A methodological approach to identifying the threshold of cooperation in regional dairy systems: a four-dimensional index and a phase transition

<p>This dataset and code archive accompanies the article <em>"Quantifying the Cooperation Threshold in Bioeconomic Dairy Clusters: A Four-Dimensional Index and Phase Transition Approach"</em> submitted to <strong>Agricultural Systems</strong> (Elsevier).</p> <p><strong>Scope.</strong> We release the complete numerical and computational basis of the paper: a panel dataset covering twenty regions of the Russian Federation over eleven years (2014–2024, n = 220), a four-year longitudinal in-depth study of Krasnodar Krai (2021–2024), a stochastic cluster simulation engine, and figure-generation scripts. Everything is reproducible from a clean machine in under five minutes.</p> <p><strong>Contents.</strong></p><ul><li><code>IIC_Q1_supplementary.xlsx</code> — Excel workbook with three sheets: 20-region panel (Regions_20), broken-line threshold dataset (Threshold_effect), empirical IES(K) surface grid (Surface_IES).</li><li><code>simulation_model.py</code> — stochastic cluster simulation defining the IES(K) response surface.</li><li><code>generate_figures.py</code> — reproduces Fig. 1 (3-D surface), Fig. 2 (broken-line scatter), Fig. 3 (phase diagram).</li><li><code>generate_excel.py</code> — builds the supplementary workbook from raw inputs.</li><li><code>requirements.txt</code>, <code>LICENSE</code>, <code>README.md</code> — environment, licence, documentation.</li></ul> <p><strong>Key results obtainable from this archive.</strong></p><ul><li>Critical cooperation threshold: K_th = 0.42 ± 0.03 (bootstrap CI, B = 5000).</li><li>Marginal returns to cooperation: dIES/dK = 0.18 below the threshold, 0.41 above.</li><li>Saturation regime: returns flatten near K = 0.85.</li><li>Spearman ρ = 0.83 (p &lt; 0.01) between IES and milk yield; OLS R² = 0.83.</li><li>Threshold invariant across northern and southern sub-panels.</li></ul> <p><strong>Methods.</strong> Four-pillar Integrated Efficiency Score (IES) — animal productivity, bioeconomic recycling, social-cooperation density, ecological efficiency — linked to cluster cooperation density K via three independent procedures: k-means clustering, broken-line regression, and second-derivative inspection of an empirical IES(K) surface coupled to a stochastic cluster simulation.</p> <p><strong>Data sources.</strong> Rosstat (Federal State Statistics Service), Ministry of Agriculture of the Russian Federation (MinSelKhoz), EMISS open-data portal, FAO GLEAM 3.0 dairy module. All raw inputs are from public sources; processing pipeline is included.</p> <p><strong>Use.</strong> Released under the MIT Licence for unrestricted reuse with attribution. See README.md for five-step replication instructions.</p>