A given number of realizations of a probability distribution (species abundances in a community) is sampled with replacement by a Poisson or Negative Binomial process, or without replacement by a hypergeometric process.
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positive integer; number of species in the community, which is the number of random deviates
generated by the probability distribution given by argument
numeric; a vector of positive real numbers depicting abundances of
species in a community or sample OR
character; root name of community sad distribution - e.g., lnorm
for the lognormal distribution
list with named arguments to be passed to the probability function defined by the argument sad.
The truncation point at which the random distribution defined in
argument sad should be truncated; see
character; if poisson the sampling process is Poisson (independent sampling of
individuals with replacement); if nbinom negative binomial
sampling is used to simulate aggregation of individuals in sampling
units with replacement;
finally, hypergeometric samples a fixed number of
positive; size parameter for the sampling binomial negative. This parameter is ignored for other sampling techniques.
logical; should zero values be included in the returned vector?
positive integer; sample size: number of draws taken from the community.
This function simulates one or more random samples taken from a community with
species. The expected species abundances in the sampled community can
(i) follow a
probability distribution given by the argument
sad or (ii) be a
numeric vector provided by the user through this same argument.
the whole set of units that made up the community (usually
individuals) is sampled. Hence the expected abundance in the sample of each
frac*n, where n is the species' expected abundance in the
Three sampling processes can be simulated.
Sampling with replacement can be done with Poisson
(individuals are sampled independently) or negative binomial sampling
(where individuals of each species are aggregated over sampling
units). The "hypergeometric" sampling scheme draws
frac * n
individuals without replacement.
For Poisson and negative binomial schemes the species abundances in
the sample are statistically independent.
In general terms, these two sampling schemes takes a Poisson or negative
binomial sampling with replacement of a vector of
S realizations of a random variable,
with the sampling intensity given by
frac. The resulting values are
realizations of a Poisson (or a Negative Binomial) random variable where the
parameter that corresponds to the mean (=expected value of the variable) follows a probability
distribution or the numeric vector given by the argument
sad. Because these two
sampling schemes assume replacement but the sampled community is
finite, they are valid only when the
fraction of the sampled community is small (
The "hypergeometric" scheme simulates a sample of a fixed total number of
individuals from the community. Therefore, abundances of the species
in the sample are interdependent (Connoly et al. 2009).
Sampling is carried out with
base::sample(..., replace = FALSE).
This scheme samples without replacement a finite community and
therefore provides valid results for any value of
For the broken-stick, logseries, MZSM and Volkov distributions, the expected value of
is deduced from the coefficients provided in the argument
coef; thus, the value of the parameter
S is ignored and may be left blank. The expressions for the number of species in each case are:
* Broken-stick: coefficient S
* Log-series: alpha log(1 + N/alpha)
* MZSM: sum_x=1^J theta/x (1 - x/J)^(theta - 1)
* Volkov: sum of the unnormalized PDF from 1 to J, see
if ssize=1 a vector of (zero truncated) abundances in the sample; if ssize>1 a data frame with sample identification, species identification, and (zero truncated) abundances.
Paulo I. Prado firstname.lastname@example.org and Andre Chalom.
Pielou, E.C. 1977. Mathematical Ecology. New York: John Wiley and Sons.
Green, J. and Plotkin, J.B. 2007 A statistical theory for sampling species abundances. Ecology Letters 10:1037–1045
Connolly, S.R., Dornelas, M., Bellwood, D.R. and Hughes, T.P. 2009. Testing species abundance models: a new bootstrap approach applied to Indo-Pacific coral reefs. Ecology, 90(11): 3138–3149.
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##A Poisson sample from a community with a lognormal sad samp2 <- rsad(S = 100, frac=0.1, sad="lnorm", coef=list(meanlog=5, sdlog=2)) ## Preston plot plot(octav(samp2)) ## Once this is a Poisson sample of a lognormal community, the abundances ## in the sample should follow a Poisson-lognormal distribution. ## Adds line of theoretical Poisson-lognormal with ## mu=meanlog+log(frac) and sigma=sdlog) ## Predicted by the theoretical Poisson-lognormal truncated at zero samp2.pred <- octavpred(samp2, sad="poilog", coef= list(mu=5+log(0.1), sig=2), trunc=0) ## Adding the line in the Preston plot lines(samp2.pred)
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