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Many institutions around Lake Erie have long-term water quality monitoring programs. These institutions, however, use several different water sampling methods and several chemical analytical methods for measuring water quality variables. The data file Eriecombined.csv include monitoring data from six institutions collected from 2010 to 2013. Figure 3.4 shows data from NOAA. One way to examine institutional differences is to use a multilevel model with institution as a factor variable, after other factors affecting water quality (TP and chlorophyll a concentrations in particular) are accounted for. These factors include (1) distance to the source of phosphorus (the Maumee River), (2) year, and (3) season (months).

(a) Use exploratory data analysis tools (e.g., Q-Q plots) to determine the nature of the difference (e.g., multiplicative or additive differences). Based on the exploratory analysis, recommend an appropriate transformation for the two water quality variables of interest (TP and chlorophyll a concentrations).

(b) Fit multilevel models for TP and chlorophyll a concentrations (TP and CHLA, respectively), using distance to Maumee River mouth (DISTANCE) as a continuous predictor and INSTITUTION, YEAR, and SEASON as three factor variables. Describe model outputs in plain language.

(c) Present the differences among institutions graphically.

Figure 3.4

Many institutions around Lake Erie have long-term water quality monitoring programs. These...

 
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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.

 
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In evaluating TITAN we used several alternative models to show the pattern of the IV s along an environmental gradient. Another natural pattern discussed by Cuffney and Qian [2013] is the Gaussian response model, where the response curve is similar to a bell-shaped curve. This response pattern is often used to represent the “subsidy-stress” response of a taxon. The initial increase in a pollutant (e.g., nutrient) provides subsidy to the growth of the organism, but the organism is stressed after the pollutant exceeds a threshold. The response pattern can be expressed as a parabola function of the gradient in log-abundance scale:

In evaluating TITAN we used several alternative models to show the pattern of the IV s along an...-1

where y is the taxon abundance and x is the environmental gradient. A logical threshold is the peak of the quadratic curve. Draw the response curve of IV similar to the curves in Figure 11.3 and discuss whether TITAN is appropriate for this type of threshold response.

Figure 11.3

In evaluating TITAN we used several alternative models to show the pattern of the IV s along an...-2

 
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