age interval long periods of lecture 29 & 30: population...

1

7.0147.014

Lecture 29 & 30:Lecture 29 & 30:

Population GrowthPopulation Growth

April 30 & May 2April 30 & May 2

20072007

Population Age Distribution

More Developed CountriesAge Interval

Number of people (Millions) FemalesMales

80 - 9070 - 8060 - 7050 - 6040 - 5030 - 4020 - 3010 - 20 0 -10

Long periods ofno net growth lead toeven distribution

Who will care for the old people?

Population Summary forthe US

2000

2025

2050

http://blue.census.gov/

2

Baby boomHere you are!*

Baby Boom Echo*

*

3

Population Age Distribution

Less Developed CountriesAge

300300Number of people (Millions) FemalesMales

Population Summary forUganda

2000

2025

2050

http://blue.census.gov/

Very high reproductive rate

4

Life Tables

x = age or interval (defined)

N0 = number of individuals in original cohort (defined)

dx = number of original cohort dying during interval

Nx = number of individuals surviving to age x (measured)

lx = proportion of individuals surviving to age x

lx = Nx / N0

mx = per capita births during age interval x to x+1 (measured)

“age specific fecundity” = female offspring produced per female

Age

Number Surviving

Proportion Surviving

X Nx lx

0 100 1.0 1 50 .5 2 40 .4 3 30 .3 4 0 0

A COHORT LIFE TABLE (for Unicorns)N0 = 100

lx = Nx/No

SURVIVORSHIP CURVES

Age

Log

(Num

ber S

urvi

ving

)

Type I

Type II

Type III

High Probabilityof Survival

Steady Survival

High Probabilityof Survival

Low Probabilityof SurvivalLow Probability

of Survival

SURVIVORSHIP CURVES

Homo sapiens

Spergula vernalis(grass)

Common BirdSpecies

Age

Log

(Num

ber S

urvi

ving

)

Age

Log

(Num

ber S

urvi

ving

)

Age

Log

(Num

ber S

urvi

ving

)

See Fig 5 4 .1Purves

5

Age

Number

Surviving

Proportion

Surviving

Average Offspring per

female of age x

(age-specific fecundity )

X Nx lx mx

0 100 1.0 0

1 50 .5 4

2 40 .4 2.5

3 30 .3 0

4 0 0 0


Age

Number

Surviving

Proportion

Surviving

Average Offspring per

female of age x

(age-specific fecundity)

Realized Fecundity

Values

X Nx lx mx lxmx

0 100 1.0 0 0

1 50 .5 4 2

2 40 .4 2.5 1

3 30 .3 0 0

4 0 0 0 0

R0 = ! lxmx = 3


R0 = Net Replacement

What if you can’t follow cohort?

Mastodon Skeleton

http://www.state.nd.us/ndfossils/Education/animals/mastodon%20%20030612.html

Age Interval

X

Number Surviving at

Beginning of X

Nx

Number Dying

dx

Proportion Surviving

by Age X

lx

0 100 50 1.0

1 50 10 .5

2 40 10 .4

3 30 30 .3

4 0 0 0

A STATIC LIFE TABLE (for Unicorns)

Sample of 100 unicorns N0 = 100

measuredNx – dx = Nx+1 lx = Nx/No

6

Lecture 30Lecture 30

Population Density (N)

Density-dependentdeath rate d

Density-independentbirth rate b

Equilibrium Density

r = (b – d)

b = d thus r = 0

thus dN/dt = 0

1 dNN dt


Density-independentdeath rate

Density-dependent birthrate

1 dNN dt


Density-dependentdeath rate

Density-dependent birthrate

Density-Dependant Factors Regulate Population Size

1 dNN dt

as N r stabilizing

US Population ClockUS Population Clockhttp://www.census.gov/cgi-bin/popclock

1212

2626

1313

88

295,974,238295,974,238

20052005

11 seconds11 seconds13131111Net gain of oneNet gain of oneperson everyperson every

27 seconds27 seconds25252222One internationalOne internationalmigrant (net) everymigrant (net) every

13 seconds13 seconds12121313One death everyOne death every

8 seconds8 seconds9988One birth everyOne birth every

301,723,494301,723,494Total PopulationTotal Population

200720072004200420032003

4/29/2007 at 14:13 AM EDT

Human Population Growth

Year

Pop

ulat

ion

(Bill

ions

)

1

2

3

4

5

6

Agriculture &domestification ofanimals

4 million 7 million

HunterGatherers

Adapted from: Cohen, “How Many People Can the Earth Support”

10,000 BC 8,000 BC 2,000 AD04,000 BC

Bubonic Plague

Industrial Revolution

(1400)

(1800)

Modern Medicine(reduced mortality)

(1900)

FossilFuel

6,591,890,041(4/29/2007)

http://www.census.gov/main/www/popclock.html

6,363,174,549(4/28/2004)

6,432,150,287(4/22/05)

Now projected toreach 9 Billion

and level off

6 Billion(1999)

6,289,870,258(4/30/2003)

7

Four “Evolutions” in Human Population Growth

Adapted from: Cohen, “How Many People Can the Earth Support”

Evolution Driver

Midpoint

Population (billions)

Doubling Time (years) before after

Local Agriculture

8000 B.C.

0.005

40,000 - 300,000

1,400 – 3,000

Global Agriculture

1750 A.D.

0.75

750 – 1,800

100 – 130

Public Health

1950

2.5

87

36

Fertility Control

1970

3.7

34 (peak)

>40 (since 1990)

F

and recall from an earlierand recall from an earlierlecture lecture …………

Popu

latio

n si

ze (b

illion

s)Po

pula

tion

size

(billi

ons)

COCO22

NN22O (310 x COO (310 x CO22))

CHCH4 4 (21x CO(21x CO22))

Population sizePopulation size

380380

340340

300300

260260

18001800

14001400

10001000

60060000 10001000500500 15001500 20002000

CO

CO

22 an

d N

and

N22O

O

ppm

Vpp

mV

Time, Calendar years (A.D.)Time, Calendar years (A.D.)

CH

CH

44 pp

bVpp

bV

66

44

22

00

Falkowski and Tchernov 2004

Demographic Transition

Stage 1

High birth rateHigh, but fluctuating

death rate

Stage 2

Declining death ratesContinuing high birth

rates

Stage 3

Declining birth anddeath rates

Stage 4

Low death rateLow, but fluctuating

birth rate

http://www.census.gov/ipc/prod/wp02/wp02-1.pdf

the tipping point

age interval long periods of lecture 29 & 30: population...

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