Don Percival         Principal Mathematician         EIS Department         Applied Physics Laboratory         University of Washington	Stellar sea lions (SSL) have declined from a population of about 250,000 in the Kodiak--Aleutian area in the 1960s to less than 50,000 in the late 1990s. While one of the factors in this population decline is thought to be commercial fishing, the present CIFAR Announcement of Opportunity calls for research into two other hypothesized factors, namely, (1) the impact of ocean climate regime shifts, and (2) changes in predator/prey relationships. APL-UW's research is directly related to number one above. Our first objective is to clarify the underlying character of North Pacific regime shifts. Loosely speaking, a regime is a stretch of time during which a time series remains predominantly either above or below its long-term average value; however, in practice, all ocean climate time series include a significant stochastic component due to interannual variability and other factors. To properly account for this inherent stochastic element, quantification and detection of regime shifts must be done within the context of particular time series models. Thus, we are comparing and contrasting different processes as candidate models for time series exhibiting regime-like characteristics. These include harmonic (oscillator) processes, chaotic processes and purely stochastic processes such as autoregressive and long memory processes. Our second objective is to compare time-space variability of North Pacific climate indices with SSL declines. Spatially dependent upwelling indices are being constructed for the Alaska coast. These indices are analyzed both for regime shifts and for lead/lag relationships using a variety of bivariate time series techniques including Fourier-based coherence analysis, wavelet-based analysis of covariance and singular spectrum analysis. Because bivariate techniques do not explicitly take into account any spatial structure, statistical methods that allow for a joint time-space assessment of the upwelling indices are also being used. The upwelling indices (and associated regimes that are derived from them) are used to address the question of how climate variability is affecting changes in the SSL population as indicated by recruitment data. This question is addressed both qualitatively through comparison of the spatially dependent upwelling indices with available SSL recruitment data, and quantitatively through a model-based approach. This latter approach consists of formulating a model in which there is a coupling parameter that is zero when SSL recruitment data is in fact uncorrelated with the upwelling data. The null hypothesis of no correlation can be assessed by testing if a maximum likelihood (ML) estimate of the coupling parameter is significantly different from zero (the ML approach has the advantage of dealing efficiently with the quite sparse recruitment data without the necessity of creating questionable interpolated values). This project provides a characterization of regime shifts, description and analysis of the space-time upwelling indices, and an assessment of the relationship between the upwelling indices and SSL recruitment data (the upwelling indices will be made available to other investigators via an appropriate website).