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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)/(w∑ l 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.