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Table 1 Summary of estimators used, their formulae and main reference.

From: A comparison of plotless density estimators using Monte Carlo simulation on totally enumerated field data sets

Estimator Formula§ Reference
Basic Distance (BD) estimators
Compound of CI, NN & 2NN (BDAV3) BDCI = 1/(4 [∑ R(1)i/N]2) [1]
  BDNN = 1/(2.778 [∑ H(1)i/N]2  
  BD 2N = 1/(2.778 [∑ H(2)i/N]2  
  BDAV3 = (BDCI + BDNN + BD2N)/3  
Kendall-Moran (KM) estimators
CI and NN Search areas pooled (KMP) KMP = {[∑ (p i + n i )] - 1}/∑ B i [5,6]
CI, NN and 2NN search areas pooled (KM2P) KM 2P = {[∑ (p i + n i + m i )] - 1}/∑ C i [5]
Ordered Distance (OD) estimators
Second Closest Individual (OD2C) OD 2C = (2N - 1)/π∑ (R(2)i)2 [7,8]
Third closest Individual (OD3C) OD3C = (3N - 1)/π∑ (R(3)i)2  
Angle-Order (AO) estimators
Second closest individual in each quadrant (AO2Q) A O 2 Q = 28 N / π 1 / R ( 2 ) i j 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyqaeKaem4ta8KaeGOmaiJaemyuaeLaeyypa0JaeGOmaiJaeGioaGJaemOta4Kaei4la8IaeqiWda3aaabqaeaacqaIXaqmcqGGVaWlcqWGsbGudaqhaaWcbaGaeiikaGIaeGOmaiJaeiykaKIaemyAaKMaemOAaOgabaGaeGOmaidaaaqabeqaniabggHiLdaaaa@4269@ [7,8]
Third closest individual in each quadrant (AO3Q) A O 3 Q = 44 N / π 1 / R ( 3 ) i j 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyqaeKaem4ta8KaeG4mamJaemyuaeLaeyypa0JaeGinaqJaeGinaqJaemOta4Kaei4la8IaeqiWda3aaabqaeaacqaIXaqmcqGGVaWlcqWGsbGudaqhaaWcbaGaeiikaGIaeG4mamJaeiykaKIaemyAaKMaemOAaOgabaGaeGOmaidaaaqabeqaniabggHiLdaaaa@4269@ [7,8]
Variable Area Transect (VAT)
Variable Area Transect V AT = (3N - 1)/(wl i ) [9]
Quadrat (QUAD)
Quadrat QUAD = ∑ q i /l i w i N) [17]
  1. CI – closest individual, NN – nearest neighbor, 2NN – second nearest neighbor. R(1)i= the distance from the ithsample point to the CI; R(2)i= the distance from the ithsample point to the second CI; R(3)i= the distance from the ithsample point to the third CI; R(3)ij= the distance from the ithsample point to the third CI for the jthquadrant; H(1)i= the distance from the ith CI to its NN; H(2)i= the distance from the NN at the ithrandom point; p i , n i , m i = the number of Cis, NNs and 2ndNNs respectively, B i = the total search area at the ithsample point for the CI and NN combined; C i , = the total search area at the ithsample point for the CI, its NN, and the second NN combine; N = the sample size (number of random sample points used to gather distance information); w i = width of quadrat; w = width of transect; l i = length of quadrat.