2505.01149
Spatial modeling of forest-savanna bistability: Impacts of fire dynamics and timescale separation
Kimberly Shen, Simon Levin, Denis D. Patterson
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper states and proves that the GBA steady state is stable to forest invasion precisely when βF B* + ΦF(G*) + μ > φG G* + φA A* (its Eq. (5)), by evaluating the full Jacobian at F = 0, observing its block lower–triangular form with a zero upper-right block, and reducing stability to the sign of the scalar top-left entry once the 2×2 GBA block is shown Hurwitz (Theorem 1) . The candidate solution follows the same block-triangular eigenvalue factorization and arrives at the identical necessary-and-sufficient inequality, matching the paper’s Proposition 3 and proof sketch .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The argument establishing the invasion-stability criterion is correct and cleanly presented: the Jacobian at the GBA state is block lower–triangular, the GBA sub-block is proven Hurwitz earlier, and the stability reduces to the sign of a single scalar entry. The candidate solution reproduces this logic faithfully. Minor notation harmonization and explicit cross-references would further aid readability, but no substantive issues remain.