Superposed Epoch Analysis: A Randomization Test of Environmental Effects on Recruitment with Application to Chub Mackerel

Abstract

Superposed epoch analysis, a nonparametric technique, can be used to test the statistical significance of associations between extreme environmental events and recruitment success. A test statistic, similar to a paired t-statistic, is used to compare recruitment in years with extreme events to recruitment in the immediately surrounding years. Because statistical significance is determined by a randomization test, superposed epoch analysis does not rely on the usual assumptions (random sampling, normality, homogeneity of variance, independence of observations) of parametric testing. Thus, the method can be used when regression analysis, correlation, or a t-test would be inappropriate. As an example, we tested the association between elevated sea level (often associated with El Nino events) and high recruitment success of chub mackerel Scomber japonicus off the coast of southern California. The association was statistically significant (P < 0.01) for the period preceding the collapse of the chub mackerel fishery in the late 1960s but not significant (P = 0.59) over the entire time series. This change may be due to statistical artifacts, a nonlinear relationship between sea level and recruitment, or biological causes. As with other statistical methods, a valid hypothesis test requires a priori formulation of the null hypothesis. Within this limitation, superposed epoch analysis is a useful method for conducting significance tests on autocorrelated time series, such as recruitment data.