1. Disturbance mosaics (treefall gaps, hurricanes, fires) Patchy, recurrent disturbance environment states vary demographically environment states change over time Dynamics includes demographic and environment transitions

2. Concepts Structured populations Mosaic of environmental states Each environmental state = one population projection matrix Entire heterogeneous landscape = set of matrices

3. Many different ways to link together... arithmetic average products of matrices (a fixed sequence) Megamatrix Stochastic sequence

4. Megamatrix Environment-by-stage classes Matrix size = no. of environments x no. stages Environmental transition matrix Aggregates over all patches of a given environment at each time step

5. Environment transition matrix

6. Environmental characteristics from a matrix? Sequence of types of environments Temporal autocorrelation Relative abundance of types of environments in the sequence over time reaches an equilibrium

7. What happens here next? Start green 50% chance of going to Red 50% chance of going to Blue Start red 50% chance of going to Green 50% chance of staying Red Start blue 100% probability of going to Green

8. Try it… Start red.

9. What happens here long term?

10. Environment transition phenology time tt+1 early change late change census

11. Megamatrix: early change

12. Megamatrix: late change

13. New sensitivity questions Environment by life history stage classification Does the same life-history event in different environments differ in elasticity values? Elasticities (can be summed) By environment By stage across all environments By stage within environments …

14. What’s next? Cumulative pop growth Stochastic sequences Stochastic elasticities Age from stage