Honey bee colony time series analysis: The influence of stationarity assumptions

Background/Question/Methods

Managed honey bee (Apis mellifera L.) colonies have been declining in numbers in both the U.S. and Europe since the 1940s but the declines have increased in the past two decades. The abundance of bees is influenced by a multitude of factors including pathogens, parasites, habitat loss, and pollutants. Honey bee colony survival can also be influenced by the weather which influences the foraging patterns and food availability for honey bees. Climate change is an emerging threat to honey bees because of the potential increases in temperature and changes in precipitation patterns.  Managed honey bee colonies are censused annually and provide an opportunity to examine how climate influences bee abundance through time. In traditional time series analysis there can be spurious correlations because of  coincidental trends and the non-stationarity of the data. Cointegration is a technique commonly used by economists to analyze non-stationary time series but little used by ecologists. Our objectives were to: (1) explore the affects of climate (precipitation, temperature, drought) on the number of managed honey bee colonies in the United States using time series analysis and (2) to compare results of traditional time series analysis with a cointegration method of time series analysis.

Results/Conclusions

We used bee colony data from 1980-2011 created by the National Agricultural Statistics Service in the time series analysis. Using multiple linear regression and differencing, we found that the number of honey bee colonies per year per state in the time series was correlated with the weather. The number of honey bee colonies per year per state could be explained up to 27% by climate factors. The yield per colony per year per state could be explained up to 40% by climate factors. Both climate and colony numbers trend through time which makes them susceptible to false associations when analyzed with multiple linear regression analysis because traditional time series methods are based on assumptions of stationarity. We tested the implications of assuming stationary of honey bee colony time series by examining the data with cointegration analysis. The cointegration results suggests that honey bee colony numbers are a non-stationary process and that the majority of the relationships we found with traditional multiple linear regression were spurious. We suggest that other factors beyond climate such as pathogens, parasites, pesticides and habitat loss are most likely responsible for bee colony declines.