1. Which of the following statements about
conventional life tables is NOT true?
A) They were first used by life insurance companies to
estimate human survival patterns
B) They show the age-specific death rates for a population
C) They are used to predict population growth
D) They can be used to construct survivorship curves
E) They are often constructed by following a cohort from
birth to death.
2. To measure the population density of monarch butterflies
occupying a park, 100 butterflies are captured, marked with
a small dot on a wing, and then released. The next day,
another 100 butterflies are captured, including the recapture
of 20 marked butterflies. One would correctly estimate the
population to be
A) 2000
B) 5000
C) 1000
D) 200
E) 500
POPULATION GROWTH
To predict how populations
will increase or decrease,
need a mathematical model.
births
+
DENSITY
-
deaths
Models of Population Growth:
1) Exponential Growth Model
- assumes continuous breeding
- assumes during each and every time interval
there is a possibility of births and deaths
Exponential Growth Model
• Change in population size (N) during a fixed time
interval (t):
N/
t = (b - d)N
• b = births, d = deaths, N = current population size
• (b – d) = r
• r = the “intrinsic rate of natural increase” or the “per
capita rate of increase”
Exponential Growth Model
dN/dt = rmaxN
• rmaxN allows us to calculate the number of new
individuals added to a population in each generation:
• if rmax > 0, the population is growing
• if rmax < 0, the population is declining
• if rmax = 0, the population is stable
Exponential Growth Example
•
•
•
•
•
•
•
If
b = 30/1000 = .03
d = 10/1000 = .01
rmax = b – d
= .03 - .01
rmax = .02
N = 10,000
• Then
• dN/dt = rmaxN = .02(10,000)
= 200 new individuals
• N2 = 10,200
• if we do this again, N3 =
10,200 + 204 new, etc.
Exponential Growth Model
Exponential Growth in Elephants
in Kruger National Park
8,000
Elephant population
6,000
4,000
2,000
0
1900
1920
1940
Year
1960
1980
BUT NO POPULATION CAN
GROW FOREVER!!!
As density increases, intraspecific
competition for resources increases,
so births decrease and deaths increase.
We have to take density into account!
Models of Population Growth:
1) Exponential Growth Model
2) Logistic Growth Model
Logistic Growth Model
Takes density into account mathematically…
dN/dt = rmaxN (K – N)
K
• K = ‘carrying capacity’, maximum stable
population size that the environment can support
Logistic Growth Model
The exponential growth model describes the increase in population
size of a population that is not constrained by resources or space.
The graph shows the elephant population in Kruger National Park,
which appears to have been reproducing exponentially from 1900 to
1963. From this graph, you can tell that
A) none of the elephants died.
B) a female elephant living around
1960 was more likely to have a
baby than a female elephant living
around 1920.
C) the elephants adapted to the new
park conditions around 1955.
D) the vegetation the elephants eat
could support more than 5,000
elephants.
E) the more elephants there are, the
more tourists will visit the park.
When will we reach our carrying capacity
and what factors will limit our growth?
Estimates of world carrying capacity range from
10-15 billion, though very difficult to estimate.
One recent technique: “Ecological footprint”
-compares supply vs demand for
ecologically productive areas
Ecological Footprint
• Ecological footprint
measures the amount of
arable land, pasture, forest,
ocean, built-up land, and
fossil energy land needed to
support one person
Most ecologists agree that people should not be
using more than 1.7 ha of resources if they want
to be sustainable. People in the United States use
an average of 10 ha. This implies that
A) the ecological footprint concept is flawed.
B) the U.S. has more land than other countries do.
C) U.S. rates of resource consumption are too high.
D) U.S. people are happier.
E) U.S. people are less likely to emigrate.
Ecological Footprint Relative to Ecological Capacity
Ecological footprint (ha per person)
16
14
12
New Zealand
10
USA
Germany
8
Australia
Canada
Sweden
Japan Netherlands
Norway
6
UK
Spain
4
2
World
China
India
0
0
2
4
6
8
10
12
Available ecological capacity
(ha per person)
Countries in red are in ecological deficit;
Countries in black still have resource surpluses
14
16