QUAST: MORPHOMETRIC VARIATION ON PACIFIC OCEAN PERCH 



Inflections and Sexual Crossover 

 in the Regressions 



I examined 216 computer-drawn scattergrams 

 for sexes within regions that represented the 

 measurement regressions (Table 2), by transpar- 

 ent overlay with incised straight line. None 

 shows obvious curvature, and only three show 

 possible inflections: In females, the regression ap- 

 pears to bend upward about 8.3° at about 262 mm 

 SL for belly measurements in the Atka-Bering 

 region; downward about 7.0° at about 242 mm SL 

 for hind-trunk ventral in the same region; and 

 possibly upward about 13.5° at about 260 mm SL 

 for the belly in the Southeastern region. Whether 

 the apparent breaks in the three regressions are 

 artifacts or real is moot. Evidence for reality in- 

 cludes their visibility in scattergrams; that all 

 occur in a single sex (females) and in a measure- 

 ment possibly influenced by sexual development 

 with growth; and that the possible break in the 

 belly regression in the Atka-Bering region has a 

 near complement in the hind-trunk ventral mea- 

 surements, which extend from the belly to the 

 tail. Also, as discussed in a succeeding paragraph, 

 mild inflections probably are hidden in variabil- 

 ity of the data. Evidence against reality includes 

 the extreme rarity of visible indications of possi- 

 ble breaks (none in 16 of 18 measurements and 

 only 3 in the remaining 24 regressions), and the 

 extreme goodness of fit (i?^) to a straight line 

 shown by the regressions with possible inflections 

 (Table 2). The measures for goodness of fit for 

 belly are the best among regions in the two re- 

 gressions with possible inflections, and both mea- 

 sures are higher than those for corresponding 

 male regressions, which show no indications of 

 inflection. The weight of evidence seems to side 

 with the visible breaks being artifacts. Yet, even 

 if the breaks represent real inflections, the mor- 

 phometric data seem to fit linear criteria well as 

 far as conventional measures are concerned. 



The regressions for sexes, within measure- 

 ments and regions (Table 2), diverge with in- 

 creasing SL, indicating that sexual dimorphism 

 increases with growth. The increases are slight, 

 however, as evidenced by the similarity in regres- 

 sion parameters between sexes, and on average, 

 characters will differ in size between sexes by 

 only a few millimeters in the standard 260 mm SL 

 fish (Fig. 2). Given normal variation, the differ- 

 ences should not be obvious or reliable in differen- 

 tiating sexes by gross examination of even the 

 largest Pacific ocean perch. 



However, divergent sexual-regression pairs 

 pose an apparent contradiction when they inter- 

 sect within their data domain. Such intersections 

 infer 1) sexual differences in fish on the juvenile 

 side of the intersection, 2) differences on the juve- 

 nile side the reverse of those on the adult side, 

 and 3) differences between sexes in juveniles that 

 increase as SL's become smaller. In the morpho- 

 metric data, the regressions for sexes do intersect, 

 and the intersections form a symmetrical unimo- 

 dal distribution with a strong peak near 230 mm 

 SL. By itself, crossover need not be a problem; 

 e.g., the symmetrical confidence limits about re- 

 gression (Sokal and Rohlf 1969) are evidence that 

 crossover within these limits is normal in sam- 

 ples from a single population. Yet, differences in 

 measurements for sexes on the juvenile side of the 

 modal point for sexual crossovers apparently are 

 greater than can be accommodated by confidence 

 limits based on the regressions. In 108 compari- 

 sons of mean estimates for measurements and 

 their confidence limits at 170 mm SL, 18 have sig- 

 nificant differences, when only about 5 are expected 

 with 95% confidence limits. Apparently, sexually 

 associated crossover is slightly too severe in the 

 morphometric data to be adequately contained by 

 confidence limits for single populations. 



The evidence is strong that most of the mea- 

 surement regressions do not fit their data per- 

 fectly and, because of the nature of the error, that 

 slight growth inflections likely are concealed by 

 variation. The three apparent inflections men- 

 tioned previously might indicate the size at in- 

 flection, but the evidence is weak. It is apparent, 

 however, that significant sexual differences in 

 measurements at SL's below the crossover mode 

 should not be taken literally. (Assuming that 

 measurement regressions may incorporate hid- 

 den inflections, most reliable estimates of juve- 

 nile measurements among sexual pairs within 

 their data domains will be from the regression 

 whose slope is nearest unity, particularly if the 

 sample number is large and the slope not signifi- 

 cantly different from unity.) Because the bulk of 

 specimens were larger than 230 mm SL, and the 

 regressions fit their data closely, conclusions re- 

 garding adult relationships in the present data, 

 particularly trends, should be reliable. 



Strength of Geographic and 



Sexual Variation Shown 



in the Characters 



Analysis of morphological diversity is most use- 



675 



