Variations in tolerance through a size range of test organisms were quantitatively represented by the function.  
$${\rm R} = {\rm \alpha } + {\rm \beta log C/}{\rm W}^{\rm b} \eqno \lpar1\rpar$$

where R = % quantal response (in probits),

C = concentration of toxicant in the ambient environment,

W = weight of test organism, and,

b = an empirically determined coefficient of weight.

This function expresses the lethal response curves of different sizes of test organisms of three species of fish following exposure to certain discrete heavy metal solutions for 96 hours. A useful derivative of Eq. 1 is,  
$$\log {\rm M} = {\rm a} + {\rm b log W}$$

where M = LC 50

The application of these weight functions in aquatic bioassay studies is discussed.

The standard bioassay procedure in aquatic toxicology simulates the principle mode of toxicant uptake from the ambient environment by exposing test organisms to aqueous solutions of chemicals for specified periods. The alternative bioassay method involves the administration of toxicants by parenteral (e.g. intraperitoneal , intravenous) or enteral (e.g. oral) routes.

It is accepted procedure in the latter bioassay studies to use a dose proportional to the body weight of the test animal. The assumption for normalizing the dose by the weight of the individual is that the magnitude of response to a given dose will change proportionally with size. For the former type of bioassay, some investigators have concluded that size of the test organism does not influence tolerance parameters (Cairns 1958; Bastos 1954) - Other studies have demonstrated that the magnitude of response varies with size (Weiss and Botts 1957; Mount 1962; Burdick et al. 1955; Skidmore 1967). The problem of size as a modifying factor may be avoided by using test organisms of similar body weight (Doudoroff et al. 1951). For those bioassay studies in which size standardization is either impractical or impossible, a rationale is needed to quantify changes in response attributable to the differences in weight of test organisms.

This paper considers the application of a weight factor-tolerance function which quantitatively represents the change in the magnitude of response with increasing size of three species of fish exposed to certain heavy metals. The quantity of the weight function is determined empirically and its value appears unique for species and toxicant. The usefulness of the weight factor in bioassay studies is discussed.

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