## Problem 185 — rank:240

**Title:** Population dynamics with complex life cycles

**Added binding assumptions (LaTeX):**

```latex
Separate transition probabilities from fecundity entries of the projection matrix: its columns need not sum to one. State the joint environmental law and whether host dynamics are stochastic or deterministic. Long-run occupation probabilities, deterministic uniform persistence and finite-horizon nonextinction are different claims. Forecast lower bounds must account for irreducible demographic uncertainty; an arbitrarily small tolerance is not guaranteed feasible.
```

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