60 
PACIFIC SCIENCE, Vol. XVII, January 1963 
Fig. 12. Fin ray index: combined number of seg- 
mented rays in the second dorsal fin and anal fin, 
divided by the number of rays in the left pectoral fin, 
multiplied by 100. Open circles, means of Pacific 
Coast populations; closed circles, means of Gulf of 
California populations; closed triangle, mean of Salton 
Sea population; horizontal lines, ranges of values. 
Pectoral Fin Asymmetry 
Species of fishes are known to differ in de- 
gree of asymmetry between the number of ele- 
ments in the right and left pectoral fins ( Hubbs 
and Hubbs, 1945). The numerical asymmetry 
between right and left pectoral fin counts in 
mirabilis was investigated to determine if in- 
dividual populations, or geographic regions, 
could be characterized by this feature (Table 4). 
Only the total amount of asymmetry, right plus 
left, was found to be useful in this respect. 
Values for the Pacific Coast and Salton Sea pop- 
ulations are usually higher (mean about 30%) 
than those from the Gulf (mean about 20%). 
The amount of asymmetry in the two most 
southerly populations on the Pacific Coast, how- 
ever, is the same as that of the Gulf forms. 
The degree of asymmetry is equally divided 
between right and left. To facilitate compari- 
sons, each population can be characterized ac- 
cording to whether there are more fish with 
higher counts in the right fin than in the left 
fin, or vice versa. If a sample has more fish with 
right fins of a higher count than the left, it 
is tallied as a "dextral”; and with more lefts 
than rights, as a "sinistral.” 
Among collections from the Pacific Coast 5 
out of 11 are dextral. In the Gulf, 3 out of 6 
are dextral, 1 is sinistral, and 2 are equal. The 
Salton Sea population vacillates from year to 
year between dextral and sinistral. Therefore, 
the distribution of rights and lefts within and 
between populations is typical of a 50-50 
chance situation, such as the toss of a coin. 
Vertebrae 
The number of vertebrae was compared in 
five populations (Table 5). In every sample 
the mode is 32, and the average is approximately 
the same value. Only the mean of the Salton 
Sea specimens differs appreciably from 32; it 
is significantly higher (t = 2.02; to . 95 (29) = 
1.70). 
In contrast to the relative uniformity of the 
means, there are patent differences between the 
variances; they are greater in the Salton Sea 
and Pacific Coast groups than in those from the 
Gulf. Each of the variances of the San Francisco 
and Salton Sea samples was tested against that 
of the northern Gulf collection; the F-ratios 
are F = 13.6, F0.975 (18, 39) = 2.4, and 
F = 8.6, F 0.97 5 (29, 39) = 2.1, respectively. 
The variances of the San Francisco and Salton 
Sea groups are not significantly different: F = 
1.6, F0.975 (18, 29) = 2.5. 
The variances of the vertebrae decrease from 
high to low latitudes. If the variances are listed 
from north to south, instead of as shown in 
Table 5, the following series of values is ob- 
tained: 0.577, 0.461, 0.182, 0.157, 0.341, 0.0. 
Considering the few populations represented, 
the correlation is surprisingly good. The pres- 
ence of a similar positive correlation between 
latitude and fin ray variance (see above) in- 
creases the confidence in the trend indicated 
by the variances of the vertebrae. 
