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To study family-specific variation in the survival of pink salmon Oncorhynchus gorbuscha, we partitioned family size into four life history divisions: (1) maternal fecundity, (2) deposition of fertilized eggs and egg loss from the redd, (3) freshwater survival (and male potency), and (4) marine survival. We directly measured the variability in fecundity and then measured the family-specific variability of freshwater survival in several Alaskan hatchery populations. Next, we measured freshwater survival in spatially clustered groups of wild pink salmon (not identified to a specific dam or sire) in Prince William Sound, Alaska. Drawing on estimates of the family-specific variation of marine survival in pink salmon from previous studies, we concluded that family-specific egg deposition processes and family-specific variability in the marine environment were the primary sources of the overall variability in pink salmon family size, at least in the populations studied. We hypothesize that the freshwater environment generally induces lower variability in family size than does the marine environment. If this is so, it appears that pink salmon populations are more finely adapted to the freshwater environment, presumably because this environment is more constant. Finally, we speculate that the marine environment is too unpredictable to permit the same level of adaptation of many traits closely linked to marine survival.

The half power method is a technique commonly used for calculating the system damping using frequency response curves. Past derivations typically assume a small damping ratio but do not keep track of the order of magnitude when simplifying results and focus mainly on displacement frequency response curves. This paper provides two separate and rigorous derivations of the half power bandwidth for displacement and acceleration frequency response functions. The exact expressions are simplified systematically using binomial expansions to include third order effects. The third order and classical approximations are compared with the exact expressions, and the truncation errors are presented for both displacement and acceleration cases. The high order effects are more apparent and the truncation errors are greater for the acceleration case. The classical method is sufficiently accurate for many practical cases where the damping ratio is less than 0.1 but higher order corrections may be used to reduce truncation error for systems where the damping ratio is higher.

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