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Maximum Entropy and Mechanism: Prospects for a Happy Marriage . John Harte, UC Berkeley INTECOL London August 20, 2013. MaxEnt Approach to Macroecology To predict patterns in: abundance d istribution e nergetics network structure
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Maximum Entropy and Mechanism: Prospects for a Happy Marriage
John Harte, UC Berkeley
August 20, 2013
Maximum Entropy? Just what is being maximized?
Here “entropy” refers to information entropy, not thermodynamic entropy.
Information entropy is a measure of the lack of structure or detail in the probability distribution describing your knowledge of a system.
A Candidate Macroecological Theory: The Maximum Entropy Theory of Ecology (METE)
Ingredients of a Fundamental Theory of Macroecology
State Variables: SNE
An inference procedure based on information theory
all species-area curves collapse onto a universal curve
the fraction of species that are rare
Harte et al., Ecology Letters, 2010; Harte, Oxford U. Press, 2011
S, N, E
Trophic interaction constraints:
Evolutionary constraints: taxonomy/ phylogeny
Order, Family, Genus
Alters size-abundance distribution
Alters predicted rarity
If (S,N,E) (F,S,N,E),
then the energy-abundance relationship is modified:
(F = family or other
higher order category)
m labels the species richness of the family (or order, …) that the species with abundance n is in.
Families of differing species richness
The Damuth rule splits apart!
Including additional resource constraints (in addition to energy, E)
r - 1 = # additional resources
The inclusion of additional resource constraints predicts increased rarity
The theory fails to predict patterns in ecosystems undergoing relatively rapid change
Abundance Distribution of Rothampsted Moths
Species-area slopes for plants in successional sites (aftermath of an erosion event) lie well above the scatter around the universal curve
Relatively undisturbed fields: Fisher log series distribution (predicted by METE)
Fields recently left to fallow and in transition: Lognormal distribution
Kempton and Taylor (1974)
Arthropod abundance distributions from Hawaiian sites of different ages and stages of speciation
Test of abundance distribution
Data from Dan Gruner
Similar pattern of success and failure for body size distributions!
To my Collaborators:
Erin Conlisk Adam Smith Xiao Xiao Mark Wilber
Justin Kitzes Andrew RomingerEthan WhiteChloe Lewis
Erica Newman David StorchTommasoZillioXiao Xiao
To Other Sources of Data:
J. Green R. Krishnamani J. Godinez W. Kunin
R. Condit P. Harnik K. Cherukumilla E. White
D. Gruner J. Goddard STRI D. Bartholomew
To the Funders:
NSF, Miller Foundation,Gordon and Betty Moore Foundation
To my Hosts during the development of METE:
Santa Fe Institute, Rocky Mountain Biological Laboratory, NCEAS, The Chilean Ecological Society, Charles University, University of Padua
Deviations from the MaxEnt theory
Measure of rapidity of change
But the pattern of deviation of abundance distributions from the predicted Fisher log series depends on whether the system is collapsing or diversifying.
This is just the first step in relating the mechanisms that disrupt an ecosystem to patterns predicted by macroecological theory.