McGurk Allometry of marine mortality of Pacific salmon 



79 



to review briefly the history of research on the weight 

 dependency of marine mortality in fishes in order to 

 establish testable hypotheses about the probable 

 values of .v and c. 



Previous research on allometry of M 



It has been known for at least 40 years that smolt- 

 adult survival of Pacific salmon is positively corre- 

 lated with smolt size (Foerster, 1954; Ricker, 1962). 

 Positive and significant correlations have been re- 

 ported within single populations of coho salmon 

 (Holtby et al., 1990) and steelhead trout (Ward and 

 Slaney, 1988), and among populations of sockeye 

 salmon (Ricker, 1962; Koenings et al., 1993). To date, 

 the relationship between smolt-adult survival and 

 adult size of Pacific salmon has not been examined, 

 nor have the interrelationships between smolt-adult 

 survival, smolt size, and adult size. 



Mathews and Buckley (1976) were the first to 

 model the functional relationship between M of Pa- 

 cific salmon and body size. They assumed that ma- 

 rine M of hatchery-reared coho salmon released into 

 Puget Sound, Washington, was proportional to W' 1 . 

 In his comprehensive review of marine M of salmon, 

 Ricker (1976) judged their assumption to be intu- 

 itively reasonable but unproven. Furnell and Brett 

 (1986, a and b) used the inverse-weight hypothesis 

 to model the marine population dynamics of Babine 

 Lake sockeye salmon, despite the lack of empirical 

 support for the hypothesis (McGurk, 1986b). 



In the nearly two decades since the inverse-weight 

 hypothesis was presented, much literature has been 



published showing that the weight-exponent of mor- 

 tality for fishes actually falls within the range of 0.25 

 to 0.40. Ursin (1967) was the first to measure the 

 mortality-size relationship offish; his review of pub- 

 lished reports showed that natural mortality scaled 

 with W-° 33 . Fenchel (1974) and Blueweiss et al. 

 ( 1978) reported that the intrinsic rate of natural in- 

 crease of animals, which is equal to M under equilib- 

 rium conditions, decreased with M~ 025 . Banse and 

 Mosher (1980) showed that the weight exponent of 

 the production-biomass ratio of animal populations, 

 which is also equivalent to M under equilibrium con- 

 ditions, was -0.37. Peterson and Wroblewski (1984) 

 derived a size-dependent equation for the mortality 

 rate of marine pelagic organisms, including inverte- 

 brates and fishes, from biomass spectrum theory and 

 concluded that M scaled with W"° 25 . 1 reported a simi- 

 lar conclusion from a review of natural mortality of 

 marine organisms that included invertebrates, fishes, 

 and marine mammals (McGurk, 1986a) and later 

 showed that M for larval and adult stages of both 

 Atlantic herring (Clupea harengus) and Pacific her- 

 ring (C. pallasi) scaled with dry weight to the power 

 of -0.4 (McGurk, 1993). 



These studies showed that data sets incorporat- 

 ing a wide variety of distantly related groups of ani- 

 mals tend to have weight exponents of M close to 

 -0.25, whereas data sets restricted to a single spe- 

 cies or a group of closely related species tend to have 

 weight exponents close to -0.40. In an attempt to 

 explain this observation, Dickie et al. ( 1987) proposed 

 that there are two size-dependent processes: 1) over 

 an entire ecosystem the slope of mortality versus 



