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Reply To: Transition Probabilities

Colin DanielColin Daniel

Yes I think what you describe can make sense in certain situations. Normally we might use a variation on the strategy you outline above to determine probabilities for succession transitions where the goal is to have a fixed annual succession probability that effectively leads to (on average) all of the area in a particular state class transitioning out of the state class over the entire age range of the class. Simple math might suggest then that if for example you transition 10% of the cells in a particular state class each year, and the state class has a 10 year age range, that after 10 years on average all of the area in the state class would have transitioned. However the math is a little more complicated than this. For example below is a table of output for 1000 cells starting in a particular state class at timestep 0 with a transition probability of 0.1/timestep:

Timestep Cells_Remaining Cells_Transitioning
0 1000 100
1 900 90
2 810 81
3 729 73
4 656 66
5 590 59
6 531 53
7 478 48
8 430 43
9 387 39
10 350

As the table shows, after 10 timesteps of applying a transition probability of 0.1, 35% of the cells will still not have transitioned. If you do the math, to transition 95% of the cells over 10 years you would need a fixed annual transition probability of 0.25!

So the first suggestion is if you do want to balance your transition probabilities across state classes, such that the transition probability on average effectively “clears” each state class over the full age range of a class, using 1/age range as the fixed probability might not be quite right. You’ll need a slightly more complicated formula to get at this.

Secondly, while we do use this approach at times for modeling a process like succession, we don’t normally do this for fire. Wihtout seeing your model, having fire probabilities be a function of the age range seems a bit counterinintuitive. Usually fire probabilities are 1/fire return interval, and while the fire return interval can vary with age, I don’t ever recall varying it with the “age range” (which is more of a modeling construct).

Hope this helps!