1. Population growth: Part 1
Ecology: Lecture 6
Population growth: Part 1

2. Disclaimer
Today’s PowerPoint does not include the material covered on the board!

3. Under what conditions might a population grow at a constant rate?
Low density
Non-limiting resources
Why would these matter?
Stable age distribution
Why would this matter?
How valid are these assumptions for most populations?

4. Geometric finite rate of increase, λ
Generation Nt λ 50 1
150 3 2
450
1350 4
4050

5. Geometric finite rate of increase, λ
Generation Nt λ 50 1
150 3 2
450
1350 4
4050

6. Geometric finite rate of increase, λ
Generation (t) N λ 50 1
150 3 2
450
1350 4
4050

7. Geometric finite rate of increase, λ
Generation Nt λ 50 1
150 3 2
450
1350 4
4050

8. Geometric finite rate of increase (λ)
How is lamda (λ) calculated?
What is the general expression for constant population growth (geometric)?

9. What is causing this change in population size?
Nt+1 = Nt +?
λ = ?
(Work through on board…)

10. Exponential vs. geometric growth [Fig. 11.1]

11. Exponential model of population growth
Key equation: Nt = N0ert
Compare to geometric growth equation for the same population
λ = ? (Do the math!)
r is the exponential rate of increase
r = ? (HINT: What factors determine whether a population grows or shrinks?)

12. Exponential growth: changing r values

13. Exponential growth: alternate equation
dN/dt = rN (derivative of Nt = N0ert)
d is not a variable, but resembles the symbol  and indicates an instantaneous rate of change.
“The change in the population size divided by the change in time equals r times the population size.”

14. Logistic growth
Takes into account some realistic constraints on population growth caused by the increasing population itself
What are some these constraints?
Are these constraints considered density-dependent or density-independent?
Includes a carrying capacity, K
Population size (for a particular area) above which an equilibrium population cannot be supported.

15. Logistic growth equation
Do on the board! (Equations in notes, also, but you need to understand each term!)
Think about mathematically…

16. Logistic growth

17. Logistic growth
Under what conditions does logistic growth most resemble exponential growth, and why?
In this case, how do birth rates compare to death rates?
Under what conditions does logistic growth approach 0, and why?

18. Logistic growth

19. dn/dt as function of population size in logistic growth
Max population growth rate at K/2.
Why so from an ecological perspective?

20. Time lag (see also equations on board)

21. Is K really a constant?