## Problem 199 — rank:172

**Title:** Ecology of cooperation across species

**Added binding assumptions (LaTeX):**

```latex
Normalize invasion exponents relative to the resident ecological life cycle and define long-run averaging for recurrent or stochastic attractors. The displayed lower-investment test is one-sided; the separately stated regulator mutants and any other claimed strategy directions need their own admissible class. Robustness over constant environments does not establish robustness under arbitrary switching between them without a specified switching law.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.