CHAMBERS ET AL.: CORRELATIONS BETWEEN EARLY LIFE HISTORY TRAITS 



Yolk at hatching was approximately a prolate 

 spheroid and we estimated this volume from 

 measurements of length and height of the yolk 

 complement minus the volume of the oil globule 

 it contained. 



We used initial yolk volume rather than initial 

 egg volume to quantify egg quahty because it 

 better represents the energy content of the egg. 

 We chose posthatching hfespan over the more 

 frequently used time to yolk-sac depletion or time 

 to irreversible starvation ("point-of-no-return", 

 Blaxter and Hempel (1963)), because the latter 

 are much more difficult to determine accurately. 

 We assumed a high correlation between these 

 components of posthatching lifespan for unfed 

 larvae. In support of this assumption we calcu- 

 lated a correlation of r = 0.88 (P < 0.001) between 

 the interval from hatching to yolk-sac depletion 

 and the interval from yolk-sac depletion to ir- 

 reversible starvation, using data from 25 marine 

 fish species presented by McGurk (1984). 



We accounted for the potential influence of 

 environmental (laboratory) variation on ELH 

 measurements by using location of the embryos 

 and larvae in the water table as a blocking varia- 

 ble. In addition, jars were inspected for hatch- 

 lings, and hatchlings were measured, in se- 

 quence by block. Block specification thus repre- 

 sented chance differences among the three static 

 tanks; locational differences (which might in- 

 clude effects of slight temperature or light 

 gi-adients on any of the ELH traits); and effects 

 of unavoidable delays in measuring hatchlings. 

 These delays were caused by the time required 

 to measure the hatchhngs. As an extreme ex- 

 ample, 30 hours were required to measure all 

 larvae hatching on the modal hatching day. 



We employed a two-way randomized block ex- 

 perimental design with female parent as the 

 treatment of interest (i.e., are there significant 

 differences among females in the ELH traits of 

 their offspring?). This design allowed us to 

 determine both the female effect on ELH traits 

 and the within-individual correlations between 

 those traits. The design was unbalanced because 

 the number of eggs used varied (12-15 per 

 female) and some mortality occurred before 

 hatching. 



We treated the six traits as a multivariate 

 response and analyzed these as a random-effects 

 multivariate analysis of variance (MANOVA) 

 with the general linear model 



(Yl, TL, Y2, G, H, L) = |x -^ female + block 



+ female x block -i- e. 



The six ELH traits of the response vector are 

 defined above, ji is the overall mean, female 

 codes for females 1-10, block codes for tank/loca- 

 tion/monitoring order 1-3, and e is random error 

 from the model. 



We calculated partial correlations between all 

 pairs of traits from residuals remaining after the 

 effects of block and the remaining four traits 

 (considered for this procedure as covariables) 

 had been statistically removed. We also calcu- 

 lated simple correlations between all pairs of 

 traits based on average gi'oup values (common 

 female parent), as has been the practice in pi-e- 

 vious work. These coiTelations were compared 

 with the partial correlations to assess differences 

 in estimated correlations based on the two ap- 

 proaches. 



We evaluated the female effect on the trait 

 vector with Wilk's lambda criterion (Timm 

 1975). After rejecting the null hypothesis of no 

 female effect we gauged the contribution of each 

 trait to this result. This was done by examining 

 the magnitude and sign of the correlation be- 

 tween each trait mean and the standardized and 

 adjusted discriminant function that maximized 

 among-female differences (Timm 1975; Wilkin- 

 son 1975). We also compared the MANOVA find- 

 ings W'ith standard F-tests and with percentage 

 of the total variance due to female source as 

 calculated from univariate ANOVA's on each 

 ELH trait. We assessed the influence of female 

 condition on the ELH traits of her offspring by 

 estimating the simple correlation between each 

 family-average ELH trait and female size, condi- 

 tion index, and hpid index. 



Prior to analysis we log transformed initial 

 yolk volumes and yolk and oil globule volumes at 

 hatching. MANOVA, discriminant analysis, and 

 l^artial correlations were performed on SYSTAT 

 (Wilkinson 1988) and the variance components 

 were estimated using SAS (SAS Institute, Inc. 

 1987). 



RESULTS 



Survival to hatch was over 98%. The quantity 

 of variation in initial yolk volume, age at hatch- 

 ing, and age at death (C.V. (= SD/mean) = 0.15, 

 0.03, and 0.24, respectively) was comparable to 

 values reported for other species (cf. Chambers 

 et al. 1988). Length, yolk, and oil globule volume 

 at hatching were more variable than expected 

 (C.V. = 0.08, 0.98, and 1.44) owing partly to 

 their rapid change during the 1-2 days after 

 hatching when measurements were taken. By 



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