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A climax vegetation coverage of Montana, the expected native vegetation under undisturbed conditions based on soils and climate, was used in this study (Fig. 4). This coverage, obtained from MAPS (Nielsen et al. 1990), was based on the climax vegetation map of Ross and Hunter (1976). The MAPS system format divides the state of Montana into 17,993 cells, each representing an area of 21.3 km2 (Nielsen et al. 1990). The climax vegetation coverage (1: 1,000,000 scale) originally expressed in long/lat plane coordinate was transformed to the Albers Equal-Area Conic projection. Sixtytwo climax vegetation types (Fig. 4), covering an area size that varies from 59 km2 up to 34,351 km2, are grouped into five geomorphological regions: Eastern Glaciated Plains, Western Glaciated Plains, Eastern Sedimentary Plains, Western Sedimentary Plains, and Foothills and Mountains (Fig. 4). To conduct the analyses at the regional level, the climax vegetation coverage (Fig. 4) was reclassified to produce a layer displaying the five geographic regions (Fig. 5). To obtain this coverage, all the vegetation types were considered except for type 61. Although this type (61) was originally described as part of the Foothills and Mountains (Ross and Hunter 1976), it occurs along the major rivers, and it is the only type that occurs in all five geographic regions (Figs. 4E, 5).
Fig. 4. Map of Montana showing the climax vegetation types (Ross and Hunter 1976). A, vegetation types coded 1-14. B, vegetation types coded 15-28, after the first 14 types have been removed. C, vegetation types coded 29-42, after the first 28 types have been removed. D, vegetation types coded 43-56, after the first 42 types have been removed. E, vegetation types coded 57-62, after the first 56 types have been removed.
Fig. 5. Map of Montana showing the geomorphological regions (Ross and Hunter 1976). The Eastern Glaciated Plains, indicated in blue; the Western Glaciated Plains, indicated in yellow; the Eastern Sedimentary Plains, indicated in brown; the Western Sedimentary Plains, indicated in green; the Foothills and Mountains, indicated in purple; vegetation type coded 61, indicated in white.
For analyses, each yearly grasshopper density coverage was classified so that only one condition (high densities, >9.6 grasshoppers m-2) was considered. Area analyses were conducted on these coverages to determine the magnitude of the differences of the percentage of high density areas among the years.
In order to investigate whether grasshopper densities are equally distributed in time across vegetation types and across geomorphological regions, each density coverage was overlayed on the climax vegetation coverage (Fig. 4) and on the region coverage (Fig. 5). For each year, the size of high density areas in each vegetation type and in each region was calculated. Because the area values were usually positively correlated with the geographic extent of a given vegetation type or geomorphological region (a problem of area effect), the areas of high densities were expressed as percentage of the total area available in each vegetation type or region. Unsurveyed areas within a given vegetation type were omitted, when the area adjustment was done. Whole vegetation types or geomorphological regions that were not surveyed over more than 50% of their area in any given year were excluded from the analysis.
We used multivariate techniques to determine the relationship between years based on the spatial distribution of high density areas. From the various multivariate techniques (Pielou 1984), we selected an ordination method (principal component analysis, PCA, Blackith and Reyment 1971) and cluster analysis (unweighted pair-group method using arithmetic averages, UPGMA, Sneath and Sokal 1973). In both methods, the percentage of high density areas in each vegetation type in each year was used to analyze the relationship between years. Two data matrices were constructed, one of eight years by 62 vegetation types for the period 1959-1966 (Table 1) and another of nine years by 62 vegetation types for the period 1984-1992 (Table 2). Q-type cluster analysis (Pielou 1984) was also conducted in order to examine if certain vegetation types tended to have similar density dynamics over time. The clustering method was chosen, because of its suitability to express categorical patterns of differentiation. The PCA was selected because it has the advantage of indicating the relative contribution of each variable to each vector. Dendrograms were based on a distance coefficient (Rohlf and Sokal 1965), and the PCA on a variance/covariance matrix. The NTSYS-PC software version 1.70 (Rohlf 1992) was used in this study.
To determine whether the outbreak areas were geographically stable in time, we overlayed the density coverages across all years within the periods studied and area analyses were conducted to determine the geographic overlap, if any.
Finally, in order to examine the spatial distribution of different density categories, each yearly grasshopper density coverage was reclassified into four broad categories of grasshopper densities recorded in the survey: very low (<3.6 grasshoppers m-2), low (3.6 to <9.6 grasshoppers m-2), high (9.6 to <17.9 grasshoppers m-2), and extreme densities (>17.9 grasshoppers m-2).
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