Detection of Environmental Influence on Recruitment Using Abundance Data

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Abstract
Environmental influences on recruitment are usually detected by correlation analysis using environmental and recruitment data. When recruitment data are unavailable, abundance data are sometimes used instead. An abundance time series can be described as a convolution of the recruitment time series, and consequently, when it is used as a proxy for recruitment, the magnitude of correlations is lower and the probability of both type I and type II errors is greater. Two approaches can restore the correlation between the environmental series and the recruitment series: (1) convolution of the environmental series and (2) deconvolution of the abundance series. Convolution of the environmental series increases the variance of computed correlation coefficients and can further increase the probability of type II errors. Deconvolution of the abundance series can recover the correlation between the environment and recruitment without increasing the variance of sample correlation coefficients or the probability of type II errors, as long as the deconvolution is stable and errors in the data are relatively small. When errors in the data are sufficiently large or the deconvolution is sufficiently unstable, the best results may be obtained by simply using abundance as a recruitment index. We evaluate application of the deconvolution technique to chinook salmon (Oncorhynchus tshawytscha) catch and spawner abundance series using both real and simulated data.