1. NL PC1: 39% of variance
Nonlinear PCA results from Marzan, Mantua, and Hare: based on 45 biotic indices from the Bering Sea and Gulf of Alaska for
NL PC2: 18% of variance
Following the earlier work of Hare and Mantua (2000), Marzan, Mantua and Hare have created a multivariate data set with 45 fishery and survey records from the Bering Sea and Gulf of Alaska for the period These data contain time series for things like annual salmon landings for 5 species and 3 regions in Alaska, rockfish and herring recruitment indices, herring biomass, and zooplankton biomass estimates for subregions of the Gulf of Alaska and Bering Sea. A neural-net based PCA is applied to identified the leading non-linear Principal Components. The results are similar to those found by Hare and Mantua (2000), where the leading PC indicates a pattern with all positive scores from , and all negative scores from The time series that load most strongly on this pattern include Alaska salmon landings, many rockfish recruitment records, while records for GoA shrimp catches load negatively on NL PC1. The explained variance in NL PC1 from this ananlysis is 39%, while PC1 from a linear analysis accounts for 27% of the variance in these data.
NLPC2 has more interannual variability than NLPC1, and suggests state shifts ~1970, 1989 and perhaps in It explains 18% of the variance in the input data. Scores for 2000 and 2001 are crude estimates based on just a small number of observations (<10), so they are not likely accurate measures for those years. This is due to the delay times in obtaining biotic series (like rockfish recruitment rates).
The error bars for the NLPC scores are obtained from a “jittering” technique that involves the introduction of small errors into the data matrix prior to computation of the NL PCs.

2. NL PC1: 32% of variance
Nonlinear PCA results from Marzan, Mantua, and Hare: based on 22 abiotic indices from the Pacific for
NL PC2: 23% of variance
These NL PC’s are based on 22 physical indices representing both large and local environmental processes. These data contain time series for large scale climate processes like the PDO, an Aleutian Low index, indices for ENSO (nino3.4), the Arctic Oscillation, as well as local measures for things like alongshore upwelling winds, coastal SSTs, and Alaska and BC annual river discharge. Note that the loadings on NLPC1 for the abiotic series have more interannual variations than those for the fishery/survey (biotic) data. The time series that load most strongly onto NLPC1 for the physical data include the PDO index, the Aleutian Low index,and coastal SST data.
The explained variance in NL PC1 from this ananlysis is 32%, while PC1 from a linear analysis accounts for 25% of the variance in these data.
NLPC2 has more interannual variability than NLPC1 and no hint of interdecadal climate regime shifts.
The error bars for the NLPC scores are obtained from a “jittering” technique that involves the introduction of small errors into the data matrix prior to computation of the NL PCs.

3. Kendall’s  trends in Alaska adult SSL data Marzban, Mantua and Hare
99% ci --
We computed the non-parametric “Kendall’s Tau” statistic to assess the statistical significance of trends in the SSL, climate and fishery data used in our analysis. A “trend" often means a linear trend. Kendall's tau assesses trend nonlinearly (though monotonically). The Z-statistic shown in this figure assesses the statistical significance of that trend.I.e. if Z >= 2.575, then the hypothesis that the true tau is zero can be rejected with 99% confidence.
The Adult SSL data show statistically significant negative trends in 5 of the 7 regions.
99% ci --
For SSL data from

4. Kendall’s  trends in Pacific fishery data Marzban, Mantua and Hare
There are many positive trends in the Alaska fishery and survey data for the period , with a few negative trends. Most of the very strong trends are in the Gulf of Alaska records, including many of the salmon catch records.
The two series with large negative trends are for indices tracking Eastern Bering Sea Turbot recruitment (#6) and Gulf of Alaska Shrimp catch per unit effort (#22).
99% ci --
Bering Sea
For fishery and survey data from

5. Kendall’s  trends in Pacific climate data Marzban, Mantua and Hare
The Kendall’s Tau statistic was also computed for climate/environmental data.
Here, we find no statisitcally significant trends for period.
99% ci --
Bering Sea
For climate data from