Table 1

Summary of estimators used, their formulae and main reference.

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

BD2N = 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 = {[∑ (pi + ni)] - 1}/∑ Bi

[5,6]

CI, NN and 2NN search areas pooled (KM2P)

KM2P = {[∑ (pi + ni + mi)] - 1}/∑ Ci

[5]

Ordered Distance (OD) estimators

Second Closest Individual (OD2C)

OD2C = (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)

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[7,8]

Third closest individual in each quadrant (AO3Q)

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[7,8]

Variable Area Transect (VAT)

Variable Area Transect

V AT = (3N - 1)/(wli)

[9]

Quadrat (QUAD)

Quadrat

QUAD = ∑ qi/liwiN)

[17]


CI – closest individual, NN – nearest neighbor, 2NN – second nearest neighbor. R(1)i = the distance from the ith sample point to the CI; R(2)i = the distance from the ith sample point to the second CI; R(3)i = the distance from the ith sample point to the third CI; R(3)ij = the distance from the ith sample point to the third CI for the jth quadrant; H(1)i = the distance from the ith CI to its NN; H(2)i = the distance from the NN at the ith random point; pi, ni, mi = the number of Cis, NNs and 2nd NNs respectively, Bi = the total search area at the ith sample point for the CI and NN combined; Ci, = the total search area at the ith sample 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); wi = width of quadrat; w = width of transect; li = length of quadrat.

White et al. BMC Ecology 2008 8:6   doi:10.1186/1472-6785-8-6

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