Extrapolation of the Species Accumulation Curve Associated to “Chao” Estimator of the Number of Unrecorded Species: A Mathematically Consistent Derivation
Annual Research & Review in Biology · pp. 1–19 · Published 9 Dec 2016
10.9734/ARRB/2016/30522Abstract
Incomplete samplings are doomed to become common practice for many inventories of biodiversity, thereby inviting to extrapolate what the rate of accumulation of newly recorded species would be if sampling was to be continued any further. For this purpose, a new derivation is provided for the extrapolation of the Species Accumulation Curve associated to the “Chao” estimator of the number of unrecorded species. This new derivation strictly complies with the general mathematical relationship constraining the shape of any expression of the Species Accumulation Curve, while the extrapolation previously proposed by Chao & Chiu [1] does not. The mathematically relevant formulation for the extrapolation R(N) of the Species Accumulation Curve associated to “Chao” estimator is thus: R(N) = R(N0) + [f12/(2 f2)](1 – exp[– (2f2/f1/N0 ). (N – N0)]), with N0 as the actual sample size, f1 and f2 as the numbers of species actually recorded once and twice and R(N) as the extrapolated number of species expected to be recorded as a function of sample size N (N> N0). Accounting for the constraining relationship mentioned above is also essential in another respect: it allows to extrapolate separately the numbers of species expected to be recorded 0-, 1-, 2-, >2- times, thereby permitting to analyse rationally the process of species accumulation during continuously growing sampling. At last, the preferred range of applicability of both “Chao” estimator and the associated extrapolation of the Species Accumulation Curve estimator is discussed, by comparison with the alternative type estimator Jackknife-2.
References (12)
- 1 Estimating Population Size Via Sample Coverage for Closed Capture-Recapture Models [DOI]
- 2 ESTIMATING SPECIES RICHNESS: SENSITIVITY TO SAMPLE COVERAGE AND INSENSITIVITY TO SPATIAL PATTERNS [DOI]
- 3 An improved nonparametric lower bound of species richness via a modified good–turing frequency formula [DOI]
- 4 Aboveground biomass and carbon stock assessment in Indian tropical deciduous forest and relationship with stand structural attributes [DOI]
- 5 Assessing biodiversity with species accumulation curves; inventories of small reptiles by pit‐trapping in Western Australia [DOI]
- 6 Wildland fires and moist deciduous forests of Chhattisgarh, India: divergent component assessment [DOI]
- 7 Theoretical Derivation of a Bias-reduced Expression for the Extrapolation of the Species Accumulation Curve and the Associated Estimation of Total Species Richness [DOI]
- 8 An Algebraic Derivation of Chao’s Estimator of the Number of Species in a Community Highlights the Condition Allowing Chao to Deliver Centered Estimates [DOI]
- 9 Butterfly fauna in Mount Gariwang-san, Korea [DOI]
- 10 Extrapolation of the Species Accumulation Curve for Incomplete Species Samplings: A New Nonparametric Approach to Estimate the Degree of Sample Completeness and Decide when to Stop Sampling [DOI]
- 11 Measuring and Estimating Species Richness, Species Diversity, and Biotic Similarity from Sampling Data [DOI]
- 12 Nonparametric Estimation and Comparison of Species Richness [DOI]
Cited by 29
Jean Béguinot · Asian Journal of Environment & Ecology · 2018
Jean Béguinot · Asian Journal of Environment & Ecology · 2018
Jean Béguinot · Asian Journal of Environment & Ecology · 2017
Jean Béguinot, Tshering Nidup · Asian Journal of Environment & Ecology · 2017
Jean Béguinot · Advances in Research · 2018
Jean Béguinot · Annual Research & Review in Biology · 2020
Jean Béguinot · Annual Research & Review in Biology · 2021
Jean Béguinot · Annual Research & Review in Biology · 2021
Maria Vigo, U. Fernandez-Arcaya, J. Navarro · Marine Biology Research · 2026
J. D. Cadena-Zamudio, J. Monribot-Villanueva, Claudia-Anahí Pérez-Torres · Functional & Integrative Genomics · 2022
Related research
- Extrapolation of the Species Accumulation Curve for Incomplete Species Samplings: A New Nonparametric Approach to Estimate the Degree of Sample Completeness and Decide when to Stop Sampling — shares topic coverage
- A Universal Key to Rationally Select Which, Among Nonparametric Species Richness Estimators, Performs Best According to Each Particular Incomplete Sampling — shares topic coverage
- The Variations of the Numbers of Species Recorded 1-, 2-, … x-times (Singletons, Doubletons, … x-tons) with Increasing Sampling-size : An Analytical Approach Using Taylor Expansion — shares topic coverage
- On General Mathematical Constraints Applying to the Kinetics of Species Discovery during Progressive Sampling: Consequences on the Theoretical Expression of the Species Accumulation Curve — shares topic coverage
- Theoretical Derivation of a Bias-reduced Expression for the Extrapolation of the Species Accumulation Curve and the Associated Estimation of Total Species Richness — shares topic coverage
Article metrics
Real usage data collected on this platform.
90
Page views
0
PDF downloads
24
Outbound clicks
29
Citations
Views over time
Views by country
Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".
Traffic sources
Referring site, by host.
Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.