Effective-founder model for balancing clonal and sexual propagation in coral restoration: analysis code and supplemental workbook

Abstract

This deposit is the computational component of An Effective-Founder Model for Balancing Clonal and Sexual Propagation in Coral Restoration (Winters, 2026, Evolutionary Applications, submitted). It reproduces every table, figure and numerical value in the manuscript. Coral restoration combines asexual fragmentation, which replicates founder genotypes, with sexual propagation, which recombines the alleles of only those founders that are bred. The model measures how founder ancestry is distributed across the resulting restored population with the effective number of founders, N_F = 1/Σpᵢ². This is a second-order Hill number, equivalent to the founder equivalent of pedigree-based management. For unrelated, non-inbred founders, it fixes the expected gene diversity of the restored population at 1 − 1/(2N_F). The code implements: the closed form for equal breeder contributions and equal ramet allocation (Eq. 3); the general form for any ramet allocation and breeder contributions (Eq. 4); the effective number of breeders, kₑ = k/(1 + CV²) (Eq. 5); the compensating and optimal ramet allocations (Eq. 6 and Section 2.4); the implementation curve, which gives the maximum sexual fraction for a target N_F (Eq. 7), and its general form (Eq. 8). Contents. The deposit is a single zip archive, which preserves the folder structure, plus this README. effective_founder_model.py: the core implementation. Run as a script, it writes a verification report (verification_output.txt) that recomputes every value stated in the manuscript, and writes Table1.csv. figures/: one self-contained script per manuscript figure (Figures 1–5), with the figures as submitted (PNG at 300 dpi, and PDF). Winters 2026.Effective_Founder_Calculator.xlsx: a calculator that applies the model to any program. Enter G, k, a target and, optionally, breeder unevenness and the breeders’ share of ramets. It returns: the maximum sexual fraction; N_F and expected gene diversity at a chosen sexual fraction; the ramet-allocation limits, with cautions on interpretation. run_all.py, requirements.txt, README.md, LICENSE, CITATION.cff. Reproducibility. There are no external data dependencies, no simulation and no random numbers. Unzip the archive and run python run_all.py (Python 3.9 or later, numpy, matplotlib) to regenerate every output in seconds. Numerical outputs are reproduced exactly; figure rendering can differ slightly with the installed fonts and matplotlib version. Reuse. The model applies to any restoration or reintroduction program that combines clonal propagation of a founder set with sexual propagation from a subset of it. To adapt it to another species or program, change G, k, the targets and, where known, the breeder contributions and ramet allocation. Generative AI disclosure. Claude (Anthropic) was used to generate Python code implementing the analytical equations described in this manuscript, to produce Table 1 and Figures 1–5, and to help develop the supplemental Excel implementation. Claude was also used during manuscript preparation to check calculations, verify citations against their sources, and suggest edits for clarity and consistency. The author reviewed and accepted, modified, or rejected each suggestion. The author reviewed and validated all AI-generated code and text and takes full responsibility for the content of the manuscript and the accuracy of all results.