Changing environments causing time delays in population dynamics

We use a linear diffusion process to approximate a stochastic density regulated population model where parameters can change through time. Contrary to stationary models, there is a difference between the expected value and the carrying capacity of a population at any given time. This time delay can be considerable and depends on the vital rates of the population and the magnitude of the change. We emphasize the importance of acknowledging this difference when assessing viability of populations. As an illustration, we consider the population of Norwegian spring spawning herring and its collapse in the 1960s. Based on our analysis, the stock was already at a critical level a decade before the collapse was observed.