Estimation of population growth and extinction parameters from noisy data

The random-walk-with-drift model of population dynamics is an important tool in conservation biology, partly because its parameters are easily estimated from periodic observations of population size. Estimating the model with noisy data is problematic, however, because the commonly used estimators of process variation are biased if population abundance measurements are imprecise, and a recently developed method that attempts to remove this bias is not robust. In this paper, I show how the random-walk-with-drift model can be applied to noisy time series of population estimates by converting the random-walk-with-drift model to state-space form and applying the Kalman filter to yield the likelihood of the data. The likelihood function allows the variances of the process error and measurement error and the growth rate of the population to be estimated in a way that is robust and fully supported by statistical theory. Comparative analysis using simulated data indicates that the Kalman-filter method reduces the bias in estimates of process variance without yielding negative variance estimates. I apply the method to California sea otter and Yellowstone grizzly bear data to illustrate how the method (and simple extensions) can be used to assess the status of real populations. California sea otters appear to have little risk of extinction over the next 100 years although the population may not be secure over the long term if a recent apparent cessation of population growth persists. The grizzly bear population appears to have responded positively to the 1988 Yellowstone fires, and if the population continues to grow at the average rate observed over the study period, it is extremely unlikely to go extinct.