Forecasting requires a model. Most forest pest forecasting models employ the idea of a trend index in one way or another. The trend index is given by

where I_N is the trend in the variable N over a unit time period, usually a year, N_t is the current value of the variable (this year's estimate), and N_t-1 is the past value of the variable (last year's estimate). The variable of interest could be numbers of acres infested by gypsy moths, numbers of trees killed by the mountain pine beetle, numbers of Douglas-fir tussock moth larvae per acre, etc. Forecasts are made by multiplying the current value of the variable by the trend index,

where N_t+1 is the projected value of the variable next year -- the expected value.

There are many modifications of the trend index:

Constant Linear trend. The trend equation derived above assumes that the trend from one year to the next is linear and constant.

Constant Geometric Trend. Knowing that populations normally grow geometrically, according to the 1^st principle of population dynamics, we might prefer the familiar step-ahead forecasting model

where ln is the natural logarithm and R_N = ln I_N.

Trend with Parasitoids. When the numbers of insects parasitoids can be estimated, say by bringing larvae collected in the field into the laboratory and rearing out the parasitoids, then we could use a model such as

where P_t is the density of parasitoids in year t.

Mortality Models. Models can be used to predict tree mortality or the value of lumber destroyed from population estimates (Slide).

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© 1998 Alan A. Berryman