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<front>
<journal-meta>
<journal-id journal-id-type="publisher">EGUsphere</journal-id>
<journal-title-group>
<journal-title>EGUsphere</journal-title>
<abbrev-journal-title abbrev-type="publisher">EGUsphere</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">EGUsphere</abbrev-journal-title>
</journal-title-group>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/egusphere-2026-6173</article-id>
<title-group>
<article-title>Technical note: MixSIAPy &amp;ndash; Bayesian stable isotope mixing models in Python with multi-backend inference and formula-based compositional regression</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yang</surname>
<given-names>Jing</given-names>
<ext-link>https://orcid.org/0000-0001-9838-5102</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Dai</surname>
<given-names>Heng</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ye</surname>
<given-names>Ming</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Cheng</surname>
<given-names>Su</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zhao</surname>
<given-names>Yonghua</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Qian</surname>
<given-names>Hui</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>School of Land Engineering, Chang’an University, Xi’an 710054, China</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>State Key Laboratory of Geomicrobiology and Environmental Changes, China University of Geosciences, Wuhan 430074, Hubei, China</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Hubei Key Laboratory of Yangtze Catchment Environmental Aquatic Science, China University of Geosciences, Wuhan 430074, Hubei, China</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee 32306, USA</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Shaanxi Biyuan Chenchuang Technology Co., Ltd., Xi&apos;an 710065, China</addr-line>
</aff>
<aff id="aff6">
<label>6</label>
<addr-line>School of Water and Environment, Chang’an University, Xi’an 710054, Shaanxi, China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>12</day>
<month>10</month>
<year>2026</year>
</pub-date>
<volume>2026</volume>
<fpage>1</fpage>
<lpage>26</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2026 Jing Yang et al.</copyright-statement>
<copyright-year>2026</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-6173/">This article is available from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-6173/</self-uri>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-6173/egusphere-2026-6173.pdf">The full text article is available as a PDF file from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-6173/egusphere-2026-6173.pdf</self-uri>
<abstract>
<p>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 &lt;em&gt;hoc&lt;/em&gt; 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.</p>
</abstract>
<counts><page-count count="26"/></counts>
<funding-group>
<award-group id="gs1">
<funding-source>National Natural Science Foundation of China</funding-source>
<award-id>42302288</award-id>
</award-group>
</funding-group>
</article-meta>
</front>
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