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John Harte, UC Berkeley INTECOL London August 20, 2013

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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John Harte, UC Berkeley INTECOL London August 20, 2013

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  1. Maximum Entropy and Mechanism: Prospects for a Happy Marriage John Harte, UC Berkeley INTECOL London August 20, 2013

  2. 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.

  3. 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

  4. 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

  5. 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

  6. 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

  7. Extending and Generalizing METE Original Theory Alters size-abundance distribution Alters predicted rarity

  8. 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)

  9. 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

  10. 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!

  11. 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.

  12. 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

  13. 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.

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