$$\alpha = (\delta^{13}C_c - \delta ^{13}C_2) /
(\delta ^{13}C_1 - \delta ^{13}C_2)$$
where \(\delta^{13}C_c\) is the isotopic value for consumer,
\(\delta^{13}C_1\) is the mean isotopic value for baseline 1 and
\(\delta^{13}C_2\) is the mean isotopic value for baseline 2.