SPATIAL ANALYSIS OF ECOLOGICAL FACTORS RELATED TO GRASSHOPPER (ORTHOPTERA: ACRIDIDAE) POPULATION DYNAMICS IN WYOMING

By Scott P. Schell

A Thesis Submitted to the Department of Plant, Soil and Insect Sciences and The Graduate School of the University of Wyoming in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in ENTOMOLOGY Laramie, Wyoming July 1994



Contents

CHAPTER II

Spatial Characteristics of Grasshopper Outbreaks in Wyoming, 1960-1993

ABSTRACT A raster-based geographic information system was used to analyze 31 yr of Wyoming's historic grasshopper survey data in an effort to understand rangeland grasshopper outbreak (> 9.6 grasshoppers per m2) dynamics and identify areas prone to grasshopper outbreaks. A nonrandom (clumped) spatial distribution pattern was observed in the grasshopper outbreaks that was consistent through time and across varying scales of outbreak size. Areas that had been infested up to 15 times were observed in close proximity to areas of apparently suitable habitat that had not had a single recorded outbreak. Sixty-two percent of Wyoming has never had a recorded outbreak and only 6.1% of Wyoming has been infested 6 or more times. Twelve years had more than 1 million ha infested (the largest outbreak was 4,325,800 ha in 1987). Outbreaks covering less than 1% of Wyoming have occurred eight years (1969-1971 and 1989-1993) with the smallest area recorded in 1993 (139,000 ha). Five major 2-yr outbreak expansion sequences showed little spatiotemporal persistence. The sequences also showed that grasshopper densities can reach outbreak levels over wide areas in a single year. Five major 2-yr outbreak collapse sequences exhibited spatiotemporal persistence. However, large areas of outbreak collapsed in a single year leaving no remnant areas. Grasshopper outbreaks in Wyoming primarily exhibit characteristics of gradient dynamics. The 31-yr composite map of outbreaks provides grasshopper managers with information on which to base survey and treatment decisions.

KEY WORDS spatial analysis, grasshoppers, outbreak dynamics 


The dynamics of rangeland grasshopper populations are difficult to predict. In an effort to predict grasshopper outbreaks, the United States Department of Agriculture's (USDA) Animal and Plant Health Inspection Service (APHIS) produces maps showing the results of the annual adult grasshopper population surveys conducted in the western United States. A rangeland grasshopper outbreak, as defined by APHIS, consists of grasshopper densities > 9.6 per m2 over a contiguous area of at least 10,000 ac (4016 ha) (USDA-APHIS 1987). The premise of this method is that, if an area supports high densities of grasshoppers this year it will probably do so the following year. However, this method has not had much success in predicting grasshopper outbreaks (Davis et. al. 1992). In fact, grasshopper populations classified as light (3-7 grasshopper per square yard) have the potential of reaching the severe category (25 or more grasshoppers per square yard) in one year, if certain species are present (Pfadt 1988). In a study conducted in southeastern Wyoming, areas up to 6000 ha in size went from very low grasshopper densities to outbreak levels in one year (Lockwood and Schell 1994).

An alternative, and potentially more effective, tool for predicting the occurrence of grasshopper outbreaks would be a map showing the spatial dynamics of grasshopper outbreaks over many years. An analogy to such a tool would be a database allowing meteorologists to predict a useful frost-free date for gardeners based on long term records, although they would not be able to predict the temperature on a specific spring day. To create a map of this sort, a geographic information system (GIS) is necessary to store, manipulate and query the large data sets (Liebhold et al. 1993). GIS has been used to examine the population dynamics of forest insect pests and tropical locust outbreaks (Liebhold et al. 1993). GIS has also been used to relate weather and physiographic landscape features to rangeland grasshopper outbreaks in Alberta, Canada, and Montana (Johnson and Worobec 1988, Johnson 1989, Cigliano et al. 1994). Fielding and Brusven (1993) used a GIS to spatially analyze the relation of grasshopper density to ecological disturbance on southern Idaho rangelands. By using a GIS on the Wyoming annual survey data, patterns and trends in grasshopper outbreaks might become apparent and perhaps predicting the areas most vulnerable to outbreaks may be feasible. We are fortunate in Wyoming that the annual adult grasshopper survey maps compiled by APHIS from 1960 to 1993 have been preserved, except for 1982 to 1984 when no surveys were funded. By manipulating these data with GIS, spatial patterns can be analyzed with the goal of answering these questions: 1) Is there a spatial pattern to the occurrence of grasshopper outbreaks in Wyoming? 2) If there is a pattern, does it change with time? 3) Does a pattern exist in years with minimal outbreak area totals or years with extensive outbreak areas? 4) Are there patterns that precede major grasshopper population collapses? 5) Are there patterns that precede major outbreak expansions?

The first question has important implications for the management of grasshoppers. If outbreaks have spatial patterns, grasshopper management resources (e.g., surveys) can be concentrated in the areas that have been repeatedly infested. The answer to the second question will be useful in determining if there is spatial stability or temporal cycling in grasshopper populations. The answer to the third question addresses the critical issue of scale-dependency of grasshopper population dynamics, (i.e., are there areas that are chronically infested regardless of the state-wide scale of infestation). The fourth question has important implications for the economics of treatment. For example, if outbreaks show a recognizable spatial pattern the year before collapse then ranchers and other land managers may rationally choose not to treat their current grasshopper infestation if that pattern is present. Finally, the fifth question is related to the eruptive-gradient dichotomy in insect outbreak theory. Current theory on pest insect population dynamics is based on work done on outbreaks of single insect species in forest ecosystems. A rather clear dichotomy can be constructed from a mathematical treatment of population dynamics in these situations (Berryman 1987). Berryman (1987) has termed the two outbreak dynamics "eruptive" and "gradient". Eruptive population dynamics are characterized by having foci from which pest populations build and spread outward through succeeding generations (Berryman 1987). Gradient population dynamics lack foci and depend on external environmental conditions, such as food resources, which the population tracks (Berryman 1987). If grasshopper outbreaks dynamics are eruptive then survey efforts to find and control eruptive foci, while they are still localized, could prevent large-scale outbreaks. If, on the other hand, grasshopper dynamics are gradient and outbreaks occur whenever environmental conditions are favorable, efforts could be directed to identifying environmental predictors of outbreaks.

Materials and Methods

Grasshopper Data. Adult rangeland grasshopper survey maps for the years 1960-1981 and 1985-1993 were obtained from USDA-APHIS (Cheyenne, Wyoming). This agency took over the adult grasshopper survey in 1985. Before 1985, the Wyoming Department of Agriculture conducted the yearly survey and submitted the results to APHIS for the production of the national map by that agency. Map areas of grasshopper densities were produced from subjective interpolation of point data generated from the results of roadside survey stops (Kemp et al. 1989). Twenty-five to fifty stops were made in each county with the number of stops depending on the size of the area with suitable grasshopper habitat (USDA-APHIS 1987). The grasshopper population density at each survey stop was determined by APHIS personnel using 18 visualized square foot samples. This method of estimating grasshopper densities is explained in detail by DeBrey et al. (1993). The method that was used by state personnel when they conducted the survey is believed to be similar, although no published methodology exists.

Individual yearly survey maps were digitized and stored in a raster format using ERDAS, Inc. PC-VGA, version 7.5, GIS. Raster-based systems assign numeric class values to individual map areas, called grid cells, which make up the total map area (ERDAS 1991). The grid cell size chosen for this study was 1000 meters square. This size represents a compromise between the resolution of the data and the ability to represent vectors, such as roads and political borders. One thousand meters is a much finer resolution than the actual annual survey maps would allow since the yearly maps were hand-drawn with only county borders for reference marks. The accuracy of outbreak locations probably deteriorated as the interpolation proceeded from a county border to the interior of a county. However, 1000 m resolution is not an egregious overestimate of the accuracy of the data based on GIS position cross-checks. The position cross-checks were done by locating, on the displayed outbreak frequency map, established APHIS survey stops with known outbreak histories with the CURSES routine (ERDAS 1991) that gives coordinate location and the attributes of grid cells. The GIS map coordinate locations and grid cell attributes agreed with known APHIS data.

GIS allowed the manipulation and analysis of all of the yearly survey data necessary to answer the five spatial-temporal questions. Initially, the 31 annual surveys were coded with a binomial grasshopper density scheme. Zero indicated areas with densities <9.6 grasshoppers per m2 and one indicated areas with >9.6 grasshoppers per m2. This scheme allowed the use of the INDEX routine (ERDAS 1991), which added the class values of corresponding grid cells of maps covering the same geographic area. For example, if grid cell 1,1 of the Wyoming state map was infested with grasshoppers 14 times in the last 31 yr, it would have the Grasshopper Outbreak Frequency Class (GOFC) value of 14 after being indexed. The maximum GOFC value a map grid cell could have with 31 yr of data would be 31.

Pattern. To determine if there was a pattern to the occurrence of grasshopper outbreaks, the 31 annual survey maps were indexed (INDEX routine; ERDAS 1991) and a single map of GOFCs was produced, and the areas of all GOFCs were computed. To test if the distribution of outbreaks departed from randomness, Morisita's index of aggregation (Im):

Im = (X/X-1)(1/µ)(2/µ+µ-1)

Im is a much better measure of departure from randomness and tendency to aggregation than the commonly used variance:mean ratio (Hurlbert 1990).

Pattern Through Time. Three decade maps, comprising the surveys conducted in the 1960s, 1970s, and 1980-1990s, were produced using the INDEX routine (ERDAS 1991). These three maps were produced to determine if there was a consistent spatial pattern of outbreaks over arbitrary time blocks during the period of data collection. The areas of all GOFC's for each decade were also computed. The maximum GOFC class value possible with these maps was 10.

Low Outbreak Years. The 8 yr with less than 300,000 ha of grasshopper outbreaks were indexed, and the areas of all GOFC's for this map were computed. This process generated a map of the spatial distribution when grasshopper outbreaks were at a low ebb. The 300,000 ha figure was chosen because it is approximately 1% of the state's area (the lowest year, 1993, had 139,000 infested ha). The maximum GOFC possible on this map was 8.

High Outbreak Years. To determine the spatial distribution when grasshopper outbreaks were extensive, the 12 yrs with at least one million hectares infested were indexed, and the areas of all GOFC's for this map were computed. One million ha is approximately 4% of the state's area (the highest year had 4,325,,800 infested ha). The maximum GOFC possible on this map is 12.

Catastrophic Expansions and Collapses. To examine the spatial dynamics of catastrophic grasshopper population expansions and collapses, it was necessary to define "catastrophic". In developing a catastrophe theory model for rangeland grasshopper populations, (Lockwood and Lockwood 1989) defined a grasshopper population catastrophe (catastrophe meaning, in mathematical usage, a sudden qualitative change in the state of a system) as a >50% change in the outbreak area from one year to the next. Using the >50% change criterion, 10 pairs of sequential years qualified for analysis. Five maps showing 2-yr expansion sequences and five maps showing 2-yr collapse sequences were produced (INDEX routine; ERDAS 1991). Each sequence was overlaid and recoded such that the outbreak areas of the year with the greater area of infestation in each pair were recoded to class value 2. After processing in this manner, each map of a two year sequence could have three possible classes: areas infested only in the low year (class 1), areas infested only in the high year (class 2), and areas infested both years (class 3). This approach is similar to that used by Cigliano et al. (1994) in Montana. The areas of the three classes for each sequence were computed for analysis. Two indices were developed to standardize and express the spatial dynamics of grasshopper populations during expansion and collapse from these data.

The first measure was the Outbreak Prevention Index (OPI), and it applied only to the expansion sequences (the first year's outbreak area being < 50% of the second year's outbreak area):
 
 

OPI =Class 3 Area /(Class 2 Area + Class 3 Area)





OPI values can range from 0.0 to 1.0. An OPI value of 0.0 would mean that there was no geographic overlap of infestations between years (i.e., the outbreaks were spatially unrelated). An OPI value of 1.0 would mean that there was complete overlap, such that with effective control measures an area equalling the entire low year's outbreak area could have been prevented assuming an effective treatment without immigration.

The second measure, the Prevention After Collapse Index (PACI), applied only to the collapse sequences (the second year's outbreak area being < 50% of the first year's outbreak area):
 
 

PACI = Class 3 Area/( Class 1 Area + Class 3 Area)





PACI values can range from 0.0 to 1.0. A PACI value of 0.0 would mean there was no overlap between the years and the outbreaks were spatially unrelated. A PACI value of 1.0 would mean a complete overlap, such that with effective control measures all of the following year's outbreaks could have been prevented, in principle.

The OPI and PACI indices are derived from and are relevant to the economics of grasshopper control. If it is shown that outbreaks persist spatially then the costs of grasshopper control measures can be amortized over two or more years because forage would be saved each year by preventing future damage.
 

Results and Discussion

Pattern. The map generated from the 31 annual grasshopper surveys (Fig. 1, updated to the1944-94 Grasshopper Outbreak Frequency Map) strongly suggests that there is a pattern to the occurrence of grasshopper outbreaks; outbreaks appear neither uniform nor random. Morisita's index of aggregation was 2.29 for the distribution of GOFCs. This value means the probability of two randomly selected infestations (i.e., a pixel infested in a given year), being from the same geographic area is 1.29 times greater than it would be if the outbreaks were randomly distributed (Hurlbert 1990).

The state historic outbreak map can be classified into three grasshopper outbreak categories. The first category consists of unsuitable habitat types (coniferous forest, alpine tundra, etc.) that have never supported an outbreak. The suitable habitat areas (mixed-grass prairie, ponderosa pine savanna, etc.) can then be divided into sporadic and chronic categories. The sporadic category includes areas with suitable habitat that have been infested zero to four times (0-13% of the years). The chronic category is defined as those areas that have been infested five or more times in the last 31 yr. The greatest GOFC on the map is 15. However, the GOFCs ranging from 13 to 15 only occupy approximately 0.1% of Wyoming's total area (Table 1). In all 31 years of data, only 37% of the state has ever been infested (Table 1).

The northwestern quarter of the state is dominated by unsuitable habitat, with large areas of coniferous forest. The southwestern quarter of the state is also unsuitable because it is dominated by large areas of desert shrubland and sagebrush steppe. Although grasshopper outbreaks occur frequently on sagebrush steppe vegetation in Idaho (Fielding and Brusven 1990), this habitat is not associated with large-scale grasshopper outbreaks in Wyoming.

Excluding those areas covered with dense coniferous forest and alpine tundra, the eastern half of Wyoming has both suitable habitat and grasshopper species capable of outbreak (Lockwood et al. 1992). However, the distribution of grasshopper outbreaks is not uniform within this area of apparently suitable habitat (Fig. 1). An example of this anomaly, are two areas that could be classified as sporadic, the Southern Powder River Basin and the Laramie-Cheyenne Plains (Fig. 2).
Neither of these areas had a recorded grasshopper outbreak in 31 years (Fig. 1). Both areas have mixed-grass prairie vegetation, and are used for grazing, and rangeland grasshopper pest species are endemic to both areas (Lockwood et al. 1993). The Southern Powder River Basin and Laramie-Cheyenne Plains are included in the annual grasshopper survey by APHIS. Cost share programs for grasshopper control programs have been available for all lands, (100% subsidy on federal lands, 50% on state and 33% on private) which would have encouraged ranchers to report grasshopper outbreaks even if government grasshopper scouts missed them. The Southern Powder River Basin is comprised of mixed private, state and federal ownership, while the Laramie-Cheyenne Plains are predominately private. Because it is improbable that large unreported outbreaks have occurred in these areas their classification as "sporadic" likely represents real ecological features. The majority of the Laramie-Cheyenne Plains area is above 1676 m (5500 ft) in elevation and frequently spring moisture is received in the form of snow well into May (Martner 1986). This could cause high mortality in emerging grasshopper nymphs. The Southern Powder River Basin receives, on average, less precipitation than the plains that surround it (Marston 1990), but has no other obvious difference from those areas that could account for the difference in outbreak frequency.

The area of the state that has had five or more outbreaks is relatively small in comparison to the total area of the state (Table 1). Six definable regions of the state can be classified as chronically infested (Fig. 1). These include the Black Hills, Laramie Mountains, Southern Big Horn Mountains, Northern Powder River Basin, Platte/Goshen/Niobrara complex, and the Thermopolis-Midwest region (Fig. 2). The Thermopolis-Midwest region includes two small areas that are separated geographically, but have chronic outbreaks that seem to be related to a common topography and vegetation (Figs. 1 and 2). Outbreaks in the Northern Powder River Basin, Southern Big Horn Mountains, and Platte/Goshen/Niobrara Complex have been the subject of more extensive control efforts than grasshopper outbreaks in the Black Hills and Laramie Mountains (J. Larsen, USDA-APHIS, pers. comm.) (Fig. 2). This difference in treatment history might be due to the greater capacity of the latter regions to absorb grasshopper damage without treatment. These regions have greater range productivity due to higher precipitation in these mountainous or foothill areas (Roberts 1989). Rangelands with high productivity have a two- to three-fold higher economic threshold (19.2 to 28.8 grasshoppers per m2 for treatment than the APHIS outbreak grasshopper density criterion (9.6 grasshopper per m2) (Davis et al. 1992). The ecological factors that may account for chronic grasshopper outbreaks on suitable habitat needs further investigation. Schell and Lockwood (1994) have suggested that these foothills areas represent an ecological transition zone with adequate temperatures to foster rapid nymphal development and enough precipitation for a consistent food base but insufficient precipitation to foster epizootics.

Pattern Through Time. The pattern of grasshopper outbreaks remained essentially the same during the 1960s, 1970s, and 1980-1993 (Fig. 3, Fig. 4 and Fig. 5 now the 1980-89 map). ( Outbreak maps from 1944-49, 1950-59 and 1990-94 are also available). Each decade had years with extensive outbreaks and periods in which high densities were relatively rare (Table 2). The decade maps confirm that the pattern of outbreaks has been generally consistent through the 31 years of data.

Low Outbreak Years. The spatial distribution of outbreaks from years with less than 300,000 ha infested (Fig. 6) is similar to the 31 yr map (Fig. 1). The only notable exception to this trend is in the Northern Powder River Basin, were outbreak activity was markedly reduced in low infestation years. Approximately 5% of the state's total area was infested at least once during the eight, low-infestation years (Table 3). The highest GOFC occurred in a very small area of the Black Hills that was infested 6 yr (Table 3). For reasons unknown, these areas can support grasshopper densities >9.6 grasshoppers per m2 during years when conditions for grasshoppers are suboptimal statewide. Perhaps these areas represent habitats which support grasshopper species which are adapted to climatic conditions unfavorable to most pest species or habitats which support a "core" population due to local factors which mitigate the generally adverse conditions. Without taxonomic data on the outbreaks these theories cannot be tested, but as the USDA-APHIS Wyoming grasshopper Information System continues to develop a taxonomic database, the nature of these persistently infested areas should become apparent.

High Outbreak Years. The pattern of outbreaks in years with more than 1 million ha infested (Fig. 7) is similar to the pattern on the 31 year map (Fig. 1). The distribution suggests that when conditions are favorable to grasshopper outbreaks, almost all areas with suitable habitat are vulnerable to infestation. A total of 35% of the state was infested at least once in the 12 high-infestation years (Table 4). A GOFC value of 9 was the highest observed on this map.

Catastrophic Collapse Sequences. The five, collapse-sequence maps suggest that outbreaks do not always collapse on themselves (Fig. 8, Fig. 9, Fig. 10, Fig. 11,and Fig. 12). However, two sequences, 1966-1967 and 1987-1988, (Fig. 8 and Fig. 11) exhibited considerable spatial persistence, with PACI's values of .54 and .75, respectively (Table 5). New outbreaks often occur in close proximity to locations infested the previous year. It appears that grasshopper outbreaks can drop below the outbreak density threshold over large areas in one year. No easily discernable spatial pattern is present that could be used as a predictor of a catastrophic reduction in outbreak area.

Catastrophic Expansion Sequences. The five, expansion-sequence maps indicate that outbreaks do not generally originate from the previous year's infestation (Fig. 13, Fig. 14, Fig. 15, Fig. 16, and Fig. 17). This observation is supported by quantitative analysis of the areas of infestation (Table 6). The greatest persistence was seen in the 1986-1987 sequence (Fig. 17), with an OPI of 0.28 (Table 6). However, the average value for the OPI for the other four expansion sequences was 0.10 (Table 6). This could explain why the annual grasshopper surveys are poor predictors of the next years' outbreaks (Davis et al. 1992).

Gradient population dynamics on the state scale are suggested by the expansion sequence maps (Fig. 13, Fig. 14, Fig. 15, Fig. 16, and Fig. 17) (Berryman 1987). Although there are localized areas that are chronically infested (Fig. 1), large scale outbreaks do not appear to originate from these areas. Therefore these dynamics do not fit Berryman's (1987) description of epicenters from which eruptive outbreak develop. Berryman (1987) specifies that his outbreak theory applies to single species dynamics only and rangeland grasshopper outbreaks are, in most cases, composed of several species (Cigliano et al. 1994). As such, the lack of a general, eruptive pattern supports a gradient dynamic only if this dichotomy is applicable to complex, multi-species systems. At smaller spatiotemporal scales rangeland grasshopper outbreaks have been found to exhibit characteristics of both eruptive and gradient dynamics (Cigliano et al. 1994, Lockwood and Schell 1994).

Summary. Regardless of the dynamics of grasshoppers outbreaks, areas that have a history of chronic infestations need to be managed differently than other Wyoming lands. Based on research conducted in the Platte/Goshen/Niobrara Complex, landowners in areas that are chronically infested may derive multi-year benefits from treating small (<4,000 ha) grasshopper outbreaks (Lockwood and Schell 1994). The benefits include maintaining grasshopper densities below outbreak levels for at least the following year and potentially preventing the expansion of the outbreak (Lockwood and Schell 1994). The efficacy of this approach is contingent upon eruptive dynamics continuing through a major large-scale outbreak, a contingency that appears to be unlikely based on the present analysis. If outbreaks can not be prevented in these chronically infested areas, continued efforts to suppress outbreaks after they develop may be unjustified (Lockwood et al. 1988). Continuing to create a livestock-grasshopper conflict in the 1% of the state with chronic infestations must be questioned. However, the history of grasshopper outbreaks in an area is only one factor of many that must be considered when managing pest populations. The other factors include aspects of rangeland ecology (e.g., productivity and climatic factors) and economics (e.g., livestock cost-and-return relationships and treatment efficacy) (Davis et al. 1992). In some of the chronically-infested areas rangeland productivity is sufficient to prevent competition between grasshoppers and livestock during most outbreaks (e.g., the Black Hills). Thus, a complex set of ecological and economic conditions function to further modify, and perhaps reduce, the area of Wyoming in which grasshoppers are a chronic, treatable pest. The present work illustrates that in most years, in most places, grasshoppers do not cause economic damage (Lockwood 1994). However, it is also evident that in some years grasshopper outbreaks can cover immense areas of the state. The analysis and maps derived from the historical data should provide managers in Wyoming previously inaccessible information on which to base effective management decisions and resource allocations with respect to survey and treatment.

Acknowledgments

I thank J. C. Larsen, Plant Protection Officer, USDA-APHIS for Wyoming for access to the annual grasshopper surveys. I also thank the USDA-APHIS Cooperative Agricultural Pest Survey Program for funding a portion of this study.

References Cited




Berryman, A. A. 1987. The theory and classification of outbreaks. pp. 3-30. In Barbosa, P. & J. C. Schultz [eds.], Insect outbreaks. Academic, New York.

Cigliano, M. M., W. P. Kemp and T. Kalaris. 1993. Spatiotemporal characteristics of rangeland grasshopper (Orthoptera: Acrididae) regional outbreaks in Montana. J. Orthop. Res. In Press.

Davis, R. M., M. D. Skold, J. S. Berry and W. P. Kemp. 1992. The economic threshold for grasshopper control on public rangelands. J. of Agric. and Res. Econ. 17: 56-65.

DeBrey, L. D., M. J. Brewer, and J. A. Lockwood. 1993. Rangeland grasshopper management. Agriculture Experiment Station B-980, University of Wyoming.

ERDAS 1991. ERDAS Field guide. ERDAS, Inc. Atlanta, GA.

Fielding, D. J. and M. A. Brusven. 1990. Historical analysis of grasshopper (Orthoptera: Acrididae) population responses to climate in southern Idaho, 1950-1980. Environ. Entomol., 19: 1786-1791.

Fielding, D. J. and M. A. Brusven. 1993. Spatial analysis of grasshopper density and ecological disturbance on southern Idaho rangeland. Agriculture, Ecosystems and Environ. 43: 31-47.

Hurlbert, S. H. 1990. Spatial distribution of the montane unicorn. Oikos. 58: 257-271.

Johnson, D. L. 1989. Spatial analysis of the relationship of grasshopper outbreaks to soil types. pp. 347-359. In L. McDonald, B. Manly, J. Lockwood, and J. Logan [eds.], Estimation and analysis of insect populations, Lecture notes in statistics 55. Springer-Q4 h DATUcomputer analysis of insects and weather: grasshoppers and rainfall in Alberta. Mem. Entomol. Soc. Can. 146:33-48

Kemp, W. P., T. M. Kalaris and W. F. Quimby. 1989. Rangeland grasshopper (Orthoptera: Acrididae) spatial variability: macroscale population assessment. J. Econ. Entomol. 82: 1270-1276.

Liebhold, A. M., R. E. Rossi and W. P. Kemp. 1993. Geostatistics and geographic information systems in applied insect ecology. Ann. Rev. Entomol. 38: 303-327.

Lockwood, J. A. 1994. Population ecology of grasshoppers. In S. K. Gangwere [ed.], Bionomics of grasshoppers and their relatives. In press.

Lockwood, J. A., W. P. Kemp and J. A. Onsager. 1988. Long-term, large-scale effects of insectidal control on rangeland grasshopper populations (Orthoptera: Acrididae). J. Econ. Entomol. 81: 1258-1264.

Lockwood, D. R. and J. A. Lockwood. 1989. Application of catastrophe theory to population dynamics of rangeland grasshopper. pp. 268-277. In L. McDonald, B. Manly, J. Lockwood, and J. Logan [eds.], Estimation and analysis of insect populations, Lecture notes in statistics 55. Springer-Verlag, New York.

Lockwood, J. A., T. J. McNary, J. C. Larsen and J. Cole. 1993. Distribution atlas for grasshoppers and the Mormon cricket in Wyoming 1988-92. University of Wyoming, Laramie, Wyoming.

Lockwood, J. A. and S. P. Schell. 1994. Outbreak dynamics of rangeland grasshoppers: eruptive, gradient, both or neither? Proceedings of the 6 th International Orthopterists' Society Meeting. Hilo, Hawaii. In press.

Martner, B. E. 1986. Wyoming climate atlas. University of Nebraska Press, Lincoln, Nebraska.

Marston, R. A. 1990. Wyoming water atlas. Wyoming Water Development Commission and University of Wyoming, Laramie, Wyoming.

Pfadt, R. E. 1988. Field guide to common western grasshoppers. Wyoming Agricultural Experiment Station Bulletin 912.

USDA-APHIS. 1987. Rangeland grasshopper cooperative management program: Final environmental impact statement. FEIS 87-1. USDA-APHIS-PPQ, Hyattsville, Maryland. 



 

Table 1. Area and percent of Wyoming occupied by each Grasshopper Outbreak Frequency Class (GOFC) (the number of years a grid cell has been infested) for the years 1960-81, 1985-93. 

GOFCa % of State
Area (ha)
0 62.25
15,939,800
12.73
3,237,700
7.44
1,892,600
4.64
1,181,700
3.56
905,300
2.87
729,600
2.29
582,500
1.81
459,600
1.04
264,200
0.51
130,900
10
0.26
65,200
11 
0.10
25,500
12 
0.05
13,100
13 
0.04
11,400
14 
0.01
2,600
15 
<0.01
1,000

a GOFC are the number of years that grasshopper outbreaks have occurred in a geographic area.



Table 2. Areas of Wyoming with grasshopper densities equalling or exceeding 9.6/m2 since 1960 (no survey was conducted in 1982, 1983 and 1984).

Year ____ Outbreak Area (ha)
1960--------------------467,500
1961--------------------387,300
1962--------------------375,500
1963------------------1,299,800
1964------------------1,560,800
1965------------------2,063,100
1966------------------2,109,400
1967--------------------849,900
1968------------------1,293,000
1969--------------------261,800
1970--------------------193,000
1971--------------------186,000
1972--------------------424,900
1973--------------------539,800
1974------------------1,838,500
1975--------------------956,500
1976--------------------458,600
1977--------------------323,800
1978--------------------435,700
1979------------------1,443,700
1980------------------1,016,600
1981--------------------514,900
1985------------------2,068,900
1986------------------1,775,700
1987------------------4,325,800
1988------------------1,799,700
1989--------------------187,600
1990--------------------289,700
1991--------------------285,200
1992--------------------211,900
1993--------------------139,000



 

Table 3. Grasshopper Outbreak Frequency Classes (GOFC) and the areas of the state they occupied for years (1969-1971, 1989-1993) in which the outbreak area was <300,000 ha or 1.18% of total state area.

GOFCa
% of State
Hectares
3.78
963,200
0.89
227,500
0.27
69,700
0.07
17,200
0.02
5,300
<0.01
600

a GOFC are the number of years that grasshopper outbreaks have occurred in a geographic area. 



 

Table 4. Grasshopper Outbreak Frequency Classes (GOFC) and the areas of the state they occupied for years (1963-1966, 1968, 1974, 1979-1980, 1985-1988) in which the outbreak area was > one million ha or 3.93% of total state area.

GOFCa
% of State
Hectares
13.24
3,368,600
7.87
2,002,600
5.39
1,372,200
3.94
1,001,900
2.54
646,400
1.34
341,600
0.44
112,100
0.08
21,200
<0.01
900

a GOFC are the number of years that grasshopper outbreaks have occurred in a geographic area. 



 

Table 5. Two year collapse sequences in which the outbreak area (>9.6 grasshoppers / m2) fell by at least 50%, the area that persisted, and a measure of spatial persistence. 

Sequence Outbreak Area (ha)
PACIa
1966 2,109,400
0.54
1967 849,900
Area that persisted: 455,800
1968 1,293,000
0.38
1969 261,800
Area that persisted: 96,400
1975 956,500
0.25
1976 458,600
Area that persisted: 116,900
1987 4,325,800
0.75
1988 1,799,700
Area that persisted: 1,265,000
1988 1,799,700
0.37
1989 187,600 
Area that persisted: 69,500

a PACI (Prevention After Collapse Index) values can range from 0.0 to 1.0. A PACI value of 0.0 would mean there was no overlap between the years. A PACI value of 1.0 would mean, theoretically, that with effective control measures all of the following year's outbreak could have been prevented. See Materials and Methods for the PACI formula. 



 

Table 6. Two year expansion sequences in which the outbreak area (>9.6 grasshoppers / m2) increased by >100%, the area that persisted, and a measure of spatial persistence. 

Sequence Outbreak Area (ha)
OPIa
1962 375,500
0.12
1963 1,299,800
Area that persisted: 153,400
1971 186,000
0.10
1972 424,900
Area that persisted: 42,900
1973 539,800
0.10
1974 1,838,500
Area that persisted: 175,000
1978 435,700
0.07
1979 1,443,700
Area that persisted: 92,300
1986 1,775,700
0.28
1987 4,325,800
Area that persisted: 1,136,700

a OPI (Outbreak Prevention Index) values can range from 0.0 to 1.0. An OPI value of 0.0 would mean that there was no overlap between the years. An OPI value of 1.0 would mean, theoretically, that with effective control measures an outbreak area equalling the low year's outbreak area could have been prevented. See Materials and Methods for the OPI formula. 


III. Spatial Analysis of Ecological Factors Related to Grasshopper Outbreaks in Wyoming