Benford Kanunu ve Genelleştirilmiş Benford Kanunu ile ekosistem doğallığının hesaplanması

Year 2021, Volume: 22 Issue: 2, 73 - 82, 29.06.2021

Kürşad Özkan

https://doi.org/10.18182/tjf.907217

Cited By: 1

Abstract

Ekosistemlerin doğallık tespitine yönelik yeni bir yöntem önerilmiştir. Bitki türleri ve örnek alanlardan oluşan (S Χ A ) üç veri seti kullanılmıştır. Bunlar Sultan Dağları Alt Bölgesi (BS) veri seti (60 Χ 96), Dedegül Dağları Alt Bölgesi (BD) veri seti (89 Χ 119) ve iki alt bölgenin birleşmesinden oluşan Beyşehir Gölü Havzası (B) veri setidir (98 Χ 215). İlk olarak BS ve BD veri setlerinden belirlenen ilk rakam olasılık değerleri (〖d_1 p〗_o ) ile Benford Kanunu teorik olasılık değerleri (d_1 p_e ) arasındaki genel uyumu belirlemek için ki kare (χ^2 ) testleri yapılmıştır. Sonuçta χ^2 (e_BS )=16,579 ve χ^2 (e_BD )=2,406 olarak bulunmuştur. İkinci olarak BS ve BD’nin gözlenen olasılık değerlerine en uyumlu teorik olasılık değerlerini belirlemek için genelleştirilmiş Benford Kanunu (GB(d;γ)) kullanılmıştır. BS ve BD için en küçük χ^2 değerleri sırasıyla γ=0,65’de ve γ=0,07’de elde edilmiştir (χ^2 (e_BD^γ )=4,992 ve χ^2 (e_BD^γ )=2,209). Beklendiği gibi genelleştirilmiş Benford Kanunu ile her iki alt bölgenin χ^2 değerleri düşmüştür. χ^2 değer düşüşü BS’de çok daha yüksek olmuştur. Alt bölgelerin örnek alan sayıları birbirlerinden farklıdır. Bu yüzden üçüncü aşamada B veri setinden her iki alt bölgenin örnek alan sayıları dikkate alınarak rastlantısal yinelemeli işlemler uygulanmış ve yineleme sayısı (K) kadar (K=10000) χ^2 değerleri elde edilmiştir. Daha sonra kalibrasyon katsayı değerlerini (kd) belirlemek için bu χ^2 değerlerinin ortalamaları ((_ ^k)(χ^2 ) ̅ (E_BS^γ )=6,747 ve (_ ^k)(χ^2 ) ̅ (E_BD^γ )=6,176) alınmıştır. Sonuçta, BS için kd=1 olduğu için BS doğallık değeri 4,992 ve BD için kd=1,093 olduğu için BD doğallık değeri 2,414 olarak bulunmuştur. Teorik olarak en doğal ekosistemler için tam doğallık değeri=0 kabul edildiğinden, elde edilen doğallık hesaplama sonuçları BD ekosistemlerinin BS ekosistemlerinden daha doğal olduğu göstermiştir.

Keywords

Hemerobi, Doğallık, Orman ekosistemleri, İlk sayı kanunu, Genelleştirme, Rastgele seçim

Estimating ecosystem naturalness using Benford’s Law and Generalized Benford’s Law

Abstract

A new method was proposed to estimate ecosystem naturalness. Three species-plot (S Χ A) datasets were used. Those data sets belong to Sultan mountain sub-district (BS) (60 Χ 96) Dedegül mountain sub-district (BD) (89 Χ 119) and, Beyşehir Watershed (B) (98 Χ 215) consisting of both of the sub-districts. Firstly, chi square test (χ^2 ) was applied to define the statistical goodness of fit between the first digit observed probabilities (〖d_1 p〗_o ) and the theoretical probabilities of Benford’s Law (d_1 p_e ). It was found that χ^2 (e_BS )=16.579 and χ^2 (e_BD )=2.406.
Secondly, to find the fittest theoretical probabilities for BS and BD, generalized Benford’s Law (GB(d;γ)) was applied. Minimal χ^2 values were obtained at γ=0.65 and γ=0.07 for BS and BD respectively (χ^2 (e_BD^γ )=4.992, χ^2 (e_BD^γ )=2.209). As expected, χ^2 values of the sub-districts decreased by generalized Benford’s Law. The most dramatic χ^2 decrease occurred in BS. The number of sample plots of the sub-districts are different. Two random iterative processes happened 10000 times were therefore performed considering the number of sample plots of the sub-districts in B dataset. As a result 10000 χ^2 values were obtained for each sub-district. Average values of those χ^2 values were then used ((_ ^k)(χ^2 ) ̅ (E_BS^γ )=6.747 and (_ ^k)(χ^2 ) ̅ (E_BD^γ )=6.176) to calculate calibration coefficients of each sub-district. Naturalness values of BS and BD were found to be 4.992 and 2.414 respectively due to calibration coefficients of BS= ((_ ^k)(χ^2 ) ̅ (E_max^γ ))⁄((_ ^k)(χ^2 ) ̅ (E_BS^γ ) )=1 and BD=((_ ^k)(χ^2 ) ̅ (E_max^γ ))⁄((_ ^k)(χ^2 ) ̅ (E_BD^γ ) )=1.093. Since the perfect naturalness value is theoretically equal to 0, the obtained results indicate that BD ecosystems are more natural than BS ecosystems.

Keywords

Hemeroby, Naturalness, Forest ecosystems, First digit rule, Generalization, Randomization

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