To emphasize central tendencies, the plots 

 were smoothed by a moving average of three 

 intervals, giving the center interval double 

 weight. The samples usually consisted of more 

 than one size class, as indicated by the pres- 

 ence of several peaks on the length- frequency 

 graphs. Only five distinct peaks could be traced 

 through three or more consecutive samples. 

 The progressions of the modal lengths of these 

 five peaks are shown in figure 9 and were used 

 to construct a hypothetical von Bertalanffy 

 growth curve of Rangia . 



The von Bertalanffy growth curve is a decay- 

 ing exponential that has been used to describe 

 growth in a variety of cases. The animal's 

 length L at any age t can be expressed as: 



L = a(l - be-l^f) 



where a, b, and k are parameters characteristic 

 of the particular animal or population. The 

 theoretical maximunn length is equal to a and 

 is approached asymptotically as t increases. 



The parameter b is the ratio of total lifetime 

 growth (after birth, or settling in the case of 

 bivalve moUusks) to total length, or: 



where c is the average length of the clam shell 

 when the larvae settle (t equal to zero). Deter- 

 mination of b obviously requires knowing the 

 length at time zero. The exponential k might 

 depend on the catabolic rate of the animal. The 

 two parameters, a and k, can easily be de- 

 termined from data only on sizes at known 

 time differences, with no knowledge of absolute 

 age. These size data are provided by the 

 progressions of modal lengths in figure 9. The 

 data were manipulated by two nnethods for 

 estimation of a and k: (1) Diaz increment 

 technique, and (2) Ford- Walford technique. The 

 resultant values for a and k are shown in 

 table 2. 



s 

 % 



o 



65 - 



60- 



55 



o 



50 



45 



40 



35 



30 



10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 J_ 2 3 4 5 67 8 9 

 1965 1966 1967 



COLLECTION DATE 



Figure 9. — Progression of modal lengths from length-frequency analysis of 12 Rangij cuneata samples. Lines A-E repre- 

 sent five peak size groups which were traceable through three or more consecutive samples. 



21 



