NOTE Matsuura and Hewitt: Changes in the spatial patchiness of Scomber japonicus 



173 



habitat, and these stations comprised the data set 

 used in the analyses. 



Size-frequency analysis 



Frequency distributions of larval catches by size were 

 assembled and a negative binomial model was fit to 

 each distribution. The negative binomial has been 

 used to describe aggregated distributions of ichthyo- 

 plankton (Hewitt, 1981; Zweifel and Smith, 1981; 

 Smith and Hewitt, 1985). The model is specified by 

 the mean (m) and the index of dispersion (k); the 

 variance (o 2 ) is related to m and k as 



m +  



m 



Lloyd's (1967) index of patchiness (P) was used to 

 describe the intensity of the distribution pattern at 

 various larval sizes where 



P=l + 



m 



m 



The index has been used by several investigators to 

 describe ichthyoplankton patchiness (Smith, 1973; 

 Hewitt, 1981; Houde and Lovdal, 1985; McGurk, 

 1987) and may be considered as a measure of how 

 many times more crowded an average individual is 

 relative to an individual in a population with the 

 same mean density, but one which is randomly dis- 

 persed. The index is independent of density and the 

 scale of sampling (Pielou, 1977; Hewitt, 1982) which 

 allows comparisons of patchiness between relatively 

 abundant yolk-sac larvae and less abundant older 

 larvae. By substituting the expression for the vari- 

 ance of the negative binomial, 



P=l + 



1 



— ' 



k 



where k was estimated by using a maximum likeli- 

 hood estimate expression (Bliss and Fisher, 1953; 

 Smith and Hewitt, 1985). The standard error of the 

 sample estimate of patchiness was estimated by fol- 

 lowing Lloyd (1967): 



se 



(P),±4 



2 Vvar(&)> 



where var(&) is the sampling variance of k. 



Adjusting for shrinkage and converting to age 



Initial size measurements were obtained from lar- 

 vae preserved in 5% buffered formalin. Preserved size 

 was converted to live size by using the shrinkage rate 

 obtained for jack mackerel larvae from Theilacker 

 (1980). To convert from larval size to larval age, we 



used the growth curve obtained from laboratory 

 reared larvae with water temperature ranging from 

 16.8 to 19.2°C (Hunter and Kimbrell, 1980): 



t = 



In {SLI 3.4432) 

 0.05968 



where t = age in days since hatching (= age), and 

 SL = standard length in live size (mm). The incuba- 

 tion period (from spawn to hatch) was assumed to be 

 2.3 days. 



Results and discussion 



Frequency distributions of larval catches by size are 

 presented in Table 1. The corresponding live sizes, 

 ages, mean abundances per tow, and patchiness pa- 

 rameters are also presented in Table 1. Larvae less 

 than 3.5 mm in length appear to be undersampled 

 in comparison to larger sizes. Pacific mackerel lar- 

 vae grow rapidly through the first two size classes 

 and therefore are vulnerable to capture for a rela- 

 tively short period of time; small larvae are also more 

 likely to be extruded through the meshes of the sam- 

 pling net (Smith and Richardson, 1977). 



The change in patchiness with age suggests that re- 

 cently hatched Pacific mackerel larvae were highly 

 aggregated and dispersed rapidly until approximately 

 five days after spawning (Fig. 1). Patchiness gradually 

 increased with age until 9.2 days, then decreased 

 slightly and continued to increase with age thereafter. 



Morphological and behavioral changes of develop- 

 ing Pacific mackerel larvae are summarized in Table 

 2 and illustrated in Figure 2. Afunctional visual sen- 

 sory organ is formed in Pacific mackerel larvae at 

 6.0-6.5 mm and completed at approximately 8 mm. 1 

 Although caudal and pectoral fins begin development 

 at 3.5 mm, swimming speed increases rapidly with 

 size only after the pelvic, anal, and dorsal fins are 

 formed at approximately 9.6 mm (Watanabe, 1970; 

 Hunter and Kimbrell, 1980). Hunter and Kimbrell 

 (1980) reported that schooling behavior did not be- 

 gin until 14 mm, although an increase in patchiness 

 at 4.6 mm is apparent from the plankton catches. It 

 may be that the ontogeny of schooling behavior in 

 Pacific mackerel involves a prolonged period of con- 

 tact between larvae that is necessary for the success- 

 ful integration of approach- withdraw and approach- 

 orient behaviors (Shaw, 1960, 1970; Williams and 

 Shaw, 1971). This phenomenon may be statistically 

 recognizable as an increase in patchiness but not 

 visually recognizable as coordinated social behavior. 



1 O'Connell, C. Southwest Fisheries Science Center, Nat. Mar. 

 Fish. Serv., NOAA, P.O. Box 271, La Jolla, California. 



