Understanding the impact of third-party species on pairwise coexistence

These are the codes in both R and Mathematica accompanying the manuscript "Understanding the impact of third-party species on pairwise coexistence" by Deng, Taylor, and Saavedra. The codes in R and Mathematica are independent, and their results match perfectly. Both codes are well commented with simple examples. So you can choose whichever you prefer.

Specifically, the codes in R provide the functions (toolbox.R) and an example (example.R) for the analytical computations of "projection contribution" and "system-level long-term effects" as described in the manuscript. The codes in Mathematica (regions.m) contain the functions and an example of "system-level long-term effects" using the Monte Carlo method.