# README # Title **Network structure shapes pollinator collapse under rapid shifts in demographic rates with random fluctuations** ## Authors * Ravi Kumar K * Partha Sharathi Dutta --- ## Description This repository contains the MATLAB codes and datasets used to generate all results presented in the manuscript: **"Network structure shapes pollinator collapse under rapid shifts in demographic rates with random fluctuations"** The study investigates rate- and noise-induced tipping (RN-tipping) in plant–pollinator mutualistic networks under time-varying demographic conditions. The repository includes all MATLAB scripts and supporting data required to reproduce the figures and statistical analyses presented in the main manuscript and Supplementary Information. --- ## Software Requirements * MATLAB R2023a (used in this study) * No additional proprietary toolboxes are required unless otherwise specified within individual scripts. --- ## Repository Structure The repository is organised into separate folders corresponding to the figures and analyses presented in the manuscript. Each folder contains: * MATLAB scripts used to generate the corresponding figure or analysis. * Supporting data files required by those scripts. * Any intermediate datasets needed for reproducing the published results. Running the main MATLAB script in a folder will reproduce the figure or analysis presented in the manuscript or the Supplementary Information. --- ## Description of Data Files and Their Origin ### 1. Empirical Plant–Pollinator Networks The empirical plant–pollinator interaction networks used in this study were obtained from the **Web of Life database**: https://www.web-of-life.es Network identifiers such as: * M_PL_018 * M_PL_022 * M_PL_023 * M_PL_027 * M_PL_030 * M_PL_031 * M_PL_038 * M_PL_050 * M_PL_052 * M_PL_053 and other networks analysed in the manuscript correspond to the original identifiers used in the Web of Life database. These files contain bipartite interaction matrices, where: * Rows correspond to plant species. * Columns correspond to pollinator species. * Matrix entries indicate the presence (1) or absence (0) of interactions. --- ### 2. Bifurcation and Basin-Instability Data Files such as: * Basin_inst_border_M038.dat * Twopara_M038.dat * kr11.dat – kr24.dat * mr11.dat – mr22.dat contain numerical continuation and bifurcation-analysis results generated by the authors in the continuation software XPPAUT. These datasets are used to construct: * Basin-instability diagrams * One-parameter bifurcation diagrams * Two-parameter bifurcation diagrams presented in Figures 2 and S1. --- ### 3. Rate- and Noise-Induced Tipping Data Files such as: * Tipping_dgm_border_data_s0_M038.dat * RNTipping_dgm_data_s05_M038.dat * rate_sigma_time_M022.dat * rate_sigma_time_M023.dat * rate_sigma_time_M027.dat * rate_sigma_time_M030.dat * rate_sigma_time_M031.dat * rate_sigma_time_M038.dat * rate_sigma_time_M050.dat * rate_sigma_time_M052.dat * rate_sigma_time_M072_09.dat contain simulation outputs. These files store information related to: * Critical-rate boundaries * Tipping outcomes * Tipping times * Rate–noise parameter sweeps used to generate Figures 3 and S4. --- ### 4. Structural-Property and Statistical-Analysis Data The statistical analyses presented in Figure 5 and Supplementary Table 1 are based on: * Connectance * Nestedness * Modularity * Network size * Critical rates computed for the 30 empirical plant–pollinator networks analysed in this study. These quantities were calculated by the authors from the empirical network data and simulation outputs. --- ## Main Manuscript Figures ### Figure 2 Basin-instability analysis and bifurcation structure for representative empirical networks. ### Figure 3 Rate-induced and rate-noise-induced tipping diagrams together with representative trajectories. ### Figure 4 Pollinator abundance time series for selected empirical plant–pollinator networks under different rates and noise levels. ### Figure 5 Relationship between network structural properties and critical tipping rates. --- ## Supplementary Figures ### Figure S1 One- and two-parameter bifurcation diagrams and phase portraits. ### Figure S2 Construction of the external forcing functions used in the study. ### Figure S3 Plant abundance time series in the high-dimensional mutualistic network model. ### Figure S4 Heatmaps illustrating the combined influence of forcing rate and noise intensity. ### Figure S5 Pairwise relationships among network structural properties. ### Figure S6 Basin-instability analysis and bifurcation structure for representative empirical networks for the second scenario. ### Figure S7 Relationship between network structural properties and critical tipping rates for the second scenario. --- ## Supplementary Tables ### Table S1 Multiple regression analysis relating network structural properties to critical rates. --- ## Reproducibility All codes and supporting datasets necessary to reproduce the published figures and analyses are included in this repository. To reproduce a figure: 1. Open MATLAB. 2. Navigate to the folder corresponding to the desired figure. 3. Run the main MATLAB script contained in that folder. 4. The script will load the required data files from the same folder and generate the corresponding figure. --- ## Data Availability The empirical plant–pollinator network data are available from the Web of Life database: https://www.web-of-life.es All processed datasets, simulation outputs, and MATLAB codes required to reproduce the results are provided in this repository. --- ## Date of README Creation 04 June 2026 --- ## Contact **Prof. Partha S. Dutta** Department of Mathematics Indian Institute of Technology Ropar Email: [parthasharathi@iitrpr.ac.in](mailto:parthasharathi@iitrpr.ac.in) --- ## Data Access and Sharing * Available via Zenodo * License: All code and data in this repository are released under the Creative Commons Attribution 4.0 International License (CC-BY 4.0). If you use this repository, please cite the associated manuscript and Zenodo DOI. ## Zenodo DOI: https://doi.org/10.5281/zenodo.20536621 --- ## Notes This repository contains all code and supporting data required to reproduce the results presented in the manuscript and Supplementary Information.