Mark Haroldson, Matthew Gould, Andrea Corradini, Cecily Costello, Justin Dellinger, Francesca Cagnacci, Frank van Manen

Demographic studies of large carnivores often deal with mixed data of individuals with
different risk profiles. Management actions can change both an animal’s true mortality
hazard and its probability of being observed. Obtaining unbiased estimates of survival
for the entire population from such data can be challenging. In the Greater Yellowstone
Ecosystem (GYE), all grizzly bears (Ursus arctos) may be randomly sampled for
research, but those involved in human-bear conflicts are targeted for capture and thus
represent a biased subpopulation. However, being a ‘managed’ bear is not a static
state; for bears that are released rather than removed, their risk profile may transition to
that of an ‘unmanaged’ bear after a period without subsequent conflict. Yet, during this
transition bears are often not collared and thus timing is unobserved (latent). To
estimate spatially-explicit survival in the GYE, we adapted a multi-state modeling
framework often used in biomedical research to wildlife: using latent states to link
observation patterns to state-specific risks. Using a large dataset (n=600 bears, F:222,
M:378) spanning 15-years (2009–2024), we developed and validated a Bayesian model
to jointly estimate (1) bidirectional transitions between managed and unmanaged states
and (2) spatially explicit survival in each state, yielding appropriately weighted
population-level estimates. Simulations showed that modeling bidirectional state
dynamics reduced bias in survival estimates compared with stratified, single-state or
one-direction recovery models. Field data indicated a mean recovery rate from a
managed state of 26.9 months. The instantaneous hazard of mortality in a managed
state (λ=0.0236) was 472x greater than that of an unmanaged state (λ=0.00005). This is
the combined hazard of management removal (λ=0.0167) and other mortalities
(λ=0.0069). Our findings highlight the need to integrate state-varying risks on
population-level estimates of survival and other events.