title: CRITICAL ILLUMINATION AND FLICKER FREQUENCY IN RELATED FISHES.
abstract: Flicker response curves have been obtained at 21.5 degrees C. for three genera of fresh water teleosts: Enneacanthus (sunfish), Xiphophorus (swordtail), Platypoecilius (Platy), by the determination of mean critical intensities for response at fixed flicker frequencies, and for a certain homogeneous group of backcross hybrids of swordtail x Platy (Black Helleri). The curves exhibit marked differences in form and proportions. The same type of analysis is applicable to each, however. A low intensity rod-governed section has added to it a more extensive cone portion. Each part is accurately described by the equation F = F(max.)/(1 + e(-p log(-p logI/I(i) ) )), where F = flicker frequency, I = associated mean critical intensity, and I(i) is the intensity at the inflection point of the sigmoid curve relating F to log I. There is no correlation between quantitative features of the rod and cone portions. Threshold intensities, p, I(i), and F(max.) are separately and independently determined. The hybrid Black Helleri show quantitative agreement with the Xiphophorus parental stock in the values of p for rods and cones, and in the cone F(max.); the rod F(max.) is very similar to that for the Platy stock; the general level of effective intensities is rather like that of the Platy form. This provides, among other things, a new kind of support for the duplicity doctrine. Various races of Platypoecilius maculatus, and P. variatus, give closely agreeing values of I(m) at different flicker frequencies; and two species of sunfish also agree. The effect of cross-breeding is thus not a superficial thing. It indicates the possibility of further genetic investigation. The variability of the critical intensity for response to flicker follows the rules previously found to hold for other forms. The variation is the expression of a property of the tested organism. It is shown that, on the assumption of a frequency distribution of receptor element thresholds as a function of log I, with fluctuation in the excitabilities of the marginally excited elements, it is to be expected that the dispersion of critical flicker frequencies in repeated measurements will pass through a maximum as log I is increased, whereas the dispersion of critical intensities will be proportional to I(m); and that the proportionality factor in the case of different organisms bears no relation to the form or position of the respective curves relating mean critical intensity to flicker frequency. These deductions agree with the experimental findings.
authors.affiliation: Biological Laboratories, Harvard University, Cambridge.
authors.forename: W J
authors.initials: WJ
authors.lastname: Crozier
authors.forename: E
authors.initials: E
authors.lastname: Wolf
authors.forename: G
authors.initials: G
authors.lastname: Zerrahn-Wolf