A Simple Method of Resolution of a Distribution into Gaussian Components

TLDR

Biological morphometric distributions are mixtures of components (species, age groups, etc.) that are usually modeled as normal, and resolving such mixtures into Gaussian components is a longstanding problem, particularly in fisheries where multimodal length distributions reveal age‑related modes. The study aims to determine the relative frequencies and frequency distribution of the mixture components by analyzing the observed distribution. The analysis of fish length distributions into Gaussian components proved useful for population studies, especially when age determination is difficult, as the skewed, multimodal distribution often reflects distinct age groups that can be separated.

Abstract

The distributionof a morphometric character inl a biological population is a mixture of components corresponding to different species, broods, sexes, etc. A problem which frequently arises is to find the relative frequencies and the frequency distribution of such components by an analysis of the observed frequency distribution. The frequency distribution of any such component is usually assumed to be normal: hence the problem is one of resolution of a distribution into Gaussiain components. For a population of fish such an analysis has been found to be very helpful for population studies, particularly when determination of age of a fish is difficult. The frequency distribution of length obtained from a sample of fish is usually skew and polymnodal: in many cases, the modes correspond to individual age-groups and are very helpful for separating them. Buchanan-Wollaston and Hodgeson [1929] disapproved of the smoothing out of 'bumpy' distributions, as practiced by the early fishery biologists, even for small samples. They suggested that the individual 'humps' indicate meaningful modes around which normal curves ought to be fitted. The problem of resolution of a distribution into two Gaussian components, and some particular cases of it, have been considered by several