Shannon entropisi temelli düzeltmeli çeşitlilik ölçümleri ve Pla kestiricisinin üst güven sınır değerini kullanarak gerçek tür çeşitliliğinin hesaplanması

Abstract

Bu çalışma Pla kestiricisinin düzeltilmiş üst güven değeri (H ̂_ ^e+1,96σ_H^* ) ve Shannon entropisi temelli düzeltmeli tür çeşitlilik (SDÇ) ölçümleri (Jackknife indisi (JK), düzeltilmiş en büyük olabilirlik kestiricisi (MLEbc), Chao ve Shen düzeltmeli çeşitlilik eşitliği (H ̂_CS ), Özkan düzeltmeli çeşitlilik kestiricisi (H ̂_O ), Bilgi teorisi temelli düzeltmeli çeşitlilik indisi (H ̂_CWJ ), Miller sapma düzeltme eşitliği (H ̂_Miller ) ve Grassberger sapma düzeltme eşitliği (H ̂_ψ )) kullanılarak gerçek tür çeşitliliğinin nasıl hesaplanabileceği bilgisini vermek amacıyla gerçekleştirilmiştir. Bu doğrultuda ilk olarak 5 toplumun JK, MLEbc, H ̂_CS, H ̂_O, H ̂_CWJ, H ̂_Miller, H ̂_ψ ve H ̂_ ^e+1,96σ_H^* değerleri hesaplanmıştır. Daha sonra her bir toplum için hesaplanan H ̂_ ^e+1,96σ_H^* değerinin altında kalan indis değerleri kullanılarak örnek toplumların gerçek tür çeşitlilik değerleri belirlenmiştir.

Keywords

• Biyolojik çeşitlilik
• Shannon indisi
• Nadir tür
• Negatif sapma
• Düzeltmeli tür çeşitliliği
• Eksik envanter

Computing true species diversity using Shannon entropy-based bias-corrected measures and upper confidence limit value of Pla estimator

Abstract

This study was conducted to illustrate how to estimate true species diversity using upper confidence limit value of Pla unbiased estimator (H ̂_ ^e+1,96σ_H^* ) and Shannon entropy-based bias-corrected diversity (SCD) measures (i.e., Jackknife index (JK), bias-corrected maximum likelihood estimator (MLEbc), Chao and Shen bias-corrected estimator (H ̂_CS ), Özkan bias-corrected estimator (H ̂_O ), information theory-based bias-corrected estimator (H ̂_CWJ ), Miller index (H ̂_Miller ) and Grassberger index (H ̂_ψ )). In this regards, firstly JK, MLEbc, H ̂_CS, H ̂_O, H ̂_CWJ, H ̂_Miller, H ̂_ψ and H ̂_ ^e+1,96σ_H^* values of five communities were calculated. Next for each community, true diversity values are calculated using the SCD values below H ̂_ ^e+1,96σ_H^* value.

Keywords

• Biodiversity
• Shannon index
• Rare species
• Negative bias
• Unbiased species diversity
• Incomplete inventory

References

1. Bonachela, J.A., Hinrichsen, H., Munoz, M.A., 2008. Entropy estimates of small data sets. Journal of Physics A: Mathematical and Theoretical, 41(20): 202001.
2. Chao, A., Ma, M.C., Yang, M.C., 1993. Stopping rules and estimation for recapture debugging with unequal failure rates. Biometrika, 80(1): 193-201.
3. Chao, A., Hwang, W.H., Chen, Y.C., Kuo, C.Y., 2000. Estimating the number of shared species in two communities. Statistica Sinica, 10: 227-246.
4. Chao A., Shen, T.J., 2003. Nonparametic estimation of Shannon’s index of diversity when there are unseen species in sample. Environmental and Ecological Statistics, 10: 429-442.
5. Chao, A., Wang, Y.T., Jost, L., 2013. Entropy and the species accumulaion curve: a novel entropy estimator via discovery rares of new species. Methods in Ecology and Evoluation, 4(11): 1091-1100.
6. Choi, J., Srivastava, H.M., 2000. Evaluation of higher-order derivatives of the gamma function. Publikacije Elektrotehničkog Fakulteta. Serija Matematika, 11: 9-18.
7. Grassberger, P., 1988. Finite sample corrections to entropy and dimension estimates. Physics Letters A, 128(6-7): 369-373.
8. Grassberger, P., 2003. Entropy Estimates from Insufficient Samplings. ArXiv Physics, e-prints 0307138.

9. Janzen, D.H., 1973a. Sweep samples of tropical foliage insects: description of study sites, with data on species abundances and size distributions. Ecology, 54(3): 659-686.
10. Janzen, D.H., 1973b. Sweep samples of tropical foliage insects: effects of seasons, vegetation types, elevation, time of day, and insularity. Ecology, 54(3): 687-708.
11. Horvitz, D. G., Thompson, D. J., 1952. A generalization of sampling without replacement from a finite universe. Journal of the American statistical Association, 47(260), 663-685.
12. Kokologiannaki, C.G., Krasniqi, V., 2013. Some properties of the k-gamma function. Le Matematiche, 68(1): 13-22.
13. Miller G.A., 1955. A note on the bias of information estimates. In: Information Theory In Psychology: Problems and Methods (Ed: Quastler, H.), The Free Press, Glencoe Illinois, pp. 95–100.
14. Özkan, K., 2020. A new proposed estimator for reducing bias due to undetected species. Gazi University Journal of Science, 33(1): 229-236.
15. Peet, R.K., 1974. The measurement of species diversity. Annual Review of Ecology and Systematics, 5(1): 285-307.
16. Pla, L., 2004. Bootstrap confidence intervals for the Shannon biodiversity index: a simulation study. Journal of Agricultural, Biological, and Environmental Statistics, 9(1): 42–56.
17. Shannon, C.E., 1948. A mathematical theory of communication. Bell System Technical Journal, 27(3): 379-423.
18. Strobl, C., 2005. Variable selection in classification trees based on imprecise probabilities. ISIPTA ’05: Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications,20-23 July, Pittsburgh, USA, pp. 339–348.
19. Zahl, S., 1977. Jackknifing an index of diversity. Ecology, 58(4): 907-913.