land as weights. Thus, the following seven variables are used to represent a state’s ecosystem:
■ Average temperature (mean January temperature)
■ Average precipitation (days of measurable precipitation per year)
■ The variance of temperature and the variance of precipitation measured using county-level
data on temperature and precipitation in each state.
■ Land index computed using principal component analysis with data on acres of cropland,
pasture, rangeland, forest, small and large urban area, and miscellaneous acres. The Land
index of the ith state is given by:
( ,τ, V ( ( Xr - X ) ʌ
Land Indexi = ∑ (αr — r-------)
∑ (Xr - X)2
r=1
where Xr (r= 1,...,R) denotes land acres in each of the categories defined above and ∀r is the
weight for the r-th category.
■ A soil and water index created in a way similar to that of the land index. The categories of
soil include sandy, silty, clay, loamy, organic and others, while those for water include water
body (less than 2, 2-40, more than 40 acres) subdivided into lakes, reservoirs, bay/gulf and
estuary, and perennial stream based on width (< 66, 66-660 and > 660 feet).
The land, soil and water index are created also using share rather than the size of each category,
which we refer to as land share, water share and soil share indexes. For each ecosystem variable,
we construct a 48x48 dissimilarity matrix as before:
z ( AL - AL )/AL ... ( AL - WY )/AL λ
4(WY - AL)/WY - (WY - WY/ WY)J48×48
Each row corresponds to the percentage difference of an ecosystem variable of a state with itself
and the other 47 states. For example, the weighted average precipitation of AL, AR and Arizona
13
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