Nested versus non-nested characterization of vegetation composition and species richness
at multiple spatial scales
Thomas R. Wentworth1
Peter S. White2
Brooke E. Wheeler2
Kristin Taverna2
Dane Kuppinger2
Lee Anne Jacobs2
Jason D. Fridley2
Jack Weiss2 ??
Robert K. Peet2
1
Department of Botany
Campus Box 7612
North Carolina State University
Raleigh, NC 27695-7612 USA
2
Department of Biology
CB#3280, Coker Hall
University of North Carolina
Chapel Hill, NC 27599-3280 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.
The fundamental difference between these designs is in how they are influenced by spatial
autocorrelation and in how well they allow characterization of change in vegetation structure
with change in grain of observation. We compared nested and non-nested designs for
characterizing species richness (using species-accumulation curves) of vascular plants using data
collected by the Carolina Vegetation Survey in 873 0.04 ha plots. Our objectives were to
compare exponential (Gleason) and power-function (Arrhenius) models for fitting speciesaccumulation curves and to determine which design allowed more effective extrapolation of the
species-accumulation relationship to larger spatial extent. The arithmetic-Arrhenius model
provided the best fit and most closely predicted 400m2 richness for both sampling designs. With
the arithmetic-Arrhenius model, the average deviation of predicted 400 m2 richness values using
the nested design was near zero, while the average deviation using the non-nested design was
positive, suggesting a consistent over-prediction of 400m2 richness for the non-nested design.
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. From a
conceptual perspective, the non-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.
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 species richness patterns 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, some of
which may be more suited to particular research questions, (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 area inventoried is fully enclosed within the next larger area; in a non-nested design areas of
different sizes are inventoried independently of one another. There is no consensus as to the
circumstances under which nested versus non-nested multi-scalar 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. [Here we need brief mention of
why Stohlgren chose the non-nested approach.] Researchers ofhe Carolina Vegetation Survey
(Peet et al. 1998) have advocated use of a nested design, also using 0.1 ha plots. 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 counterarguments favoring the nested approach, there is a pressing need for an empirical evaluation of
the effectiveness of nested versus non-nested designs in characterizing species richness patterns.
Beyond the issue of nested versus non-nested subplot arrangement, there is a secondary problem
of the appropriate model for fitting species-area relationships obtained using either design. It
may be that both nested and non-nested subplot arrangements are appropriate methods for
characterizing species-richness patterns, but their efficacy must be evaluated by application of
different models. Such model-fitting has a long history, 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. While the Gleason model is
appropriately fit using simple linear regression, two alternatives exist for fitting the Arrhenius
model. 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 simple linear regression.
However, Wright (1981) recommended using non-linear regression techniques to estimate the
parameters of the Arrhenius model in its non-linear form, S = cAz. We chose to compare the
results using both linear regression (referred to hereafter as the log-Arrhenius model) and nonlinear regression (referred to hereafter as the arithmetic-Arrhenius model). Of the three, the logArrhenius model is the most difficult to apply to small-scale data due to the prevalence of zero
richness values at the smallest scales. [This might be our first major decision in translating the
poster to manuscript form: how much do we want to focus on the issue of log- vs. non-log
Arrhenius? The point has been made before (haven’t read the Wright paper, but Rosenzweig
1995 discusses this a bit); is this analysis essential to our argument? Should we just pick one?
Also, how much model-fitting redundancy should we have with the fine-scale sparcs paper? I am
more worried about the issue of redundancy with the SPACS paper. A case could be made for
omitting this stuff her, assuming the SPARCS paper will be submitted at nearly the same time. I
rather like the one paper – one idea approach here. Perhaps we could simply reference the
SPARCS paper in place of repeating it here.]
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 nonnested 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. However, it can be shown that the SPARCs
developed by averaging both nested and non-nested sets of data collected from within the same
larger area are expected to be identical; efforts to compare them would thus be uninteresting.
[But the issue of replication is an important one; although mean values of subplot richness
should be the same, CVS design allows for several semi-independent estimates of small-scale
species-area curves; this is not as easily achieved with non-nested data because you’d have to
“jump around” in space to construct replicate curves. Yup] However, SPACCs developed from
nested and non-nested data collected from within the same larger area may be different, and this
paper focuses exclusively on comparison of species-area relationships described by SPACCs.
Because SPACCs developed from non-nested data encompass greater spatial extent than those
developed from nested data, the cumulative species list will generally be greater than the
corresponding list developed from nested data. [This assumes that, unlike our comparisons
below, nested and non-nested approaches are not both nested within the representative largest
area (ie, 0.1 ha plot). In Gleason and Rosenzweig’s examples of SPACCs with nested and nonnested data, the ends of the curves are fixed, and the shape of the non-nested curve is convex.]
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). We compared SPACCs developed from nested data with SPACCs
developed from non-nested data to evaluate the following questions. (1) For both nested and
non-nested designs, which model provides the best fit to the species richness-area relationship?
(2) Does one design result in consistently better model fitting? (3) Do nested or non-nested
subplot designs provide more accurate predictions of richness at larger scales? [Given the much
larger-scale focus of our other paper, perhaps we should be more specific with our “projecting
upward” analysis to relatively small scales, say within a community? Yup]
[The major component missing from this current introduction is the rationale for choosing nested
vs. non-nested designs in the first place, without regard to model fitting. What did we know
about nested vs. non-nested techniques BEFORE our analysis? How does then our analysis
change what we thought we knew (or does it)? We at least knew that: 1) nested samples are
generally logistically easier to perform, more efficient use of field time; 2) nested samples are
most appropriate for concerns over confounding grain and extent; 3) nested samples are more
mathematically desirable because they are strictly monotonic; 4) non-nested samples are often
thought to be more statistically desirable because richness values of different quadrats are more
statistically independent; 5) extrapolation of small-scale data to larger-scales is ALWAYS
performed in a nested framework, so nested designs at small scales are methodologically
consistent with larger-scale curves; 6) given equal sampling time, non-nested quadrats will
almost always find more species because they can cover a greater spatial extent. So the question
becomes how model fitting procedures add to this previous perspective (and perhaps more
rigorous shore-up some of our preconceived notions, or perhaps even change some). We also
need some rationale for our stated 3 goals: why is prediction of richness at larger scales
important? Why is it necessary to have a consistent model for fine-scale sparcs?]
[I agree with Jason’s concerns expressed in the previous paragraph. Note, however, that to
address them would add length to an already much, much too long introduction. This leads me
to think we need a structural change in the paper. We should have a short intro that is at most 2
paragraphs long where we explain the need for an analysis of the conceptual merits and
advantages of both methods, and the need to empirically test model fits. This should be followed
by a section on theory and logic, wherein Jason’s points are addressed. Then we move on to the
empirical section wherein we start with methods.]
Methods
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) [wanna use the figure from the other
paper, or a subset of it? – issue?]. 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 richness values 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 quadrat (cf.
Williamson 2003) The four 10x10m modules were nested within larger 1000m2 plots, but we
focus on the contiguous block of 10x10m modules, with a combined area of 400m2. Four
separate sets of nested richness values were generated for each plot using values collected within
each of the four 10x10m modules. Four separate sets of non-nested richness values 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 values 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.
Gleason and Arrhenius models were fit to each of the four nested and four non-nested sets of
richness data in each plot; we fit the Arrhenius model using both linear (log-Arrhenius) and
nonlinear (arithmetic-Arrhenius) regression. [Here I wonder if we should say we fit both
untransformed and log-transformed Arrhenius models but got consistently better fits for the
untransformed, and omit all subsequent discussion of log-Arr? – I like this idea] We will
subsequently refer to each of these three approaches to curve-fitting as a separate “model.”[I
guess I prefer two models only. Me too] Figures 2a-c illustrate our curve-fitting procedure for
nested data from one plot representing median richness from the Carolina Vegetation Survey
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 values is individually depicted (resulting in
873x4 points per scatter plot) for data from both non-nested and nested designs (a and b,
respectively, in Figures 3-5).
[Could use brief rationale for the following here.] The absolute deviations of the 400m2 richness
predictions from the actual 400m2 richness values for the eight replicates (four nested and four
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. 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 3-5). 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 what we call the null distribution of no difference between the sampling designs. in
what…
[probably don’t need to mention this in Methods, just results – I think I agree]
Results
[This focuses immediately on functions rather than nested or non-nested; is this too close to the
other paper? – I think it is too close] Of the models investigated, the arithmetic-Arrhenius had
the highest average R2 values and the lowest average absolute deviations from actual richness for
both nested and non-nested sampling designs (Table 1). The Gleason model generally underpredicted species richness for both sampling designs (Fig. 3a,b; actual deviations in Table 1). In
the rank sum distribution (Fig. 3c), the non-nested distribution fell to the left of the null
distribution, showing that the Gleason model applied to non-nested data better predicted 400m2richness, and both absolute and actual deviations for the Gleason model applied to non-nested
data were less than those for nested data (Table 1). The log-Arrhenius model generally over
predicted species richness for both sampling designs (Fig. 4a,b; actual deviations in Table 1). In
the rank sum distribution (Fig. 4c), the nested distribution fell to the left of the null distribution,
showing that the log-Arrhenius model applied to nested data better predicted 400m2-richness,
and both absolute and actual deviations for the Gleason model applied to nested data were less
than those for non-nested data (Table 1). The arithmetic-Arrhenius model predicted species
richness well for both sampling designs (Fig. 5a,b; actual deviations in Table 1). The rank sum
distribution for both designs closely approximated the null distribution (Fig. 5c), suggesting no
advantage for either design, and absolute deviations were also similar for both designs (Table 1).
However, the arithmetic-Arrhenius model applied to data from the nested design had a lower
average actual deviation than the same model applied to data from the non-nested design,
suggesting greater accuracy of the nested approach (Table 1). [Need to add in tests of
significance. I also am still a little concerned about the mixing of choosing models (GvsA)
versus choosing designs (NvsNN). The reader might be pretty confused at this point. I agree ]
Discussion
[Again, better to start with NvsNN rather than model choice?] Choice of an appropriate model
for fitting the relationship of species richness to area must be made prior to the realization of
other objectives, such as estimation of the slope parameter, extrapolation of species-area or
species-accumulation curves to larger spatial scales, etc. Our analyses of Carolina Vegetation
Survey data at four spatial scales revealed differences in the goodness-of-fit of the three models
we evaluated, with some advantage to using the arithmetic-Arrhenius model. These analyses
also revealed an interaction between the model used and the predictive ability of speciesaccumulation curves fit to data derived from both nested and non-nested sampling designs. Of
the three models tested, the Gleason model provided the poorest fit and consistently underpredicted 400m2 richness for both sampling designs, but it more closely predicted 400m2
richness when applied to data collected using the non-nested design. The log-Arrhenius model
provided a better fit than did the Gleason model. This model consistently over-predicted 400m2
richness for both sampling designs, but it more closely predicted 400m2 richness when applied to
data collected using the nested design. However, the arithmetic-Arrhenius model provided the
best fit and most closely predicted 400m2 richness for both sampling designs.
Since publication of Gleason’s seminal work in 1922 (1925 more general treatment?), other
authors have suggested that the Gleason model is most appropriate for fitting the relationship of
species richness to increasing spatial scale when the maximum spatial scale is small (e.g.,
Rosenzweig 1995, He and Legendre 1996), as was the case in our study [much overlap with
other paper here]. Some investigators, such as Stohlgren et al. (1995), have thus adopted the
Gleason model without consideration of alternatives, such as the Arrhenius models evaluated in
the present study. Although average coefficients of determination were in excess of 0.9 for all
models applied to both nested and non-nested data in the present study, we found a general
advantage to using the Arrhenius models, with slightly better performance from the arithmeticArrhenius 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 and better performance in extrapolating species richness to a larger scale. Had we
used only the Gleason model, as did Stohlgren et al., we would have arrived at the same
conclusion. However, the higher coefficients of determination encountered when using the
arithmetic-Arrhenius model led us to adopt this model for further evaluation of the two sampling
designs. [Because Stohlgren’s 1995 analysis was so fishy anyway, one wonders whether he
would have got our answer if he did the analysis right. Should we point out the problems in his
analysis here? Probably – let’s try it pout and see how it reads Also, a critic might point out
that, if Gleason curves point to the superiority of non-nested designs as Stohlgren argued, and the
difference in GvsA model fitting is an R2 difference less than 5%, perhaps non-nested designs
are just as legit as nested designs. This might argue against focusing on model-fitting as the
most important criterion for choosing nested vs. non-nested designs—I worry about this
especially since we’re fitting models to only 4 data points! Bubt we have lots of replicates]
Like Stohlgren et al. (1995), we compared capability of models based on data from nested and
non-nested designs to predict species richness at a larger scale. While the rank sum analysis
suggested advantages of using non-nested data with the Gleason model and nested data with the
log-Arrhenius model, this analysis provided little guidance in evaluating the two sampling
designs using the arithmetic-Arrhenius model, as rank sums from both designs closely
approximated the null distribution. [again, the impression is that the NvsNN decision is not that
important, IF the model fitting/extrapolation criterion is most important] With the log-Arrhenius
model, the average deviations of predicted from actual 400m2 richness values were also nearly
identical for both designs when the absolute value of the deviation was used. However, when the
sign of the deviation was taken into account (actual deviations in Table 1), the average deviations
were different for the two designs. The average actual deviation for the non-nested design was
positive, suggesting a small but consistent over-prediction of 400m2 richness, while that for the
nested design was close to zero, indicating little bias. We suggest that this less biased
distribution supports using a nested design with an arithmetic-Arrhenius model for predictive
purposes.
While our empirical analyses provide support for use of the nested sampling design, there are
also conceptual reasons for choosing this design. 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 expectation was reflected in our analyses, in which
the non-nested data led to average actual deviations higher than those for nested data, regardless
of the model chosen for curve-fitting (Table 1). While nested data showed no tendency to underor over-predict larger-scale richness when used with the arithmetic-Arrhenius model (average
actual deviation close to zero in Table 1), the non-nested data still showed some tendency toward
over-prediction. [the arguments for and against NvsNN would be nicely displayed in a table]
We find other advantages to using a nested inventory design for collection of species richness
data at multiple spatial scales. Only nested subplots allow for a meaningful way to obtain
multiple sets of fine-scale species-area or species-accumulation relationships within a larger area,
because nested subplots can sample a restricted areal extent. Although either design can be used
to examine species-area or species-accumulation relationships, the nested design constrains the
result to the desired monotonic response for each replicate. For some objectives, a nested
sampling design may not be the most appropriate. 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.
Researchers concerned with inventory of species richness at multiple scales must consider an
array of different options available to them. Among these are the particular scales selected for
inventory, the criteria used to score a species’ presence within a subplot representing a particular
spatial scale; the use of nested versus non-nested inventory designs; the ultimate nesting of a
particular set of subplots within a larger inventory area; whether or not multiple sets of subplots
will be established within a larger inventory area; and the replication of the larger inventory
areas themselves. Other options include the choice among various models that might be used to
fit the relationship of species richness and spatial scale. Researchers must also decide whether
they wish to portray species-area or species-accumulation relationships. If the goal is to predict
species richness for a larger area using subsampled areas, our results also show that a nested
sampling design is more appropriate. [I don’t like this final paragraph. We don’t need the long
fist portion of the paragraph to support the straight-forward final sentence. So as to keep the
ending pithy, perhaps break off the final sentence as a separate paragraph, but with one or two
sentences added at its beginning.
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.
Gleason, H.A. 1922. On the relation between species and area. Ecology 3:158-162.
He, F. & P. Legendre. 1996. On species-area relations. American Naturalist 148:719-737.
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.
Stohlgren, T.J., M.B. Falkner, & L.D. Schell. 1995. A modified-Whittaker nested vegetation
sampling method. Vegetatio 117:113-121.
Wright, S.J. 1981. Intra-archipelago vertebrate distributions: the slope of the species-area
relation. American Naturalist 118:726-748. (not yet seen by TRW)
Acknowledgments
We greatly appreciate the thorough and insightful assistance of Jack Weiss regarding data
analysis. Members of the Plant Ecology Lab at UNC 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 [These need to be fleshed out just a little]
Figure 1. Plot layout for data collected by the Carolina Vegetation Survey.
Figures 2a-c. Model fitting of four replicates (color-coded) of nested data for one plot
representing median richness in the Carolina Vegetation Survey data set. The SPACCs were fit
with Gleason (a), log-Arrhenius (b), and arithmetic-Arrhenius (c) models.
Figures 3a-c. Predicted vs. actual richness values under the Gleason model for SPACCs at
400m2 (a,b) and rank sum distribution (c).
Figures 4a-c. Predicted vs. actual richness values under the log-Arrhenius model for SPACCs at
400m2 (a,b) and rank sum distribution (c).
Figures 5a-c. Predicted vs. actual richness values under the arithmetic-Arrhenius model for
SPACCs at 400 m2 (a,b) 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.