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

Publication Type:

Journal Article


Journal of the North American Benthological Society, Volume 26, Issue 4, p.642-662 (2007)




Aquatic foodweb models for 2 seasons (relatively high- [March] and low-flow [August] conditions) were constructed for 4 reaches on the Truckee River using δ13C and δ15N 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 δ13C and δ15N 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 <0.005 to 0.05‰ based on the results of the 500 runs, indicating that the modeling approach was very robust. However, sensitivity analysis of calculated detritus and seston δ13C and δ15N values indicated that the robustness of the approach is dependent on having accurate measures of all observed foodweb-component δ13C and δ15N values. Model results from the 500 runs using the mean isotope values for detritus and seston indicated that upstream food webs were the simplest, with fewer feeding groups and trophic interactions (e.g., 21 interactions for 10 feeding groups), whereas food webs for the reach downstream of the Reno–Sparks metropolitan area were the most complex (e.g., 58 interactions for 16 feeding groups). Nonnative crayfish were important omnivores in each reach and drew energy from multiple sources, but appeared to be energetic dead ends because they generally were not consumed. Predatory macroinvertebrate diets varied along the river and affected estimated trophic positions of fish that consumed them. Differences in complexity and composition of the food webs appeared to be related to season, but could also have been caused by interactions with nonnative species, especially invasive crayfish.