# Stochastic versus deterministic disturbance

Stochastic and deterministic disturbance have very different effects on the age of the forest, even when the average time between disturbances is exactly the same. I illustrated this in a paper from my PhD (man moons ago), but I think it is still useful (McCarthy and Burgman 1995).

The occurrence of unplanned fire is a good example of a stochastic disturbance. In some places of the world, fires are very likely to occur, but their exact occurrence is uncertain. The best we can do is make probabilistic predictions. For example, we might be able to estimate that the probability of a particular point in a forest burning within the next year is 0.01 (1 in 100).

In contrast, logging of forests by humans tends to be systematic, occurring at prescribed intervals – the rotation age of the forest.

When I was a post-doc at NCEAS, I developed a webpage to illustrate the difference between the two forms of disturbance. Here it is. This simple example shows that the average age of a forest under deterministic disturbance is about half that of a forest under stochastic disturbance, even though the average interval between disturbance is the same.

A comparison of two forests, one with deterministic disturbance, and one with stochastic disturbance. The average interval between disturbances is 100 years in both cases, but the resulting age structure is different.

Deterministic disturbance as an analogue to timber harvesting is easy to simulate. We simply break the forest up into a particular number of areas, and disturb the oldest one each year. That returns the forest age for that area to zero (or one year, whatever is used as the youngest age), and all other sites increase in age by one year. The number of areas determines the average time between disturbance events.

Stochastic disturbance is different by allowing forest areas of any age to be disturbed. If the probability of each site being disturbed each year is 1/N then the average interval between disturbances is N years. Under this model, no areas will be disturbed in some years, in other years 1, 2, 3, etc areas will be disturbed.

These two models (and a model in which one site is disturbed in each year, but its identity is selected at random) are simulated in this Excel spreadsheet. Sure, Excel might not be the world’s most reliable stochastic simulation program, but it is handy for illustrating the ideas.

Reference

McCarthy, M.A., and Burgman, M.A. (1995). Coping with uncertainty in forest wildlife planning. Forest Ecology and Management 74: 23-36. [Online] [Abstract] [#PDFtribute]

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