## Problem 148 — rank:235

**Title:** Reinforcement

**Added binding assumptions (LaTeX):**

```latex
The relevant derivative changes a rare mutant's mating trait while holding the resident population fixed, not the trait of the whole population at once. Define the resident-normalized invasion gradient $s(a;m,w_H)$ at mutant trait $a_m=a$ and take its response to hybrid cost at fixed demographic conventions. A positive local gradient still requires feasibility, linkage and an accessible evolutionary trajectory; it does not establish global fixation.
```

**Direct edits:** 3. **Fresh external checks:** None; supplied sources retained as provenance.