FISHERY BULLETIN: VOL. 73, NO. 2 



proportion of immatures and males in the uniform 

 group must be known, and this requires some 

 knowledge of mortality rates. 



A rough estimate of mortality can be made from 

 the transect data and the known color composition 

 of each age. The yearly survival rate is calculated 

 using a modification of a simple fisheries estimate 

 (Ricker 1958). The rate is assumed to be constant, 

 and can be estimated as: 



s = 



N, 



where A'^ is the number of individuals in a par- 

 ticular age class in a sample. Where a large 

 number of age classes are available, one can 

 weight the classes according to their abundance 

 and separate two or more ages from the numera- 

 tor and denominator, giving, for example: 



N^ + N, + ... + N,_, 



For the Catalina population of P. pulchrum, the 

 formula used was: 



In this first approximation we assume that 

 bicolored fishes are all 8 or more years old, and 

 younger fish (ages 2 through 7) are uniform. The 

 decision to use age 7 as the dividing point comes 

 from Figure 9, where between ages 7 and 8 the 

 proportion of females drops to a low level and the 

 males become predominant. 



From Catalina transect data, s is estimated by: 



s6 = _33 and s = 0.735. 

 183 



The transect ratio can then be adjusted to com- 

 pensate for bicolored individuals younger than age 

 8 and uniform individuals older than age 7 by us- 

 ing proportions derived from Table 4, and each 

 age's contribution to the numerator or denomina- 

 tor can be weighted according to the first estimate 

 of survival derived above. The new estimate of 

 survival from the adjusted transect ratio is not 

 very different from the original, s = 0.71. 



A similar estimate for the Guadalupe Island 

 population, assuming in this case that the uniform 

 individuals are ages 2 through 7 (see Figure 9) and 

 adjusting as before, is s = 0.69. 



Mature sex ratios can now be estimated. Using 

 0.7 as the yearly survival rate, about 36% of the 

 uniform individuals seen at Catalina should be 



mature, and approximately 5% of those individuals 

 would be male. The ratio of mature males to ma- 

 ture females from field transects would then be 

 derived as: 



33 + (183 X 0.36 x 0.05) 36 



183 X 0.36 X 0.95 



=l = "-s' 



or about two females for every mature male. 



For Guadalupe, about a third (34%) of the 

 uniform individuals should be mature, and 90% of 

 these would be female. The sex ratio at Guadalupe 

 would then best estimated as: 



64 -I- (343 X 0.34 x 0.1) 76 



343 X 0.34 X 0.9 



105 



= 0.72 



or approximately three females for every two 

 males. 



An artifact of protogynous hermaphroditism is 

 the concentration of females in the younger ages. 

 Thus, the observed sex ratio depends on when the 

 animals change sex, and upon the mortality oc- 

 curring from year to year. Mortality causes sex 

 ratios to be biased towards females and these 

 become even more biased the greater the average 

 age of transformation is in the population. This 

 effect can be seen by comparing the estimated sex 

 ratio of the Guadalupe population (0.72), where 

 most females change sex within 3 yr after ma- 

 turity, with that of Catalina (0.57), where trans- 

 formation is relatively delayed. 



The deviations of sex ratio from unity seen here 

 should not be taken as contradictions of the 

 theories put forth on the adaptiveness of the 1:1 

 ratio (Fisher 1930; Bodmer and Edwards 1960; 

 Kalmus and Smith 1960), as these were developed 

 for nonhermaphroditic species, and sought to 

 equalize the lifetime reproductive potentials for 

 males and females. In sequential hermaphrodites, 

 the same individual functions as both male and 

 female at sometime in its life, and the question 

 becomes one of changing sex at the proper time to 

 maximize the individual's reproductive potential 

 (Warner in press). 



SUMMARY 



Year-round sampling of a population of the 

 California sheephead, Pimelometopon pulchrum, 

 was carried out at Catalina Island, Calif., and 

 comparative material was collected from a 

 population at Guadalupe Island, Mexico. 



Age determinations indicate individuals in the 

 Guadalupe population are dwarfed relative to 



280 



