Prime brood intervals minimise predator overlap
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
notes.md
# Prime brood intervals minimise predator overlap **Verdict: Supported.** Prime intervals have a mean overlap of 0.21 across predator cycles 2-12, against 0.45 for composite intervals of 7-31 years; the best interval is 13 and the worst is 24. ## Design Exact overlap arithmetic over lcm(m,p) for emergence intervals 7-31 years and predator cycles 2-12 years, plus a noisy predator-biomass simulation for intervals 12-20. ## Result - Mean overlap, primes: 0.211 - Mean overlap, composites: 0.449 - Best interval: 13 yr - Worst interval: 24 yr ## Limits - The arithmetic minimises overlap with predator cycles of fixed period; it says nothing about whether predators are the actual selective driver. - Intervals 13 and 17 are the only well-documented periodical cicadas, so the empirical range is far narrower than the 7-31 years tested here. - Real predator cycles are noisy and not fixed; the simulation perturbs them, but a 15% noise level is an assumption. - A composite interval that avoids the specific predator cycles present at a site could do as well as a prime one; the result is an expectation over predator cycles, not a universal law.