SYKES and BOTSFORD: CHINOOK SALMON SPAWNING ESCAPEMENT 



medium (70-80 cm), medium plus (81-85 cm), or 



large (>85 cm). 

 Sex: Male or female. 

 Condition: Alive, fresh (eyes clear), decayed 



minus (eyes cloudy, flesh firm), decayed (flesh 



soft), decayed plus (flesh very soft), or skeleton 



(flesh falling off). 



Carcasses were individually tagged with fingerling 

 fish tags which were attached around the maxillary 

 bone. Data on place of release for each released car- 

 cass were recorded as follows: 



Pool, pool/riffle, or riffle. 



The presence or absence of obstructions which 



would trap and remove a carcass. 

 The speed of water flow. 



Thus movements of individual carcasses and their 

 condition, both of which might affect catchability 

 and survival, could be examined on an individual 

 basis. During the sampling process about one-third 

 of the unmarked, captured carcasses was random- 

 ly removed from the population by cutting the fish 

 in two. This was done because of limited time 

 available for recording data. These individuals were 

 considered "trap mortalities" (i.e., they are counted 

 in the sample size but not in the total releases for 

 that time period). Because the mark-recapture 

 methods used allow for capture loss, removal of 

 these fish has no effect on errors other than lower- 

 ing sample sizes. 



Two existing methods, those of Jolly and Seber 

 (Seber 1982) and Manly and Parr (1968), and a third, 

 a modified Jolly-Seber method, were used to es- 

 timate population sizes, recruitment, survival, and 

 their standard errors (when expressions were 

 available). The corrected estimates of Seber (1982) 

 were used for the Jolly-Seber method. When sur- 

 vival was estimated as greater than unity, or immi- 

 gration as <0.0, those values were replaced with 1.0 

 and 0.0 respectively in subsequent calculations. In 

 the third method, standard Jolly-Seber estimates 

 were calculated after modifying the mark-recapture 

 data so that all decayed (decayed minus or worse) 

 carcasses (marked and unmarked) were assumed to 

 have been destroyed upon capture. This method 

 simulates the way CDF&G has traditionally col- 

 lected data. 



After these estimates had been calculated, the 

 estimated escapement, E, was calculated as the 

 number present at the first sample period, plus the 

 number of individuals immigrating during each 

 subsequent period. 



E = n x + 2 - R, * *,)/(*!) b ) 



+ D 2 + D 3 + D 4 (1) 



where n x = the number sampled at the first sam- 

 ple time, 



R x = the number tagged and released at 

 the first sample time, 



N 2 = the estimated population size at sam- 

 ple time two, 



A = Mn 5 , 



<t>i = the survival rate from i to i + 1, and 



B { = the estimated number of carcasses 



still present at the sample time i + 



1 which immigrated between i and i 



+ 1. 



In this expression the initial number present at time 

 period 1 is conservatively taken to be the sample 

 size at time period 1 {n{). The number immigrating 

 during the subsequent period is taken to be the 

 estimated population at time period 2, minus the 

 number of tagged fish which had been accounted for 

 in the first sample. Immigration during the next two 

 periods are standard estimates. Each immigration 

 rate is divided by the square root of the survival rate 

 (the survival rate for half the sample period), to ac- 

 count for fish that enter the population and leave 

 it between sampling periods, and thus are never 

 sampled (Stauffer 1970). 



Estimates of immigration during the last time 

 period are not computed in standard multiple mark- 

 recapture experiments; however, this immigration 

 (.B 4 here) can be estimated from the standard Jolly- 

 Seber expression (Seber 1982), if the final numbers 

 (N b ) and survival rate (<t> 4 ) can be estimated. If sur- 

 vival varies little from sample to sample, <t> 4 can be 

 estimated by assuming that mortality is equal to the 

 value estimated over an earlier period in this study. 

 Since survival varied little between sampling periods 

 and the x 2 test of Seber (1982) failed to reject the 

 null hypothesis of constant survival (x 2 = 0.4648, 

 df = 2), we estimated survival from period 3 to 

 period 4 as the average of 4> 1; 4> 2 > ana " ^3- To esti- 

 mate iV 5 , we estimated the capture probability at 

 sample period 5 (P 5 ) as the ratio of the number of 

 carcasses released at sample 4 and recaptured at 

 sample 5 (r 4 ) to the number released at sample 4 

 (R 4 ) times survival to sample 5 (4> 4 ), 



P 5 = rJ(R, * 4> 4 ). 



(2) 



We then estimated the population size at sample 5 



263 



