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A frequently used indicator of stream ecosystem conditions is the species richness (number of species or taxa found in a sample). In the EUSE example, we often use (1) total number of macroinvertebrate taxa (richness) and (2) the number of taxa belonging to three orders known to be sensitive to pollution. These three orders are Ephemeroptera (mayflies), Plecoptera (stone flies), and Trichoptera (caddisflies). Taxa in these three orders are collectively known as EPT taxa. EPT taxa richness is often more indicative of water quality than total taxa richness. The data file posted on USGS web page (http://pubs.usgs.gov/ sir/2009/5243/data/EUSE_USGSReportData.csv) includes total richness (RICH) and EPT taxa richness (EPTRICH).

(a) Develop a multilevel model to model the response of total taxa richness (RICH) to changes in watershed urbanization represented by the national urban intensity index (NUII), as well as to regional level climate conditions.

(b) Develop a multilevel model to study the response of EPT taxa richness (EPTRICH) to changes in urban intensity, as well as to regional level variables such as mean temperature and precipitation.

(c) Another way to examine the changes in biological community is to examine the changes in the relative EPT taxa richness (i.e., EPT taxa richness as a fraction of total number of macroinvertebrate taxa) along the urban gradient. Develop a multilevel logistic regression model to study the changes of relative EPT taxa richness and compare the results to the EPT taxa richness model.

(d) Considering the connection between multinomial and Poisson models discussed in Chapter 8, discuss how the connection can be used in a multilevel setting.