Macroecology & uneven distributions of wealth Ken Locey

183,913,348 records of birds in the Global Biodiversity Information Facility database

Abundance: n i /N Distribution: f(k;λ) = λ k e -λ /k! Diversity: H’ = -Σp i *ln(p i ) …study of ecological relationships that involves characterizing and explaining statistical patterns of… Macroecology

Land birds Land mammals Geographic range patterns North-South (km) East-West (km) 100 1,000 10,000

Metabolic Theory of Ecology (MTE) Ecological phenomenon ∝ M 3/4 e -E/kt Temp. corrected max. rate of whole organism biomass production Slope = 0.76 R 2 = 0.99

Species Abundance Distribution Abundance Class frequency (frequency distribution)

DATA

Computing GIS Math & Stats Metabolic rate ∝ M 3/4 e -E/kt Information: Tools

COLLABORATION & SHARING Code development Sharing Source networks

GIS Programming Published Research Data management Math & Stats Collaboration Undergraduate & Graduate research Skills Jobs Grad School

Center for Macroecology, Evolution, & Climate macroecology.ku.dk whitelab.weecology.org

Species Abundance Distribution Abundance Class frequency (frequency distribution)

Species Abundance Distribution Rank in Abundance Abundance (Rank-abundance distribution)

Wheat Production (tons) tons

Poverty in Rural America, 2008 Percent in Poverty – – – 3.1

Distributions of Wealth (DOW) Supreme importance attaches to one economic problem, that of the distribution of wealth. Is there a natural law according to which the wealth of society is divided? – John Bates Clark Wealth: sources of human welfare which are material, transferable, and limited in quantity.

Total quantity ( Q) Community abundance Global Oil Consumption GDP, GNP Number of entities ( N) Species Nations Economic classes Distributions of Wealth (DOW)

If Q = 10 and N = 3, then: 8 unordered ways to sum N positive integers to obtain Q Distributions of Wealth (DOW)

Do we observe the average of possible DOWs?

The feasible set (all possible shapes of the DOW) 16,958 shapes for Q = 50 & N = 10 Rank Wealth

Combinatorial Explosion QNSize of feasible set , × × 10 21

Heat mapping the feasible set (or a random sample) ln(wealth) Rank Q=1,000 N=80

Heat mapping the feasible set (or a random sample) ln(abundance) Rank in abundance ca. 4.02x10 29 possible shapes for N=1000 & S=80

Q = Total community abundance ( i.e. number of individuals) N = Species richness (i.e. number of species) Ecological DOWs (species-abundance distributions)

Observed wealth Predicted wealth R 2 per site OBSERVED: [1, 2, 10, 12, 20, 30, 40, 60, 110] PREDICTED: [1, 2, 11, 11, 22, 28, 43, 50, 117] R 2 = 0.99

Observed abundance Predicted abundance R 2 per site R 2 = 0.99 R 2 = 0.89 R 2 = 0.80 R 2 = 0.75

Observed abundance Predicted abundance R 2 per site R 2 = 0.99 R 2 = 0.89 R 2 = 0.80 R 2 = 0.75 R 2 per site

Observed abundance Predicted abundance R 2 per site R 2 = 0.93

Food & Agriculture Organization of the UN US Dept of Energy, Energy Information Admin.

Predicted supply Observed supply Food supply among nations ( ) grams/capita/day * 0.1tons * grams/capita/day

Predicted pop. size Observed pop. size Population sizes among nations ( , millions of people)

Predicted Observed Oil use among nations ( , barrels per day * 0.01)

Predicted home runs Observed home runs ( )

Are DOWs similar to the average of possible shapes? …very often Do Q and N constrain the DOW more than ever realized? …Yup Is the feasible set good for more than predictions? …Absolutely Is combinatorial explosion a pain in the *expletive*? …Not for long…?

Funding USU College of Science – Willard L. Eccles Fellowship NSF CAREER award to Ethan White Research grant from Amazon Web Services

Acknowledgments Individuals, agencies, organizations responsible for the collection and management of the: – Breeding Bird Survey, Christmas Bird Count, Forest Inventory and Analysis, Mammal Community Database, North American Butterfly Association, Argonne National Laboratory’s MG-RAST metagenomic server Colleagues & Collaborators – USU: Ethan White, Xiao Xiao, Dan McGlinn – Berkeley Harte Lab: Justin Kitzes – SESYNC: Bill Burnside UCO college of Math and Science

The feasible set as a framework Understanding Comparing Inequality

Percentile of the feasible set Gini’s coefficient of inequality

The feasible set (all possible values of species evenness) Species evenness Species richness, S Total abundance, N = 60

Combinatorial Explosion QNSize of feasible set ,745,696,653, ,194,941,264,401,427,042,462,944, ,569,292

Feasible sets are dominated by hollow-curves Q=50, N=20 Q=50, N=10 Evenness (Smith & Wilson, 1996)

MTE prediction: species richness decreases with temperature (S ∝ Ae -E a /kT ) Computer Science Student: Biology student: Chemistry Student models based on chemical kinetics/activation energy microbe data, reasons why MTE should (not) work for microbes model development data scraping & management Temperature-richness predictions of MTE do not hold for diverse microbe communities as tested using several models of chemical kinetics. This may be explained by microbial dormancy and dispersal. + Conclusion(?)

Body mass (g) Land birdsLand mammals Body-size distributions Number of species continental regional patch