MIT Department of Biology
7.014 Introductory Biology, Spring 2005
7.014
Lecture 29 & 30:
Population Growth
Lecture Slides
April 25 & 27, 2005
2005
Population Age Distribution
MORE DEVELOPED COUNTRIES
80-90
AGE INTERVAL
70-80
60-70
50-60
40-50
30-40
20-30
10-20
0-10
MALES
NUMBER OF PEOPLE (MILLIONS)
FEMALES
Figure by MIT OCW.
1
Population Summary for
the US
2000
2025
2050
http://blue.census.gov/
Population Age Distribution
LESS DEVELOPED COUNTRIES
AGE
300
MALES
300
NUMBER OF PEOPLE (MILLIONS)
FEMALES
Figure by MIT OCW.
2
Population Summary for
Uganda
2000
2025
2050
http://blue.census.gov/
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 l x = Nx / N0
mx = per capita births during age interval x to x+1 (measured)
“age specific fecundity” = female offspring produced per female
3
A COHORT LIFE TABLE (for Unicorns)
N0 = 100
Age
Number
Surviving
Proportion
Surviving
X
0
1
2
3
4
Nx
100
50
40
30
0
lx
1.0
.5
.4
.3
0
SURVIVORSHIP CURVES
High Probability
of Survival
Log (Number Surviving)
Type I
Steady Survival
Type II
Low Probability
of Survival
Low Probability
of Survival
Type III
High Probability
of Survival
Age
4
Log (Number Surviving)
SURVIVORSHIP CURVES
HOMO SAPIENS
SPERGULA VERNALIS
(GRASS)
Log (Number Surviving)
Log (Number Surviving)
AGE
AGE
COMMON BIRD
SPECIES
AGE
Figure by MIT OCW.
A COHORT LIFE TABLE (for Unicorns)
N0 = 100
Age
Number
Surviving
Proportion
Surviving
Average
Offspring
per female
of age x
X
0
1
2
3
4
Nx
100
50
40
30
0
lx
1.0
.5
.4
.3
0
mx
0
4
2.5
0
0
5
A COHORT LIFE TABLE (for Unicorns)
N0 = 100
Age
Number
Surviving
Proportion
Surviving
Average
Offspring
per female
of age x
X
0
1
2
3
4
Nx
100
50
40
30
0
lx
1.0
.5
.4
.3
0
mx
0
4
2.5
0
0
Realized
Fecundity
Values
lxmx
0
2
1
0
0
R0 = Σ lxmx = 3
R0 = Net Replacement
A STATIC LIFE TABLE (for Unicorns)
Sample of 100 unicorns N0 = 100
Age Interval
Number Surviving at
Beginning of X
Number Dying
Proportion Surviving
by Age X
X
Nx
dx
lx
0
1
2
3
4
100
50
40
30
0
50
10
10
30
0
1.0
.5
.4
.3
0
6
A COHORT LIFE TABLE (for Unicorns)
N0 = 100
Age
Number
Surviving
Proportion
Surviving
Average
Offspring
per female
of age x
X
0
1
2
3
4
Nx
100
50
40
30
0
lx
1.0
.5
.4
.3
0
mx
0
4
2.5
0
0
Realized
Fecundity
Values
lxmx
0
2
1
0
0
lxmxX
0
2
2
0
0
R0 = Net Replacement = ∑ lxmx = 3
G ~ (∑ lxmxx) / (∑ lxmx) = (∑ lxmxx) / R0 = 4/3
years
Intrinsic
Rate of
Increase
r ≈ (ln R0) / G ≈ (ln 3)/1.33 ≈ 0.82 yr -1
Density-Dependant Factors Regulate Population Size
Density-dependent
death rate - d
Density-dependent birth
rate
1 dN
N dt
1 dN
N dt
Density-independent
birth rate - b
Density-independent
death rate
Population Density (N)
Population Density (N)
Equilibrium
Density
r = b-d
Density-dependent
death rate
1 dN
N dt
Density-dependent birth
rate
as N r stabilizing
Population Density (N)
7
Human Population Growth
6,432,150,287
(4/22/05)
6,363,174,549
(4/28/2004)
Now projected to
reach 9 Billion
and level off
6,289,870,258*
(4/30/2003)
6
Population (Billions)
5
3
2
Hunter
Gatherers
1
4 million
10,000 BC
6 Billion
(1999)
Modern Medicine
(reduced mortality)
(1900)
4
Agriculture &
domestification of
animals
Fossil
Fuel
Industrial Revolution
(1800)
Bubonic Plague
(1400)
7 million
8,000 BC
4,000 BC
0
2,000 AD
Year
Adapted from: Cohen, “How Many People Can the Earth Support”
http://www.census.gov/main/www/popclock.html
Four “Evolutions” in Human Population Growth
Evolution
Driver
Midpoint
Population
(billions)
Doubling Time (years)
before
after
40,000 - 300,000
1,400 – 3,000
750 – 1,800
100 – 130
2.5
87
36
3.7
34 (peak)
>40
(since 1990)
Local
Agriculture
8000 B.C. 0.005
Global
Agriculture
1750 A.D. 0.75
Public
Health
1950
Fertility
Control
1970
F
Adapted from: Cohen, “How Many People Can the Earth Support”
8
and recall from lecture 20……
6
380
CO2
1800
2
0
N2O (310 x CO2)
340
Population size
1400
300
CH4 ppbV
Population size (billions)
4
CO2 and N2O ppmV
CH4 (21x CO2)
1000
260
600
0
500
1000
1500
Time, Calendar years (A.D.)
2000
Falkowski and Tchernov 2004
http://www.census.gov/ipc/prod/wp02/wp02-1.pdf
9
DEMOGRAPHIC TRANSITION
BIRTH RATE
D
TH
EA
TO
TA
L
PO
PU
LA
TI
O
N
TE
RA
Time
STAGE 1
High birth rate
High, but fluctuating
death rate
STAGE 2
Declining death rates
Continuing high
birth rates
STAGE 3
Declining birth and
death rates
STAGE 4
Low death rate
Low, but fluctuating
birth rate
Figure by MIT OCW.
10