1. 1. Which of the following statements about conventional life tables is NOT true?
They were first used by life insurance companies to estimate human survival patterns
They show the age-specific death rates for a population
They are used to predict population growth
They can be used to construct survivorship curves
They are often constructed by following a cohort from birth to death.

2. 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
2000
5000
1000
200
500

3. - POPULATION GROWTH To predict how populations
will increase or decrease,
need a mathematical model. +
births -
DENSITY
deaths

4. 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

5. 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”

6. 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

7. Exponential Growth ExampleIf
b = 30/1000 = .03
d = 10/1000 = .01
rmax = b – d =
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, new, etc.

8. Exponential Growth Model

9. Exponential Growth in Elephants in Kruger National Park
1900
1920
1940
1960
1980
Year
2,000
4,000
6,000
8,000
Elephant population

10. 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!

11. Models of Population Growth:
1) Exponential Growth Model
2) Logistic Growth Model

12. 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

13. Logistic Growth Model

16. 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 From this graph, you can tell that
A) none of the elephants died.
B) a female elephant living around 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.
Answer: d

18. When will we reach our carrying capacity
and what factors will limit our growth?

19. 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

20. 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

21. Most ecologists agree that people should not be using more than 1
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.
Answer: c

22. Ecological Footprint Relative to Ecological Capacity16 14 12 10 8 6 4 2
New Zealand
Australia
Canada
Sweden
World
China
India
Available ecological capacity (ha per person)
Spain UK
Japan
Germany
Netherlands
Norway
USA
Ecological footprint (ha per person)
U.S. is in ecological deficit – we have an ecological footprint of 8.4 ha / person (it takes 8.4 ha to support us) but we have only 6.2 ha per person
Countries in red are in ecological deficit;
Countries in black still have resource surpluses