VETTER: NATURAL MORTALITY IN FISH STOCKS 



Thus, horizontal curves are subject to the ex- 

 tremely restrictive assumption that the groups 

 from which the data were collected must be in 

 steady state relative to each other, i.e., their rela- 

 tive abundances must be constant through time. 

 If this is true, then a graph of data collected at a 

 single point in time, which may include, for ex- 

 ample, individuals from 5 consecutive year 

 classes displayed as frequencies at 5 consecutive 

 ages, will look the same as the 5 graphs of data 

 that will result from collecting samples during 5 

 consecutive years (ages) from each of the 5 year 

 classes. If these conditions are not met, simple 

 linear fitting to determine a single estimate for 

 mortality will be inappropriate. 



The second type of catch curve, longitudinal, 

 includes data collected from a single identifiable 

 group over a protracted period of time. Most often, 

 this will be a single cohort of fish such as single 

 year class, sampled during successive years. Lon- 

 gitudinal curves are not subject to the assumption 

 of steady state, but do share with horizontal catch 

 curves several other severe disadvantages. These 

 include 1) groups must be adequately identifi- 

 able; 2) groups must be closed to migration, so 

 that changes in abundance are due only to fishing 

 or natural mortality, or if migration does occur, it 

 must occur in proportion to the age distributions 

 in the local groups; 3) samples must represent 

 adequately the true composition of the groups in 

 nature; 4) rate(s) of mortality must be relatively 

 constant between groups over time, so that the 

 log-transformed frequency distributions are truly 

 linear (e.g., Jensen 1984); 5) compensatory rela- 

 tionships between stock levels and natural mor- 

 tality, or fishing mortality and natural mortality, 

 must not be present. 



Methods for estimating M, which assume to 

 greater or lesser degrees that the conditions listed 

 above are met, have been described repeatedly. 

 The methods tend to fall into two categories. 

 Methods in the first category estimate M from 

 catch records of unexploited or lightly exploited 

 groups of fish. In these groups, F equals or ap- 

 proximates zero. Therefore, the observed rate of 

 decrease (Z ) equals or approximates M, because Z 

 equals the sum of F and M (e.g., Heincke 1913; 

 Baranov 1918; Ricker 1947; Beverton and Holt 

 1957; Robson and Chapman 1961; Pauly 1982; 

 Munro 1982; and among others). 



Methods in the second category estimate M by 

 determining Z at various levels of fishing effort, 

 then using the observed relationship between Z 

 and effort to predict, via regression analysis or 



manipulation of various ratios, the value of Z 

 at zero effort (e.g., Silliman 1943; Beverton and 

 Holt 1957; Paloheimo 1961; Lander 1962; Chap- 

 man and Murphy 1965; Paulik and Robson 1969; 

 Gulland 1983; Butler and MacDonald 1979; 

 Fournier and Archibald 1982; Caddy 1984; and 

 others). 



These methods are most appropriate for analyz- 

 ing catches of unmarked fish. Accurate results 

 depend strongly on accurate measures of catch 

 per unit effort (CPUE) and constant catchability 

 (q) because if these conditions (in addition to 

 those listed above) are not met, observed relation- 

 ships between abundances in different sample 

 groups may not reflect true differences between 

 groups in situ. 



Marked fish present fewer problems. Advan- 

 tages include 1) concentration on measuring rela- 

 tive rather than absolute differences between 

 abundances of different groups, 2) immigration 

 need not be considered, as entire original groups 

 are known to carry marks, and 3) with suffi- 

 ciently large samples, it becomes possible to test 

 for differences in mortality rate between different 

 groups (e.g., between ages, between sexes, or be- 

 tween sampling sites), rather than having to as- 

 sume that such effects are negligible. 



Reviews and descriptions of various mark- 

 recapture methods appear in papers by Seber 

 (1973), Ricker (1975), Jones (1979), and Brownie 

 et al. (1985). Some of the newer types of marking 

 analyses can solve many of the most vexing prob- 

 lems associated with traditional catch curve anal- 

 ysis (e.g.. Reed and Davies 1980; Hochbaum and 

 Walters 1984; Burnham and Andersen 1984; 

 Burnham et al. 1984; Brownie et al. 1985). 



Several disadvantages unique to marking oper- 

 ations counteract these advantages, however, 

 even with the newer methods. These disadvan- 

 tages include various types of mark-induced 

 effects on mortality rates, behavior, and vulnera- 

 bility to capture, as well as mark loss, unrepre- 

 sentative mixing of marked fish with their origi- 

 nal groups prior to recapture (e.g., Ricker 1975), 

 and especially in commercial fisheries, under- 

 reporting or incorrect reporting of recaptures. 



Both analysis of catch curves from unmarked 

 fish and analysis of mark-recapture data have the 

 advantage of requiring only catch (and usually 

 effort) data, and these data can generally be col- 

 lected by sampling catches from commercial fish- 

 eries. However, in addition to problems specific to 

 each method, they have in common one or more 

 other major disadvantages: 1) inability to distin- 



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