TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters



## Appendix B-13: Mapping Continuous Biological Index Values to BCG TiersTSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B13-1 

### Appendix B-13. Mapping Continuous Biol ogical Index Values to BCG Tiers
The Florida Department of Environmental Prot ection (FDEP) conducted a workshop to calibrate a biological condition gradient (BCG) using macroinvertebrate da ta collected from streams in Florida. During the workshop, macroinvertebrate sa mples (a list of taxa and their abundances) from 30 streams spanning the human disturban ce gradient were provi ded to a panel of 22 biologists with expertise and experience with Flor ida streams. Each biologist then assigned each sample to one of the six BCG tiers. A stream c ondition index value (SCI) was also computed for each sample, but this SCI value was not provi ded to the biologists during the calibration workshop.

BCG tiers represent categories of stream condition, ranging from “as naturally occurs” (Tier 1) to “severely degraded” (Tier 6). Modeling the relationship between the SCI value associated with each sample and the BCG tiers assigned to the sa mple requires that one taken into account the categorical nature of the data. One approach for modeling the relations hip between a continuous variable (e.g., SCI) and a categ orical response (e.g., BCG tier) is a proportional odds logistic regression model (Guisan and Harr ell 2000). This model estimates the cumulative probability of a site’s being assigned to a given tier (e.g., Tier 3) or to any higher-quality tier (Tier 1 or 2). The model equation can be written as follows:

)( 1 ln SCIba g g

j j j

        

 Eqn. B13-1

Where gj is the probability of a site’s being assigned to Tiers 1 through j , and j ranges from 1 to 5. Note that the regression coefficient, aj , can differ depending on the value of j , but the regression coefficient that scales the effects of SCI is constant fo r all tiers. Five parallel models are fit, modeling the probability of assignment to Tier s 5 to 1, Tiers 4 to 1, Tiers 3 to 1, Tiers 2 to 1, and Tier 1 only. Once these five models are fit, the probability of assi gnment to any single tier can be extracted from the model results.

In Figure B13-1, the mean predictions of a proportional odds logistic regression model are plotted as solid lines. The lines are color-coded and labeled by di fferent tiers, and each line can be interpreted as the proportion of experts that assigned samples with the indicated SCI value to a particular tier. For example, approximately 90% of experts assigned a sample with SCI = 0 to Tier 6 (brown line), while the remaining 10% of experts assigned the sample to Tier 5 (purple line). The solid circles represent the actual expert assignments recorded from the workshop for each SCI value. The size of the ci rcle is proportional to the number of experts that assigned a sample to a particular tier, and the circles are color-coded by tier.

Expert consensus in tier assignments was high for very degraded sites. That is, sites with SCI < 15 were assigned only to Tier 5 or 6. Consequent ly, the maximum values for the curves for Tiers 6 and 5 were relatively high. Similarly, expert consensus was high for high-quality sites because most sites with SCI > 58 were scored as Tier 1 or 2. The range of expert assignments at midrange SCI values was much broader.TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B13-2 At the workshop, experts were also asked to identify a point on the BCG where they thought streams were impaired, and approximately half th e experts identified the transition between Tier 4 and Tier 5 as the impairment threshold. The ot her half identified the boundary between Tier 3 and Tier 4 as the impairment threshold. Most ex perts also agreed that Tiers 1 and 2 corresponded to reference conditions.

One approach for using the results from the BCG calibration workshop to support a biocriterion threshold established by candidate reference sites is to identify an SCI value that corresponds with both a low probability of assignment to Tier 5 (impaired) and corresponds with a low probability of assignment to Tier 2 (reference cond itions). For these data, this point occurs at approximately SCI = 40–44, where both the purple and the blue lines are low (i.e., less than about 0.15). In a sense, thresholds selected in this range of values balance the probability of mistakenly assessing a degraded site as meeting aquatic life use goals w ith the probability of mistakenly assessing a refe rence site as impaired.

The same modeling approach can be applied to e xpert assignments of lake vegetation samples to a BCG. Here, lake vegetation can also be summ arized as a Lake Vegetation Index (LVI).

The consensus among experts was somewhat weaker compared to the resu lts for the SCI. For example, most experts assigned the lake with the highest LVI value (LVI = 94) to Tier 1 or 2, but one expert assigned it to Tier 4. Similarly, at the other end of the condition gradient, a lake with LVI = 18 was assigned by experts to Tiers 3–6.

The same logic can be applied to interpreting thes e results to support criter ion selection. In this case, the probabilities of assignment to Tiers 5 and 2 were less than about 0.15 for LVI = 50–58.

Figure B13-1. BCG tier assignments modeled w ith a proportional odds logistic regression.TSD for U.S. EPA’s Proposed Numeric Nutrient Criteria for FL Inland Surface Fresh Waters

B13-3 Figure B13-2. BCG tier assignments based on lake vegetation. LVI: Lake Vegetation Index.