table 1). Of the four design-model combinations examined, the nested design used with the Arrhenius model provided the best average model fit (R2 = 0.963), and the smallest average actual deviation of predicted from observed 400 m2 richness (7.720 species). However, the non-nested design used with the Gleason model provided the lowest average absolute deviation of predicted from observed 400m2 richness (11.188 species). The rank-sum test indicated superiority of the non-nested design when used with the Gleason model (Figure 3c), but superiority of the nested design when used with the Arrhenius model (Figure 4c).

Discussion

Choosing an appropriate inventory design for multi-scale sampling involves many decisions, some of which can be evaluated empirically; other decisions must weigh the merits of various conceptual issues. Our empirical analyses provide insights into the difficulties inherent in comparing inventory designs, while offering some conclusive outcomes. We followed the lead of Stohlgren et al. (1995) in using goodness-of-fit of common models to the species-accumulation relationship as one basis for discriminating among inventory designs. Average coefficients of determination were in excess of 0.9 for both Gleason and Arrhenius models applied to nested and non-nested data. The high coefficients of determination are not surprising, given that we were fitting two-parameter models to only four data points. However, we did find a small advantage to using the Arrhenius model. In their comparison of nested and non-nested designs, Stohlgren et al. (1995) found that data from the non-nested design produced models with higher coefficients of determination. Had we used only the Gleason model, as did Stohlgren et al. (1995), we would have arrived at the same conclusion – the average coefficient of determination for the non-nested-Gleason combination (0.939) exceeded that for the nested-Gleason combination (0.916). However, the nested-Arrhenius combination produced a slightly higher coefficient of determination (0.963) than did the non-nested-Arrhenius combination (0.957). Based solely on coefficients of determination, then, we would prefer the nested-Arrhenius combination of inventory design and model form.

Like Stohlgren et al. (1995), we also evaluated inventory designs by extrapolating species-accumulation curves to predict species richness at the scale of the larger plot within which our subplots were nested. These analyses revealed an interaction between the model used and the predictive ability of species-accumulation curves fit to data derived from the two sampling designs. The non-nested design outperformed the nested design when the Gleason model was used, as evidenced by lower average deviations of predicted from observed values of 400m2 richness and the superior performance of non-nested data in the rank-sum test. Had we only examined the Gleason model, we would have concluded, as did Stohlgren et al. (1995), that the data collected using a non-nested design resulted in better extrapolation. In our analyses, however, the nested design outperformed the non-nested design when the Arrhenius model was used, as evidenced by lower average deviations of predicted from observed values of 400m2 richness and the superior performance of nested data in the rank-sum test. From these results, it is difficult to identify a combination of inventory design and model that is clearly superior. However, given the slightly better fit of the Arrhenius model to data collected using both nested and non-nested inventory designs, plus other recent results demonstrating the superiority of the Arrhenius model for fitting small-scale species-area relationships (Fridley et al., unpublished), use of this model is better supported. With the Arrhenius model, data collected using the nested inventory design resulted in better prediction of species richness at the 400m2 scale.

While our empirical analyses provide support for use of the nested sampling design, there are also conceptual reasons for choosing this design. The majority of conceptual issues reviewed earlier in this paper would lead one to adopt a nested design. Among these issues, we feel that the following is of particular significance: the nested design is generally more appropriate if the goal is to assess changes in species richness with changing grain size of observation, because the non-nested design confounds the influence of grain with that of extent, making the search for mechanisms controlling richness difficult. The nested design, in contrast, minimizes the confounding of scale and extent. Prediction of species richness at larger scales using data from smaller subplots is inherently a “nested” approach, so a nested design is preferred for this purpose to maintain model consistency. Data collected using a non-nested design cover greater areal extent and are therefore prone to over-predict richness in larger areas within which they are inherently nested. This hypothesized expectation was reflected in our analyses, in which the non-nested data led to consistent over-prediction of 400m2 richness, when fitted with the Arrhenius model.

Selection of a design for multi-scale inventory of species richness should involve consideration of both conceptual/practical issues and empirical evaluation of data collected using both nested and non-nested approaches. The preponderance of conceptual and practical considerations argues for adoption of a nested approach. If the goal is to predict species richness for a larger area using subsampled areas, our empirical results also show that a nested sampling design is more appropriate. We agree with Stohlgren et al. (1995) that the Whittaker plant diversity sampling method (Shmida 1984) could be improved by adopting a consistent subplot shape and dispersing the subplots throughout the larger plot. The sampling design utilized by the Carolina Vegetation Survey (Peet et al. 1998) incorporates these improvements by using a consistent and compact square subplot shape, dispersed throughout the 400m2 subsampled area. However, we disagree with the conclusion of Stohlgren et al. (1995) that nesting of subplots in multi-scale inventories is undesirable. Indeed, we find multiple conceptual, practical, and empirical advantages to incorporating a nested approach for inventory of vegetation composition and richness at multiple scales. The Carolina Vegetation Inventory design thus retains the inherently nested approach originally promoted by Whittaker (Shmida 1984), while incorporating several important enhancements.

Literature Cited

Arrhenius, O. 1921. Species and area. Journal of Ecology 9:95-99.

Barnett, D.T. & T.J. Stohlgren. 2003. A nested-intensity design for surveying plant diversity. Biodiversity and Conservation 12:255-278.

Chase, J.M. and Liebold, M.A. 2002. Spatial scale dictates the productivity-biodiversity relationship. Nature 416: 427-430.

Fridley, J.D. 2001. The influence of species diversity on ecosystem productivity: how, where, and why? Oikos 93:514-526.

Fridley, J.D., R.K. Peet, T.R. Wentworth, and P.S. White. Connecting fine- and broad-scale patterns of species diversity: Species-area relationships of southeastern U.S. flora.

Gleason, H.A. 1922. On the relation between species and area. Ecology 3:158-162.

Gleason, H.A. 1925. Species and area. Ecology 6:66-74.

Grace, J.B. 1999. The factors controlling species density in herbaceous plant communities: an assessment. Perspectives in Plant Ecology, Evolution and Systematics 2: 1-28.

He, F. & P. Legendre. 1996. On species-area relations. American Naturalist 148:719-737.

Huston, M.A. 1979. A general hypothesis of species diversity. American Naturalist 113: 81-102.

Huston, M.A. 1994. Biological diversity: the coexistence of species on changing landscapes. Cambridge University Press, Cambridge, U.K.

Loreau, M., Naeem, S., Inchausti, P., Bengtsson, J., Grime, J.P., Hector, A., Hooper, D.U., Huston, M.A., Raffaelli, D., Schmid, B., Tilman, D., and Wardle, D.A. 2001. Biodiversity and ecosystem functioning: current knowledge and future challenges. Science 294: 804-808.

Palmer, M. & P.S. White. 1994. Scale dependence and the species-area relationship. American Naturalist 144:717-740.

Peet, R.K., T.R. Wentworth, & P.S. White. 1998. A flexible, multipurpose method for recording vegetation composition and structure. Castanea 63:262-274.

Rosenzweig, M.L. 1995. Species diversity in space and time. Cambridge University Press. Cambridge, UK.

Shmida, A. 1984. Whittaker’s plant diversity sampling method. Israel Journal of Botany 33:41-46.

Stohlgren, T.J., M.B. Falkner, & L.D. Schell. 1995. A modified-Whittaker nested vegetation sampling method. Vegetatio 117:113-121.

Rosenzweig, M.L. 1995. Species diversity in space and time. Cambridge University Press, Cambridge.

Williams, C.B. 1964. Patterns in the balance of nature. Academic Press, London.

Williamson, M. 2003. Species-area relationships at small scales in continuum vegetation. Journal of Ecology 91: 904-907.

Acknowledgments

We greatly appreciate the thorough and insightful assistance of Jack Weiss regarding data analysis. Members of the Plant Ecology Lab at University of North Carolina - Chapel Hill provided valuable feedback and discussion during the development of this project. We are also indebted to the countless volunteers who contributed time, effort, and expertise to the Carolina Vegetation Survey. We appreciate permission to use data from the Carolina Vegetation Survey plot database. This paper is based upon work supported by the National Science Foundation under Grant Nos. DBI-9905838 and DBI-0213794.

Figure Legends [RKP: These still need to be fleshed out just a little]

Figure 1. Plot layout for data collected by the Carolina Vegetation Survey.

Figures 2a-b. Model fitting of four replicates of nested data for one plot representing median richness in the Carolina Vegetation Survey data set. The species-accumulation curves were fit with Gleason (a) and Arrhenius (b) models.

Figures 3a-c. Predicted vs. actual richness values under the Gleason model for SPACCs at 400m2 (a: nested data; b: non-nested data) and rank sum distribution (c).

Figures 4a-c. Predicted vs. actual richness values under the Arrhenius model for SPACCs at 400m2 (a: nested data; b: non-nested data) and rank sum distribution (c).

Table Legend

Table 1. Average R2, average predicted richness at 400m2, average of the actual deviation and average of the absolute value of the deviation of the predicted from actual richness at 400m2 for each model applied to data from both nested and non-nested sampling designs.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download