162 



Fishery Bulletin 91(1). 1993 



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Figure 2 



Plots of (A) sagitta weight vs. fork length, and (B) sagitta 

 length, height, and sulcal width vs. fork length for age-0+ 

 Pagrus auratus, 1987 and 1988 year-classes, sampled during 

 Periods 1-4 (see Table 1). 



Increases in sagitta size-variables between Periods 

 2 and 3 are also consistent with a growth rate 

 effect: snapper with lower growth rates (Period 3) 

 had larger sagittae than those with higher growth rates 

 (Period 2). Snapper growth rate generally declines be- 

 tween summer and winter (Paul 1976), so the pattern 

 of increasing sagitta size over Periods 1-4 (summer- 

 winter) is also consistent with a growth-rate effect. 



Between Periods 4 and 5, the slopes of single-sample 

 plots of size-variables vs. FL decreased. A reduction in 

 slope during the winter months suggests that somatic 

 growth slows faster in small than in large snapper, 

 leading to relatively larger sagittae in the former. The 

 reduction in slope is responsible for the curvilinear 

 trends observed when data from all periods are pooled 

 (Fig. IB). A similar effect of season on sagitta-somatic 

 relationships has been reported in other species (Reay 

 1972, Thomas 1983). 



When sagitta and somatic growth rates are un- 

 coupled, back-calculated lengths may be biased 

 (Campana 1990). To reduce this bias, Campana (1990, 

 eq. 4) connected the growth trajectory end-points (i.e., 

 sagitta and somatic sizes-at-capture) with a "biological 

 intercept" (he suggested sagitta and somatic size- 

 at-hatching). Snapper larvae are about 2mmSL 

 (equivalent to ~2.5mmFL) at hatching, and have cir- 

 cular sagittae that are 0.010-0.012 mm in diameter 

 (M.P Francis, unpubl. data). These values would 

 form an appropriate biological intercept for daily in- 

 crement back-calculations using measurements in ei- 

 ther the anterio-posterior (length) or dorso-ventral 

 (height) axes. 



Francis (1990) reviewed back-calculation methods, 

 but was not aware of Campana's (1990) study. Francis 

 identified two back-calculation hypotheses: scale 

 (=sagitta) proportional, and body (=somatic) propor- 

 tional. He pointed out that the commonly used Fraser-Lee 

 equation follows neither hypothesis, and recommended that 

 it be replaced with an equation that does. Campana's equa- 

 tion 4 is a modification of the Fraser-Lee equation, and also 

 does not follow scale- or body-proportional hypotheses. This 

 is easily shown by considering the point at which growth 

 trajectories converge. For scale-proportional methods, this 

 point is on the body-size axis; for body-proportional meth- 

 ods, the point is on the scale-size axis; for Campana's method, 

 the point is at the biological intercept which will usually 

 have some small, positive value on both axes (Campana 

 1990, Francis 1990). Campana's method, therefore, repre- 

 sents a third back-calculation hypothesis, which is based on 

 the idea that the proportional relationship between scale 

 and body size is initiated at some growth stage, such as 

 hatching. (The Fraser-Lee equation was also based on this 

 idea, but, in practice, most authors using that equation cal- 

 culated the intercept from a regression line rather than 

 from biological data [Francis 19901). 



