## Problem 190 — rank:169

**Title:** Paradox of the plankton

**Added binding assumptions (LaTeX):**

```latex
Fix positive starting biomasses above the detection thresholds when requiring persistence from time zero. Distinguish externally imposed immigration from internal coexistence and account for measured forcing in the probability law. Classical competitive-exclusion results apply to restricted equilibrium models, not every consumer--resource system. The target is quantitative mechanism discrimination in the specified community, not a claim that multispecies persistence is mathematically unexplained in all models.
```

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