Bounded random walks as a null model for evaluating population trends

Management of wildlife and protection of endangered species depend on determination of population trends. Because population changes are stochastic and autoregressive, there is reason to believe that population trends might not be properly determined by simple regression over short time periods. A bounded random walk (BRW) model is introduced as a null model for evaluating population trends. The BRW model shows long-term stability but rising and falling sequences of up to many decades. For a given variability and survey length, there will be an expected probability of finding a greater than X% slope simply by chance. This false positive probability needs to be considered when evaluating trends. Breeding Bird Survey data for 128 species over 46 years for two states were analyzed for trends for different series lengths. Trends estimated from short series were likely to not agree with the 46-year trends. Very short series (e.g., 5 years) tended to indicate no trend due to loss of statistical power. A 101-year series for sandwich term (Sterna sandvicensis) revealed that even for 40 year-long series, 33% of subset series had a negative trend compared to the strong 101 year full series positive trend. The BRW model simulations and both data sets pointed to 20 years as a minimum time period for estimating trends reliably, though this can be longer for species that tend to cycle. Proper inference should thus consider the implications of inherent time series variability.