68 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



results just as significantly accurate could be 

 obtained by merely plotting the data, fitting the 

 lines by eye, and estimating the Li's and L.'s 

 from the graph. 



Between September 20 and 25, 1939, we 

 measured in ^-cm. units and marked a number of 

 shrimp in the Gulf of Mexico. We measured the 

 shrimp again upon recapture. 



I divided the returns (sexes combined) into four 

 equal time intervals of 10 days each — to 9 days 

 out, 10 to 19 days out, 20 to 29 days out, and 30 

 to 39 days out — and arranged the number of 

 returns in tabular form with lengths at tagging 

 against lengths at return. I fitted lines by least 

 squares to these data, with X= length at tagging 

 and Y= length at return. See tabulation follow- 

 ing and figure 2. 



In the tabulation, L„ for 0-9 days out was not 

 used in calculating the sum or the mean L„ as it 

 represents only an average of 5 days' growth. In 

 using this technique I wish to caution against 

 taking too short a time interval or too large a 

 measuring unit. There is always the possibility 

 under these circumstances that !<«, will be either 

 too large or too small. When the growth line 

 tends to parallel the 45° line, L„ will be too large. 

 When L„ tends to represent the larger individuals 

 at time of marking, it generally will be too small. 



In this instance the tendency was to approximate 

 the 45° line, probably making L„ too large. 



In each instance, I calculated L m from the 



a 



constants in the line formula and from Z„ 



0.678 



1-6 



=42.38 



For example, for 0-9 days out Z„ 



K-cm units or 211.9 mm. 



I calculated Li from two successive lines and the 

 _L n+ i — Z„ 



formula Zi= 



kn 



For example, Li calculated from the 0-9 and 

 3.850-0.678 



10-19 day lines is Z^ "'""" "•"'" =3.22 %-cm. 



units. 



I obtained Walford's 10-day growth line from 

 the mean L„ and the mean Li and from the 



1- 



2.51 



=0.9292. 



formula k=\ — ^i; k — 



LJ 35.46 



Hence, Walford's line for 10-day intervals for 

 this group of shrimp is Y=2.51 + 0.9292X. 



However, in order to compare growth calculated 

 in this fashion with monthly size distributions of 

 the shrimp populations, I found it necessary to 

 have a 30-day instead of a 10-day Walford line. 

 In other words, I needed an L 3 instead of an Li line. 

 This was obtained by 



Z 3 =Z 1 ^=2.51 ^44^=7.01; ' 



l-jfc 



1-0.9292 



7.01 



35.46 



= 0.8023. 



Hence, for a 30-day Walford fine in K-cm units 

 Y=7.01+0.8023X. 



LITERATURE CITED 



Walford, Lionel A. 



1946. A new graphic method of describing the growth 

 of animals. Biological Bull., vol. 90, No. 2 (June), 

 pp. 141-147. 



