Technical note: MixSIAPy – Bayesian stable isotope mixing models in Python with multi-backend inference and formula-based compositional regression

Abstract. Bayesian stable isotope mixing models quantify source contributions, but environmental studies increasingly require testing how multiple interacting drivers alter entire source compositions. The widely used R package MixSIAR restricts covariate structures, while post hoc regression of estimated proportions neither propagates posterior uncertainty nor preserves compositional dependence. Its reliance on a separately installed JAGS engine also constrains direct evaluation of gradient based samplers and accelerator-aware computation. We here introduce MixSIAPy, an open-source Python framework addressing these statistical and computational limitations while retaining established MixSIAR model structures. Its principal methodological contribution is formula-based compositional regression embedded directly in the mixing-model likelihood. Multiple categorical and numerical predictors and their interactions act jointly on source compositions in isometric log-ratio coordinates, with regression, grouping, source, and error parameters estimated in one posterior. A single PyMC model can be fitted through four interchangeable No-U-Turn Sampler backends, enabling CPU sampling and optional GPU execution. A shared engine supports scripted, local graphical, and hosted web workflows with reproducible outputs. Across 20 paired benchmarks, 19 converged in both implementations and showed close posterior correspondence; MixSIAPy reached an acceptable posterior faster in 13 cases. Backend performance was model dependent, and GPUs became advantageous only for some models at high chain parallelism. In an additional crop-water-uptake case study, the model identified a biomass associated shift from shallow to middle soil water in linseed, whereas broader effects remained uncertain. MixSIAPy thus enables interacting environmental controls to be tested within source-partitioning models instead of through separate analyses of uncertain estimated proportions.