FISHERY BULLETIN: VOL. 74, NO. 2 



confined to shallow waters less than 50 m depth 

 and appear fairly uniform along the Oregon coast 

 based on commercial landings of legal-sized 

 adults (Waldron 1958). This implies that the dis- 

 tribution of larvae along the entire Oregon near- 

 shore area would be relatively homogeneous from 

 year to year. Wind induced turbulence and mix- 

 ing would tend to increase the homogeneity of the 

 larval population despite any initial patchiness. 



If we assume that the total number of C magis- 

 ter larvae combined over the four inshore stations 

 (NHOl, NH03, NH05, NHIO) is representative of 

 the total population on a local basis, then the 

 question may be asked whether there is a signif- 

 icant difference in the population means between 

 the 2 yr, 1970 and 1971, and can a difference 

 be explained using the concomitant observations 

 of time, temperature, and salinity? 



An analysis of multiple covariance was used to 

 test this hypothesis on two sets of data for C. 

 magister larvae. The first set of data compares the 

 sampling period from 29 January 1970 to 29 July 

 1970 with that of 18 January 1971 to 21 July 

 1971. This period includes, for these 2 yr, the first 

 major larval release through the time at which no 

 megalopae were present in the water column. 

 Larval density estimates from both sizes of mesh 

 of the 0.2-m bongo net sampler were used in the 

 analyses. Surface temperatures and salinities 

 comprised the only complete data set for the two 

 larval seasons and the average values of the four 

 inshore stations were used for each sampling 

 period. Nevertheless, sea surface temperatures 

 and salinities are representative of nearshore 

 subsurface conditions during the winter period 

 from November through March-April as exten- 

 sive wind mixing occurs in the shallow areas pro- 

 ducing isothermal conditions (Renfro et al. 1971). 

 During the spring and summer, a weak thermo- 

 cline of less than 2°C exists in the nearshore area 

 (<20 m). Larval and environmental data used in 

 the analyses are given in Appendix Table 1. 



The mathematical model used for the initial 

 analysis was of the form: 



Y = b + bo(y) + bi it) + b^m + b:,(S) 

 + b^{T^) + 65(52) + b^{T X S) 



where, Y = logio(X -I- 1) number of larvae per 

 4,000 m^ of water, 6 = a mean effect, y = a year 

 effect, ^ = a time effect (days elapsed since 1 

 January), T = linear effect of sea surface temper- 

 ature (°C), S = linear effect of sea surface salinity 



360 



(%o), T"^ = quadratic effect of temperature, S^ — 

 quadratic effect of salinity, and T x S = interac- 

 tion effect between temperature and salinity. 



The b's in the model were estimated from a 

 general linear hypothesis testing computer pro- 

 gram contained in the Oregon State University 

 Statistical Program Library. Various hypotheses 

 can be specified by the user to test the importance 

 of the individual parameters in the model. 



A summary of the analysis on the initial run is 

 given in Table 2. A highly significant difference 

 {1% level) was found between j' means after being 

 adjusted for all the covariates in the model. How- 

 ever, only t was found to be highly significant in 

 explaining the yearly difference. That is, the ap- 

 pearance of larvae in the plankton was of shorter 

 duration in 1971 than in 1970. Subsequently, a 

 new model was generated using only f as a 

 covariate: 



Y = b + bo(y) + 61U). 



The importance of t was again found to be 

 highly significant in explaining the difference be- 

 tween y population means of C. magister larvae 

 (Table 3). 



Table 2. — A comparison of the total number of Cancer magis- 

 ter larvae for 1970 and 1971 (January through July) by analysis 

 of multiple covariance (full model). 



Source of 

 vanation 



Degrees of 

 freedom 



Sum of 

 squares 



Mean 

 square 



f-level 



Table 3. — A comparison of the total number of Cancer magis- 

 ter larvae for 1970 and 1971 (January through July) by analysis 

 of multiple covariance (reduced model). 



