Journal of Fish Biology (1996) 49, 277–286 A statistical power analysis of the ‘ internal reference ’ technique for comparing growth and growth depensation of tilapia strains Z. U. B*, R. W. D†  A. L. A* *SEAFDEC Aquaculture Department, Binangonan Freshwater Station, Binangonan, Rizal, Philippines and †Department of Biology, Dalhousie University, Halifax, Nova Scotia, B3H 4J1, Canada (Received 19 May 1994, Accepted 8 December 1995) Experiments were conducted to compare the growth and growth compensation of three strains of juvenile Oreochromis niloticus. Ten full sib families (10 replicates) per strain were split and grown under crowded and uncrowded conditions for 3 weeks (the treatment). Both treatments were then grown an additional 12 weeks under less crowded conditions (the compensation). Standard length measurements were made at the end of crowding and the end of compensation. Each replicate included a size-matched control population of a fourth (red) reference strain. ANCOVA with the reference strain used as a cofactor revealed significant strain effects on specific growth throughout the experiment. The reference strain removed most of the random among-replicate error variance as shown by an increase of r 2 from 0·06 to 0·91 when it was included in the statistical models. If the reference fish had not been used, approximately 450 replicate families would have been needed to achieve the sensitivity of the present experiment (a difference of 7% among strains significant at P=0·05). We conclude that the CLSU strain grows significantly more slowly than the Israel and NIFI strains under the experimental conditions, that the crowding effect was essentially eliminated after 12 weeks of compensation, and that the reference strain greatly improved the resolution of the strain-testing experiment.  1996 The Fisheries Society of the British Isles Key words: genetic; growth; compensation; depensation; strain; tilapia; Oreochromis. INTRODUCTION In fish populations, social interaction is known to affect individual growth rates, resulting in size–frequency distributions with large variances (Brown, 1946; Allee et al., 1948; Magnuson, 1962; Yamagishi, 1962; Purdom, 1974; Doyle & Talbot, 1986a; Davis & Olla, 1987). Magnuson (1962) suggested that competition for a limited food supply could give rise to growth depensation. However, growth depensation occurs even when food is not a limiting factor (Yamagishi et al., 1974; Li & Brocksen, 1977; Jobling, 1985). Physical interactions and agonistic encounters are believed to induce hierarchy formation leading to growth depensation. However, visual and chemical contact between conspecifics are hypothesized to affect growth pattern and development (Henderson-Arzapalo et al., 1980; Liley, 1982). Rearing space is usually limited in hatchery facilities and hatchery fish are often maintained in high population densities in small confined units. Severe crowding and confinement in small units might have adverse influence on the growth pattern and development of normal social behaviour. 277 0022–1112/96/080277+10 $18.00/0  1996 The Fisheries Society of the British Isles