Quantifying foodweb interactions with simultaneous linear equations: Stable isotope models of the Truckee River, USA

Aquatic foodweb models for 2 seasons (relatively high- [March] and low-flow [August] conditions) were constructed for 4 reaches on the Truckee River using ??13C and ??15N data from periphyton, macroinvertebrate, and fish samples collected in 2003 and 2004. The models were constructed with isotope values that included measured periphyton signatures and calculated mean isotope values for detritus and seston as basal food sources of each food web. The pseudo-optimization function in Excel's Solver module was used to minimize the sum of squared error between predicted and observed stable-isotope values while simultaneously solving for diet proportions for all foodweb consumers and estimating ??13C and ??15N trophic enrichment factors. This approach used an underdetermined set of simultaneous linear equations and was tested by running the pseudo-optimization procedure for 500 randomly selected sets of initial conditions. Estimated diet proportions had average standard deviations (SDs) of 0.03 to 0.04??? and SDs of trophic enrichment factors ranged from