Macroecology & uneven distributions of wealth

Ken Locey

http://tchester.org/srp/plants/communities/figures/global_biodiversity_by_area.gif

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

Abundance: ni/N

Distribution: f(k;λ) = λke-λ/k!

Diversity: H’ = -Σpi*ln(pi)

…study of ecological relationshipsthat involves characterizing and explaining statistical patterns of…

Macroecology

Land birds

Landmammals

Geographic range patternsN

orth

-Sou

th (k

m)

East-West (km) 100 1,000 10,000

Metabolic Theory of Ecology (MTE)Ecological phenomenon ∝ M3/4e-E/kt

Temp. corrected max. rate of whole organism biomass production

Slope = 0.76R2 = 0.99

1 3 6 10 14 19 33 38 69 93150

0123456789

10

Species Abundance Distribution

Abundance Class

freq

uenc

y(frequency distribution)

http://encyclopediaurantia.org/images/ROM11.JPG

DATA

Computing

GISMath & Stats

Metabolic rate ∝ M3/4e-E/kt

Information:

Tools

COLLABORATION & SHARING

Code

dev

elop

men

t Sharing

Source networks

GISProgrammingPublished ResearchData managementMath & StatsCollaboration

Undergraduate &Graduate research

Skills

Jobs

Grad School

Center for Macroecology, Evolution, & Climate www.macroecology.ca

macroecology.ku.dk

whitelab.weecology.org

Species Abundance Distribution

Abundance Class

freq

uenc

y(frequency distribution)

1 3 6 10 14 19 33 38 69 93150

0123456789

10

1 6 11 16 21 26 31 361

10

100

Species Abundance Distribution

Rank in Abundance

Abun

danc

e(Rank-abundance distribution)

Wheat Production (tons)

tons62.9 104588178.7

Poverty in Rural America, 2008

Percent in Poverty54.5 - 25 25 - 20 20 – 14.3 14.2 – 12.2 12.1 - 10 10 – 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 abundanceGlobal Oil ConsumptionGDP, GNP

Number of entities (N)SpeciesNationsEconomic classes

Distributions of Wealth (DOW)

If Q = 10 and N = 3, then:8 unordered ways to sum Npositive integers to obtain Q 8+1+1 7+2+1 6+3+1 6+2+2 5+4+1 5+3+2 4+4+2 4+3+3

Distributions of Wealth (DOW)

Do we observe the average of possible DOWs?

The feasible set(all possible shapes of the DOW)

16,958 shapes forQ = 50 & N = 10

Rank

Wea

lth

Combinatorial Explosion

Q N Size of feasible set

50 10 16,928

500 10 2.013 × 1012

5000 10 1.531 × 1021

Heat mapping the feasible set(or a random sample)

ln(w

ealth

)

Rank

Q=1,000N=80

Heat mapping the feasible set(or a random sample)

ln(a

bund

ance

)

Rank in abundance

ca. 4.02x1029 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)

Obs

erve

d w

ealth

100 101 102

Predicted wealth

102

101

100

R2 per site

OBSERVED: [1, 2, 10, 12, 20, 30, 40, 60, 110]PREDICTED: [1, 2, 11, 11, 22, 28, 43, 50, 117]

R2 = 0.99

Obs

erve

d ab

unda

nce

100 101 102

Predicted abundance

102

101

100

R2 per siteR2 = 0.99R2 = 0.89R2 = 0.80R2 = 0.75

Obs

erve

d ab

unda

nce

100 101 102

Predicted abundance

102

101

100

R2 per siteR2 = 0.99R2 = 0.89R2 = 0.80R2 = 0.75

R2 per site

0.0 1.0

Obs

erve

d ab

unda

nce

100 101 102

Predicted abundance

102

101

100

R2 per site0.0 1.0

R2 = 0.93

Food & Agriculture Organization of the UN

US Dept of Energy, Energy Information Admin.

0.83 0.91 0.93

Predicted supply

Obs

erve

d su

pply

Food supply among nations(1960-2010)

grams/capita/day * 0.1tons * 0.0001grams/capita/day

0.69 0.77 0.91

Predicted pop. size

Obs

erve

d po

p. si

zePopulation sizes among nations

(1960-2009, millions of people)

0.88 0.92 0.92

Predicted

Obs

erve

d

Oil use among nations(1980-2009, barrels per day * 0.01)

Predicted home runs

Obs

erve

d ho

me

runs

0.93 0.88 0.90

0.91 0.91 0.89

0.94 0.93

(2002-2010)http://mlb.mlb.com

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

Perc

entil

e of

the

feas

ible

set

Gini’s coefficient of inequality

The feasible set(all possible values of species evenness)Sp

ecie

s eve

nnes

s

Species richness, S

Total abundance, N = 60

Combinatorial Explosion

Q N Size of feasible set

1000 10 886,745,696,653,253

1000 100 302,194,941,264,401,427,042,462,944,147

1000 900 190,569,292

Feasible sets are dominatedby hollow-curves

Evar

Prob

abili

ty d

ensit

y fu

nctio

nN = 50, S = 205,507 macrostates

N = 50, S = 1016,928 macrostates

Q=50, N=20

Q=50, N=10

Evenness(Smith & Wilson, 1996)

MTE prediction: species richness decreases with temperature (S ∝ Ae-Ea/kT )

Computer Science Student:Biology student:

Chemistry Studentmodels based on chemical kinetics/activation energy

microbe data,reasons why MTEshould (not) workfor microbes

model developmentdata 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 birds Land mammals

Body-size distributions

Num

ber o

f spe

cies continental

regional

patch