APPELDOORN: VARIATION IN GROWTH RATE OF MYA ARENARIA 



variance of each age mode. Therefore, variation 

 in the original data is reflected in the variance 

 estimates of the model parameters, and poorly 

 represented age modes, where estimates of mean 

 length and variance might be subject to error, 

 are weighted less. The resulting growth curves 

 are based on the assumption that growth varies 

 from year to year only to the extent expected 

 owing to normal fluctuations in growing condi- 

 tions. Hence, they are an estimation of "average" 

 growth within a population, representing an in- 

 tegration of several variable processes affecting 

 growth. 



The environmental data listed in Table 1 were 

 used to characterize Mya armaria habitats. 

 These data were subjected to principal compo- 

 nents analysis (PCA) to reduce the observed var- 

 iables to a more meaningful and manageable 

 number of factors without excessive loss of infor- 

 mation. PCA locates hidden components which 

 have generated dependence in the observed var- 

 iables (Morrison 1976). Each resulting compo- 

 nent is a composite variable — a linear combina- 

 tion of the original variables. The components 

 are independent and ordered, so that the first 

 component accounts for most of the observed var- 

 iation, the second for most of the residual varia- 

 tion, and so on. The loadings given for each com- 

 ponent represent the correlation coefficient (r) 

 between a variable and a component. The analy- 

 sis was run on the Pearson product-moment cor- 

 relation matrix of the environmental parameters 

 (to allow for standardization of the units of mea- 

 sure) by using the CORR, FACTOR, and SCORE 

 procedures of SAS79 (Helwig and Council 1979). 



The components produced by PCA are limited 

 by the input data and can only reflect the factors 

 represented by those data. In the present study 

 the selection of factors was constrained by the 

 sampling design, and no direct measurements 

 were made on a number of factors which would 

 be expected to influence growth (e.g., current 

 flow, food concentration). However, several of 

 the factors represent an integration of processes, 

 incorporating factors not measured directly. For 

 example, current flow is represented to some de- 

 gree by tidal range, tidal position, and sediment 

 characteristics (see Discussion). This integration 

 effect will help offset the limitations of the input 

 data. 



The growth rate parameter was transformed 

 to log 10 (co) for the analysis of growth variations. 

 Since logio(ZO and logio(L J are inversely propor- 

 tional (Pauly 1979), it isfeltthatlogio(aj)isamore 



suitable measure of growth (Appeldoorn in 

 press). A difference in logio(co) would then indi- 

 cate a fundamental difference in growth — not 

 just a reciprocal change in Kand L^. [See Pauly 

 1979, 1980 for a discussion of the analogous P = 

 \ogw{K-W x ) parameter of the VBGF for weight.] 

 Variations in growth rate were analyzed using 

 a stepwise functional regression of logio(a;) on the 

 components generated by PCA, where the resid- 

 uals of the regression of the logio(ou) on Compo- 

 nent 1 were regressed against Component 2 and 

 so on. The geometric mean functional regression 

 was deemed appropriate because of variability 

 in both ai and the components, small sample size, 

 and uncertainties about the distribution of the 

 data (Ricker 1973; Laws and Archie 1981). In 

 normal predictive regressions the regression co- 

 efficient (slope) is b\ functional regression yields 

 a coefficient of v — b/r where r is the correlation 

 coefficient. The standard error of v (SE,) equals 

 the standard error of 6(SE/,) and 95% confidence 

 limits on rare approximated by v± 2SE, (Ricker 

 1973). Estimates of b, r 2 , and SE* were obtained 

 using the GLM procedure of SAS79 (Helwig and 

 Council 1979) and used to calculate v and its 95% 

 confidence limits. The significance of the regres- 

 sion is tested by determining if the confidence 

 limits bracket v = 0. If not, the null hypothesis 

 Ho: v = is rejected. 



RESULTS 



The mean lengths at age as determined 

 through length-frequency analysis are given in 

 Appendix Table 1 for the 19 populations analyzed 

 here. The parameters of the VBGF and logio(to) 

 are given in Table 2. Using the 95% confidence 

 limits around logmM, statistically significant 

 growth differences become readily apparent. A 

 functional regression of logioMon latitude yield- 

 ed: logio(to) = 4.8184 - 0.0878 latitude with r = 

 0.8220. Although the regression accounts for the 

 majority of the observed variation in growth, it 

 does not indicate what underlying processes may 

 be responsible for this relationship. 



The results of the PCA are shown in Table 3. 

 The terms used in the table follow the definitions 

 in Morrison ( 1976). In order to simplify the table, 

 those loadings <0.30 have been left out, although 

 all variables contribute to all components to 

 some degree. The first five components have 

 been retained and account for 88% of the observed 

 variation. Of these, the first three were exam- 

 ined in greater detail. 



79 



