specaccum: Species Accumulation Curves
In vegan: Community Ecology Package
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Function specaccum finds species accumulation curves or the
number of species for a certain number of sampled sites or
individuals.
Usage
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specaccum(comm, method = "exact", permutations = 100,
conditioned =TRUE, gamma = "jack1", w = NULL, subset, ...)
## S3 method for class 'specaccum'
plot(x, add = FALSE, random = FALSE, ci = 2,
ci.type = c("bar", "line", "polygon"), col = par("fg"), ci.col = col,
ci.lty = 1, xlab, ylab = x$method, ylim,
xvar = c("sites", "individuals", "effort"), ...)
## S3 method for class 'specaccum'
boxplot(x, add = FALSE, ...)
fitspecaccum(object, model, method = "random", ...)
## S3 method for class 'fitspecaccum'
plot(x, col = par("fg"), lty = 1, xlab = "Sites",
ylab = x$method, ...)
## S3 method for class 'specaccum'
predict(object, newdata, interpolation = c("linear", "spline"), ...)
## S3 method for class 'fitspecaccum'
predict(object, newdata, ...)
specslope(object, at)
Arguments
comm
Community data set.
method
Species accumulation method (partial match). Method
"collector"
adds sites in the order they happen to be in the data,
"random" adds sites in random order, "exact" finds the
expected (mean) species richness, "coleman" finds the
expected richness following
Coleman et al. 1982, and "rarefaction" finds the mean when
accumulating individuals instead of sites.
permutations
Number of permutations with method = "random".
Usually an integer giving the number permutations, but can also be a
list of control values for the permutations as returned by the
function how, or a permutation matrix where
each row gives the permuted indices.
conditioned
Estimation of standard deviation is conditional on
the empirical dataset for the exact SAC
gamma
Method for estimating the total extrapolated number of species in the
survey area by function specpool
w
Weights giving the sampling effort.
subset
logical expression indicating sites (rows) to keep: missing
values are taken as FALSE.
x
A specaccum result object
add
Add to an existing graph.
random
Draw each random simulation separately instead of
drawing their average and confidence intervals.
ci
Multiplier used to get confidence intervals from standard
deviation (standard error of the estimate). Value ci = 0
suppresses drawing confidence intervals.
ci.type
Type of confidence intervals in the graph: "bar"
draws vertical bars, "line" draws lines, and
"polygon" draws a shaded area.
col
Colour for drawing lines.
ci.col
Colour for drawing lines or filling the
"polygon".
ci.lty
Line type for confidence intervals or border of the
"polygon".
xlab,ylab
Labels for x (defaults xvar) and
y axis.
ylim
the y limits of the plot.
xvar
Variable used for the horizontal axis:
"individuals" can be used only with
method = "rarefaction".
object
Either a community data set or fitted specaccum model.
model
Nonlinear regression model (nls). See Details.
lty
line type code (see par.
newdata
Optional data used in prediction interpreted as
number of sampling units (sites). If missing, fitted values are
returned.
interpolation
Interpolation method used with newdata.
at
Number of plots where the slope is evaluated. Can be a
real number.
...
Other parameters to functions.
Details
Species accumulation curves (SAC) are used to compare diversity
properties of community data sets using different accumulator
functions. The classic method is "random" which finds the mean
SAC and its standard deviation from random permutations of the data,
or subsampling without replacement (Gotelli & Colwell 2001). The
"exact" method finds the expected SAC using sample-based
rarefaction method that has been independently developed numerous
times (Chiarucci et al. 2008) and it is often known as Mao Tau
estimate (Colwell et al. 2012). The unconditional standard deviation
for the exact SAC represents a moment-based estimation that is not
conditioned on the empirical data set (sd for all samples > 0). The
unconditional standard deviation is based on an estimation of the
extrapolated number of species in the survey area (a.k.a. gamma
diversity), as estimated by function specpool. The
conditional standard deviation that was developed by Jari Oksanen (not
published, sd=0 for all samples). Method "coleman" finds the
expected SAC and its standard deviation following Coleman et
al. (1982). All these methods are based on sampling sites without
replacement. In contrast, the method = "rarefaction" finds the
expected species richness and its standard deviation by sampling
individuals instead of sites. It achieves this by applying function
rarefy with number of individuals corresponding to
average number of individuals per site.
Methods "random" and "collector" can take weights
(w) that give the sampling effort for each site. The weights
w do not influence the order the sites are accumulated, but
only the value of the sampling effort so that not all sites are
equal. The summary results are expressed against sites even when the
accumulation uses weights (methods "random",
"collector"), or is based on individuals
("rarefaction"). The actual sampling effort is given as item
Effort or Individuals in the printed result. For
weighted "random" method the effort refers to the average
effort per site, or sum of weights per number of sites. With
weighted method = "random", the averaged species richness is
found from linear interpolation of single random permutations.
Therefore at least the first value (and often several first) have
NA richness, because these values cannot be interpolated in
all cases but should be extrapolated. The plot function
defaults to display the results as scaled to sites, but this can be
changed selecting xvar = "effort" (weighted methods) or
xvar = "individuals" (with method = "rarefaction").
The summary and boxplot methods are available for
method = "random".
Function predict for specaccum can return the values
corresponding to newdata. With method "exact",
"rarefaction" and "coleman" the function uses analytic
equations for interpolated non-integer values, and for other methods
linear (approx) or spline (spline)
interpolation. If newdata is not given, the function returns
the values corresponding to the data. NB., the fitted values with
method="rarefaction" are based on rounded integer counts, but
predict can use fractional non-integer counts with
newdata and give slightly different results.
Function fitspecaccum fits a nonlinear (nls)
self-starting species accumulation model. The input object
can be a result of specaccum or a community in data frame. In
the latter case the function first fits a specaccum model and
then proceeds with fitting the a nonlinear model. The function can
apply a limited set of nonlinear regression models suggested for
species-area relationship (Dengler 2009). All these are
selfStart models. The permissible alternatives are
"arrhenius" (SSarrhenius), "gleason"
(SSgleason), "gitay" (SSgitay),
"lomolino" (SSlomolino) of vegan
package. In addition the following standard R models are available:
"asymp" (SSasymp), "gompertz"
(SSgompertz), "michaelis-menten")
(SSmicmen), "logis" (SSlogis),
"weibull" (SSweibull). See these functions for
model specification and details.
When weights w were used the fit is based on accumulated
effort and in model = "rarefaction" on accumulated number of
individuals. The plot is still based on sites, unless other
alternative is selected with xvar.
Function predict for fitspecaccum uses
predict.nls, and you can pass all arguments to that
function. In addition, fitted, residuals and
coef, AIC and deviance work on the result
object.
Function specslope evaluates the derivative of the species
accumulation curve at given number of sample plots, and gives the
rate of increase in the number of species. The function works with
specaccum result object when this is based on analytic models
"exact", "rarefaction" or "coleman", and with
non-linear regression results of fitspecaccum.
Nonlinear regression may fail for any reason, and some of the
fitspecaccum models are fragile and may not succeed.
Value
Function specaccum returns an object of class
"specaccum", and fitspecaccum a model of class
"fitspecaccum" that adds a few items to the
"specaccum" (see the end of the list below):
call
Function call.
method
Accumulator method.
sites
Number of sites. For method = "rarefaction" this
is the number of sites corresponding to a certain number of
individuals and generally not an integer, and the average
number of individuals is also returned in item individuals.
effort
Average sum of weights corresponding to the number of
sites when model was fitted with argument w
richness
The number of species corresponding to number of
sites. With method = "collector" this is the observed
richness, for other methods the average or expected richness.
sd
The standard deviation of SAC (or its standard error). This
is NULL in method = "collector", and it
is estimated from permutations in method = "random", and from
analytic equations in other methods.
perm
Permutation results with method = "random" and
NULL in other cases. Each column in perm holds one
permutation.
weights
Matrix of accumulated weights corresponding to the
columns of the perm matrix when model was fitted with
argument w.
fitted, residuals, coefficients
Only in fitspecacum:
fitted values, residuals and nonlinear model coefficients. For
method = "random" these are matrices with a column for
each random accumulation.
models
Only in fitspecaccum: list of fitted
nls models (see Examples on accessing these models).
Note
The SAC with method = "exact" was
developed by Roeland Kindt, and its standard deviation by Jari
Oksanen (both are unpublished). The method = "coleman"
underestimates the SAC because it does not handle properly sampling
without replacement. Further, its standard deviation does not take
into account species correlations, and is generally too low.
Author(s)
Roeland Kindt r.kindt@cgiar.org and Jari Oksanen.
References
Chiarucci, A., Bacaro, G., Rocchini, D. & Fattorini,
L. (2008). Discovering and rediscovering the sample-based rarefaction
formula in the ecological literature. Commun. Ecol. 9:
121–123.
Coleman, B.D, Mares, M.A., Willis, M.R. & Hsieh,
Y. (1982). Randomness, area and species richness. Ecology 63:
1121–1133.
Colwell, R.K., Chao, A., Gotelli, N.J., Lin, S.Y., Mao, C.X., Chazdon,
R.L. & Longino, J.T. (2012). Models and estimators linking
individual-based and sample-based rarefaction, extrapolation and
comparison of assemblages. J. Plant Ecol. 5: 3–21.
Dengler, J. (2009). Which function describes the species-area
relationship best? A review and empirical evaluation.
Journal of Biogeography 36, 728–744.
Gotelli, N.J. & Colwell, R.K. (2001). Quantifying biodiversity:
procedures and pitfalls in measurement and comparison of species
richness. Ecol. Lett. 4, 379–391.
See Also
rarefy and rrarefy are related
individual based models. Other accumulation models are
poolaccum for extrapolated richness, and
renyiaccum and tsallisaccum for
diversity indices. Underlying graphical functions are
boxplot, matlines,
segments and polygon.
Examples
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data(BCI)
sp1 <- specaccum(BCI)
sp2 <- specaccum(BCI, "random")
sp2
summary(sp2)
plot(sp1, ci.type="poly", col="blue", lwd=2, ci.lty=0, ci.col="lightblue")
boxplot(sp2, col="yellow", add=TRUE, pch="+")
## Fit Lomolino model to the exact accumulation
mod1 <- fitspecaccum(sp1, "lomolino")
coef(mod1)
fitted(mod1)
plot(sp1)
## Add Lomolino model using argument 'add'
plot(mod1, add = TRUE, col=2, lwd=2)
## Fit Arrhenius models to all random accumulations
mods <- fitspecaccum(sp2, "arrh")
plot(mods, col="hotpink")
boxplot(sp2, col = "yellow", border = "blue", lty=1, cex=0.3, add= TRUE)
## Use nls() methods to the list of models
sapply(mods$models, AIC)
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3
Warning message:
In cor(x > 0) : the standard deviation is zero
Species Accumulation Curve
Accumulation method: random, with 100 permutations
Call: specaccum(comm = BCI, method = "random")
Sites 1.00000 2.00000 3.00000 4.00000 5.0000 6.00000 7.00000
Richness 90.97000 122.01000 139.03000 150.89000 159.4300 165.85000 171.27000
sd 7.14561 7.87593 7.29252 7.01642 6.2833 5.65931 5.22205
Sites 8.00000 9.00000 10.00000 11.00000 12.00000 13.00000 14.00000
Richness 175.53000 179.05000 182.45000 185.59000 187.76000 190.17000 192.33000
sd 5.13151 4.99975 4.79978 4.64518 4.55964 4.52837 4.46548
Sites 15.0000 16.00000 17.00000 18.00000 19.00000 20.00000 21.00000
Richness 194.2800 196.05000 197.90000 199.38000 201.01000 202.22000 203.50000
sd 4.4132 4.34468 4.24383 4.04215 3.89896 3.93785 3.93508
Sites 22.00000 23.00000 24.00000 25.00000 26.0000 27.00000 28.0000
Richness 204.88000 206.15000 207.36000 208.45000 209.3000 210.29000 211.1600
sd 3.76126 3.82014 3.78866 3.73456 3.7457 3.59656 3.4516
Sites 29.00000 30.00000 31.00000 32.00000 33.00000 34.00000 35.00000
Richness 212.08000 212.94000 213.90000 214.65000 215.35000 216.06000 216.77000
sd 3.45733 3.27778 3.13179 3.04304 3.00294 2.96041 2.93999
Sites 36.0000 37.00000 38.00000 39.00000 40.00000 41.00000 42.00000
Richness 217.3900 218.02000 218.80000 219.52000 220.12000 220.65000 221.13000
sd 2.7776 2.82478 2.60148 2.52054 2.33671 2.21736 2.02337
Sites 43.00000 44.00000 45.00000 46.00000 47.00000 48.00000 49.00000
Richness 221.65000 222.07000 222.55000 223.08000 223.62000 224.08000 224.52000
sd 1.81673 1.78238 1.53987 1.45422 1.27747 1.09802 0.74508
Sites 50
Richness 225
sd 0
1 sites 2 sites 3 sites 4 sites 5 sites
Min. : 77.00 Min. :103.0 Min. :119 Min. :132.0 Min. :144.0
1st Qu.: 85.00 1st Qu.:117.0 1st Qu.:134 1st Qu.:146.0 1st Qu.:156.0
Median : 91.00 Median :122.5 Median :139 Median :151.0 Median :160.0
Mean : 90.97 Mean :122.0 Mean :139 Mean :150.9 Mean :159.4
3rd Qu.: 97.25 3rd Qu.:127.0 3rd Qu.:145 3rd Qu.:156.2 3rd Qu.:164.0
Max. :109.00 Max. :144.0 Max. :154 Max. :164.0 Max. :171.0
6 sites 7 sites 8 sites 9 sites
Min. :150.0 Min. :159.0 Min. :162.0 Min. :165.0
1st Qu.:163.0 1st Qu.:168.0 1st Qu.:173.0 1st Qu.:176.8
Median :166.0 Median :171.0 Median :175.5 Median :179.0
Mean :165.8 Mean :171.3 Mean :175.5 Mean :179.1
3rd Qu.:170.0 3rd Qu.:175.0 3rd Qu.:179.0 3rd Qu.:182.2
Max. :178.0 Max. :184.0 Max. :186.0 Max. :190.0
10 sites 11 sites 12 sites 13 sites
Min. :168.0 Min. :172.0 Min. :175.0 Min. :178.0
1st Qu.:179.0 1st Qu.:182.0 1st Qu.:185.0 1st Qu.:187.0
Median :183.0 Median :186.0 Median :188.0 Median :190.0
Mean :182.4 Mean :185.6 Mean :187.8 Mean :190.2
3rd Qu.:186.0 3rd Qu.:189.0 3rd Qu.:191.0 3rd Qu.:193.0
Max. :192.0 Max. :195.0 Max. :197.0 Max. :200.0
14 sites 15 sites 16 sites 17 sites
Min. :180.0 Min. :182.0 Min. :184.0 Min. :187.0
1st Qu.:189.8 1st Qu.:191.8 1st Qu.:193.0 1st Qu.:195.0
Median :193.0 Median :195.0 Median :197.0 Median :198.0
Mean :192.3 Mean :194.3 Mean :196.1 Mean :197.9
3rd Qu.:195.2 3rd Qu.:197.0 3rd Qu.:199.0 3rd Qu.:201.0
Max. :204.0 Max. :206.0 Max. :208.0 Max. :209.0
18 sites 19 sites 20 sites 21 sites 22 sites
Min. :189.0 Min. :190 Min. :190.0 Min. :191.0 Min. :194.0
1st Qu.:197.0 1st Qu.:199 1st Qu.:200.0 1st Qu.:201.0 1st Qu.:202.8
Median :199.0 Median :201 Median :203.0 Median :204.0 Median :205.0
Mean :199.4 Mean :201 Mean :202.2 Mean :203.5 Mean :204.9
3rd Qu.:202.0 3rd Qu.:204 3rd Qu.:205.0 3rd Qu.:206.0 3rd Qu.:207.2
Max. :210.0 Max. :211 Max. :213.0 Max. :215.0 Max. :215.0
23 sites 24 sites 25 sites 26 sites
Min. :196.0 Min. :196.0 Min. :197.0 Min. :197.0
1st Qu.:204.0 1st Qu.:205.0 1st Qu.:207.0 1st Qu.:207.8
Median :207.0 Median :208.0 Median :209.0 Median :209.0
Mean :206.2 Mean :207.4 Mean :208.4 Mean :209.3
3rd Qu.:208.0 3rd Qu.:210.0 3rd Qu.:211.0 3rd Qu.:212.0
Max. :215.0 Max. :217.0 Max. :217.0 Max. :218.0
27 sites 28 sites 29 sites 30 sites
Min. :200.0 Min. :202.0 Min. :202.0 Min. :204.0
1st Qu.:208.0 1st Qu.:209.0 1st Qu.:210.0 1st Qu.:211.0
Median :210.0 Median :211.5 Median :212.5 Median :213.0
Mean :210.3 Mean :211.2 Mean :212.1 Mean :212.9
3rd Qu.:213.0 3rd Qu.:213.0 3rd Qu.:215.0 3rd Qu.:215.2
Max. :219.0 Max. :219.0 Max. :220.0 Max. :221.0
31 sites 32 sites 33 sites 34 sites
Min. :205.0 Min. :206.0 Min. :207.0 Min. :207.0
1st Qu.:212.0 1st Qu.:212.8 1st Qu.:213.0 1st Qu.:214.0
Median :214.0 Median :215.0 Median :215.0 Median :216.0
Mean :213.9 Mean :214.7 Mean :215.3 Mean :216.1
3rd Qu.:216.2 3rd Qu.:217.0 3rd Qu.:217.2 3rd Qu.:218.0
Max. :222.0 Max. :222.0 Max. :222.0 Max. :222.0
35 sites 36 sites 37 sites 38 sites 39 sites
Min. :207.0 Min. :208.0 Min. :208 Min. :209.0 Min. :211.0
1st Qu.:215.0 1st Qu.:216.0 1st Qu.:216 1st Qu.:217.0 1st Qu.:218.0
Median :216.0 Median :218.0 Median :218 Median :219.0 Median :220.0
Mean :216.8 Mean :217.4 Mean :218 Mean :218.8 Mean :219.5
3rd Qu.:219.0 3rd Qu.:219.0 3rd Qu.:220 3rd Qu.:221.0 3rd Qu.:221.0
Max. :222.0 Max. :222.0 Max. :223 Max. :223.0 Max. :224.0
40 sites 41 sites 42 sites 43 sites
Min. :214.0 Min. :215.0 Min. :216.0 Min. :217.0
1st Qu.:219.0 1st Qu.:219.0 1st Qu.:220.0 1st Qu.:220.0
Median :220.0 Median :221.0 Median :221.0 Median :222.0
Mean :220.1 Mean :220.7 Mean :221.1 Mean :221.7
3rd Qu.:222.0 3rd Qu.:222.0 3rd Qu.:223.0 3rd Qu.:223.0
Max. :224.0 Max. :225.0 Max. :225.0 Max. :225.0
44 sites 45 sites 46 sites 47 sites
Min. :217.0 Min. :218.0 Min. :220.0 Min. :220.0
1st Qu.:221.0 1st Qu.:221.0 1st Qu.:222.0 1st Qu.:223.0
Median :222.0 Median :223.0 Median :223.0 Median :224.0
Mean :222.1 Mean :222.6 Mean :223.1 Mean :223.6
3rd Qu.:223.0 3rd Qu.:224.0 3rd Qu.:224.0 3rd Qu.:225.0
Max. :225.0 Max. :225.0 Max. :225.0 Max. :225.0
48 sites 49 sites 50 sites
Min. :221.0 Min. :222.0 Min. :225
1st Qu.:223.8 1st Qu.:224.0 1st Qu.:225
Median :224.0 Median :225.0 Median :225
Mean :224.1 Mean :224.5 Mean :225
3rd Qu.:225.0 3rd Qu.:225.0 3rd Qu.:225
Max. :225.0 Max. :225.0 Max. :225
Asym xmid slope
258.440682 2.442061 1.858694
[1] 94.34749 121.23271 137.45031 148.83053 157.45735 164.31866 169.95946
[8] 174.71115 178.78954 182.34254 185.47566 188.26658 190.77402 193.04337
[15] 195.11033 197.00350 198.74606 200.35705 201.85227 203.24499 204.54643
[22] 205.76612 206.91229 207.99203 209.01150 209.97609 210.89054 211.75903
[29] 212.58527 213.37256 214.12386 214.84180 215.52877 216.18692 216.81820
[36] 217.42437 218.00703 218.56767 219.10762 219.62811 220.13027 220.61514
[43] 221.08369 221.53679 221.97528 222.39991 222.81138 223.21037 223.59747
[50] 223.97327
[1] 323.0717 341.3868 332.6834 342.4211 358.0178 345.2216 315.1033 322.4612
[9] 320.1974 317.3514 327.5915 316.9724 302.3015 281.7547 316.1479 348.1764
[17] 352.4154 353.2717 317.7539 337.9884 344.3120 318.1150 360.9480 327.0056
[25] 299.7821 342.1344 331.7578 363.4896 344.9060 329.9862 333.5556 339.5104
[33] 307.6372 336.0589 346.2054 284.1864 263.3566 285.0028 358.1501 321.8131
[41] 344.2241 338.7433 306.6802 354.2406 306.2675 348.1462 342.4255 315.5634
[49] 323.2725 292.0440 339.8582 322.2898 371.9230 352.1725 306.2792 329.0107
[57] 304.2660 361.3904 339.0634 354.6308 316.5934 298.0690 349.8517 312.0757
[65] 341.8240 333.0405 343.8575 327.7161 340.0718 321.3245 329.4584 304.2948
[73] 351.5482 351.9405 315.4029 319.0922 336.9580 337.4708 338.4089 332.1611
[81] 344.7823 322.6134 362.8288 358.2178 323.7816 345.2883 324.0142 360.9966
[89] 352.9998 332.9889 334.2561 323.0296 348.9373 349.7626 340.6058 321.9601
[97] 321.3303 320.9482 342.7446 319.3514
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Function specaccum finds species accumulation curves or the
number of species for a certain number of sampled sites or
individuals.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | specaccum(comm, method = "exact", permutations = 100,
conditioned =TRUE, gamma = "jack1", w = NULL, subset, ...)
## S3 method for class 'specaccum'
plot(x, add = FALSE, random = FALSE, ci = 2,
ci.type = c("bar", "line", "polygon"), col = par("fg"), ci.col = col,
ci.lty = 1, xlab, ylab = x$method, ylim,
xvar = c("sites", "individuals", "effort"), ...)
## S3 method for class 'specaccum'
boxplot(x, add = FALSE, ...)
fitspecaccum(object, model, method = "random", ...)
## S3 method for class 'fitspecaccum'
plot(x, col = par("fg"), lty = 1, xlab = "Sites",
ylab = x$method, ...)
## S3 method for class 'specaccum'
predict(object, newdata, interpolation = c("linear", "spline"), ...)
## S3 method for class 'fitspecaccum'
predict(object, newdata, ...)
specslope(object, at)
|
Arguments
comm |
Community data set. |
method |
Species accumulation method (partial match). Method
|
permutations |
Number of permutations with |
conditioned |
Estimation of standard deviation is conditional on the empirical dataset for the exact SAC |
gamma |
Method for estimating the total extrapolated number of species in the
survey area by function |
w |
Weights giving the sampling effort. |
subset |
logical expression indicating sites (rows) to keep: missing
values are taken as |
x |
A |
add |
Add to an existing graph. |
random |
Draw each random simulation separately instead of drawing their average and confidence intervals. |
ci |
Multiplier used to get confidence intervals from standard
deviation (standard error of the estimate). Value |
ci.type |
Type of confidence intervals in the graph: |
col |
Colour for drawing lines. |
ci.col |
Colour for drawing lines or filling the
|
ci.lty |
Line type for confidence intervals or border of the
|
xlab,ylab |
Labels for |
ylim |
the y limits of the plot. |
xvar |
Variable used for the horizontal axis:
|
object |
Either a community data set or fitted |
model |
Nonlinear regression model ( |
lty |
line type code (see |
newdata |
Optional data used in prediction interpreted as number of sampling units (sites). If missing, fitted values are returned. |
interpolation |
Interpolation method used with |
at |
Number of plots where the slope is evaluated. Can be a real number. |
... |
Other parameters to functions. |
Details
Species accumulation curves (SAC) are used to compare diversity
properties of community data sets using different accumulator
functions. The classic method is "random" which finds the mean
SAC and its standard deviation from random permutations of the data,
or subsampling without replacement (Gotelli & Colwell 2001). The
"exact" method finds the expected SAC using sample-based
rarefaction method that has been independently developed numerous
times (Chiarucci et al. 2008) and it is often known as Mao Tau
estimate (Colwell et al. 2012). The unconditional standard deviation
for the exact SAC represents a moment-based estimation that is not
conditioned on the empirical data set (sd for all samples > 0). The
unconditional standard deviation is based on an estimation of the
extrapolated number of species in the survey area (a.k.a. gamma
diversity), as estimated by function specpool. The
conditional standard deviation that was developed by Jari Oksanen (not
published, sd=0 for all samples). Method "coleman" finds the
expected SAC and its standard deviation following Coleman et
al. (1982). All these methods are based on sampling sites without
replacement. In contrast, the method = "rarefaction" finds the
expected species richness and its standard deviation by sampling
individuals instead of sites. It achieves this by applying function
rarefy with number of individuals corresponding to
average number of individuals per site.
Methods "random" and "collector" can take weights
(w) that give the sampling effort for each site. The weights
w do not influence the order the sites are accumulated, but
only the value of the sampling effort so that not all sites are
equal. The summary results are expressed against sites even when the
accumulation uses weights (methods "random",
"collector"), or is based on individuals
("rarefaction"). The actual sampling effort is given as item
Effort or Individuals in the printed result. For
weighted "random" method the effort refers to the average
effort per site, or sum of weights per number of sites. With
weighted method = "random", the averaged species richness is
found from linear interpolation of single random permutations.
Therefore at least the first value (and often several first) have
NA richness, because these values cannot be interpolated in
all cases but should be extrapolated. The plot function
defaults to display the results as scaled to sites, but this can be
changed selecting xvar = "effort" (weighted methods) or
xvar = "individuals" (with method = "rarefaction").
The summary and boxplot methods are available for
method = "random".
Function predict for specaccum can return the values
corresponding to newdata. With method "exact",
"rarefaction" and "coleman" the function uses analytic
equations for interpolated non-integer values, and for other methods
linear (approx) or spline (spline)
interpolation. If newdata is not given, the function returns
the values corresponding to the data. NB., the fitted values with
method="rarefaction" are based on rounded integer counts, but
predict can use fractional non-integer counts with
newdata and give slightly different results.
Function fitspecaccum fits a nonlinear (nls)
self-starting species accumulation model. The input object
can be a result of specaccum or a community in data frame. In
the latter case the function first fits a specaccum model and
then proceeds with fitting the a nonlinear model. The function can
apply a limited set of nonlinear regression models suggested for
species-area relationship (Dengler 2009). All these are
selfStart models. The permissible alternatives are
"arrhenius" (SSarrhenius), "gleason"
(SSgleason), "gitay" (SSgitay),
"lomolino" (SSlomolino) of vegan
package. In addition the following standard R models are available:
"asymp" (SSasymp), "gompertz"
(SSgompertz), "michaelis-menten")
(SSmicmen), "logis" (SSlogis),
"weibull" (SSweibull). See these functions for
model specification and details.
When weights w were used the fit is based on accumulated
effort and in model = "rarefaction" on accumulated number of
individuals. The plot is still based on sites, unless other
alternative is selected with xvar.
Function predict for fitspecaccum uses
predict.nls, and you can pass all arguments to that
function. In addition, fitted, residuals and
coef, AIC and deviance work on the result
object.
Function specslope evaluates the derivative of the species
accumulation curve at given number of sample plots, and gives the
rate of increase in the number of species. The function works with
specaccum result object when this is based on analytic models
"exact", "rarefaction" or "coleman", and with
non-linear regression results of fitspecaccum.
Nonlinear regression may fail for any reason, and some of the
fitspecaccum models are fragile and may not succeed.
Value
Function specaccum returns an object of class
"specaccum", and fitspecaccum a model of class
"fitspecaccum" that adds a few items to the
"specaccum" (see the end of the list below):
call |
Function call. |
method |
Accumulator method. |
sites |
Number of sites. For |
effort |
Average sum of weights corresponding to the number of
sites when model was fitted with argument |
richness |
The number of species corresponding to number of
sites. With |
sd |
The standard deviation of SAC (or its standard error). This
is |
perm |
Permutation results with |
weights |
Matrix of accumulated weights corresponding to the
columns of the |
fitted, residuals, coefficients |
Only in |
models |
Only in |
Note
The SAC with method = "exact" was
developed by Roeland Kindt, and its standard deviation by Jari
Oksanen (both are unpublished). The method = "coleman"
underestimates the SAC because it does not handle properly sampling
without replacement. Further, its standard deviation does not take
into account species correlations, and is generally too low.
Author(s)
Roeland Kindt r.kindt@cgiar.org and Jari Oksanen.
References
Chiarucci, A., Bacaro, G., Rocchini, D. & Fattorini, L. (2008). Discovering and rediscovering the sample-based rarefaction formula in the ecological literature. Commun. Ecol. 9: 121–123.
Coleman, B.D, Mares, M.A., Willis, M.R. & Hsieh, Y. (1982). Randomness, area and species richness. Ecology 63: 1121–1133.
Colwell, R.K., Chao, A., Gotelli, N.J., Lin, S.Y., Mao, C.X., Chazdon, R.L. & Longino, J.T. (2012). Models and estimators linking individual-based and sample-based rarefaction, extrapolation and comparison of assemblages. J. Plant Ecol. 5: 3–21.
Dengler, J. (2009). Which function describes the species-area relationship best? A review and empirical evaluation. Journal of Biogeography 36, 728–744.
Gotelli, N.J. & Colwell, R.K. (2001). Quantifying biodiversity: procedures and pitfalls in measurement and comparison of species richness. Ecol. Lett. 4, 379–391.
See Also
rarefy and rrarefy are related
individual based models. Other accumulation models are
poolaccum for extrapolated richness, and
renyiaccum and tsallisaccum for
diversity indices. Underlying graphical functions are
boxplot, matlines,
segments and polygon.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | data(BCI)
sp1 <- specaccum(BCI)
sp2 <- specaccum(BCI, "random")
sp2
summary(sp2)
plot(sp1, ci.type="poly", col="blue", lwd=2, ci.lty=0, ci.col="lightblue")
boxplot(sp2, col="yellow", add=TRUE, pch="+")
## Fit Lomolino model to the exact accumulation
mod1 <- fitspecaccum(sp1, "lomolino")
coef(mod1)
fitted(mod1)
plot(sp1)
## Add Lomolino model using argument 'add'
plot(mod1, add = TRUE, col=2, lwd=2)
## Fit Arrhenius models to all random accumulations
mods <- fitspecaccum(sp2, "arrh")
plot(mods, col="hotpink")
boxplot(sp2, col = "yellow", border = "blue", lty=1, cex=0.3, add= TRUE)
## Use nls() methods to the list of models
sapply(mods$models, AIC)
|
Example output
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-3
Warning message:
In cor(x > 0) : the standard deviation is zero
Species Accumulation Curve
Accumulation method: random, with 100 permutations
Call: specaccum(comm = BCI, method = "random")
Sites 1.00000 2.00000 3.00000 4.00000 5.0000 6.00000 7.00000
Richness 90.97000 122.01000 139.03000 150.89000 159.4300 165.85000 171.27000
sd 7.14561 7.87593 7.29252 7.01642 6.2833 5.65931 5.22205
Sites 8.00000 9.00000 10.00000 11.00000 12.00000 13.00000 14.00000
Richness 175.53000 179.05000 182.45000 185.59000 187.76000 190.17000 192.33000
sd 5.13151 4.99975 4.79978 4.64518 4.55964 4.52837 4.46548
Sites 15.0000 16.00000 17.00000 18.00000 19.00000 20.00000 21.00000
Richness 194.2800 196.05000 197.90000 199.38000 201.01000 202.22000 203.50000
sd 4.4132 4.34468 4.24383 4.04215 3.89896 3.93785 3.93508
Sites 22.00000 23.00000 24.00000 25.00000 26.0000 27.00000 28.0000
Richness 204.88000 206.15000 207.36000 208.45000 209.3000 210.29000 211.1600
sd 3.76126 3.82014 3.78866 3.73456 3.7457 3.59656 3.4516
Sites 29.00000 30.00000 31.00000 32.00000 33.00000 34.00000 35.00000
Richness 212.08000 212.94000 213.90000 214.65000 215.35000 216.06000 216.77000
sd 3.45733 3.27778 3.13179 3.04304 3.00294 2.96041 2.93999
Sites 36.0000 37.00000 38.00000 39.00000 40.00000 41.00000 42.00000
Richness 217.3900 218.02000 218.80000 219.52000 220.12000 220.65000 221.13000
sd 2.7776 2.82478 2.60148 2.52054 2.33671 2.21736 2.02337
Sites 43.00000 44.00000 45.00000 46.00000 47.00000 48.00000 49.00000
Richness 221.65000 222.07000 222.55000 223.08000 223.62000 224.08000 224.52000
sd 1.81673 1.78238 1.53987 1.45422 1.27747 1.09802 0.74508
Sites 50
Richness 225
sd 0
1 sites 2 sites 3 sites 4 sites 5 sites
Min. : 77.00 Min. :103.0 Min. :119 Min. :132.0 Min. :144.0
1st Qu.: 85.00 1st Qu.:117.0 1st Qu.:134 1st Qu.:146.0 1st Qu.:156.0
Median : 91.00 Median :122.5 Median :139 Median :151.0 Median :160.0
Mean : 90.97 Mean :122.0 Mean :139 Mean :150.9 Mean :159.4
3rd Qu.: 97.25 3rd Qu.:127.0 3rd Qu.:145 3rd Qu.:156.2 3rd Qu.:164.0
Max. :109.00 Max. :144.0 Max. :154 Max. :164.0 Max. :171.0
6 sites 7 sites 8 sites 9 sites
Min. :150.0 Min. :159.0 Min. :162.0 Min. :165.0
1st Qu.:163.0 1st Qu.:168.0 1st Qu.:173.0 1st Qu.:176.8
Median :166.0 Median :171.0 Median :175.5 Median :179.0
Mean :165.8 Mean :171.3 Mean :175.5 Mean :179.1
3rd Qu.:170.0 3rd Qu.:175.0 3rd Qu.:179.0 3rd Qu.:182.2
Max. :178.0 Max. :184.0 Max. :186.0 Max. :190.0
10 sites 11 sites 12 sites 13 sites
Min. :168.0 Min. :172.0 Min. :175.0 Min. :178.0
1st Qu.:179.0 1st Qu.:182.0 1st Qu.:185.0 1st Qu.:187.0
Median :183.0 Median :186.0 Median :188.0 Median :190.0
Mean :182.4 Mean :185.6 Mean :187.8 Mean :190.2
3rd Qu.:186.0 3rd Qu.:189.0 3rd Qu.:191.0 3rd Qu.:193.0
Max. :192.0 Max. :195.0 Max. :197.0 Max. :200.0
14 sites 15 sites 16 sites 17 sites
Min. :180.0 Min. :182.0 Min. :184.0 Min. :187.0
1st Qu.:189.8 1st Qu.:191.8 1st Qu.:193.0 1st Qu.:195.0
Median :193.0 Median :195.0 Median :197.0 Median :198.0
Mean :192.3 Mean :194.3 Mean :196.1 Mean :197.9
3rd Qu.:195.2 3rd Qu.:197.0 3rd Qu.:199.0 3rd Qu.:201.0
Max. :204.0 Max. :206.0 Max. :208.0 Max. :209.0
18 sites 19 sites 20 sites 21 sites 22 sites
Min. :189.0 Min. :190 Min. :190.0 Min. :191.0 Min. :194.0
1st Qu.:197.0 1st Qu.:199 1st Qu.:200.0 1st Qu.:201.0 1st Qu.:202.8
Median :199.0 Median :201 Median :203.0 Median :204.0 Median :205.0
Mean :199.4 Mean :201 Mean :202.2 Mean :203.5 Mean :204.9
3rd Qu.:202.0 3rd Qu.:204 3rd Qu.:205.0 3rd Qu.:206.0 3rd Qu.:207.2
Max. :210.0 Max. :211 Max. :213.0 Max. :215.0 Max. :215.0
23 sites 24 sites 25 sites 26 sites
Min. :196.0 Min. :196.0 Min. :197.0 Min. :197.0
1st Qu.:204.0 1st Qu.:205.0 1st Qu.:207.0 1st Qu.:207.8
Median :207.0 Median :208.0 Median :209.0 Median :209.0
Mean :206.2 Mean :207.4 Mean :208.4 Mean :209.3
3rd Qu.:208.0 3rd Qu.:210.0 3rd Qu.:211.0 3rd Qu.:212.0
Max. :215.0 Max. :217.0 Max. :217.0 Max. :218.0
27 sites 28 sites 29 sites 30 sites
Min. :200.0 Min. :202.0 Min. :202.0 Min. :204.0
1st Qu.:208.0 1st Qu.:209.0 1st Qu.:210.0 1st Qu.:211.0
Median :210.0 Median :211.5 Median :212.5 Median :213.0
Mean :210.3 Mean :211.2 Mean :212.1 Mean :212.9
3rd Qu.:213.0 3rd Qu.:213.0 3rd Qu.:215.0 3rd Qu.:215.2
Max. :219.0 Max. :219.0 Max. :220.0 Max. :221.0
31 sites 32 sites 33 sites 34 sites
Min. :205.0 Min. :206.0 Min. :207.0 Min. :207.0
1st Qu.:212.0 1st Qu.:212.8 1st Qu.:213.0 1st Qu.:214.0
Median :214.0 Median :215.0 Median :215.0 Median :216.0
Mean :213.9 Mean :214.7 Mean :215.3 Mean :216.1
3rd Qu.:216.2 3rd Qu.:217.0 3rd Qu.:217.2 3rd Qu.:218.0
Max. :222.0 Max. :222.0 Max. :222.0 Max. :222.0
35 sites 36 sites 37 sites 38 sites 39 sites
Min. :207.0 Min. :208.0 Min. :208 Min. :209.0 Min. :211.0
1st Qu.:215.0 1st Qu.:216.0 1st Qu.:216 1st Qu.:217.0 1st Qu.:218.0
Median :216.0 Median :218.0 Median :218 Median :219.0 Median :220.0
Mean :216.8 Mean :217.4 Mean :218 Mean :218.8 Mean :219.5
3rd Qu.:219.0 3rd Qu.:219.0 3rd Qu.:220 3rd Qu.:221.0 3rd Qu.:221.0
Max. :222.0 Max. :222.0 Max. :223 Max. :223.0 Max. :224.0
40 sites 41 sites 42 sites 43 sites
Min. :214.0 Min. :215.0 Min. :216.0 Min. :217.0
1st Qu.:219.0 1st Qu.:219.0 1st Qu.:220.0 1st Qu.:220.0
Median :220.0 Median :221.0 Median :221.0 Median :222.0
Mean :220.1 Mean :220.7 Mean :221.1 Mean :221.7
3rd Qu.:222.0 3rd Qu.:222.0 3rd Qu.:223.0 3rd Qu.:223.0
Max. :224.0 Max. :225.0 Max. :225.0 Max. :225.0
44 sites 45 sites 46 sites 47 sites
Min. :217.0 Min. :218.0 Min. :220.0 Min. :220.0
1st Qu.:221.0 1st Qu.:221.0 1st Qu.:222.0 1st Qu.:223.0
Median :222.0 Median :223.0 Median :223.0 Median :224.0
Mean :222.1 Mean :222.6 Mean :223.1 Mean :223.6
3rd Qu.:223.0 3rd Qu.:224.0 3rd Qu.:224.0 3rd Qu.:225.0
Max. :225.0 Max. :225.0 Max. :225.0 Max. :225.0
48 sites 49 sites 50 sites
Min. :221.0 Min. :222.0 Min. :225
1st Qu.:223.8 1st Qu.:224.0 1st Qu.:225
Median :224.0 Median :225.0 Median :225
Mean :224.1 Mean :224.5 Mean :225
3rd Qu.:225.0 3rd Qu.:225.0 3rd Qu.:225
Max. :225.0 Max. :225.0 Max. :225
Asym xmid slope
258.440682 2.442061 1.858694
[1] 94.34749 121.23271 137.45031 148.83053 157.45735 164.31866 169.95946
[8] 174.71115 178.78954 182.34254 185.47566 188.26658 190.77402 193.04337
[15] 195.11033 197.00350 198.74606 200.35705 201.85227 203.24499 204.54643
[22] 205.76612 206.91229 207.99203 209.01150 209.97609 210.89054 211.75903
[29] 212.58527 213.37256 214.12386 214.84180 215.52877 216.18692 216.81820
[36] 217.42437 218.00703 218.56767 219.10762 219.62811 220.13027 220.61514
[43] 221.08369 221.53679 221.97528 222.39991 222.81138 223.21037 223.59747
[50] 223.97327
[1] 323.0717 341.3868 332.6834 342.4211 358.0178 345.2216 315.1033 322.4612
[9] 320.1974 317.3514 327.5915 316.9724 302.3015 281.7547 316.1479 348.1764
[17] 352.4154 353.2717 317.7539 337.9884 344.3120 318.1150 360.9480 327.0056
[25] 299.7821 342.1344 331.7578 363.4896 344.9060 329.9862 333.5556 339.5104
[33] 307.6372 336.0589 346.2054 284.1864 263.3566 285.0028 358.1501 321.8131
[41] 344.2241 338.7433 306.6802 354.2406 306.2675 348.1462 342.4255 315.5634
[49] 323.2725 292.0440 339.8582 322.2898 371.9230 352.1725 306.2792 329.0107
[57] 304.2660 361.3904 339.0634 354.6308 316.5934 298.0690 349.8517 312.0757
[65] 341.8240 333.0405 343.8575 327.7161 340.0718 321.3245 329.4584 304.2948
[73] 351.5482 351.9405 315.4029 319.0922 336.9580 337.4708 338.4089 332.1611
[81] 344.7823 322.6134 362.8288 358.2178 323.7816 345.2883 324.0142 360.9966
[89] 352.9998 332.9889 334.2561 323.0296 348.9373 349.7626 340.6058 321.9601
[97] 321.3303 320.9482 342.7446 319.3514
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