1. Cypripedium acaule Complex Life Histories: A Cryptic Orchid as an Example

2. Analysis of the Life-Cycle Graph: The Transition Matrix Modeling Approach

3. Converting a Life-Cycle Diagram to a Matrix Representation Coryphantha robbinsorum Matrix Representation

4. Source State Small juveniles Large juveniles Adults Small juveniles Large juveniles Adults Subsequent State Codifying the Transition Matrix

5. Source State Small juveniles Large juveniles Adults Small juveniles Large juveniles Adults Subsequent State Staying in the Same State

6. Source State Small juveniles Large juveniles Adults Small juveniles Large juveniles Adults Subsequent State Increasing in Size

7. Source State Small juveniles Large juveniles Adults Small juveniles Large juveniles Adults Subsequent State Reproduction

8. Source State Small juveniles Large juveniles Adults Small juveniles Large juveniles Adults Subsequent State Other Possibilities: Decreasing in Size

9. Source State Small juveniles Large juveniles Adults Small juveniles Large juveniles Adults Subsequent State Other Possibilities: Increasing in Size

10. What Good is This Stuff?

11. Parameterized Model Matrix Analysis in Three Habitats Coryphantha robbinsorum

12. Parameterized Model Matrix Analysis: Population Growth Population Growth Rate  = 0.998  = 0.997  = 1.12

13. Parameterized Model Matrix Analysis: Stable Size Class Distribution Asymptotic Size Class Distribution

14. Parameterized Model Matrix Analysis: Population Growth Population Growth Rate  = 0.998  = 0.997  = 1.12 Asymptotic Size Class Distribution

15. Matrix Analysis: Population Projection Simple MatrixMatrix Multiplication: Population Projection Matrix Multiplication: What it represents

16. Parameterized Model Matrix Analysis: Population Projection Projection of Population into Future

17. Sensitivity Analysis How does (population growth rate) change in response to a small change in transition rate? = 1.12 +.04 = 1.12 = 1.14

18. Sensitivity Analysis

19. Sensitivity Analysis: A Couple of Problems High sensitivities may be associated with transitions that don’t occur in nature. There is a basic difference in values associated with survivorship and fecundity.

20. Elasticity Analysis: a potential solution How does (population growth rate) change in response to a proportional change in transition rate? = 1.12 + 10% = 1.12 = 1.13

21. Parameterized Model Elasticity Analysis

22. Model Predictions Life table Matrix = 1 < 1 > 1 Key assumptions?

23. Density Effects Population change over time Birth and Death Rates

24. Density Effects Birth and Death Rates Impact of increasing density Decrease in Light Nutrients H 2 0 Space Impact of increasing density on the population Increase in death rate Decrease in reproduction Increase in disease herbivory