Comparison of Scale Reading and Length-frequency Results
A method has also been described (Cassie 1954, p. 517) by which the results of scale readings may be co-ordinated with those from length-frequencies. In the example given, significant discrepancies were found between the results given by the two methods for certain age groups, suggesting that one or other method was invalid. In only six small-fish trawl catches were the numbers of snapper sufficient for adequate analysis, but not one of these shows complete consistency between scale reading and length-frequency determinations of age. The difficulty in interpretation is further increased by the high proportion of unreadable scales, but for the purposes of illustration it has been possible to choose a set of results (Text-fig. 3) where 90 per cent, of the scales have been interpreted. Similar results were obtained from each of the other five samples.
Text-fig. 3a shows the length frequency of the catch (totalling 201 fish) plotted in histogram form. Superimposed on this the hatched areas depict the hypothetical normally distributed population curves as estimated by the probability paper analysis. Although the histogram appears somewhat irregular compared with the smooth curve, it must be remembered that the number of fish in each class is small, leaving a considerable margin for chance variation. A test of goodness of fit gives χ2 = 12.158
Text-fig 3.—Analysis of age groups of a sample of 201 snapper by length-frequency (a) and scale-reading (b-g).
with 14* degrees of freedom, the probability of a higher value of χ2 occurring by chance being approximately 0.5, so that there is no reason on this score to doubt the validity of the analysis The estimated age-class parameters are shown in Table 1.
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Where n = number of fish.
x = mean length in inches.
s = standard deviation of length.
[Footnote] * After grouping to avoid expected numbers less than 5 in any size class, 27 size classes remain From this figure must be subtracted one degree of freedom for each of the 13 parameters shown in Table 1, leaving 14 degrees of freedom.
The corresponding parameters as determined by scale-reading (Text-fig. 3, b-g) are given in Table II.
t test of significance of differences from Table I.
Comparing the two tables, it is clear that in each of the three larger age groups one or more parameters differ significantly. Thus in classes 1+ and 2+, n differs by a number greater than can be accounted for by unreadable scales, while the difference in x is highly significant. In 3+, n and x do not differ greatly, but the difference in s is highly significant. There is no clear indication in Tables I and II which is more likely to be the correct version, but referring once again to Text-fig. 3, it will be noted that the length-frequency distribution of the scale-reading age groups is in some cases quite clearly divergent from normal. For instance, the 2+ class has at least two modes which appear to correspond to the 1+ and 2+ classes in the length-frequency analysis, while the isolated block on the right might well belong to the 3+ class. A similar interpretation might be placed on nearly all the scale-reading age classes. It will be noted that the unreadable section (Text-fig. 3, g) has a very similar distribution to the parent sample, except that (as might be expected) there is a tendency for more unreadable scales to be found in the larger sizes. The discrepancy between the results of the two methods is also made apparent in the figure by the dark horizontal bars along the bases of the histograms, representing the interval mean ± 2 × standard error for each apparent age-class.
From the above considerations it is concluded that the length-frequency solution is the more acceptable of the two. Although it is by no means axiomatic that measurement characters in any homogeneous group such as an age group should be normally distributed, when a normal distribution can be fitted to a series of apparent age-groups, such a solution is more convincing than an erratic series of polymodal classes. The latter can quite reasonably be explained on the assumption that, although there is a tendency for one annulus to be formed every year, annuli may sometimes be omitted or duplicated, owing perhaps to variations in seasons or in the behaviour of the fish. Some weight is lent to this supposition by the fact that snapper scales taken from the west coast of the North Island and Tasman Bay have more regularly spaced annuli and are more easily read. The scale shown in Plate 28, Fig. 1, for example, was taken in Tasman Bay and, for its size, is much more legible than any taken in Hauraki Gulf. Compared with the Hauraki Gulf, the west coast is a relatively exposed region with few sheltered bays and harbours. Thus the Hauraki Gulf snapper may, by relatively short-range wanderings, experience in any one year a number of different hydrographic conditions which may induce or suppress annuli. The west coast snapper on the other hand must either be subjected to regular annual changes in its aquatic environment or make annual migrations, either of which would tend to produce an annual pattern of scale growth. It is perhaps significant that both in Tasman Bay and Manukau Harbour, seasonal migrations distinguished by changes in the size composition of the catch are well-known to the fishermen, while in the Hauraki Gulf such movements are less obvious. Thus, even if scale-
[Footnote] ** significant at 1% level.
[Footnote] *** significant at 0.1% level.
[Footnote] * significant at 5% level.
readings are rejected as unreliable for Hauraki Gulf snapper, it is possible that this technique may still produce valid results for other localities.
While the length-frequency method appears, on the basis of the above evidence, to be a more satisfactory method of age determination, it is still necessary to examine the possibility that modes might be manifestations not of age groups but of some other form of discontinuous grouping in the population sampled. It is known, for instance, that some species of fish tend to congregate in schools of individuals all approximately the same size A trawl passing through a series of such schools would produce a polymodal sample, each mode representing a school which is not necessarily homogeneous for age. This possibility cannot be altogether discounted until more comprehensive data have been collected, but, as will be shown in the next section, all the length-frequency data so far collected yield results consistent with the age group hypothesis. Such agreement would scarcely be expected unless age is at least a major component in determining the position of modes.
Although scale reading has been rejected for present purposes, the structure of snapper scales may still repay further investigation, since the same irregularities which render them unreliable for age-determination may be of value for other purposes. If annuli are formed as a response to variations in hydrographic conditions, it is not unlikely that scale pattern may serve in some instances as an index of geographical races. For instance, there would be little difficulty in distinguishing, on the basis of scales alone, between two samples of large snapper, one from Hau [ unclear: ] Gulf and one from Tasman Bay.