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.

DENSITYbirths deaths-+

Models of Population Growth:

1) Exponential Growth Model

- assumes continuous breeding

- assumes during each and every time intervalthere 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

• 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

dN/dt = rmaxN

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

1900 1920 1940 1960 1980

Year

0

2,000

4,000

6,000

8,000

Ele

phan

t po

pula

tion

BUT NO POPULATION CANGROW FOREVER!!!

As density increases, intraspecificcompetition for resources increases,so births decrease and deaths increase.

We have to take density into account!

2) Logistic Growth Model

Models of Population Growth:

1) Exponential 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 capacityand what factors will limit our growth?

Estimates of world carrying capacity range from10-15 billion, though very difficult to estimate.

One recent technique: “Ecological footprint”

-compares supply vs demand forecologically 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

16

14

12

10

8

6

4

2

00 2 4 6 8 10 12 14 16

New Zealand

AustraliaCanada

Sweden

World

ChinaIndia

Available ecological capacity (ha per person)

Spain

UK

Japan

Germany

NetherlandsNorway

USA

Eco

logi

cal f

ootp

rint (

ha p

er p

erso

n)

Countries in red are in ecological deficit; Countries in black still have resource surpluses