Publication describes how sample size and other factors affect estimates of wildlife population trends

Government agencies and conservation organizations often identify species at risk of extinction based on factors such as the size of their geographic range, threats, and population declines. All populations fluctuate naturally over time, however, and it is important to account for this variation when estimating population trends. Furthermore, size and the number of years for which population data are available can influence conclusions about population trends.

Recently, Dr. Craig Loehle of NCASI and Dr. Nasser Arghami (deceased) used a 46-year series of data from the Breeding Bird Survey in the US to evaluate how sample size and the number of years for which population estimates were available influenced inferences about wildlife population trends. In addition, they used a 100-year-long data set for breeding Sandwich terns from the German North Sea coast. In their analyses, they attempted to account for random influences on population trends.

Results of the authors’ analyses indicate that there was considerable variability in population trends for short survey lengths with the direction of trends estimated for short time periods (e.g., 5-10 years) sometimes differing from the trend direction when estimated from the full data sets. Results from the study have important implications, particularly for estimating trends for species for which survey data are limited.

The abstract for the paper follows.

“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.”  


Loehle, C., and N. Arghami. 2017. Bounded random walks as a null model for evaluating population trends. Population Ecology 59(2):109–117.