THE FLICKER RESPONSE CONTOUR FOR THE CRAYFISH. I

The F - log I curve for threshold response to visual flicker has been determined for the crayfish Cambarus bartoni. As predicted on the basis of the higher curvature of the optic surface, the flicker response contour is more asymmetrical than for bee and dragonfly nymph under comparable conditions of temperature and light time fraction of flash cycle. The mechanical origin of this asymmetry is thus confirmed, and is further supported by the similar forms of the F - log I curves in bee, dragonfly larva, and crayfish in the lower portion of the curves (up to F = 70 per cent F_max.). The slope of the fundamental curve for crayfish, deduced by analysis of the data, is lower than for bee, dragonfly nymph, or Asellus. This signifies a wider spread of the effective distribution of elemental log I thresholds involvable in the response to flicker, and may be traced either to the greater curvature of the eye-surfaces or to their position upon movable pedicles. The results are therefore consistent with the statistical conception of the nature of effects recognizable as due to the activity of excitable elements.     

CRITICAL ILLUMINATION AND FLICKER FREQUENCY IN RELATED FISHES

Flicker response curves have been obtained at 21.5°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.     

CRITICAL INTENSITY AND FLASH DURATION FOR RESPONSE TO FLICKER: WITH ANAX LARVAE

Determinations of the flicker response curve (F – log I_m) with larvae of Anax junius (dragonfly) for various ratios t_L/t_D of light time to dark time in a flash cycle provide relations between t_L/t_D and the parameters of the probability integral fundamentally describing the F – log I function, including the variability of I. These relations are quantitatively of the same form as those found for this function in the sunfish, and are therefore non-specific. Their meaning for the theory of reaction to visual flicker is discussed. The asymmetry of the Anax curve, resulting from mechanical conditions affecting the reception of light by the arthropod eye, is (as predicted) reduced by relative lengthening of the fractional light time in a cycle.     

CRITICAL ILLUMINATION AND FLICKER FREQUENCY,AS A FUNCTION OF FLASH DURATION: FOR THE SUNFISH

From the relations between critical illumination in a flash (I_m) and the flash frequency (F) for response of the sunfish to visual flicker when the proportion of light time to dark time (t_L/t_D) in a flicker cycle is varied at one temperature (21.5°) the following results are obtained: At values of t_L/t_D between 1/9 and 9/1 the F - log I_m curves are progressively shifted toward higher intensities and lower F_max.. F_max. is a declining rectilinear function of the percentage of the flash cycle time occupied by light. The rod and the cone portions of the flicker curve are not shifted to the same extent. The cone portion and the rod region of the curve are each well described by a probability integral. In terms of F as 100 F/F_max. the standard deviation of the underlying frequency distribution of elemental contributions, summed to produce the effect proportional to F, is independent of t_L/t_D. The magnitude of log I_m at the inflection point (r''), however, increases rectilinearly with the percentage light time in the cycle. The proportionality between I_m and σ_II1 is independent of t_L/t_D. These effects are interpreted as consequences of the fact that the number of elements of excitation available for discrimination of flicker is increased by increasing the dark interval in a flash cycle. Decreasing the dark interval has therefore the same kind of effect as reducing the visual area, and not that produced by decreasing the temperature.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : IV. ANAX NYMPHS

At fixed flash frequency (_F = 20, _F = 55) and with constant light time fraction (50 per cent) in the flash cycle, the critical illumination I for response of Anax nymphs to visual flicker falls continuously as the temperature rises. The temperature characteristic µ for the measure of excitability (1/I) increases continuously with elevation of temperature. The form of the F - log I curve does not change except at quite high temperature (35.8°), and then only slightly (near F = 55); F_max. is not altered. The very unusual form of the 1/I curve as a function of temperature is quantitatively accounted for if two processes, with respectively µ = 19,200 and µ = 3,400, contribute independently and simultaneously to the control of the speed of the reaction governing the excitability; the velocities of these two processes are equal at 15.9°.     

THE FLICKER RESPONSE CONTOUR FOR THE ISOPOD ASELLUS

The flicker response contour for the isopod Asellus is a simple probability integral (F - log I) over the whole determinable range (F = 1 to 51). This contrasts with the "distorted" asymmetrical curves obtained with Apis, Anax, and other arthropods with large convex eyes. The explanation of the distortion as due to mechanical conditions affecting photoreception is therefore confirmed, as the structure of the Asellus eye does not make such a factor likely to be expected for this case. The Asellus curve agrees with the only other available complete and uncomplicated flicker response contour (from Pseudemys, turtle with rod-free retina), in showing the superiority of the probability integral formulation as compared with certain others which have been suggested. It is noted as a curious and probably important fact that the relative dispersion of the intensity thresholds (σ''_{log I}) for the elements implicated in determining the flicker contour appears to be identical in bee, dragon fly nymph, and isopod. Other relevant information derived from similar experiments with vertebrates shows that this quantity is specifically determined by the organization of the animal. The nature of the common feature of neural organization in three such diverse arthropods, as contrasted with the diversity seen within one class of vertebrates (e.g., teleosts), remains to be discovered.     

THE FLICKER RESPONSE CURVE FOR FUNDULUS

After Fundulus heteroclitus have been for some time in the laboratory, under conditions favorable for growth, and after habituation of the fishes to the simple routine manipulations of the observational procedure required, they are found to give reproducible values of the mean critical flash illumination (I_m) resulting in response to visual flicker. The measurements were made with equality of light time and dark time in the flash cycle, at 21.5°C. Log I_m as a function of flash frequency F has the same general form as that obtained with other fishes tested, and for vertebrates typically: the curve is a drawn-out S, with a second inflection at the low I end. In details, however, the curve is somewhat extreme. Its composite form is readily resolved into the two usual parts. Each of these expresses a contribution in which log I, as a function of F, is accurately expressed by taking F as the summation (integral) of a probability distribution of d log I, as for the flicker response contour of other animals. As critical intensity I increases, the contribution of rod elements gradually fades out; this decay also adheres to a probability integral. The rod contribution seen in the curve for Fundulus is larger, absolutely and relatively to that from the cones, than that found with a number of other vertebrates. The additive overlapping of the rod and cone effects therefore produces a comparatively extreme distortion of the resulting F-log I curve. The F-log I_m curve is shifted to lower intensities as result of previous exposure to supranormal temperatures. This effect is only very slowly reversible. The value of F _max. for each of the components of the duplex curve remains unaffected. The rod and cone segments are shifted to the same extent. The persisting increase of excitability thus fails to reveal any chemical or other differentiation of the excitability mechanism in the two groups of elements. Certain bearings of the data upon the theory of the flicker response contour are discussed, with reference to the measurements of variation of critical intensity and to the form of the F-log I curve. The quantitative properties of the data accord with the theory derived from earlier observations on other forms.     

CRITICAL ILLUMINATION AND CRITICAL FREQUENCY FOR RESPONSE TO FLICKERED LIGHT,IN DRAGONFLY LARVAE

Curves relating flicker frequency (F) to mean critical illumination (I_m) for threshold response to flickered light, with equal durations of light and no light intervals, and relating illumination (I) to mean critical flicker frequency (F_m) for the same response, have been obtained from homogeneous data based upon the reactions of dragonfly larvae (Anax junius). These curves exhibit the properties already described in the case of the fish Lepomis. The curve for F_m lies above the curve of I_m by an amount which, as a function of I, can be predicted from a knowledge either of the variation of I_m or of F_m. The law of the observable connection between F and I is properly expressed as a band, not as a simple curve. The variation of I_m (and of F_m) is not due to "experimental error," but is an expression of the variable character of the organism''s capacity to exhibit the reaction which is the basis of the measurements. As in other series of measurements, P.E. _I is a rectilinear function of I_m; P.E. _F passes through a maximum as F (or I) increases. The form of P.E. _F as a function of I can be predicted from the measurements of P.E. _I. It is pointed out that the equations which have been proposed for the interpretation of curves of critical flicker frequency as a function of intensity, based upon the balance of light adaptation and dark adaptation, have in fact the character of "population curves;" and that their contained constants do not have the properties requisite for the consistent application of the view that the shape of the F - I curve is governed by the steady state condition of adaptation. These curves can, however, be understood as resulting from the achievement of a certain level of difference between the average effect of a light flash and its average after effect during the dark interval.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : X. MODIFICATIONS OF THE FLICKER RESPONSE CONTOUR,AND THE SIGNIFICANCE OF THE AVIAN PECTEN

1. When there is projected on the retina (man, monocularly) the shadow of a grid which forms a visual field in several distinct pieces (not including the fovea in the present tests), the ordinary properties of the flicker recognition contour (F vs. log I) as a function of the light-time cycle fraction (t_L) can be markedly disturbed. In the present experiments flicker was produced by the rotation of a cylinder with opaque vertical stripes. In the absence of such a grid shadow the "cone" segments of the contours form a set in which F_max. and the abscissa of inflection are opposite but rectilinear functions of t_L, while the third parameter of the probability integral (σ''_{log I}) remains constant. This is the case also with diverse other animals tested. In the data with the grid, however, analysis shows that even for low values of t_L (up to 0.50) there occurs an enhancement of the production of elements of neural effect, so that F_max. rises rather than falls as ordinarily with increase of t_L, although σ''_{log I} stays constant and hence the total number of acting units is presumed not to change. This constitutes valid evidence for neural integration of effects due to the illumination of separated retinal patches. Beginning at t_L = 0.75, and at 0.90, the slope of the "cone" curve is sharply increased, and the maximum F is far above its position in the absence of the grid. The decrease of σ''_{log I} (the slope constant) signifies, in terms of other information, an increase in the number of acting cone units. The abscissa of inflection is also much lowered, relatively, whereas without the grid it increases as t_L is made larger. These effects correspond subjectively to the fact that at the end-point flicker is most pronounced, on the "cone" curve, along the edges of the grid shadow where contrast is particularly evident with the longer light-times. The "rod" portion of the F - log I contour is not specifically affected by the presence of the grid shadow. Its form is obtainable at t_L = 0.90 free from the influence of summating "cone" contributions, because then almost no overlapping occurs. Analysis shows that when overlapping does occur a certain number of rod units are inhibited by concurrent cone excitation, and that the mean contribution of elements of neural action from each of the non-inhibited units is also reduced to an extent depending on the degree of overlap. The isolated "rod" curve at t_L = 0.90 is quite accurately in the form of a probability integral. The data thus give a new experimental proof of the occurrence of two distinct but interlocking populations of visual effects, and experimentally justify the analytical procedures which have been used to separate them. 2. The changing form of the F - log I contour as a function of t_L, produced in man when the illuminated field is divided into parts by a shadow pattern, is normally found with the bird Taeniopygia castenotis (Gould), the zebra finch. The retina has elements of one general structural type (cones), and the F - log I contour is a simplex symmetrical probability integral. The eye of this bird has a large, complex, and darkly pigmented pecten, which casts a foliated shadow on the retina. The change in form of the F - log I curve occurs with t_L above 0,50, and at t_L = 0.90 is quite extreme. It is more pronounced than the one that is secured in the human data with the particular grid we have used, but there is no doubt that it could be mimicked completely by the use of other grids. The increase of flicker acuity due to the pecten shadow is considerable, when the dark spaces are brief relative to the light. The evidence thus confirms the suggestion (Menner) drawn from comparative natural history that the visual significance of the avian pecten might be to increase the sensory effect of small moving images. It is theoretically important that (as in the human experiment) this may be brought about by an actual decrease of effective retinal area illuminated. It is also significant theoretically that despite the presence of shadows of pecten or of grid, and of the sensory influences thus introduced, the probability integral formulation remains effective.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : V. XIPHOPHORUS,PLATYPOECILIUS, AND THEIR HYBRIDS

For the teleosts Xiphophorus montezuma, Platypoecilius maculatus, and their F ₁ hybrids the temperature characteristics (µ in Arrhenius'' equation) are the same for the shift of the low intensity and the high intensity segments of the respective and different flicker response contours (critical intensity I as a function of flash frequency F, with light time fraction constant, at 50 per cent). The value of µ is 12,500 calories or a very little less, over the range 12.5 to 36°. This shows that 1/I can be understood as a measure of excitability, with F fixed, and that the excitability is governed by the velocity of a chemical process common to both the classes of elements represented in the duplex performance curve (rods and cones). It is accordingly illegitimate to assume that the different shapes of the rod and cone branches of the curves are determined by differences in the chemical mechanisms of excitability. It is also forbidden to assume that the differing form constants for the homologous segments in the curves for two forms (X. and P.) are the reflections of a difference in the chemical factors of primary excitability. These differences are determined by statistical factors of the distribution of excitabilities among the elements implicated in the sensory effect vs. intensity function, and are independent of temperature and of the temperature characteristic. It must be concluded that the physicochemical nature of the excitatory process cannot be deduced from the shape of the performance contour. The form constants (σ''_{log I} and F_max.) for F vs. log I are specifically heritable in F ₁, although µ is here the same as for X. and P. In an intergeneric cross one cannot in general expect Mendelian simplicity of segregation in subsequent generations, and in the present case we find that F ₂ individuals are indistinguishable from F ₁, both as regards F vs. log I and as regards the variation of I within a group of 17 individuals. The result in F ₂ definitely shows, however, that certain specific statistical form constants for the F-log I contour are transmissible in inheritance. It is pointed out that there thus is provided an instance in which statistical (distribution) factors in performance characteristics involving the summating properties of assemblages of cellular units are heritable in a simple manner without the implication of detectable differences in chemical organization of the units involved. This has an important bearing upon the logic of the theory of the gene.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : II. SUNFISH

The curve connecting mean critical illumination (I_m) and flicker frequency (F) for response of the sunfish Lepomis (Enneacanthus gloriosus) to flicker is systematically displaced toward lower intensities by raising the temperature. The rod and cone portions of the curve are affected in a similar way, so that (until maximum F is approached) the shift is a nearly constant fraction of I_m for a given change of temperature. These relationships are precisely similar to those found in the larvae of the dragonfly Anax. The modifications of the variability functions are also completely analogous. The effects found are consistent with the view that response to flicker is basically a matter of discrimination between effect of flashes of light and their after effects,—a form of intensity discrimination. They are not consistent with the stationary state formulation of the shape of the flicker curve. An examination of the relationships between the cone portion and the rod portion of the curves for the sunfish suggests a basis for their separation, and provides an explanation for certain "anomalous" features of human flicker curves. It is pointed out how tests of this matter will be made.     

THE FLICKER RESPONSE CONTOURS FOR GENETICALLY RELATED FISHES. II

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 I_m) 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 F ₁ hybrids (H'''') of X. montezuma x P. variatus show dominance of the X. properties with respect to cone F_max. 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 F_max. 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.     

TEMPERATURE AND CRITICAL ILLUMINATION FOR REACTION TO FLICKERING LIGHT : I. ANAX LARVAE

The curve of mean critical illumination (I_m) for response to flicker as a function of flicker frequency (F) for the larvae of the dragonfly Anax junius is progressively shifted toward higher intensities the lower the temperature. The maximum flicker frequency (one half the cycle time of light and no light) and the maximum intensity with which it is associated are very little if at all affected by change of temperature. These facts are in agreement with the requirements of the conception that recognition of critical illumination for reaction to flicker involves and depends upon a kind of intensity discrimination, namely between the effects of flashes and the after effects of these flashes during the intervals of no light. The shift of the F-I_m curve with change of temperature is quite inconsistent with the stationary state conception of the determination of the shape of the curve. The dispersion (P.E. _II1) of the measurements of I ₁ is directly proportional to I_m, but the factor of proportionality is less at high and at low temperature than at an intermediate temperature; the scatter of the values of P.E. _II1 is also a function of the temperature. These facts can also be shown to be concordant with the intensity discrimination basis for marginal recognition of flicker.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : V. FLASH DURATION AND CRITICAL INTENSITY FOR RESPONSE TO FLICKER

The relation between flash duration and mean critical intensity (white light) for threshold recognition of visual flicker, as a function of flash frequency, was investigated by means of measurements at five values of the light-time fraction: 0.10, 0.25, 0.50, 0.75, 0.90, with flash frequencies of the interrupted beam ranging from 2 to 60 per second. A square area, 6.1 x 6.1°, centrally fixated) was viewed monocularly; the discriminometer used provides automatically an artificial pupil 1.8 mm. in diameter. Except for the slight day-to-day fluctuation in the magnitudes of the parameters, the data for the observer used are shown to form an essentially homogeneous group. As for other animals tested, the F - log I_m curve is enlarged and moved toward lower flash intensities as the light-time fraction is decreased. The high intensity segments of the duplex curves are fitted by normal probability integrals for which F _max. and the abscissa of inflection are rectilinear functions of t_L(t_L + t_D), with opposite slopes. The third parameter, (σ''_{log I}, is invariant. The low intensity segments are composites, their shapes determined by the summation of the lower part of the high intensity curve with an overlapping low intensity population of effects. Both the rising and the declining branches of this latter assemblage suffer competitive partial suppression by the effects in the high intensity population. The detailed analysis shows that these results are consistent with the theory of the central, rather than peripheral, location of the dynamically recognizable elements in the determination of flicker.     

THE FLICKER RESPONSE CONTOUR FOR THE FROG

The flicker response contour for the frog Rana pipiens exhibits the duplex character typical for most vertebrates. By comparison (under the same conditions of temperature, 21.5°, and light-time fraction, = 0.5), the low intensity section of the F - log I curve is the smallest thus far found. The cone portion of the curve is satisfactorily described by a probability integral. The rod part represents the addition of a small group of sensory effects upon the lower end of the cone curve, from which it can be analytically separated. The relation between the two groups of sensory effects permits certain tests of the rule according to which (in homogeneous data) I_m and σ_1I1 are in direct proportion.     

THE FLICKER RESPONSE CONTOUR FOR THE GECKO (ROD RETINA)

The flicker response contour for the gecko Sphaerodactylus (retina with only rods) agrees in all essential respects (intensity range, shape) with that for the turtle Pseudemys (cone retina), as determined under equivalent conditions with the same apparatus. With experimentally determined correction for the expansion of the iris at the very lowest intensities, the F - log I contour for the gecko is a simple probability integral. Its maximum F is lower than that for other animals; this means simply a smaller number of available sensory elements. The quantitative parallelism in the magnitudes of the intensities at the inflection of F - log I and the shape constants for rod and cone animals show that assumptions from comparative histological evidence concerning the properties of rods and cones in relation to visual performance may be quite misleading.     

REACTION TO VISUAL FLICKER IN THE NEWT TRITURUS

The flicker response curve for the newt Triturus viridescens (water phase) has much the same quantitative structure as that found with various fresh-water teleosts at the same temperature (21.5°). The variability of critical intensity and of critical flash frequency likewise follows the same rules. The cone portion of the F - log I curve is much more widely spread, however. This, and the rather low maximum to which the rod curve rises, produce a considerable overlapping of the two parts additively fused. In addition, and to an extent which differs in various individuals, there is apparent a slight departure from the probability integral form of the cone curve. Reasons are given for considering that this is possibly connected with the role of an additional (small) number of (perhaps temporary, or developmental) retinal elements in addition to the typical rods and cones.