A Method of Analysing a Polymodal Frequency Distribution and its Application to the Length Distribution of the Porgy, Taius tumifrons (T. and S.)

Publisher Website
Google Scholar
Abstract
By utilizing the fact that normal frequency distributions become parabolas when logarithms are taken, a simple graphical method has been devised for analyzing polymodal distributions into their components. Briefly, the method consists of (a) plotting the observed frequencies on semi-log paper; (b) drawing on transparent paper the parabolas corresponding to a series of values of o (2 or 3 copies); (c) fitting these parabolas to the observed frequency distribution. An an example, Rao''s data were treated in this way, and the result was compared with what he obtained by the maximum likelihood method. Though the results do not coincide perfectly, there seems to be adequate agreement. For a second example the length distribution of the porgy was analyzed in this way and compared with what is obtained by (1) using probability graph paper, and (2) fitting parabolas by least squares. The method proposed here is less cumbersome than either of these and it yields good results. Using the graphical method, the length distributions of porgy were analysed using the data from September 1950 to December 1952, and the age composition, mean fork length, and standard deviation in length were obtained for the separate year-classes. The annual rate of decrease is about 0.7, and the abundance of recent year-classes seems to have declined. Growth in length is linear and amounts to about 4.0 cm per year. The standard deviation in length increases with age, while the coefficient of variation decreases. The effectiveness of stratification by length for estimating age distribution has been examined. The ratio of the variance between strata to the variance within strata is about 4, hence, stratification by length is expected to be extremely efficient.

This publication has 0 references indexed in Scilit: