1. Population Dynamics
The Growth and Decline of Populations

2. Populations
What is a population?

3. Population Dynamics
• Populations grow when birth rate + immigration rate > death rate + emigration rate
• Populations decline when birth rate + immigration rate < death rate + emigration rate

4. Population Dynamics
Resources determine how a given population will grow.
In general, any population of organisms with plenty of resources and ideal conditions tends to grow fast.
This is called exponential growth

5. Exponential Growth

6. Exponential Growth
“…give me one grain of wheat for the first square, two for the second and so on, doubling the grains for each of the 64 squares of the chess board.”
How much wheat?
A pyramid with a base of 28 miles and a height of 4.5 miles…. More wheat than exists on the planet!

7. Exponential Growth

8. Exponential Growth
EXPONENTIAL GROWTH
Occurs when resources are plentiful relative to population size
Usually occurs early in population’s growth
Characterized by constant growth rate and doubling time

9. Logistic Growth
Logistic growth curves demonstrate the natural (logical) phases of population growth: slow; moderate; fast; steady state or collapse.
EVENTUALLY THE GROWTH WILL LEVEL OFF OR COLLAPSE. THIS ENTIRE PROGRESSION IS KNOWN AS LOGISTIC GROWTH.

10. Stable Population – Steady State
As resources run low population growth may level off, reaching a steady state.
This is also sometimes referred to as an S–Curve.

11. Population Decline - Collapse
As resources run low, the other possibility is that the population will collapse, sometimes referred to as a J–curve.

12. Carrying Capacity
Theoretical point beyond which a population can no longer be sustained is known as the carrying capacity.
Normal part of population logistics because resources are finite.
Do populations undergo steady state growth or collapse when they reach carrying capacity?

13. Limiting Factors
Resources – nutrients and energy – in short supply, limit population growth
These resources are considered limiting factors

14. Limiting Factors Density-dependent limiting factors
Limit population size when a population is large and crowded
Examples include: food, predation, disease, stress
Density-independent limiting factors
Limit population size regardless of whether a population is large or small
Examples include: geothermal activity, extreme weather

15. Mathematics of Population Growth
Populations grow when there are more births than deaths
Populations decline when there are more deaths than births
The growth rate (r) is the difference between
the death rate and the birth rate.

16. Mathematics of Population Growth
Growth rate (r) is always calculated as an average for a specific time period, i.e. average yearly growth rate or average daily growth rate
If a population of 100 added 4 people in a year,
the average yearly growth rate would be r = 0.04 or 4%.
This means that 0.04 new people were added for every person in the original population.
It also means that 0.4 were added for every 10 or 4 people were added for every 100!

17. Mathematics of Population Growth
Practice
Using the fruit fly data from the textbook:
What is the growth rate for the fruit fly population between day 15 and day 20?
Using the rabbit data from the textbook:
What is the growth rate for the rabbit population between generation 2 and generation 25?

18. Mathematics of Population Growth
Once a population’s average growth rate is known, we can make predictions - both future population and doubling time.
These predictions make the assumption that the old growth rate will be the growth rate in the future!

19. Mathematics of Population Growth
Practice
Using the fruit fly data from the textbook:
What is the average daily growth rate for the fruit fly population between day 15 and day 20?
Based on the average daily growth rate between day 15 and day 20, what do you predict the population will be on day 60?
Based on the average daily growth rate between day 30 and day 35, what do you predict the population will be on day 60?

20. Mathematics of Population Growth
Practice
Using the rabbit data from the textbook:
What is the average generational growth rate for the rabbit population between generation 2 and generation 25?
Based on the average generational growth rate between generation 2 and generation 25, what do you predict the population will be on generation 125?
Based on the average generational growth rate between generation 86 and generation 100, what do you predict the population will be on generation 125?