Gypsy moth populations spread via stratified dispersal which is a combination of (1) long-distance dispersal which results in establishment of small isolated colonies beyond the population front, and (2) short-distance dispersal which results in growth of isolated colonies until they coalesce. Long-distance dispersal results mainly from inadvertent transportation of egg masses and other life-stages by humans (e.g., on campers, logs, etc.). Short-distance dispersal results from larval dispersal.

It was suggested that detection and eradication of isolated colonies beyond the population front may reduce the rate at which gypsy moth populations are spreading. The idea was partially implemented in the Appalachian IPM project, and later fully implemented in the Slow the Spread project. A barrier zone was set just ahead of the population front with a dense grid of pheromone traps. Detected isolated colonies were treated.

The notion of a barrier-zone is usually associated with a constant area which
prevents further progression of the population front. Here we are talking about
the *shifting* barrier zone which only slows the spread of gypsy moth.
OK, why not to stop its spread? Stopping gypsy moth spread is feasible but not
rational because it will require spraying large forest areas with strong pesticides.
This is environmentally dangerous and unreasonably expensive.

I have developed a model of stratified dispersal which quantified the effect of a barrier zone on the rate of population spread. However, this model is too abstract to provide guidelines for optimization of the management of the barrier zone. Here I present a discrete version of this model which can be directly applied to pest management. The model is written in Microsoft Excel (ver. 5.0) for Windows. It can be run on Macintosh computers as well.

To optimize the allocation of pheromone traps you will need a Solver which is a tool that comes with Microsoft Excel. Solver may be not installed on your computer if you used the standard installation option of Excel. In this case, use installation disks to add the Solver.

To __download__ the model, click on the icon below.

Excel spreadsheet "stsopt4.xls"

The third column (C) shows the colonization rate, which is a linear function
of distance from the population front (see fig. at the right). Two parameters
are used: *x _{max}* is the maximum distance from the defoliation
front at which new colonies can become established, and

Numbers in the table (D5:T23) show the number of colonies (colony centers)
per 1 sq.km. These numbers are shifted diagonally because the number of colonies
in age *a* at time *t* is the same as the number of colonies at age
*a*+1 at time *t*+1.

At the bottom of the table (C25:U25) there are population numbers (total egg
masses in a colony of specific age) which are assumed to increase exponentially.
The last column in the table (*V*) shows the average population density
as a function of distance from the defoliation front.

The probability of detecting a colony is proportional to colony area (C81:U81) and to the density of pheromone traps (AA29:AA80). Initial density of pheromone traps is assumed to be 0.02 per sq.km. at all distances from the population front. This allocation of traps is not optimal: it is clear that we don't need traps too close to the population front or too far from it. Later we will find the optimum allocation of traps.

We assume that all detected colonies are eradicated using pesticides. Knowing the area of colonies (C81:U81) it is easy to estimate the area where pesticides are applied for eradication. Eradication costs are $3,500 per sq.km and the cost of one trap is $50. Average expenses on trapping and eradication within 1 sq.km. are shown in (W29:W80) and (X29:X80), respectively. Total sums (W81 and X81) are multiplied by the rate of spread to get the total annual cost of maintaining 1 km of a barrier zone measured along the population front. The total cost of maintaining 1 km of the barrier zone (prior to optimization) is $33,869. Then to maintain a 100-km barrier zone it will cost annually $3,386,900. This sum of money is very large because we have not optimized trap allocation yet.

The graph below the lower table shows the density of traps and the proportion of area treated with pesticides at different distances from the defoliation front.

The most interesting part is the optimization of trap allocation. We start
from the uniform density of traps. Then we use the Solver to find the best trap
allocation. Open **"Tools/Solver**". Let's examine the Solver dialog box.
At the top we put the cell that contains total costs (Y81). The value of this
cell should be minimized (thus we select **"min**"). Now we need to specify
model parameters which can be modified automatically by the computer in order
to minimize the costs. In this field we put the entire column of trap densities
(AA29:AA80). The last thing is to specify two constraints: (1) trap density
cannot be negative, and (2) the average population density at the defoliation
front should be the same in both tables (Z80=V24). The second constraint is
better written in the form Z80 ≤ V24 because this will improve the stability
of the optimization process. However, this will not affect the final result
(you may check it later): after optimization the value of Z80 will be equal
to the value of V24.

Now let's run the Solver. At the bottom we see how costs are reduced with each iteration. The Solver finally converged to a minimum of $9,078 per 1 km length of population front annually (there may be small variations in this number depending on initial conditions and Solver options). Now you can see on the graph below the table that the traps should be set from 81 to 225 km from the defoliation front. Both trap density and treatment area are higher at the proximal portion of the barrier zone than in the distant portion.

You can change the parameters of the model (Z6:Z13) and run the optimization again. I did these simulations for different target spread rates from 5 to 17 km/yr, and the results are presented in Sheet 2.

For more information, please contact Patrick Tobin or Andy Roberts

Maintained By Jiang Wu