Table 1 General format, power law and random placement models for SAR, EAR and OAR
From: Application of fundamental equations to species−area theory
Parameters | General format | Power law model | Random placement model |
|---|---|---|---|
SAR EAR | S a + E A-a = S A = E A S A-a + E a = S A = E A | S a = ca z E a = cA z − c(A − a)z | \(S_{a} = S_{a}^{1} = S_{A} - \sum \limits_{i = 1}^{{S_{A} }} \left(1 - \frac{a}{A}\right)^{{N_{i} }}\) |
\(E_{a} = S_{a}^{N} = \sum \limits_{i = 1}^{{S_{A} }} (\frac{a}{A})^{{N_{i} }}\) | |||
OAR | \(O_{a, A - a} = S_{a} - E_{a}\) \(O_{a, A - a} = S_{a} + S_{A - a} - S_{A}\) \(O_{a, A - a} = S_{A} - E_{a} - E_{A - a}\) \(O_{a, A - a} = O_{A - a, a}\) | \(O_{a, A - a} = ca^{z} + c(A - a)^{z} - cA^{z}\) | \(O_{a, A - a} = S_{A} - \sum \limits_{i = 1}^{{S_{A} }} \left[ {\left( {1 - \frac{a}{A}} \right)^{{N_{i} }} + \left( {\frac{a}{A}} \right)^{{N_{i} }} } \right]\) |
h | \(h = \frac{{O_{a, A - a} }}{{S_{a} }} = \frac{{S_{a} - E_{a} }}{{S_{a} }} = 1 - \frac{{E_{a} }}{{S_{a} }}\) | \(h = 1 - \frac{{A^{z} - (A - a)^{z} }}{{a^{z} }}\) | \(h = 1 - \frac{{ \sum \nolimits_{i = 1}^{{S_{A} }} \left(\frac{a}{A}\right)^{{N_{i} }} }}{{S_{A} - \sum \nolimits_{i = 1}^{{S_{A} }} \left(1 - \frac{a}{A}\right)^{{N_{i} }} }}\) |
h, a = A/2 | \(h = \frac{{2S_{A/2} - S_{A} }}{{S_{A/2} }} =\) 2−\(\frac{{S_{A} }}{{S_{A/2} }}\) | h = 2 − 2z | \(h = 2 - \frac{1}{{1 - \frac{{ \sum \nolimits_{i = 1}^{{S_{A} }} \left(\frac{1}{2}\right)^{{N_{i} }} }}{{S_{A} }}}}\) |
h′ | \(h^{'} = \frac{{O_{a, A - a} }}{{S_{A} }} = \frac{{S_{a} + S_{A - a} }}{{S_{A} }} - 1\) | \(h^{'} = \frac{{ca^{z} + c(A - a)^{z} }}{{cA^{z} }} - 1\) | \(h^{'} = \frac{{2S_{A} - \sum \nolimits_{i = 1}^{{S_{A} }} \left[ {\left( {1 - \frac{a}{A}} \right)^{{N_{i} }} + \left( {\frac{a}{A}} \right)^{{N_{i} }} } \right] }}{{S_{A} }} - 1\) |
h′, a = A/2 | \(h^{'} = \frac{{O_{a, A - a} }}{{S_{A} }} = \frac{{2S_{A/2} }}{{S_{A} }} - 1\) | h ’ = 21−z − 1 | |
\(\eta\) | \(\eta = \frac{{S_{a} }}{{S_{A} }} = 1 - \frac{{E_{A - a} }}{{S_{A} }}\) | \(\eta = c(\frac{a}{A})^{z}\) | \(\eta = 1 - \frac{{ \sum \nolimits_{i = 1}^{{S_{A} }} (1 - \frac{a}{A})^{{N_{i} }} }}{{S_{A} }}\) |
λ | \(\lambda = \frac{{E_{a} }}{{S_{A} }} = 1 - \frac{{S_{A - a} }}{{S_{A} }}\) λ = (1 − h)η | \(\lambda = 1 - c(1 - \frac{a}{A})^{z}\) | \(\lambda = \frac{{ \sum \nolimits_{i = 1}^{{S_{A} }} (\frac{a}{A})^{{N_{i} }} }}{{S_{A} }}\) |