Appendix A. Derivational details for Eqs. 16a, 16b, and 17.

Derivational details for Eqs. 16a, 16b, and 17

Appendix C. Statistical estimation issues.

Statistical estimation issues

Appendix B. More comparisons of the two formulas for alpha diversity.

More comparisons of the two formulas for alpha diversity

Appendix D. Unveiling the species-rank incidence distribution for incidence data.

Unveiling the species-rank incidence distribution for incidence data

Appendix A. Simulation results based on two theoretical abundance distributions and four large empirical surveys.

Simulation results based on two theoretical abundance distributions and four large empirical surveys

Appendix B. A generalization of Good-Turing sample coverage theory.

A generalization of Good-Turing sample coverage theory

Supplement 1. R code for JADE (Joint species-rank Abundance Distribution/Estimation) based on individual-based (abundance) and sampling-unit-based (incidence) data.

<h2>File List</h2><div> <p><a href="JADE.R">JADE.R</a> (MD5: 31757e7a2d9de9266d235d61d8e48f61)</p> </div><h2>Description</h2><div> <p>JADE.R –R code for computing the estimated complete species-rank abundance distribution (RAD) based on individual-based (abundance) and sampling-unit-based (incidence) data. The estimated complete RAD includes two parts: (i) the adjusted relative abundances for the set of species detected in the sample, and (ii) the estimated relative abundances for the set of species undetected in the sample but inferred to be present in the assemblage. Then the two parts are jointly combined to obtain the complete RAD estimator.</p> </div

Appendix C. Other models for the relative abundances of the undetected species.

Other models for the relative abundances of the undetected species

Consistency of empirical data with IAM based on the Dopamine receptor D4 (<i>DRD4</i>) alleles data.

<p>Empirical and expected values by treating each of the four subpopulations as an isolated population following IAM for mutation. Data are shown in Table A (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.s005" target="_blank">S5 Appendix</a>). See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.t001" target="_blank">Table 1</a> for the expected formulas and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.s004" target="_blank">S4 Appendix</a> for statistical methods to obtain empirical values. The proportional difference PD ≡ (expected value−estimated value)/expected value. All s.e. estimates were obtained by a bootstrap method based on 1000 resamples generated from the observed allele frequency distribution.</p><p>^#The expected parameters under IAM for the four subpopulations: <i>Nμ</i> = (1.0113, 1.6552, 2.2610, 2.1280); see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.e004" target="_blank">Eq 1</a>.</p><p>Consistency of empirical data with IAM based on the Dopamine receptor D4 (<i>DRD4</i>) alleles data.</p

Consistency of empirical data with IAM-FIM based on the Dopamine receptor D4 (<i>DRD4</i>) alleles data.

<p>Empirical and IAM-FIM expected values for total-population, subpopulation and differentiation measures under IAM-FIM. Data are shown in Table A (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.s005" target="_blank">S5 Appendix</a>). See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.t001" target="_blank">Table 1</a> for the expected formulas and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.s004" target="_blank">S4 Appendix</a> for statistical methods to obtain empirical values. The proportional difference PD ≡ (expected value−estimated value)/expected value. All s.e. estimates were obtained by a bootstrap method based on 1000 resamples generated from the observed allele frequency distribution.</p><p>^# The expected parameters under IAM-FIM: <i>Nμ</i> = 0.6058, <i>Nm</i> = 3.0748; see Eqs. D5 and D6 of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.s004" target="_blank">S4 Appendix</a>.</p><p>^* Total population entropy value calculated from total population-heterozygosity under IAM via <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.e009" target="_blank">Eq 3A</a>: ¹<i>H</i>_<i>T</i> = <i>ψ</i>[1/(1−²<i>H</i>_<i>T</i>)]+0.5772.</p><p>^§ Subpopulation entropy is calculated from heterozygosity via a link described in Eq. D7 in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125471#pone.0125471.s004" target="_blank">S4 Appendix</a>.</p><p>Consistency of empirical data with IAM-FIM based on the Dopamine receptor D4 (<i>DRD4</i>) alleles data.</p