Shareholder Quorum Subsampling was introduced by John Alroy (2010). Chao and Jost (2012) provided analytical solutions for an almost equivalent method, which they called “Coverage-based rarefaction”. Past follows the algorithm of Alroy (2010).
Like rarefaction, SQS can be used to standardize species counts across samples of different size, but standardizing on a fixed “coverage” rather than a fixed sample size. Coverage is defined as the proportion of individuals in the population that are represented by the species recovered in the sample. If all species are recovered in the sample, coverage is 1. If only one species is recovered, but 50% of the individuals in the population belong to this species, coverage is 0.5. SQS gives a more fair sampling of communities with different evenness than classical rarefaction, which suffers from a “compression effect” where differences in richness are artificially dampened. SQS is therefore gradually replacing classical rarefaction in the literature.
The module expects one or more columns of count data. The following parameters can be selected:
Quorum: The desired subsampled coverage level (0-1). This value should be larger than 0.4. A value of e.g. 0.9 might be better, but for small samples this coverage may not be achieved, giving an error message. The quorum value is not critical: Larger values will give higher SQS species richness, but this is of little consequence for the comparison of several samples.
Trials: The number of subsampling runs. Higher values give more exact results, but takes longer.
Ignore singletons and Ignore dominant: Disregard species with abundance 1; disregard the single most common species. The possible advantage of this is slightly unclear.
The module outputs the original sample size (N), the number of observed species (S_obs), and Good’s u which is a simple estimator of sample coverage: u = 1 - f1/N, where f1 is the number of singletons (Chao & Jost 2012 give an improved estimator), in addition to the SQS richness.
References
Alroy, J. 2010. Geographical, environmental and intrinsic biotic controls on Phanerozoic marine diversification. Palaeontology 53:1211–1235.
Chao, A., Jost, L. 2012. Coverage-based rarefaction and extrapolation: standardizing samples by completeness rather than size. Ecology 93:2533-2547