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Mapping Grasshopper Population Dynamics

### By Kiana Zimmerman, Jeffrey Lockwood, Rex Gantenbein, and Scott Schell University of Wyoming, Laramie, Wyoming

Editor's note: The authors have developed an extension for ArcView GIS that applies Markov chain analysis, a type of mathematical model, to grasshopper survey data. This methodology is used to determine the likelihood of infestation at a detrimental density for a specific area so that landowners and managers can weigh the cost-effectiveness of treatment.

 The Markov chain extension helps determine the probability of grasshopper infestation.

More than \$22 million was spent in 1985 and 1986 to combat the last major grasshopper infestation in Wyoming. Since that time, inflation and federal policies have tripled the cost of control. With shrinking resources available to control grasshoppers, landowners and managers must make informed decisions on how to deal with these outbreaks. Perhaps the most important question is whether the cost of treatment can be effectively amortized over multiple years. In many cases, treatment can only be justified if the outbreak is likely to persist beyond the current year.

To decide whether and how to treat a grasshopper outbreak, managers need to know the probability that an area that is currently infested will be infested next year or in succeeding years.

To answer these questions, a two-state Markov chain analysis was applied to rangeland grasshopper infestation data gathered by the United States Department of Agriculture Animal and Plant Health Inspection Service (USDA-APHIS) Plant Protection Quarantine (PPQ). Markov chains are used to analyze stochastic (chance) processes. The future of a system is predicted based on its current state or condition. Given a series of events or states, a Markov chain predicts three things-the probability of a system being in a particular state at a specific time, the time until a state is first reached, and the period of time the system will be in that state.

## Acquiring Data

The infestation maps were created using grasshopper survey data obtained from USDA-APHIS. For the period between 1944 and 1996, this agency conducted grasshopper surveys at between 25 and 50 locations in each county in Wyoming. Many of the survey sites were located in the eastern half of the States, where grasshopper outbreaks are most frequent. At each location, 18 visualized square-foot counts for grasshopper population density estimation were taken. Hand-drawn maps were created by subjectively interpolating the survey point data.

These hand-drawn maps were digitized into a raster GIS with a 1,000-square-meter grid cell size and stored in Lambert Conformal Conic projection. The data was imported into ArcView GIS with each year's data represented as a separate grid. Each cell was coded with "0" if the cell was uninfested or "1" if the cell was infested.

Infestation was defined as a population equal to or greater than 9.6 grasshoppers per square meter. This was the only population density consistently encoded in the maps across all years of the survey. Although infestation at this level is no longer considered by entomologists to be economically injurious, this population density has ecological meaning because it approximates the grasshopper population density that can be supported. At the 9.6-grasshoppers-per-square-meter threshold, the damage caused by grasshoppers does not equal the cost of control because factors such as rangeland productivity, forage and livestock prices, and grasshopper species composition are not included.

## The Two-State Markov Chain Extension

This extension was designed using ArcView GIS 3.2 with the ArcView Spatial Analyst extension. When the extension is loaded, a new menu choice, Markov chain, is added to the ArcView GIS GUI. Avenue scripts attached to the choices in this menu execute all the steps required for analysis. To run the extension, the user opens a view containing at least two grid themes. For each menu choice, a new view is created, and the information is displayed as a grid theme.

Figure 1: Markov Chain Extension Menu Choices

 Menu Choice Function Outbreak Frequency This routine computes the frequency with which each cell was infested at the threshold level by summing up the values in each cell over the time period. One-Year Transition Probabilities This choice creates four grids in a new view that represent the one-step transition matrix. These four grids answer the question, "If a cell is uninfested/infested this year, what are the chances it will be uninfested/infested next year?" Expected Number of Years This choice, available after the four one-step transition grids have been generated, computes the time that each cell will be in each state before switching to another state. The One-Year Transition Probabilities grids are used to compute the expected number of years, variance, and 95 percent confidence interval grids that answer the question, "How long will the uninfested/infested conditions last?" Probabilities in 2, 3, 4, and 5 Future Years This function predicts the probability of each cell being in state 0 or 1 at a time beyond the next year. This option computes the n-step transition matrix in the form of 16 grids and displays the information in a new view. Percent of Time in 5 Years in Each State/Condition This function creates a view that displays the number of years and percent of time each cell is expected to be in each state in the next five years, given an initial infested or uninfested state.

## Analysis of Maps Produced

The central question in dealing with grasshopper infestations is whether ranchers can receive multiyear benefits from using insecticides to treat outbreaks. This question has sparked an intense and long-lasting debate among entomologists, and there has been little empirical insight available to resolve the issue. Markov chain analysis revealed that most locations in Wyoming tend to become or remain uninfested and that the vast majority of the landowners and managers cannot count on multiyear benefits. They must base treatment decisions solely on the cost benefit for the current year.

The maps generated by the Markov chain extension provide further information relevant to ranchers and pest managers. For purposes of rangeland grasshopper management, the most important transition is from an infested or uninfested state to an infested state, and the most important timescale is the one-year transition. Devoting limited survey and control resources to mapping these transitions could significantly improve the efficiency of resource allocation.

 This extension answers the important question, "Will this area be infested next year?"

For a rancher or a weed and pest district with limited resources for control programs, it may be necessary to focus management efforts in areas that have the greatest potential for economic return. In this triage approach, one of the most important elements of assuring a profitable treatment is to control populations that are likely to persist if nothing is done. This accrues multiyear benefits from treatment in the current year. Conversely, if an infestation has a low probability of persisting beyond the current year, the economic returns from a control program will be limited to the forage that is protected in a single growing season. With all other factors being equal, management priority should be allocated to land that has the longest expected duration of infestation and the greatest probability of continued infestation.

## Some Qualifications

Although this analysis provides far greater and more objective insights into rangeland grasshopper population dynamics than ever before, this approach is not without limitations. The user of this extension or of maps generated from it must consider three qualifications.

First, as with financial investments, past performance is no guarantee of future returns. In an ecological sense, this analysis assumes that all of the factors that were responsible for grasshopper population dynamics over the last 50 years will continue to operate in the same manner. Any changes in the inputs that accounted for the transitions in the past will affect the accuracy of current forecasts.

Next, the only grasshopper population density that was consistently recorded was the previously stated threshold. Although this density rarely represents the economic threshold, it may be close to the ecological carrying capacity of the rangeland and portend an increase in population. However, all of the probabilities and durations are predicated on this particular density. The chances of an infestation at a different level persisting for more than a single year may differ greatly from the probability indicated by analysis for the cited threshold.

Finally, this analysis was conducted using a 1,000-square-meter spatial scale. Each grid cell on the map represents a fixed area of rangeland. It is possible that the analysis would have yielded different results if a substantially larger or smaller scale had been used. However, a 1,000-square-meter grid cell size was small enough to provide an appropriate level of detail but large enough to be relevant to management practices.

Kiana Zimmerman
Cooperative Agricultural Pest Survey (CAPS)
Department of Renewable Resources
University of Wyoming
Box 3354
Laramie, Wyoming 82071
Tel.: 307-766-5278
E-mail: caps@uwyo.edu
Web site: www.sdvc.uwyo.edu/grasshopper/

Kiana Zimmerman, a computer programmer with the University of Wyoming, does GIS and programs for the Cooperative Agricultural Pest Survey (CAPS) program. She holds bachelor and master's degrees in computer science from the University of Wyoming.

Jeffrey Lockwood is an associate professor of entomology in the Department of Renewable Resources at the University of Wyoming.

Rex Gantenbein is a professor of computer science at the University of Wyoming.

Scott Schell is a research associate in the entomology section of the Department of Renewable Resources at the University of Wyoming.

## In Print

Berry, J.S., J.A. Onsager, W.P. Kemp, T. McNary, J. Larsen, D. Legg, J.A. Lockwood, N. Foster. "Assessing Rangeland Grasshopper Populations," United States Department of Agriculture Grasshopper Integrated Pest Management User Handbook. 1995.
Davis, R.M., M.D. Skold, J.S. Berry, and W.P. Kemp. "The Economic Threshold for Grasshopper Control on Public Rangelands." Journal of Agricultural and Resource Economics, Vol. 17, No. 1, pp. 56–65 1992.
Schell, S.P. and J.A. Lockwood, "Spatial Analysis Optimizes Grasshopper Management." GIS World, Vol. 8, No. 11, pp. 68–73, November 1995.
Stewart, W.J. Introduction to the Numerical Solution of Markov Chains. (Princeton University Press:Princeton, New Jersey, 1994.

## On the Web

The Field Guide to Common Western Grasshoppers by Robert E. Pfadt is available at The University of Wyoming College of Agriculture Web site at www.sdvc.uwyo.edu/grasshopper/.

The Wyoming Grasshopper Information System (WGIS) Web site can be found at w3.uwyo.edu/~caps/caps.html.