code for "A minimalistic probabilistic model for salt marsh establishment"

This model is used for the manuscript "Footholds for pioneers: how geomorphic features accelerate early marsh assembly"

Authors: Mingxuan Wu*, Zhiyuan Zhao, Gregory Fivash, Jim van Belzen1, Tjeerd J. Bouma,  Yuxi Ma, Tim Grandjean, Xiaowei Ding, Roeland C. van de Vijsel, Johan van de Koppel


*Corresponding author. Mingxuan Wu 
Affiliation: Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research; Yerseke, The Netherlands
Email: mingxuan.wu@nioz.nl



 -----------Fig. 3 and Fig.S3 Simulation Code------------

**Description:**  
This script simulates how marsh establishment probability and mean time to establishment depend on seed production (N_s) and per-seed establishment probability (P_ind).  
It reproduces both the main Figure 3 (heatmaps) and Supplementary Figure S3 (section curves) in the manuscript.


**Outputs:**  
- **Figure 3A:** Heatmap of establishment probability ($P_{est}$), with experimental scenarios (with/without creek) indicated.
- **Figure 3B:** Heatmap of mean time to establishment ($E(t)$), same experimental references.
- **Fig. S3A:** E(t) as a function of N_s at a representative $P_{ind}$ value.
- **Fig. S3B:** E(t) as a function of P_ind at experimental $N_s$.

**How to run:**  
- Requires Python 3.x and `matplotlib`, `numpy`.







-----------Fig. S4 Simulation Code------------

Title:
Simulation of population establishment dynamics with and without tidal creek under different seed establishment probabilities

Description:
This Python script simulates population trajectories of marsh plants over 50 years, comparing "with creek" and "without creek" scenarios under two different single-seed establishment probabilities (P_ind).
The output reproduces Fig. S4 in the manuscript Footholds for pioneers: how geomorphic features accelerate early marsh assembly.

Panel A: P_ind = 0.01
Panel B: P_ind = 0.005

Both panels visualize the number of established plants each year, with and without creek effects, up to the carrying capacity.




The experimental data we integrate into the model, can be found at: https://doi.org/10.5281/zenodo.15838150