Sampling variability in Hill diversity

A simulated dataset with mean absolute error and log sd for sample and asymptotic Hill diversity estimates based on finite samples from simulated species abundance distributions. Hill diversity was estimated with the naïve estimator, rarity(sample_freq, l) and the Chao and Jost 2015 non-parametric asymptotic estimator Chao_Hill_abu(sample_freq, l), and parameterized by richness and evenness

err_plot_data

Format

A data.frame with 2,196 rows and 15 variables:

  • evenness Factor, approximately the ratio of Hill-Simpson to richness

  • distribution Factor, family, one of "lnorm" or "gamma"

  • ell: Scalar, scaling parameter for Hill diversity

  • sample_sdlog: Numeric, standard deviation of natural log of sample Hill diversity

  • estimator_sdlog: Numeric, standard deviation of natural log of estimated Hill diversity of the SAD based on asymptotic estimator

  • sample_bias Numeric, mean log ratio of sample diversity to expected sample diversity

  • naive_bias Numeric, mean log ratio of sample diversity to true diversity

  • estimator_bias Numeric, mean log ratio of estimated asymptotic diversity to true diversity

  • sample_rmsle Numeric, square root of the mean squared log ratio of sample diversity to expected sample diversity

  • estimator_rmsle Numeric, square root of the mean squared log ratio of estimated asymptotic diversity to true diversity

  • estimator_rmsle Numeric, square root of the mean squared log ratio of estimated asymptotic diversity to true diversity

  • true_diversity Numeric, Hill diversity of the SAD

  • mean_sample Numeric, mean of sample diversity for combination of ell, evenness, distribution, and SS.

  • mean_asymptotic Numeric, mean of estimated asymptotic diversity for combination of ell, evenness, distribution, and SS.

  • sample_size Integer, number of individuals sampled

References

Chao A, Jost L (2015). “Estimating diversity and entropy profiles via discovery rates of new species.” Methods in Ecology and Evolution, 6(8), 873--882. ISSN 2041210X, doi:10.1111/2041-21 . Chao A, Ricotta C, Aldo P (2019). “Quantifying evenness and linking it to diversity, beta diversity, and similarity.” Ecology, 1--15. ISSN 0012-9658, doi:10.1002/ecy.2852 .