Logistic-growth models measuring density feedback are sensitive to population declines, but not fluctuating carrying capacity

Analysis of long-term trends in abundance of animal populations provides insights into population dynamics. Population growth rates are the emergent interplay of inter alia fertility, survival, and dispersal. However, the density feedbacks operating on some vital rates ("component feedback") can be decoupled from density feedbacks on population growth rates estimated using abundance time series ("ensemble feedback"). Many of the mechanisms responsible for this decoupling are poorly understood, thereby questioning the validity of using logistic-growth models versus vital rates to infer long-term population trends. To examine which conditions lead to decoupling, we simulated age-structured populations of long-lived vertebrates experiencing component density feedbacks on survival. We then quantified how imposed stochasticity in survival rates, density-independent mortality (catastrophes, harvest-like removal of individuals) and variation in carrying capacity modified the ensemble feedback in abundance time series simulated from age-structured populations. The statistical detection of ensemble density feedback from census data was largely unaffected by density-independent processes. Long-term population decline caused from density-independent mortality was the main mechanism decoupling the strength of component versus ensemble density feedbacks. Our study supports the use of simple logistic-growth models to capture long-term population trends, mediated by changes in population abundance, when survival rates are stochastic, carrying capacity fluctuates, and populations experience moderate catastrophic mortality over time.