# Quantitative Ecotoxicology, Page 189, Example 4.12, QICAR-Model

This is example 4.12 on page 189 of Quantitative Ecotoxicology - reproduced with R.

### Introduction

Quantitative Ion Character-Activity Relationships (QICAR) are models that are used to predict toxicity from metal ion characteristics.

One such metal ion characteristic is the *‘softness’*:

metal ions can be classified into

- hard (e.g., Be2, Al3, Fe3)
- soft (e.g., Cu, Ag, Hg, Pt2)
- borderline (e.g., Fe2, Co2 , Ni2, Zn2,Cu2) metal ions.

Hard acids preferentially bind to O or N, soft acids to S, and the borderline ions form stable complexes with S, O, or N (Ownby and Newman, 2003).

In this example, the softness of 20 metal ions is given, as well as associated toxicity data (EC50 values from a bacterial assay).

We want to relate softness to toxicity by a linear model.

### Analysis

Get the data from here and read it into R:

As always our first step is to look at the data:

Data consists of a three column table: TOTLEC is the log10 of EC50 values and SOFTCON is a measure of metal ion softness. Plotting the data reveals that there is a strong relationship between both.

To build a linear model we use the `lm()`

function.
We specify the model via the formula notation `repose ~ predictor`

and store it as an object names `mod`

.

Since we are interested in the model properties we take a look at the model summary:

This output shows us the intercept (2.617) and slope (SOFTCON, - 2.931) of our model, the R-Square (0.866) as well as some other useful information.

To make a quick plot of our data and model we can use `abline`

:

### Polishing the plot

The above plot isn’t very nice, so let’s try to reproduce the plot from Figure 4.15.

To get greek symbols, sub- and superscripts etc into R plots we have to use some special mathematical annotation (see `?plotmath`

for more information).

As above we plot the data and our model. The model is display as a dashed line (`lty = 'dashed'`

), the raw data as solid (`pch = 16`

) and bigger (`cex = 1.4`

) points.
Moreoever, the axis labels were customized. All `plotmath`

annotations have to be wrapped into expressions, `sigma[con]`

is equal to the greek letter sigma subscript with con.

We can also add the model equation to this plot via `text()`

which is slightly trickier:

First we extract the model coefficients via `coef()`

.
If we want to access these numbers (and not type them manually) in the equation, we have to embed the equation into `bqoute()`

. `bqoute()`

works like `expression()`

above, except that objects wrapped in `.()`

will be replaced by their respective values.

Once again we reproduced the same results as in the book using R :) Code and data are available on my github-repo under file name ‘p189’.

### References

[1] D. Ownby and M. Newman. “Advances in Quantitative Ion
Character-Activity Relationships (QICARs): Using Metal-Ligand
Binding Characteristics to Predict Metal Toxicity”. In: *QSAR \&
Combinatorial Science* 22.2 (Apr. 2003), pp. 241-246. DOI:
10.1002/qsar.200390018. <URL:
http://dx.doi.org/10.1002/qsar.200390018>.