Turkish Journal of Forestry (Jun 2021)
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.
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