ENVE3503 – Environmental EngineeringPopulation Growth
dXX
dt
The Sorcerer’s Apprentice
Exponential Growth
dXX
dt
104857652428826214413107265536327681638481924096204810245122561286432168421
Exponential Growth
dXX
dt
0t
tX X e
0
100000
200000
300000
400000
500000
600000
700000
800000
900000
1000000
0 5 10 15 20 25
Popu
lati
on S
ize
Time
exponential growth model, with
X0 = 1 = 0.69 d-1
104857652428826214413107265536327681638481924096204810245122561286432168421
The Death Term
d
dXk X
dt
0t
tX X e 0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 5 10 15 20 25
Popu
lati
on S
ize
Time (d)
another intrinsic characteristic of the organism.
dk
( )ddX
k Xdt
Limits to Exponential Growth(non-renewable and renewable resources)
http://wildgoosechasing.blogspot.com/2007/12/experts-world-population-will-explode.html
non-renewable resources
Logistic Growth (limitation by non-renewable resources)
1dX X
Xdt K
( )0
0
1 d
t
k t
KX
K Xe
X
0
1000
2000
3000
4000
5000
6000
7000
0 10 20 30 40 50
Popu
lati
on S
ize
Time (d)
carrying capacity, KWhile some organisms may reach a population size that is limited by non-renewable resources, higher organisms would be expect to encounter limitation by renewable resources first.
http://www.cbc.ca/gfx/images/news/photos/2008/06/27/f-un-food-distribution-584.jpg
renewable resources
Limits to Exponential Growth(non-renewable and renewable resources)
The Monod Model (limitation by renewable resources)
max ds
dX Sk X
dt K S
Substrate Concentration
Gro
wth
Rat
eHalf-saturation constant: substrate level at which the growth rate is at one-half it’s maximum.
The Monod Model (limitation by renewable resources)
max ds
dX Sk X
dt K S
0
2
4
6
8
10
0
10
20
30
40
0 20 40 60 80 100
Food
Sup
ply
Popu
lati
on S
ize
Time (d)
Should that population grow beyond its equilibrium size or if it were to experience an interruption in food supply, e.g. a famine, the population would decline and ultimately disappear.
A population in equilibrium with its food supply is maintained at a constant level.
The Yield Coefficient (linking substrate depletion and growth
max ds
dX Sk X
dt K S
max
1d
s
dS Sk X
dt Y K S
dX mgXY
dS mgS
0
100
200
300
400
500
0 5 10 15 20 25
Biom
ass,
Sub
stra
teTime
Life at carrying capacity …
Carrying capacity holds populations in check through density-driven phenomena such as,
• lack of space• increased incidence of disease• increased susceptibility to predation
0
1000
2000
3000
4000
5000
6000
7000
0 10 20 30 40 50
Popu
latio
n Si
ze
Time (d)
carrying capacity, K
Consider the differences in life at carrying capacity for non-human and human populations.
A catastrophe of Malthusian proportion …
How may humans experience “misery and vice” in a catastrophe of Malthusian proportions?
The 18th Century British economist recognized that populations grew exponentially, checked only by “misery or vice”, by which he meant . He asserted that because the “means of subsistence” increased in a linear fashion, demand would eventually outstrip supply with catastrophic results.
0
2
4
6
8
10
12
14
0 10 20 30 40 50
Popu
lati
on S
ize
Time
Soiling the global nest …
Paul Chefurka, a Canadian photojournalist and computer scientist, has suggested that as we pile environmental insult upon environmental insult, we diminish the carrying capacity of our global ecosystem. In this sense, we are not moving toward the crisis, the crisis is moving toward us!
What is the role of the environmental engineer in restoring the Earth’s carrying capacity?
Can you think of an example where this has been accomplished?
Popu
lati
on S
ize
Time
carrying capacity, K
IPAT: the elephant in the global living room
I P A T impact affluencepopulation technology
IPAT and the environmental engineer
I P A T impact affluencepopulation technology
thetechnological
solution
IPAT and us
I P A T impact affluencepopulation technology
thesocial
solution
Farmer Bean and Her Pigs
Drawings by Bill Sproule