1. How populations grow, reproduce and distribute themselves
Population Ecology
How populations grow, reproduce and distribute themselves

2. Mathematical modeling principles
Models are a gross simplification of reality.
Models are only as accurate as your:
Equations – variables included in model
Data used for model
Consider weather prediction:
Accurate only to a few days.
Often right for big picture, wrong for details.
Best models have dozens and dozens of variables.
Real world is still much more complicated.

3. Population growth What factors increases the size of a population?
Decreases a population?
How can we represent this mathematically?

4. Population growth
Births (B)
Deaths (D)
ΔN = B – D

5. r = B – D

6. Exponential growth
Continuous
Nt = N0ert
Discrete
Nt+1 = λNt

8. Carrying capacity Are there limits to population size?
How do we represent such limits?

9. Logistic growth More realistic than exponential growth
Includes carrying capacity variable (K)
Nt = K/1+[(K-N0)/N0]e-rt

10. Other missing variables
What other variables are missing in effectively modeling population growth? ?

11. Leslie matrix modeling
Includes many factors ignored in other models.
Based on 2 matrices (boxes of numbers).
1 - Number of individuals in each age group/stage.
2 - Survival/fertility probabilities
Now
Future

13. Add carrying capacity of environment
EXPONENTIAL
Add ages/stages
Predation/Competition/Disease, etc.
LOGISTIC
MATRIX MODELS

14. Life history (r/K)

15. Human demography