At branch points, two or more separate reactions compete for the same reactant. This affects the isotopic composition of all products downstream of the branch point. To illustrate this, consider the network below:
Here, the flux of material into pool B (φ) is balanced by two fluxes, one into pool C and the other into pool D (φ and φ respectively). The mass balance for the heavier isotope in this system is represented by
Define f = φ / (φ + φ) = φ/φ as the fractional yield of C. Dividing through by φ gives
Applying the approximation introduced in the previous section, δ ≈ δ + ε. Further, δ ≈ δ + ε and δ ≈ δ + ε. Substituting these relations into the mass balance and solving for δ gives
The isotopic composition of pool B is clearly dependent on the fractional yield of C. Since there are no fluxes out of pools C or D, δ = δ, δ = δ. Thus, the isotopic compositions of these pools are offset from δ by ε and ε respectively. The figure at right summarizes these results.