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

B13-1 

Appendix B-13. Mapping Continuous Biological Index Values to BCG Tiers 

The Florida Department of Environmental Protection (FDEP) conducted a workshop to calibrate 

a biological condition gradient (BCG) using macroinvertebrate data collected from streams in 

Florida. During the workshop, macroinvertebrate samples (a list of taxa and their abundances) 

from 30 streams spanning the human disturbance gradient were provided to a panel of 22 

biologists with expertise and experience with Florida streams. Each biologist then assigned each 

sample to one of the six BCG tiers. A stream condition index value (SCI) was also computed for 

each sample, but this SCI value was not provided 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 sample requires that one taken into account the 

categorical nature of the data. One approach for modeling the relationship between a continuous 

variable (e.g., SCI) and a categorical response (e.g., BCG tier) is a proportional odds logistic 

regression model (Guisan and Harrell 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: 

)( 1ln 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 for all tiers. Five parallel models 

are fit, modeling the probability of assignment to Tiers 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 assignment 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 different 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 circle 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. Consequently, 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 the experts identified the transition between Tier 

4 and Tier 5 as the impairment threshold. The other half identified the boundary between Tier 3 

and Tier 4 as the impairment threshold. Most experts 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 conditions). 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 with the probability of 

mistakenly assessing a reference site as impaired. 

The same modeling approach can be applied to expert assignments of lake vegetation samples to 

a BCG. Here, lake vegetation can also be summarized as a Lake Vegetation Index (LVI). 

The consensus among experts was somewhat weaker compared to the results 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 these results to support criterion 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 with 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.