VALENTINE. SOULE. and SAMOLLOW: ASYMMETRY ANALYSIS IN FISHES 



begun between the first anal fin spine and the 

 vent, extending dorso-anteriorly along a natural 

 scale row to the pored lateral line scales. 



5. Pored lateral line scales: A count begun 

 with the first anterior pored lateral line scale, 

 usually located under or adjacent to the oper- 

 cular series, and extending posteriorly to the 

 end of the hypural plate. When the hypural 

 plate is reached, a straight pin is inserted in 

 the last pored scale counted and pushed through 

 the caudal peduncle. When the scales are counted 

 on the other side of the fish, the pin designates 

 the point at which counting should cease. 



6. Length of the dentaries: Measured from 

 the symphysis to a small notch at the posterior 

 edge of the dentary. 



7. Length of the posterior lateral projection 

 of the epiotic: Measured from the medial notch 

 defining the projection to the tip of the pro- 

 jection. 



Where practical, all characters were counted 

 under a binocular microscope. For specimens 

 too large to fit under a microscope, a magnifying 

 glass was used. 



Statistical Analysis 



The procedure for meristic (countable and 

 discrete) characters follows. For each individual 

 in a sample, the count taken from the left side is 

 subtracted from the corresponding count on the 

 right to obtain the signed difference. Next, the 

 standard deviation of the signed differences 

 i^r-0 i^ calculated for each sample. Then, the 

 mean of the character (^^+;) is calculated for 

 each sample by adding the absolute scores for 

 both sides and dividing by the sample size. 

 Finally, the squared coefficient of asymmetry 

 variation (CV^) for each population is defined 

 as follows: 



Crete, measurable), each measurement (item) is 

 divided by a suitable "general size" measure- 

 ment (e.g., we utilize the length of the cranium 

 as the standardizing measurement when study- 

 ing bilateral bones in the cranial region). Each 

 morphometric measurement is so treated before 

 obtaining the signed difference. The variance of 

 the resulting differences is then treated as if 

 it were a CV^ value. 



After the above analyses had been performed 

 on a series of barred sand bass from southern 

 {N = 74) and Baja California {N = 101), we 

 decided to restrict further asymmetry analyses 

 to total gill raker and pectoral fin ray counts 

 since asymmetry in all of the other characters 

 showed a significant association with asymmetry 

 in these (Table 1). Furthermore, pectoral fin 

 rays and gill rakers are the easiest characters 

 to quantify and appear to be the most accurate 

 counts that can be taken on barred sand bass. 

 For both grunion and barred surfperch only 

 the pectoral fin ray and total gill raker counts 

 were used for asymmetry analysis. 



Locality Designations 



We consider Point Fermin, the first major 

 point north of the Los Angeles-Long Beach 

 Harbors, to be our pivotal locality. Point Fermin 

 is situated approximately equidistant between 

 Point Conception and the California-Mexico 

 border, the northern and southern boundaries 

 for southern California. The distances between 

 Point Fermin and the other localities men- 

 tioned in this paper are indicated in Table 2. 



RESULTS 

 Barred Sand Bass 



CV^a- 



S^_,X100\2 



.V 



r + t 



F tests are employed to test for significant 

 differences in asymmetry. We follow Lewontin 

 (1966) in using the squared coefficient of varia- 

 tion as an analogue to the variance. 



To obviate scaling problems associated with 

 growth in morphometric characters (nondis- 



In our original analyses of barred sand bass 

 asymmetry data, we used all characters pre- 

 viously listed. Results from these analyses are 

 presented in Table 1. For all characters, both 

 meristic and morphometric, asymmetry values 

 for southern California barred sand bass are 

 significantly higher than for Baja California 

 or Mexican barred sand bass. 



Of interest is the relation between asymmetry 

 and length. Mexican barred sand bass were 



359 



