Theoretical Basis of Allometric Relationships in Juvenile Brachyura: Data from a West African Mangrove Swamp Crab Population

The carapace length-weight relationship in juvenile Brachyura (crabs) was studied theoretically to assess the relevance of the allometric factor and the validity of the condition factor as these factors are often not determined because most fishery investigations are conducted for adult population. The allometric factor appears to be the main parameter in the equation: W = aLb (where W = weight, a is a constant and L = carapace length). Parameters a (also called the condition factor K, known as the ponderal index) and k = 103 W/L3 were found to be of less significance and they were closely related to b. The theoretical value of b = 3 was found to be rarely met in crab fishery studies; rather much wider range was observed. It was, therefore, recommended that the assumed theoretical value of b = 3 would not be applied in all ichthiofauna surveys as it is generally commonly done by fishery scientists. The present analytical studies has opened a new approach to the elucidation of the biological significance of the allometric factor b, through the theories of tractal geometry (where b is seen as a fractal dimension equivalent and salutatory ontogeny where b is a critical point in the early life history of crabs. Introduction The early development of Brachyura is characterized by several distinct stages of growth during which rapid physiological and structural changes occur. Growth is by ecdysis, resulting in distinct “Stanza” which are separated by the presence of morphological changes or by sudden change in growth rate (Abby-kalio & Warner, 1984; Cott, 1929; Davidson & Marsdon, 1987; Huxley, 1932; Lee. 1992; Harcourt, 1978; Safran, 1992). It has been observed that length varies in relation to weight within a distinct stage of development (Safran, 1992). Ricker (1980) emphasized the necessity for obtaining fauna in a wide size range when a general length-weight relationship for a population is required. Most brachyuran surveys are focused on large adults and, thus, the growth parameters of length and weight are described only for adult individuals of the various species. Estimated parameters, when only adult specimens are used, can deviate enormously from their actual values. Based on the large number of juvenile crabs collected during a 3-year (1986–1988) field study of crab ecology in the Bonny estuary, the present investigation assesses the value of allometric factors connecting length and weight and re-evaluates the validity of the condition factor which is widely applied in ichthyological researches. This paper presents an analytical concept of the length-weight relationship in crab juveniles based on the fractal (Mandelbrot, 1984; Frontier, 1987) and saltatory ontogeny (Balon, 1984) theories. Materials and methods Different species of crab juveniles were caught during a nursery ecosystem survey along the Bonny-Port Harcourt estuarine system during 1986–1988 (Ewa-oboho,1988; 1993). Crab specimens were preserved in a 40% solution of buffered formalin and stored for later sorting, identification and analyses. Carapace width was measured to the nearest millimeter while the weight of each species was determined to the nearest gram. Analyses of stomach content were also carried out. A formulation of the length-weight relationship generally applicable to many species and body forms was introduced by Le Cren (1951). In most aquatic forms this relationship may be expressed by the formula: W = aL, where W = weight, L = Length (or carapace width (CW) in crabs). a is a constant (the condition factor, so called because it indicates the physiological condition of the studied fauna relative to a specific standard), and b is the allometric factor. This relationship can also be expressed as: Log W = log a + b log L (CW). In which case the weight-length data for crab of the same weight VS carapace width relationship will fall roughly on a straight line if plotted on a log – log paper (Weatherley, 1972). Since an individual crab cannot be measured and weighed in successive years of its life, this expression cannot be applied at its best. Rather, the value of b is determined by plotting the logarithm of length against the logarithm of weight for a large number of crabs of various sizes, the gradient of the fitted line is estimated as b (Ricker, 1980) and passes through the average point o of many points, with log CW and log W as co-ordinates, b = 6 log W/log CW, and log a as the origin co-ordinate. Parameters b and a are characteristics of the species within the study period (interval) when the cluster of points is rectilinear. Since the interval in juveniles is usually small and the mean point fixer the condition factor, a becomes a very critical parameter for fitting the allometric line and log a inversely proportional to allometric factor b (Fig. 1).