= Competitive index
{title2=$\mathrm{CI}$}
A \b[competitive index] measures the change in the relative representation of two competing <biological strains>. With test strain $T$ and reference strain $R$, a common convention is
$$
\mathrm{CI}=\frac{T_{\mathrm{out}}/R_{\mathrm{out}}}{T_{\mathrm{in}}/R_{\mathrm{in}}},
$$
where input and output denote abundances measured before and after the comparison. The order of the two <biological strains> must be stated: swapping them gives the reciprocal when all four abundances are positive.<Clostridioides difficile proline fermentation in response to commensal clostridia by Christopher A. Lopez and others>[section4.6, Competition assay, output ratio divided by input ratio]{ref}
An original numerical example starts with 100 test and 100 reference units and ends with 200 test and 800 reference units. Then $\mathrm{CI}=(200/800)/(100/100)=0.25$. The test strain doubled in absolute abundance while declining fourfold relative to the reference. If the input had instead been 100 test and 400 reference units, that same output would give $\mathrm{CI}=1$. Input normalization therefore matters.
The measurement can connect a molecular difference to <microbial ecology>. A primary study compared a <proline>-fermenting bacterial strain with a <mutant> unable to perform that fermentation, then tested how additional community members changed their relative recovery. The observed advantage depended on the surrounding community and medium.<Clostridioides difficile proline fermentation in response to commensal clostridia by Christopher A. Lopez and others>[section2.4 and Figure4; section4.6]{ref}
An index above one favors the strain placed in the numerator for that comparison. It is not a context-independent measure of <biological fitness>. The abundance assay, reference strain, sampling interval and environment define the question. Counts of <colony-forming units>, for example, measure recoverable colony-producing units under the assay conditions. Zero reference counts make the displayed ratio undefined; substituting an arbitrary number changes the statistic.
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