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

Ecological DOWs(species-abundance distributions)

• North American Breeding Bird Survey (1,583 sites)• Forest Inventory and Analysis (7,403 sites)• Mammal Community Database (42 sites)• North American Butterfly Association (306 sites)• Aquatic prokaryotes (92 metagenomes)

– Arctic surface waters, Deep-sea Hydrothermal vents

• Terrestrial prokaryotes (48 metagenomes) – Arctic soils, agricultural soils

• Indoor fungi (124 metagenomes)– All continents except Antarctica

Total: 9,598 different sites of diverse communities

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

Obs

erve

d ab

unda

nce

R2 = 0.931,583 sites in the Breeding Bird Survey

100 101 102

102

101

100

R2 per site

Predicted abundance

0.0 1.0

R2 = 0.84

7,403 treecommunities

R2 = 0.80

306 butterflycommunities

R2 = 0.78

42 mammal communities

Observed abundance vs. Abundance at the center of the feasible set

Count data

R2 = 0.58

48 terrestrial prokaryote

Observed abundance vs. Abundance at the center of the feasible set

R2 = 0.83

92 aquatic prokaryote

R2 = 0.76

124 indoor fungi

Metagenomes

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

pdf10,173 sites

R2 (obs vs. random sample)

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

pdf

1,583 sites in the Breeding Bird Survey

0.2 0.4 0.6 0.8

0.8

0.6

0.4

0.2

R2 (obs vs. random sample)

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