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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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slide1

Maximum Entropy and Mechanism: Prospects for a Happy Marriage

John Harte, UC Berkeley

INTECOL

London

August 20, 2013

slide2

MaxEnt Approach to Macroecology

  • To predict patterns in:
  • abundance
  • distribution
  • energetics
  • network structure
  • across taxonomic groups
  • across spatial scales
  • across habitat categories
  • without adjustable parameters,
  • without arbitrary choice of governing mechanisms
  • and thereby to reach insight into mechanism.
slide3

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.

P(x)

P(x)

Lower Entropy

Higher Entropy

x

x

slide4

A Candidate Macroecological Theory: The Maximum Entropy Theory of Ecology (METE)

Ingredients of a Fundamental Theory of Macroecology

INPUT DATA

State Variables: SNE

THEORYMaxEnt:

An inference procedure based on information theory

  • PREDICTIONS(Metrics of Ecology)
  • Species-Area Relationships
  • Endemics-Area Relationships
  • Abundance & Body Size Distributions
  • Spatial Aggregation Patterns
  • Web Structure & Dynamics
  • Species Distribution across Genera, Families, etc.
  • APPLICATIONS
  • Species Loss under Habitat Loss
  • Reserve design
  • Web Collapse under Deletions
  • Scaling up Biodiversity
slide5

Examples of Validated Predictions

MaxEnt predicts:

all species-area curves collapse onto a universal curve

MaxEntpredicts:

the fraction of species that are rare

z =1/4

log(N(A)/S(A))

Harte et al., Ecology Letters, 2010; Harte, Oxford U. Press, 2011

slide6

At the Frontier of METE

Core theory

Resource constraints:

S, N, E

Water, Phosphorus,..

Trophic interaction constraints:

Evolutionary constraints: taxonomy/ phylogeny

Order, Family, Genus

Linkages

slide7

Extending and

Generalizing METE

Original Theory

Alters size-abundance distribution

Alters predicted rarity

slide8

Including higher taxonomic levels as constraints

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.

Log(abundance)

Families of differing species richness

The Damuth rule splits apart!

Log(metabolic rate)

slide9

Including additional resource constraints (in addition to energy, E)

The log-series

SAD becomes:

r - 1 = # additional resources

The inclusion of additional resource constraints predicts increased rarity

slide10

The theory fails to predict patterns in ecosystems undergoing relatively rapid change

1.

2.

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

X

X

Kempton and Taylor (1974)

3.

150 y

4 My

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!

slide11

SUMMARY:

  • METE is a relatively successful theory of macroecology.
  • Success does not imply mechanism does not matter!
  • Mechanisms are incorporated into the values of the state variables, and we still need to understand what they are.
  • Failure of the core theory tells us that more mechanistic information than is captured by the state variables is needed to predict patterns in ecology.
  • Testing various extensions of the theory allow us to identify the role of particular mechanisms.
slide12

Thanks:

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

slide14

Hypothesis:

Deviations from the MaxEnt theory

x

x

x

x

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.