Models fitted to 1980–2019 Isle Royale counts predict most of the 2019–2026 moose decline only when they include wolves, but the wolf share depends on model form

Question: can moose growth models fitted only to counts before the 2018-2019 wolf restoration on Isle Royale (USA) forecast the decrease from 2,060 moose in 2019 to 524 in 2026, and how much of it do they assign to wolves? Approach: we fitted Gompertz state-space models (drift; density; wolf:moose ratio; density plus ratio; density plus wolf count; density plus ratio plus three climate terms) to the public NPS winter counts for 1980-2019. Then we forecast 2020-2026 from the 2019 state with the observed wolf counts and with a no-restoration counterfactual (2 wolves). We used six fit configurations, rolling-origin hindcasts from 1995-2012, and a block jackknife. Findings: models without a wolf term put the observed 2026 count in the lowest 0.4-4.5% of their forecasts; density alone predicted a 31-43% decrease. Models with density and a wolf term predicted a 52-67% median decrease, and the 2026 count was inside their 95% intervals (PIT 0.03-0.25). Under no restoration, all models with a wolf term put the 2026 count below their 0.4% quantile. The wolf models also had lower hindcast error before restoration (mean CRPS 0.27-0.30 against 0.40 for drift, 126 forecasts). But the wolf share of the observed log decrease was 36-47% for the ratio form and 62-88% for the wolf-count form, because the moose level with few wolves is poorly identified. Limitations: one forecast origin and five test counts (no census in 2021 and 2025); wolves are exogenous; the strong density dependence depends on the 1995-1997 crash; no kill-rate, recruitment, forage or tick data were used.

Isle Royale · wolf · moose · predator-prey · reintroduction · ecological forecasting · out-of-sample test · Gompertz state-space model · density dependence · counterfactual · ratio dependence