1. Previous Lecture Populations are Structured
Basic descriptive attributes of populations:
Density
Distribution
Dispersion

2. All Populations Potentially Grow Exponentially
Lecture 2
All Populations Potentially Grow Exponentially
A. Exponential population growth (Ricklefs Chap. 15)
B. Exponential growth modified by age structure (next time)
C. Exponential growth and stage structure (next time)

3. Exponential Growth
The ‘Law of Exponential Growth’ is the Fundamental Theorem of Ecology
All populations potentially grow exponentially
Where does this law come from?

4. Exponential Growth
Individuals have some maximum birth rate per capita (b)
Individuals have some minimum death rate per capita (d)
The “per capita population growth rate”, or the exponential growth rate r = b - d (for all species this is >0)

5. Exponential Growth Total rate = per capita rate * N
Translated into population growth rate (dN/dt):
Note: This equation can also be written as:

6. Exponential Growth
This is an equation for a line, whose slope is r:

7. Exponential Growth
BUT, what kind of population growth (N vs. time) is predicted by this equation?

8. Figure 15 -1,
Ricklefs

9. Exponential Growth In the REAL World?
Reindeer on the Pribilof Islands

10. More Actual Exponential Growth
Historical increases have been approximately exponential for periods in human history

11. Realized Exponential Growth
Rabbits in Australia
Gypsy moth in North America
Locusts in Africa
Plague in Europe
Lemmings in the Arctic
Etc...

12. HOW TO BECOME A MILLIONAIRE or WHY THE RICH GET RICHER!

13. How Does Money Grow? (1) Interest (t) = Interest rate x Balance (t)
(2) Balance (t+1) = Balance (t) + Interest (t)

14. How Does Money Grow? (cont’d)
Compounding of interest:
Iteration of two equations:
Example:

15. So You Want to Be a Millionaire?

16. Another sample problem!
If you wanted to leave $1,000,000 to one grandchild in 60 years, how much would your initial investment have to be in order to accomplish this, assuming a 10% continuously compounded interest rate?

17. Exponential Population Growth
Another expression for exponential population growth:
This is the SAME model, written differently

18. Sample Problem
E. coli cells propagate by binary fission. They don’t ‘give birth’ in the traditional sense. However, if the effective ‘birth rate’ of these cells is 6 cells/cell*hr, and death rate is 0, and the initial population consists of 100 cells, how long would it take to reach a population size of 4.92 x 1043 cells, enough to cover the Earth 1 meter deep in bacteria?

19. French School Children and Exponential Growth
A pond is completely covered by duckweed (a floating plant that reproduces by doubling it’s leaf size, then splitting once per day) on day 32. On what day is the pond 1/8 covered?

20. Pop Quiz Time!
Which of the following equations describes the population growth rate, in exponential growth theory?
The correct answer is C; dN/dt is the population growth rate

21. Pop Quiz (cont’d)
2. Which equation allows you to calculate the time it takes for a population to go from N at time 0 to a different N at time t, according to the exponential growth equation?
The correct answer is C, solved for t

22. Question 3
If a pond is completely covered with duckweed on Day 32, and the duckweed leaves split once every two days, on what day is the pond 1/4 covered???
Day 28. To answer this question, no equations are needed. Simply ask yourself on what day the pond would be half covered? Day 30, right? (recall they double every two days!) Then the pond is 1/4 covered 2 days further back, on Day 28)