# Population EcologyPage 3

#### WATCH ALL SLIDES

In animals, parental care of smaller broods may facilitate survival of offspring.

Some plants, like the dandelion, produce a large number of small seeds, ensuring that at least some of them will grow and eventually reproduce.

Other types of plants, like the coconut tree, produce a moderate number of large seeds that provide a large store of energy that will help seedlings become established.

Slide 16

Variation in the size of seed crops in plants

(a) Dandelion

(b) Coconut palm

Slide 17

## The exponential model describes population growth in an idealized, unlimited environment

It is useful to study population growth in an idealized situation.

Idealized situations help us understand the capacity of species to increase and the conditions that may facilitate this growth.

Slide 18

Zero population growth occurs when the birth rate equals the death rate.

Most ecologists use differential calculus to express population growth as growth rate at a particular instant in time:

where N = population size, t = time, and r = per capita rate of increase = birth – death

Slide 19

## Exponential Growth

Exponential population growth is population increase under idealized conditions.

Under these conditions, the rate of reproduction is at its maximum, called the intrinsic rate of increase.

Exponential population growth results in a J-shaped curve

Exponential Growth is not sustainable.

Slide 20

Exponential Growth Model

Number of generations

0

5

10

15

0

500

1,000

1,500

2,000

1.0N

=

dN

dt

0.5N

=

dN

dt

Population size (N)

Slide 21

The J-shaped curve of exponential growth characterizes some rebounding populations

8,000

6,000

4,000

2,000

0

1920

1940

1960

1980

Year

Elephant population

1900

Slide 22

## The logistic model describes how a population grows more slowly as it nears its carrying capacity

Exponential growth cannot be sustained for long in any population. A more realistic population model limits growth by incorporating carrying capacity.

Carrying capacity (K) is the maximum population size the environment can support.

In the logistic population growth model, the rate of increase declines as carrying capacity is reached.

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