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Five Common Graphs

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Five Common Graphs

Several graphs are commonly seen in ecology

for example

- Linear progressions
- J - CURVES
- S - CURVES
- Climb and collapse
- Bell shaped curve

An arithmetic number sequence grows by repeated additions of like amounts

and produces a linear graph

Examples

1...2...3...4...5...6...7...8...9...

3...6...9...12...15...18...21

110...220...330...440...

1...2...3...4...5...6...7...8...9...

3...6...9...12...15...18...21

110...220...330...440...

Each of these

arithmetic progressions when graphed,produces a straight-line graph

Such number sequences are predictable and easy to understand

An exponential progression

produces a classical J – CURVElike the one shown here

J-curves are both powerful and deceptive

They result from number sequences that growby repeated multiplications by like amounts

Examples

1...2...4...8...16...32...64...128

1...3...9...27...81...243

Most of the growth in an exponential sequence

occurs at the end of the sequence

Examples

- A graph of a nuclear detonation
- Populations undergoing ecological release
- A graph of human population growth between 8000 BC and 2000 AD

Many populations exhibit anS - CURVE

- Takes into account environmental factors limiting growth.
- Contains 5 stages.
- Initial Growth/slow
- Exponential Growth/fast
- Slowing Growth
- Slower Growth
- Steady State, which will fluctuate moderately.

During the early stages of a population’s growth,theS-CURVE follows an exponential pattern

As the population grows larger, competition and other limiting factors begin to slow its rate of growth

Eventually,

birth rates and death rates become equal

and the population stabilizesnear the carrying capacity of its environment

We often see

S– CURVES

in k-strategists

such as whales and gorillas

..... unless they undergo ecological release .....

This graph depicts a population pattern known as

Climb and Collapse

Can you see why?

The population shown here grew exponentially for many generations

This was eventually followed by a catastrophicdie-off over a relatively short span of time

This graph shows the climb-and-collapse of a reindeer population

on St. Matthews Island, Alaska

In 1944, 29 reindeer were placed on the island

Since the island had no competitors or predators

The reindeer herd underwent

ecological release

(Definition?)

By 1963, more than 6000 reindeerdamaged the vegetation needed to survive

More than 99% of the herd died during the winter of 1963-1964

… only 42 individuals survived …

And with fewer reindeer, Santa had to try a different approach.

Biologists who study populations often run across data that produce

Bell-Shaped Curves

Such data often involve patterns of variation within a population

Example

Suppose we analyze all the oranges on a given tree for their vitamin Ccontent per gram

Some will have a very high amount of vitamin C per gram

Others

will have very little

vitamin C

per gram

But most will have some average amount of vitamin C per gram

producing a bell-shaped curve when graphed

C’s

B’s

D’s

A’s

Bell shape curves are what we often use in education when evaluating student work.

What’s fair about this? What’s not?