A Model of Phototaxis and Its Evaluation With Anuran Amphibians
Authors: Hailman Jack P. , Jaeger Robert G. 
Published: April 2008

Abstract
I. We propose a model of phototaxis based on the brightness-intensity function of the eye. Brightness (ψ) is a positive, monotonic function of the physical intensity (I). Electroretinographic studies of the anuran eye show brightness to be a sigmoid curve with intensity (measured logarithmically) - rather than obeying the WEBER-FECHNER Law or STEVENS' Power Law. Brightness-discrimination is best at the inflection-point of the curve (where d2/ψI2 = o). 2. In our model the inflection-point determines the optimum ambient illumination (O.A.I.) for the animal. If ambient illumination is greater than the O.A.L, the animal is photonegative; if less than the O.A.L, the same animal is photopositive. When behaving photopositively, anuran amphibians show a blue color-preference, and when behaving photonegatively show a U-shaged spectral response, which may not involve color vision. When the ambient intensity is at the O.A.L, the animal shows a random response to spectral stimuli. 3. Four factors besides phototactic movements help the eye to maintain its best operating range for brightness-discrimination : (a) visual duplexity, or possession of different kinds of photoreceptor cells with different operating ranges; (b) pupillary responses, which control the amount of light falling on the retina; (c) migration of the pigment-epithelium, which controls the amount of light striking the individual photoreceptor cells; and (d) dark- and light-adaptation of receptor cells, which increase sensitivity in the dark and decrease it in the light. 4. Nine new experiments tested predictions of the effects of stimulus-intensity on phototactic preferences to intensity. Eight sets of results were consistent with the model. The exception was later shown to be due to two factors of uncontrolled variables. 5. Seven new experiments tested predictions of the effects of stimulus-intensity on phototactic preferences to spectral stimuli. All seven sets of results were consistent with the model. 6. Five new experiments and four previously reported experiments tested predictions of the effects of adaptational state on phototactic preferences to intensity. All nine sets of results were consistent with the model. 7. Five new experiments and four previously reported experiments tested predictions of the effects of adaptational state on the phototactic preferences to spectral stimuli. All nine sets of results were consistent with the model. 8. The model shows that species are not classifiable as "photopositive" or "photonegative" because every species shows both kinds of phototactic behavior. The model suggests that the physiological mechanisms for response to intensity and spectral stimuli are intimately related. Furthermore, the model interprets species-differences as due primarily to the intensity of the O.A.L, a set-point that could be under genetic control. We suggest that genetic experiments on the phototaxis of Drosophila would yield higher "heritability" scores if the intensity of the stimuli and the state of the animal's adaptation were brought under experimental control.