The flicker response contour has been determined for several species and types of the teleosts Xiphophorus (X.) and Platypoecilius (P.) under the same conditions. The curve (F vs. log Im) is the same for representatives of each generic type, but is different for the two genera. Its duplex nature is analyzable in each instance by application of the probability integral equation to the rod and cone constituent parts. The parameters of this function provide rational measures of invariant properties of the curves, which have specific values according to the genetic constitution of the animal. The F1 hybrids (H'') of X. montezuma x P. variatus show dominance of the X. properties with respect to cone Fmax. and σ' log I, but an intermediate value of the abscissa of inflection (τ'). The rod segment shows dominance of σ' log I from P., but an intermediate value of Fmax. and of τ'. The composite flicker curve involves the operation of two distinct assemblages of excitable elements, differing quantitatively but not qualitatively in physicochemical organization, probably only secondarily related to the histological differentiation of rods and cones because almost certainly of central nervous locus, but following different rules in hereditary determination, and therefore necessarily different in physical organization. The interpretation of the diverse behavior of the three parameters of the probability summation is discussed, particularly in relation to the physical significance of these parameters as revealed by their quantitative relations to temperature, retinal area, and light time fraction in the flash cycle, and to their interrelations in producing the decline of rod effects at higher intensities.
It is stressed that in general the properties of the parameters of a chosen interpretive analytical function must be shown experimentally to possess the physical properties implied by the equation selected before the equation can be regarded as describing those invariant properties of the organic system concerned upon which alone can deduction of the nature of the system proceed. The importance of genetic procedures in furthering demonstration that the biological performance considered in any particular case exhibits constitutionally invariant features provides a potentially powerful instrument in such rational analysis.