Population Growth

1
Population Growth
U.S. population passes 300 million milestone
US clock 303,125,670
World clock 6,624,662,442
2
Population Growth

• ? N t1/ Nt
• ? change in N in a discreet period of time
• Populations grow continuously
• US Population
• One birth every................7 seconds
• One death every..............13 seconds
• One immigrant (net) every............ 31
  seconds
  
• Net gain of one person every..... 11 seconds
• dN/dt rate of growth
• change in numbers with change in time

3
Rate of Growth

• dN/dt rmaxN
• rmax intrinsic rate of increase
• maximum per capita rate of increase under ideal
  conditions
  
• birthrate - death rate
• As N ? dN/dt ?
• The rate of growth increases
• the exponential growth

4
Exponential Growth

• Instantaneous change dN/dt rmaxN
• Integrate to estimate Nt
• Nt N0ermaxt
• Rearrange and take the log of both sides
• r ln (Nt/No)
• t
• Substitute Nt/No Ro then
• R ln Ro when T generation time
• T

5
Exponential Growth
6
Exponential Growth

• When does it happen?
• Favorable environment with low starting density

7
Scots Pine
50,000 25,000 0
Pollen accumulation rate in lake sediments (an
index of population size)
0 250
500
Years after colonizing in Great Britain
8
Whooping Cranes
Since protection in 1940 population has grown
from 22 to 220 in 2005
200 150 100 50 0
cranes
Problems were hunting and habitat destruction
1940 1960 1980 2000
year
9
Exponential Growth

• Will there be whooping cranes everywhere?
• No
• As resources ? pop growth ? and eventually stops

10
Eurasian Collared Dove
250,000 200,000 150,000 100,000 50,000

0
birds
After colonizing Great Britain
In less than 20 years, growth slowed
1955 1960 1965 1970 1975
year
11
Environmental Limitation

• Environment can support a limited of
  individuals of a population
  
• Carrying capacity K
• As N -- K pop growth slows and then stops

12
Logistic Growth

• Growth limited by the environment

250,000 200,000 150,000 100,000 50,000

0
birds
1955 1960 1965 1970 1975
13
Logistic Growth

• Exponential
• dN/dt rmaxN

14
Logistic Growth

• Logistic
• dN/dt rmaxN K-N
  K
  

15
Population Growth
16
Yeast Logistic Growth
17
Barnacle Logistic Growth
18
Daphnia Growth
Predicted observed
K-N
if N K then is negative and dN/dt is
negative
K
19
Birth and Death Rates

• Affected by
• Biotic factors
• Disease, predators, food, competitors
• Abiotic factors
• Rainfall, temperature, light, pollution
• Can be density dependent or density independent
• Can be extrinsic or intrinsic

20
Limits to Growth

• Medium Galapagos finch
• Droughts (fewer seeds)
• Death rate increases
• Birth rate decreases
• High rainfall (more seeds and caterpillars)
• Death rate decreases
• Birth rate increases

21
Finches Rainfall