Statistical Interrelation of Length, Growth, and Scale Circulus Spacing: Appraisal of a Growth Rate Estimator for Fish

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Abstract
Biological and statistical properties of spacing of the marginal circuli of scales (CIRC) were examined in an experimental population of tilapia (Oreochromis mossambicus/hornorum) hybrids. Biological, or "causal," interrelationships of body length, growth, and CIRC were analysed by maximum likelihood solution of a simultaneous equation model involving the three variables. Spacing varies directly with growth rate and inversely with fish length, and growth varies inversely with length. Consequently, spacing is relatively constant along the radial axis of the scale except where variation in ration level or other facotrs varies the rate of growth as a function of length. The correlation of CIRC with current growth rate in populations of mixed parentage, sizes, and ages is sufficiently high (r = 0.65-0.71) to render it a useful growth estimator in aquaculture and natural situations where ages are unknown and sequential size measurements are difficult to obtain. Statistical and procedural conditions for maximizing the utility of the growth estimator in several applications are examined: (a) comparison of individual growth rates within a population, (b) comparison of mean growth of populations in different environments, (c) indirect selection for growth in aquaculture genetic programs, and (d) response of growth to exogenous variables such as parasite load, behaviour, and microhabitat.

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