## Problem 180 — rank:165

**Title:** Determinants of natural population density

**Added binding assumptions (LaTeX):**

```latex
The equality of per-capita birth and death is only the focal-density equilibrium condition; resource and predator derivatives must also vanish and full-state stability must be checked. A persistence-conditioned mean must use a specified quasi-stationary or finite-age law, with extinction risk reported separately. Site-transfer uncertainty includes initial basin assignment and mechanism changes, not only parameter-estimation error within one fixed model.
```

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