The length distribution in a sample from a specific population is the product of recruitment, growth, mortality and sampling errors. Annual variations in recruitment and individual variability in growth frequently mask the interpretation of modal classes in length frequency.
These methods are based on the assumption that each modal class in a frequency distribution will correspond to a cohort and represent different age classes determined at regular intervals. The presence of modes in the length distribution depends on the distance between the medians, the extent of the variance, the proportion of each age class in the population and the size of the sample studied (MacDonald and Pitcher, 1979; Fournier, 1983).
Methods of growth determination based on length-frequency analysis can be applied to populations with a markedly seasonal recruitment, where the identity of the year classes is maintained, and when growth is sufficiently swift to avoid excessive superimposition of the lengths of successive age classes.
Gear selectivity can influence the type of length frequency. The smaller lengths, for instance, not fully recruited to the gear, will be under-represented. Selectivity can be corrected by calculating the capture probability (Brey and Pauly, 1986). When the gear is also selective with respect to larger-sized fish, as with trammels and long-lines (Ralston, 1990), it is much harder and sometimes impossible to use methods based on length frequency analysis.
Hosmer (1973) showed that the estimation of the parameters of each age class, such as average length and relative abundance, are enormously facilitated by having separate samples from one or more age class. This author formulated the calculations needed to identify two normal components in the frequency distribution. Based on these original calculations, more general systems were developed for a larger number of components.
A time sequence of length frequency distributions makes it possible to separate age classes which might otherwise be obscured by the super-imposition of frequencies. Changes over time in each cohort can be analysed visually (Petersen, 1891), or by computerized methods developed from Hasselblad (1966), which separate the modal classes of the length-frequency (MacDonald and Pitcher, 1979; Schnute and Fournier, 1980). Pauly and David (1981) analysed the time series, assuming that the mode of each class followed a von Bertalanffy curve (1938; 1957; 1964).
Various approaches have been utilized in the process of selecting modes in a single frequency; graphic methods which determine the area of the cumulative frequency (Cassie 1954; Bhattacharya, 1967) and statistical methods based on maximum likelihood. Growth parameters in the second group can be determined by adapting complex models to length-frequency (Schnute and Fournier, 1980). These hypotheses can be determined and verified when specific characteristics are attributed to the processes (e.g. normal length distribution in each age class) and likelihood functions are maximized.
Assumed growth models can be adjusted by a minimum chi-squared method or other technique to the modal classes observed in the frequency (Pauly, 1984; Pauly and Gaschutz, 1979; Pauly and Morgan, 1985). Recently, Wetherall et al., (1987) developed an ingenious method for calculating Loo and Z/K based on scant length-frequency data.
The determination of median lengths and relative abundance in each cohort is more precise when a subsample of age data is available for one or more of the age classes present in the length-frequency (Hosmer, 1973). Given the close correlation of the von Bertalanffy parameters, Loo and K, errors in plotting from the same set of length-frequency data will be avoided by including in the calculation data which is not dependent on growth. Age determination of a length-frequency subsample makes it possible to know the number of age classes in the population and make the calculations more accurate.
MacDonald and Pitcher (1979) stated that the use of age data limits the number of possible components in length distribution and implies adjustments of greater biological significance. Comparably, Morgan (1987) applied age data to improve growth parameters calculated from length-frequency. A modification of Morgan's method was developed by Gayanilo et al (1988).
The necessary age subsample for the application of the above methods can be selected at random from the length-distribution, or by stratified sampling. The catch of most species is made up of various age classes of different abundances, and therefore the size-stratified sample will eliminate the errors introduced by the relative abundance of lengths and will allow more of the bigger fish to be sampled where the superimposition of lengths is greater.
