Ecological Neutral Theory — Hubbell Model
Zero-sum ecological drift · Species abundance distribution · Fisher log-series
Community Parameters
Community size J:
400
Speciation rate ν:
0.020
Immigration rate m:
0.100
Steps per frame:
20
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Species richness S:
—
Θ = 2Jν:
—
Shannon H:
—
Simpson D:
—
Hubbell's neutral theory:
all individuals are ecologically equivalent; community changes by birth-death-immigration.
Θ = 2Jν
(biodiversity number)
At equilibrium, SAD follows the
Ewens sampling formula
; Fisher log-series in the limit:
E[Sₙ] = Θ xⁿ/n
(n individuals)
Immigration m controls metacommunity coupling. Low m → drift dominates → fewer species.