McFARLANP F.T AL.: KKCKI'ITMKNT I'AITKRNS IN FKP:N('H CRUNTS 



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SAMPLING DATES 



15 - 



1980 



Fkjure 3. - Relationship (if fertilization dates of recently settled postlarval grunts to time of the year. Upper graph represents the dates and 

 the numbers of postlarvae collected for aging from the backreef of Tague Bay barrier reef. Lower graph represents the frequencies for back- 

 calculated dates of fertilization of the collected samples in the upper graph. 



fewer postlarvae (Fig. 3). The actual day of fertiliza- 

 tion for each of these 1,478 French grunts indicates 

 that recently settled individuals were spawned with 

 a consistent periodicity (Fig. 3) that is similar to the 

 settlement periodicity (Fig. 2). These derived spawn- 

 ing data suggest, however, the presence of a more 

 pronounced short cycle. 



Periodic Analysis, Times of 



Settlement and Reproductive Activity, 



and Patterns of Settlement 



Periodic Analysis 



To evaluate the periodicity of postlarval settlement 

 and of fertilization times of recently recruited 

 French grunts (Figs. 2. 3), we used a Rayleigh-test 

 (see Batschelet 1965). The method involves a Fourier 

 transform of sequential data (see McFarland and 

 Kotchian 1982 for details). A data set is first sequen- 

 tially summed for a specified period, and these pool- 

 ed data are used to evaluate the degree of deviation 

 from a nonperiodic random distribution. By compar- 

 ing dimensions of the mean vectors obtained for dif- 



ferent specified periods, the most dominant period is 

 usually revealed (Fig. 4). 



Analysis of the 1980 settlement and fertilization 

 data reveals that a rhythm with a period of about 15 

 d dominates (Table 1). Examination of the census 

 and fertilization data (Figs. 2, 3) indicates that weak 

 secondary appearances of PL-l's and different ferti- 

 lization dates may occur. Indeed, their presence (e.g., 

 4 peaks in Fig. 2) hints at a weekly rhythm super- 

 imposed on the semilunar periodicity. It is difficult to 

 assess this possibility with periodic analysis, 

 however, because a natural harmonic of the domi- 

 nant 15-d rhythm can occur at about 7.5 d, even if a 

 weekly rhythm does not exist (Fig. 4). 



With less mathematical elegance the periodicity in 

 the data sets can be estimated by averaging intervals 

 between peaks. Both the 1980 census data for the 20 

 discrete study sites (Fig. 2) and the fertilization date 

 data (Fig. 3) provide similar estimates of about 13.9 

 d and 15.1 d (Table 2), which do not differ significant- 

 ly from the mean semilunar period of 14.64 d that ac- 

 tually occurred. The possible presence of a weekly 

 rhythm often interspersed between the biweekly 

 rhythm is revealed by 5 obvious short-period pulses 



417 



