Resource polygon geometry predicts Bayesian stable isotope mixing model bias

Abstract

Bayesian mixing model analyses of re - source and consumer stable isotope composition are commonly used to infer elemental, energetic, and trophic pathways in aquatic and terrestrial food webs. However, the outputs of these models may be biased towards prior or null generalist assumptions, but the magnitude of this potential bias is unknown. I con- ducted a series of experiments to determine how this bias is affected by the geometry and end-member un- certainty of resource polygons. These experiments showed that bias is mostly due to isotopic overlap be- tween resources and is very strongly cor related in a sigmoid manner with the normalized surface area of stable isotope resource polygons. The normalized sur- face area, a classic signal to noise ratio in bivariate space, is calculated by scaling the x and y ordinates by the mean standard deviations (SD) for δ 13 C and δ 15 N, respectively. When equilateral 3-resource poly- gons have a surface area <3.4 SD 2 , the outputs of Bayesian mixing models primarily reflect the prior generalist assumption. The back-calculated bias for 85 recently published triangular polygons averaged 50 ± 28% (± SD). Analyses of regular resource poly- gons with 4 to 6 resources required 3.1 to 8.0 times larger normalized surface areas to constrain bias. Fur- thermore, polygons with 4 or more resources gave poor outcomes for minor diet components. There was a strong bias for resources similar, and against re- sources dissimilar, to the dominant resource. Overall, Bayesian methods applied to underdetermined mod- els and poorly resolved data very often give results that are highly biased towards centrist and generalist solutions.