Identifying the Stock–Recruitment Relationship for Age-Structured Populations Using Time-Invariant Matched Linear Filters

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Abstract
Theory is introduced which permits the identification and removal of part of the environmental (density-independent) noise influencing the recruitment to age-structured populations. The biological assumptions under which this noise may be safely removed from the recruitment data without distorting the analysis of the density-dependent dynamics are outlined, and the permissible level of filtering is shown to depend on the age structure of the population in question. As examples of the method, filters were designed and applied to stock–recruitment data available for 16 commercially exploited marine fish populations. A substantial improvement is demonstrated in the statistical precision with which the stock–recruitment relationship can be defined, with standard errors on parameter estimates frequently decreasing by a factor of 2 or 3 after filtering. In general, use of filtering theory should allow a more precise definition of the nature of the stock–recruitment relationship in essentially all age-structured populations.

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