Two new methods for Regime Change Analyses

Abstract

There is currently a good deal of concern about a recently recognized decline in the numbers of several pelagic fish species in the Sacramento-San Joaquin Delta in California, USA. Several research groups are investigating possible reasons for this decline. One part of this study addresses whether the decline is the result of some recent regime change in the ecosystem, and more generally whether one or more regime changes have occurred since regular sampling of fish, zooplankton and mysids shrimps began in 1967. There are many statistical methods of analysis that have been proposed to detect regime changes. These are reviewed, but it is noted that none of them is immediately suitable for analysing the basic data collected from the Sacramento-San Joaquin Delta, which consists of counts from trawl hauls and other sampling gears used in the field. Two new methods are therefore proposed for this type of data, which is commonly collected. One method searches for times when the mean level and trend in the abundance of an organism changed, assuming that in the absence of a regime change the abundances will exhibit a linear trend with time. The other method assumes that in the absence of a regime change the abundances will exhibit a polynomial trend in time, and searches for times when the mean level changed significantly. Both methods rely on bootstrap resampling of the data for assessing the significance of apparent regime changes. Simulation studies to verify the properties of the proposed analyses are described, and also some examples of the results of the analyses on the Sacramento-San Joaquin data.