fisher.rSAC estimates the expected number of species represented at least
r times in a random sample, based on the initial sample.
The estimator was originally proposed by Fisher et al. (1943) for estimating
the SAC. We generalize this estimator for predicting the r-SAC.
A two-column matrix. The first column is the frequency j = 1,2,…; and the second column is N_j, the number of species with each species represented exactly j times in the initial sample. The first column must be sorted in an ascending order.
A positive integer. Default is 1.
The estimator for the r-SAC. The input of the estimator is a vector of sampling efforts t, i.e., the relative sample sizes comparing with the initial sample. For example, t = 2 means a random sample that is twice the size of the initial sample.
Fisher, R., Corbet, A., & Williams, C. (1943). The Relation Between the Number of Species and the Number of Individuals in a Random Sample of an Animal Population. Journal of Animal Ecology, 12(1), 42-58. doi:10.2307/1411
Deng, C., Daley, T., Calabrese, P., Ren, J., & Smith, A.D. (2016). Estimating the number of species to attain sufficient representation in a random sample. arXiv preprint arXiv:1607.02804v3.
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## load library library(preseqR) ## import data data(WillButterfly) ## construct the estimator for SAC fisher1 <- fisher.rSAC(WillButterfly, r=1) ## The number of species represented at least once in a sample, ## when the sample size is 10 or 20 times of the initial sample fisher1(c(10, 20)) ## construct the estimator for r-SAC fisher2 <- fisher.rSAC(WillButterfly, r=2) ## The number of species represented at least twice in a sample, ## when the sample size is 50 or 100 times of the initial sample fisher2(c(50, 100))
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