FLICKER RESPONSE CONTOURS FOR THE SPARROW,AND THE THEORY OF THE AVIAN PECTEN

The flicker contour for the house sparrow Passer domesticus is duplex, corresponding to the presence of both rods and cones in the retina. The presence of the pecten brings about changes in the "cone" part of the contour when the light-time in the flash cycle is varied. These changes are of the same sort as those we have already described for the visually simplex zebra finch, and for man provided with an artificial "pecten shadow." The changes are such as to greatly enhance flicker acuity for small dark-times (moving stripe technique). The form of the scotopic part of the duplex contour (also as in the case with man) gives no evidence that rod excitation is specifically influenced by the presence of the pecten. The changing integration of "rod" and "cone" effects as the light-time fraction is altered provides another means of testing the theory used for the analytical separation of the two components of the duplex flicker contour.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : VI. WAVE-LENGTH AND FLASH DURATION IN FLICKER

For spectral regions associated with violet, blue, green, and red the relation between mean critical flash intensity I_m for visual flicker and the flash frequency F is modified as already found with white light when the light time fraction t_L in the flash cycle is changed. For a square image 6.13° on a side, foveally fixated, the "rod" and "cone" contributions to the duplex contour are analyzed in the way already used for white. It is pointed out that several customary qualitative criteria for cone functioning do not necessarily give concordant results. The analysis shows that the three parameters of the probability summations giving the "rod" and "cone" curves are changed independently as a function of wave-length composition of the light, and of the light time fraction. The correlation of these changes, and of those found in the associated variability functions, can be understood in terms of differences in (1) the numbers of neural units potentially excitable and (2) in the numbers of elements of neural effect obtained from them. In a multivariate situation of this kind it is necessary to compare intensities of luminous flux required to activate half the total population of potentially available elements when this total size is held constant for the different conditions. The results of this comparison, for the filtered lights used, are discussed in relation to certain aspects of excitation vs. wave-length. The problem is a general one, arising where the effects produced as a function of a particular variable are concerned. In the distinction between (1) units excited and (2) the actions they produce may be found the clue for the curious fact that with certain wave-lengths the critical intensities are lower than for white. The extension of the observations to other parts of the retina may be expected to further this analysis.     

THEORY AND MEASUREMENT OF VISUAL MECHANISMS : VIII. THE FORM OF THE FLICKER CONTOUR

Flicker response curves (man) obtained with images formed entirely within the fovea are like those secured with lower animals having only one general class of retinal receptors. They are normal probability integrals (F vs. log I_m), and the properties of their parameters agree with those for visually simplex animals and for the "cone" portions of contours exhibiting visual duplexity. By several different procedures, involving experimental modifications of the "cone" curve, the "rod" part of the typical human duplex curve can be obtained free from overlapping by the extrapolated "cone" curve. It then has the probability integral form which the lower segment does not directly exhibit when combined with "cone" effects. These results are discussed with reference to the statistical nature of the fundamental form of the flicker contour and to the interpretation of duplex curves produced by the neural integration of two independently modifiable groups of sensory effects.     

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.     

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.     

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 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 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.     

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.     

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.     

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.     

CRITICAL ILLUMINATION FOR RESPONSE TO FLICKERED LIGHT,WITH DRAGONFLY LARVAE (ANAX), IN RELATION TO AREA OF EYE

Arthropods with large convex eyes provide curves of critical illumination for response as a function of flicker frequency (or of visual acuity) which depart from the probability integral type characteristically found for F – log I with vertebrates. By means of experiments with Anax nymphs in which various parts of the eye have been opaqued it is shown that the special shape of the flicker curve is due to the mechanical disadvantage of the periphery of the eye in the reception of light, which is overcome by higher intensities. It is not due to a fixed spatial pattern of intrinsic individual excitabilities of the ommatidia. Reduction of retinal area decreases F_max., and increases log I for F/F_max. = 50 per cent. The direct proportionality of I_m to P.E._1I is independent of area. Certain relations of these facts to the theory of response to flicker have been discussed.     

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 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.     

THE FLICKER RESPONSE CONTOUR FOR PHRYNOSOMA (HORNED LIZARD; CONE RETINA)

The lizard Phrynosoma, with purely cone retina, provides a simplex flicker response contour (log critical flash intensity as a function of flash frequency). It is well described as a normal probability integral (F - log I). The Phrynosoma curve differs markedly, in higher slope and in higher median intensity level, from that obtained under the same conditions for the turtle Pseudemys, also with entirely cone retina. Other comparisons having a bearing on the duplexity doctrine are discussed.     

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.     

ON THE VARIABILITY OF CRITICAL ILLUMINATION FOR FLICKER FUSION AND INTENSITY DISCRIMINATION

From the data of experiments with bees in which threshold response is employed as a means of recognizing visual discrimination between stripes of equal width alternately illuminated by intensities I ₁ and I ₂, it is shown that the detectable increment of intensity ΔI, where ΔI = I ₂ - I ₁, is directly proportional to σ_I2 (I ₁ being fixed). From tests of visual acuity, where I ₁ = 0 and the width of the stripes is varied, σ_I2 = kI ₂ + const.; here I ₂ = ΔI, and ΔI/I ₂ = 1. When the visual excitability of the bee is changed by dark adaptation, λI ≡ kΔI (= k'' σ_ΔI) = k'''' I + const. For the measurements of critical illumination at threshold response to flicker, σ_I2 (= σ_ΔI) = k I ₂ = k'' ΔI + const. The data for critical illumination producing threshold response to flicker in the sun-fish Lepomis show for the rods σ_I2 = K I ₂ for the cones σ_I2 = K''(I ₂ + const.). The data thus indicate that in all these experiments essentially the same visual function is being examined, and that the recognition of the production of a difference in effect by alternately illuminated stripes takes place in such a way that d (ΔI)/d (σ_I2) = const., and that ΔI is directly proportional to I (or "I ₂," depending on the nature of the experiment). It is pointed out that the curve for each of the cases considered can be gotten equally well if mean I or σ_I is plotted as a function of the independent variable involved in the experiment. Certain consequences of these and related facts are important for the treatment of the general problem of intensity discrimination.     

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.