Testing for compensation in a multi-species community

The dynamics of a community are said to be compensatory if aggregate biomass is less variable over time than the biomass of the individual components of the system. In broad terms, the presence of compensation reflects interactions between components that tend to stabilize the overall community. A common quantitative measure used to detect compensation is the ratio of the temporal variance of total biomass to the sum of the biomass variances of the components, with a ratio less than 1 indicative of compensation. The purpose of this note is to describe a test for compensation when the variance ratio is estimated from biomass time series data. The test involves a bootstrap procedure that accounts for serial correlation in biomass. Failure to account for positive serial correlation can lead to spurious detection of compensation. The test is illustrated using biomass data for fish stocks on Georges Bank.