Robustness of Machine Learning Algorithms to Skewness, Spatial Dependence, and Sample Size Compared to BME in Soil Fertility Prediction

Robustness of Machine Learning Algorithms to Skewness, Spatial Dependence, and Sample Size Compared to BME in Soil Fertility Prediction | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Robustness of Machine Learning Algorithms to Skewness, Spatial Dependence, and Sample Size Compared to BME in Soil Fertility Prediction MARTHE PAULETTE GUEDEZOUME BEHANZIN, Codjo Emile Agbangba, D. Gustave Dagbenonbakin, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8738598/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Finally, BME remains the benchmark for spatially explicit predictions in limited and asymmetric datasets. However, the integration of ML’s non-linear predictive capacity with BME’s spatial rea­soning offers a promising hybrid BME–ML framework, combining statistical robustness with spatial adaptability to advance digital soil mapping and guide more reliable soil fertility management strate­gies. Accurate prediction of soil fertility parameters is essential for sustainable agricultural management and environmental conservation. However, the performance of predictive models often depends on data characteristics such as spatial dependence, skewness, and sample size. This study compared the robustness of three Machine Learning (ML) algorithms Random Forest (RF), Support Vector Machine (SVM), and Artificial Neural Network (ANN) with the geostatistical Bayesian Maximum Entropy (BME) method in predicting key soil fertility attributes, including Organic Matter (OM), Potassium (K), Phosphorus (P), Potential of Hydrogen (pH), Copper (Cu), Zinc (Zn), Iron (Fe), Mag­nesium (Mg), Nitrogen (N), Boron (B), Electrical Conductivity (EC), Calcium Carbonate (CaCO 3 ), Cation Exchange Capacity (CEC), and Organic Carbon (OC). A comprehensive simulation experiment was conducted based on twelve scenarios that systemati­cally combined variations in sample size (200, 500, 1,000, and 10,000), degrees of skewness (sym­metric, moderately skewed, and highly skewed), and spatial dependence levels (weak, moderate, and strong) under Spherical, Exponential, and Gaussian semivariogram models. Model performance was evaluated using multiple accuracy and spatial consistency metrics, including the Coefficient of Determination (R 2 ), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Spatial Efficiency (SE), and Moran’s I of residuals, while uncertainty quantification employed Prediction Interval Coverage Probability (PICP), Mean Prediction Interval Width (MPIW), and Continuous Ranked Probability Score (CRPS). The results indicate that BME consistently outperformed all ML models under conditions of strong spatial dependence and small sample sizes (R 2 > 0.75, RMSE < 0.18, SE ≈ 0.82, and Moran’s I < 0.05). In contrast, ML algorithms, particularly ANN and SVM, showed significant perfor­mance degradation in highly skewed datasets (R 2 0.25), while RF demonstrated relative resilience (R 2 ≈ 0.70). Increasing the sample size from 200 to 10,000 markedly improved the performance of all ML models, thereby narrowing their performance gap with BME (average ∆R 2 = 0.10). BME also exhibited superior uncertainty quantification, with higher PICP (0.93) and lower CRPS (0.12) compared to ML models. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 11 Mar, 2026 Reviews received at journal 08 Mar, 2026 Reviews received at journal 27 Feb, 2026 Reviews received at journal 25 Feb, 2026 Reviewers agreed at journal 13 Feb, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers agreed at journal 11 Feb, 2026 Reviewers invited by journal 11 Feb, 2026 Editor invited by journal 11 Feb, 2026 Editor assigned by journal 04 Feb, 2026 Submission checks completed at journal 04 Feb, 2026 First submitted to journal 30 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8738598","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":590709108,"identity":"83351f82-477d-499d-b589-421b9a49f934","order_by":0,"name":"MARTHE PAULETTE GUEDEZOUME BEHANZIN","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYBAC+/Yz5p8//vknZ3Aj//mHDzWHeeRnMDB++NiGW4vBmRwzZskGNmODO2/YGGccey7HJsHALDnzHB4tN3jMmHkb2BI33H/DBmT8NwZqYePm/UdQC0/ihts5bI9tG24ntgG1MPNuw+OXGTzmj3l/SAC15B83ziVGi4HEG5AtBiBbGKRz+4jSkgPSkpC44QZQi2Xb4XqIFnwhBtFyAKSFTZqx7TDYFm68WnjS0oCBfMBYckYOs2HPMZAWxmbJmfi0sB8+Do5Kfon8hw9+1BxOnD//8EG8UYkNMDaQpn4UjIJRMApGAQYAAF+JYZxdCXtkAAAAAElFTkSuQmCC","orcid":"","institution":"Université d'Abomey-Calavi","correspondingAuthor":true,"prefix":"","firstName":"MARTHE","middleName":"PAULETTE GUEDEZOUME","lastName":"BEHANZIN","suffix":""},{"id":590709109,"identity":"3635148b-94e2-4863-bfd3-c81b4ede61a8","order_by":1,"name":"Codjo Emile Agbangba","email":"","orcid":"","institution":"Université d'Abomey-Calavi","correspondingAuthor":false,"prefix":"","firstName":"Codjo","middleName":"Emile","lastName":"Agbangba","suffix":""},{"id":590709110,"identity":"275e2887-70be-4f08-9f6e-bbff4a07624e","order_by":2,"name":"D. 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However, the integration of ML’s non-linear predictive capacity with BME’s spatial rea­soning offers a promising hybrid BME–ML framework, combining statistical robustness with spatial adaptability to advance digital soil mapping and guide more reliable soil fertility management strate­gies.\u003c/p\u003e\n\u003cp\u003eAccurate prediction of soil fertility parameters is essential for sustainable agricultural management and environmental conservation. However, the performance of predictive models often depends on data characteristics such as spatial dependence, skewness, and sample size. This study compared the robustness of three Machine Learning (ML) algorithms Random Forest (RF), Support Vector Machine (SVM), and Artificial Neural Network (ANN) with the geostatistical Bayesian Maximum Entropy (BME) method in predicting key soil fertility attributes, including Organic Matter (OM), Potassium (K), Phosphorus (P), Potential of Hydrogen (pH), Copper (Cu), Zinc (Zn), Iron (Fe), Mag­nesium (Mg), Nitrogen (N), Boron (B), Electrical Conductivity (EC), Calcium Carbonate (CaCO\u003cem\u003e3\u003c/em\u003e), Cation Exchange Capacity (CEC), and Organic Carbon (OC).\u003c/p\u003e\n\u003cp\u003eA comprehensive simulation experiment was conducted based on twelve scenarios that systemati­cally combined variations in sample size (200, 500, 1,000, and 10,000), degrees of skewness (sym­metric, moderately skewed, and highly skewed), and spatial dependence levels (weak, moderate, and strong) under Spherical, Exponential, and Gaussian semivariogram models. Model performance was evaluated using multiple accuracy and spatial consistency metrics, including the Coefficient of Determination (R\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Spatial Efficiency (SE), and Moran’s I of residuals, while uncertainty quantification employed Prediction Interval Coverage Probability (PICP), Mean Prediction Interval Width (MPIW), and Continuous Ranked Probability Score (CRPS).\u003c/p\u003e\n\u003cp\u003eThe results indicate that BME consistently outperformed all ML models under conditions of strong spatial dependence and small sample sizes (R\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e \u0026gt; 0.75, RMSE \u0026lt; 0.18, SE ≈ 0.82, and Moran’s I \u0026lt; 0.05). In contrast, ML algorithms, particularly ANN and SVM, showed significant perfor­mance degradation in highly skewed datasets (R\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e \u0026lt; 0.60; RMSE \u0026gt; 0.25), while RF demonstrated relative resilience (R\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e ≈ 0.70). Increasing the sample size from 200 to 10,000 markedly improved the performance of all ML models, thereby narrowing their performance gap with BME (average ∆R\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e = 0.10). BME also exhibited superior uncertainty quantification, with higher PICP (0.93) and lower CRPS (0.12) compared to ML models.\u003c/p\u003e","manuscriptTitle":"Robustness of Machine Learning Algorithms to Skewness, Spatial Dependence, and Sample Size Compared to BME in Soil Fertility Prediction","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-16 06:27:56","doi":"10.21203/rs.3.rs-8738598/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-11T16:43:24+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-09T02:57:16+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-27T11:45:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-25T09:38:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"160881421732417861526521431063262913861","date":"2026-02-13T07:34:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"99164472996283433767216656803329489747","date":"2026-02-11T10:22:00+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"128464389045969147682593446672956254784","date":"2026-02-11T08:26:43+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-11T06:57:07+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-02-11T06:03:29+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-04T07:28:13+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-04T07:18:27+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Artificial Intelligence","date":"2026-01-30T07:37:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-artificial-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"diai","sideBox":"Learn more about [Discover Artificial Intelligence](https://www.springer.com/44163)","snPcode":"","submissionUrl":"","title":"Discover Artificial Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5d6e175b-ddc1-4d82-b3ba-06f40ef5cc12","owner":[],"postedDate":"February 16th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T19:38:45+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-16 06:27:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8738598","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8738598","identity":"rs-8738598","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}