Function specaccum finds species accumulation curves or the
number of species for a certain number of sampled sites or
individuals.
specaccum(comm, method = "exact", permutations = 100,
conditioned =TRUE, gamma = "jack1", w = NULL, subset, ...)
# S3 method for specaccum
plot(x, add = FALSE, random = FALSE, ci = 2,
ci.type = c("bar", "line", "polygon"), col = par("fg"), lty = 1,
ci.col = col, ci.lty = 1, ci.length = 0, xlab, ylab = x$method, ylim,
xvar = c("sites", "individuals", "effort"), ...)
# S3 method for specaccum
boxplot(x, add = FALSE, ...)
fitspecaccum(object, model, method = "random", ...)
# S3 method for fitspecaccum
plot(x, col = par("fg"), lty = 1, xlab = "Sites",
ylab = x$method, ...)
# S3 method for specaccum
predict(object, newdata, interpolation = c("linear", "spline"), ...)
# S3 method for fitspecaccum
predict(object, newdata, ...)
specslope(object, at)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):
Function call.
Accumulator method.
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.
Average sum of weights corresponding to the number of
sites when model was fitted with argument w
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.
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.
Permutation results with method = "random" and
NULL in other cases. Each column in perm holds one
permutation.
Matrix of accumulated weights corresponding to the
columns of the perm matrix when model was fitted with
argument w.
Only in fitspecacum:
fitted values, residuals and nonlinear model coefficients. For
method = "random" these are matrices with a column for
each random accumulation.
Only in fitspecaccum: list of fitted
nls models (see Examples on accessing these models).
Community data set.
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.
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.
Estimation of standard deviation is conditional on the empirical dataset for the exact SAC
Method for estimating the total extrapolated number of species in the
survey area by function specpool
Weights giving the sampling effort.
logical expression indicating sites (rows) to keep: missing
values are taken as FALSE.
A specaccum result object
Add to an existing graph.
Draw each random simulation separately instead of drawing their average and confidence intervals.
Multiplier used to get confidence intervals from standard
deviation (standard error of the estimate). Value ci = 0
suppresses drawing confidence intervals.
Type of confidence intervals in the graph: "bar"
draws vertical bars, "line" draws lines, and
"polygon" draws a shaded area.
Colour for drawing lines.
line type (see par).
Colour for drawing lines or filling the
"polygon".
Line type for confidence intervals or border of the
"polygon".
Length of horizontal bars (in inches) at the end of
vertical bars with ci.type = "bar".
Labels for x (defaults xvar) and
y axis.
the y limits of the plot.
Variable used for the horizontal axis:
"individuals" can be used only with
method = "rarefaction".
Either a community data set or fitted specaccum model.
Nonlinear regression model (nls). See Details.
Optional data used in prediction interpreted as number of sampling units (sites). If missing, fitted values are returned.
Interpolation method used with newdata.
Number of plots where the slope is evaluated. Can be a real number.
Other parameters to functions.
Roeland Kindt r.kindt@cgiar.org and Jari Oksanen.
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 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, nobs,
coef, AIC, logLik 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.
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.
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)
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