Random temporal variation in selection intensities: One-locus two-allele model

Summary The paper formulates a one locus two allele diploid model influenced by temporal random selection intensities. The concept of stochastic local stability for equilibria states is formulated. Necessary and sufficient conditions are derived for the stochastic local stability of the fixation states for non-dominant and dominant traits. A general model, where a fixed polymorphic equilibrium is maintained is investigated. The complete local evolutionary picture is derived and some cases of global convergence are established.Supported in part by N. I. H. Grant GM 10452-09 and N. S. F. Grant 7507129.     

Effect of fast moving stimuli and saccadic eye movements on cell activity in visual areas V1 and V2 of behaving monkeys

Extracellular recordings were carried out in the visual cortex of behaving monkeys trained on a fixation/detection task, during which a target light was displayed stationary or suddenly moving on a tangent translucent screen. The responses of visual cortical cells to fast moving stimuli during steady fixation and those obtained during rapid eye movements (saccades) which moved their receptive field across a stationary stimulus, were studied. Areas V1 and V2 were explored. When tested with rapidly moving stimuli (500 deg/sec) during steady fixation, neurons in each area behaved in almost the same way. About one fourth of them were activated, the remainder showing either no response (little more than a half of them) or a reduction of the spontaneous firing rate. In both areas, some of the neurons activated during steady fixation did not respond or responded very weakly during eye motion at saccadic velocity (500 +/- 50 deg/sec). Neurons of this type, which we refer to as 'real motion' cells, could somehow contribute to the maintenance of visual stability during the execution of large eye movements.     

Influence of Retinal Image Shifts and Extra-Retinal Eye Movement Signals on Binocular Rivalry Alternations

Previous studies have indicated that saccadic eye movements correlate positively with perceptual alternations in binocular rivalry, presumably because the foveal image changes resulting from saccades, rather than the eye movement themselves, cause switches in awareness. Recently, however, we found evidence that retinal image shifts elicit so-called onset rivalry and not percept switches as such. These findings raise the interesting question whether onset rivalry may account for correlations between saccades and percept switches.We therefore studied binocular rivalry when subjects made eye movements across a visual stimulus and compared it with the rivalry in a ‘replay’ condition in which subjects maintained fixation while the same retinal displacements were reproduced by stimulus displacements on the screen. We used dichoptic random-dot motion stimuli viewed through a stereoscope, and measured eye and eyelid movements with scleral search-coils.Positive correlations between retinal image shifts and perceptual switches were observed for both saccades and stimulus jumps, but only for switches towards the subjects'' preferred eye at stimulus onset. A similar asymmetry was observed for blink-induced stimulus interruptions. Moreover, for saccades, amplitude appeared crucial as the positive correlation persisted for small stimulus jumps, but not for small saccades (amplitudes < 1°). These findings corroborate our tenet that saccades elicit a form of onset rivalry, and that rivalry is modulated by extra-retinal eye movement signals.     

Mathematical models of eye movements in reading: a possible role for autonomous saccades

 An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory – almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes. Received: 21 March 2000 / Accepted in revised form: 10 January 2001     

Both Lexical and Non-Lexical Characters Are Processed during Saccadic Eye Movements

On average our eyes make 3–5 saccadic movements per second when we read, although their neural mechanism is still unclear. It is generally thought that saccades help redirect the retinal fovea to specific characters and words but that actual discrimination of information only occurs during periods of fixation. Indeed, it has been proposed that there is active and selective suppression of information processing during saccades to avoid experience of blurring due to the high-speed movement. Here, using a paradigm where a string of either lexical (Chinese) or non-lexical (alphabetic) characters are triggered by saccadic eye movements, we show that subjects can discriminate both while making saccadic eye movement. Moreover, discrimination accuracy is significantly better for characters scanned during the saccadic movement to a fixation point than those not scanned beyond it. Our results showed that character information can be processed during the saccade, therefore saccades during reading not only function to redirect the fovea to fixate the next character or word but allow pre-processing of information from the ones adjacent to the fixation locations to help target the next most salient one. In this way saccades can not only promote continuity in reading words but also actively facilitate reading comprehension.     

Different programming modes of human saccadic eye movements as a function of stimulus eccentricity: Indications of a functional subdivision of the visual field

1. Voluntary saccadic eye movements were made toward flashes of light on the horizontal meridian, whose duration and distance from the point of fixation were varied; eye movements were measured using d.c.-electrooculography.—2. Targets within 10°–15° eccentricity are usually reached by one saccadic eye movement. When the eyes turn toward targets of more than 10°–15° eccentricity, the first saccadic eye movement falls short of the target by an angle usually not exceeding 10°. The presence of the image of the target off the fovea (visual error signal) subsequent to such an undershoot elicits, after a short interval, corrective saccades (usually one) which place the image of the target on the fovea. In the absence of a visual error signal, the probability of occurrence of corrective saccades is low, but it increases with greater target eccentricities. These observations suggest that there are different, eccentricity-dependent modes of programming saccadic eye movements.—3. Saccadic eye movements appear to be programmed in retinal coordinates. This conclusion is based on the observations that, irrespective of the initial position of the eyes in the orbit, a) there are different programming modes for eye movements to targets within and beyond 10°–15° from the fixation point, and b_ the maximum velocity of saccadic eye movements is always reached at 25° to 30° target eccentricity. —4. Distributions of latency and intersaccadic interval (ISI) are frequently multimodal, with a separation between modes of 30 to 40 msec. These observations suggest that saccadic eye movements are produced by mechanisms which, at a frequency of 30 Hz, process visual information. —5. Corrective saccades may occur after extremely short intervals (30 to 60 msec) regardless of whether or not a visual error signal is present; the eyes may not even come to a complete stop during these very short intersaccadic intervals. It is suggested that these corrective saccades are triggered by errors in the programming of the initial saccadic eye movements, and not by a visual error signal. —6. The exitence of different, eccentricity-dependent programming modes of saccadic eye movements, is further supported by anatomical, physiological, psychophysical, and neuropathological observations that suggest a dissociation of visual functions dependent on retinal eccentricity. Saccadic eye movements to targets more eccentric than 10°–15° appear to be executed by a mechanism involving the superior colliculus (perhaps independent of the visual cortex), whereas saccadic eye movements to less eccentric targets appear to depend on a mechanism involving the geniculo-cortical pathway (perhaps in collaboration with the superior colliculus).     

Attention governs action in the primate frontal eye field

While the motor and attentional roles of the frontal eye field (FEF) are well documented, the relationship between them is unknown. We exploited the known influence of visual motion on the apparent positions of targets, and measured how this illusion affects saccadic eye movements during FEF microstimulation. Without microstimulation, saccades to a moving grating are biased in the direction of motion, consistent with the apparent position illusion. Here we show that microstimulation of spatially aligned FEF representations increases the influence of this illusion on saccades. Rather than simply impose a fixed-vector signal, subthreshold stimulation directed saccades away from the FEF movement field, and instead more strongly in the direction of visual motion. These results demonstrate that the attentional effects of FEF stimulation govern visually guided saccades, and suggest that the two roles of the FEF work together to select both the features of a target and the appropriate movement to foveate it.     

Human visual search does not maximize the post-saccadic probability of identifying targets

Researchers have conjectured that eye movements during visual search are selected to minimize the number of saccades. The optimal Bayesian eye movement strategy minimizing saccades does not simply direct the eye to whichever location is judged most likely to contain the target but makes use of the entire retina as an information gathering device during each fixation. Here we show that human observers do not minimize the expected number of saccades in planning saccades in a simple visual search task composed of three tokens. In this task, the optimal eye movement strategy varied, depending on the spacing between tokens (in the first experiment) or the size of tokens (in the second experiment), and changed abruptly once the separation or size surpassed a critical value. None of our observers changed strategy as a function of separation or size. Human performance fell far short of ideal, both qualitatively and quantitatively.     

Studies of cyclic AMP action using mutant tissue culture cells

Summary S49 mouse lymphoma cell mutants, each with a specific defect in its ability to generate or respond to cyclic AMP, have been isolated. Analysis of the properties of these cells has begun to provide information on complex and significant biologic problems related to the cyclic AMP system. Presented in the Opening Symposium on Nutritional Factors and Differentiation at the 28th Annual Meeting of the Tissue Culture Association, New Orleans, Louisiana, June 6–9, 1977. The work was supported in part by National Science Foundation Grant BMS 75-06764 and National Institutes of Health Grants GM 16496 and GM 00001. P.C. is the recipient of National Institutes of Health Research Career Development Award GM 00308. P. A. I. is an Established Investigator of the American Heart Association.     

Open-loop simulations of the primate saccadic system using burst cell discharge from the superior colliculus

 Saccade-related burst neurons (SRBNs) in the monkey superior colliculus (SC) have been hypothesized to provide the brainstem saccadic burst generator with the dynamic error signal and the movement initiating trigger signal. To test this claim, we performed two sets of open-loop simulations on a burst generator model with the local feedback disconnected using experimentally obtained SRBN activity as both the driving and trigger signal inputs to the model. First, using neural data obtained from cells located near the middle of the rostral to caudal extent of the SC, the internal parameters of the model were optimized by means of a stochastic hill-climbing algorithm to produce an intermediate-sized saccade. The parameter values obtained from the optimization were then fixed and additional simulations were done using the experimental data from rostral collicular neurons (small saccades) and from more caudal neurons (large saccades); the model generated realistic saccades, matching both position and velocity profiles of real saccades to the centers of the movement fields of all these cells. Second, the model was driven by SRBN activity affiliated with interrupted saccades, the resumed eye movements observed following electrical stimulation of the omnipause region. Once again, the model produced eye movements that closely resembled the interrupted saccades produced by such simulations, but minor readjustment of parameters reflecting the weight of the projection of the trigger signal was required. Our study demonstrates that a model of the burst generator produces reasonably realistic saccades when driven with actual samples of SRBN discharges. Received: 25 October 1994/Accepted in revised form: 20 June 1995     

Comments on lack of interference in the four strand model of crossing over

Summary Assuming a four strand model and no chromatid interference, lack of chiasma interference is known to be equivalent to the assumption that the formation of chiasmata follows a Poisson process. We prove that lack of chiasma interference is also equivalent to the assumption that a random gamete shows recombination on any given interval of a chromosome independently of recombination on all disjoint intervals. Both assumptions are sufficient, but not necessary, for Haldane's formula relating recombination to map distance to be true, as we demonstrate by specific counterexamples. These issues are discussed in the context of the theory of stochastic point processes.Research supported by: University of California at Los Angeles, NIH Special Resources Grant RR-3, and USPHS Predoctoral Traineeship GM 7104.     

The effect of the visual stimulation of the leading and nonleading eye on the value of the saccadic latency period and on the peak latency of rapid presaccadic potentials]

Visual targets were presented monocularly to the leading and nonleading eyes. The complex of rapid positive and negative potentials was studied using the reverse summation from the onset of saccades. The latencies of saccades and peak latencies of the averaged presaccadic potentials were measured. The dependence of the saccade latencies and peak latencies of the complex of potentials on stimulation of the leading or nonleading eye and saccade direction was not simple and was largely determined by the individual profile of asymmetry. It is suggested that during stimulation of the leading eye the processes of attention fixation and switching as well as of the space visual processing are faster than during stimulation of the nonleading eye. Thus, the leading role of the right eye is reflected not only in fixation processes but also in movement anticipation.     

Abnormal Fixational Eye Movements in Amblyopia

Purpose

Fixational saccades shift the foveal image to counteract visual fading related to neural adaptation. Drifts are slow eye movements between two adjacent fixational saccades. We quantified fixational saccades and asked whether their changes could be attributed to pathologic drifts seen in amblyopia, one of the most common causes of blindness in childhood.

Methods

Thirty-six pediatric subjects with varying severity of amblyopia and eleven healthy age-matched controls held their gaze on a visual target. Eye movements were measured with high-resolution video-oculography during fellow eye-viewing and amblyopic eye-viewing conditions. Fixational saccades and drifts were analyzed in the amblyopic and fellow eye and compared with controls.

Results

We found an increase in the amplitude with decreased frequency of fixational saccades in children with amblyopia. These alterations in fixational eye movements correlated with the severity of their amblyopia. There was also an increase in eye position variance during drifts in amblyopes. There was no correlation between the eye position variance or the eye velocity during ocular drifts and the amplitude of subsequent fixational saccade. Our findings suggest that abnormalities in fixational saccades in amblyopia are independent of the ocular drift.

Discussion

This investigation of amblyopia in pediatric age group quantitatively characterizes the fixation instability. Impaired properties of fixational saccades could be the consequence of abnormal processing and reorganization of the visual system in amblyopia. Paucity in the visual feedback during amblyopic eye-viewing condition can attribute to the increased eye position variance and drift velocity.     

Study of the relationship between eye movements and the geometry of fovea

The objective of this research was to compare the features of the shape of the foveolar area with the characteristics of eye movements in reading. To measure the size of the fovea, we used the method of optical coherence tomography of the retina. Based on this method, the diameter of the upper part of fovea (fovea diameter) and fovea bottom (foveola diameter) were determined. We found a negative correlation between the fovea diameter and fixation duration and positive correlations at the level of tendency between the foveola diameter and the number of saccades performed and between the foveola diameter and the number of characters captured by eye per fixation.     

Dyslexic children are confronted with unstable binocular fixation while reading

Reading requires three-dimensional motor control: saccades bring the eyes from left to right, fixating word after word; and oblique saccades bring the eyes to the next line of the text. The angle of vergence of the two optic axes should be adjusted to the depth of the book or screen and--most importantly--should be maintained in a sustained manner during saccades and fixations. Maintenance of vergence is important as it is a prerequisite for a single clear image of each word to be projected onto the fovea of the eyes. Deficits in the binocular control of saccades and of vergence in dyslexics have been reported previously but only for tasks using single targets. This study examines saccades and vergence control during real text reading. Thirteen dyslexic and seven non-dyslexic children read the French text "L'Allouette" in two viewing distances (40 cm vs. 100 cm), while binocular eye movements were measured with the Chronos Eye-tracking system. We found that the binocular yoking of reading saccades was poor in dyslexic children (relative to non-dyslexics) resulting in vergence errors; their disconjugate drift during fixations was not correlated with the disconjugacy during their saccades, causing considerable variability of vergence angle from fixation to fixation. Due to such poor oculomotor adjustments during reading, the overall fixation disparity was larger for dyslexic children, putting larger demand on their sensory fusion processes. Moreover, for dyslexics the standard deviation of fixation disparity was larger particularly when reading at near distance. We conclude that besides documented phoneme processing disorders, visual/ocular motor imperfections may exist in dyslexics that lead to fixation instability and thus, to instability of the letters or words during reading; such instability may perturb fusional processes and might--in part--complicate letter/word identification.     

The effect of illumination on involuntary eye saccades]

A study was made of the influence of sudden illumination micromovements of the eyes. Sudden contour illumination of the eye by a 15 degrees field with a crossing in the centre and a brightness of 100 nit reduced the amplitude of involuntary saccades and their frequency. The effect was particularly distinct with preliminary recording of the eye micromovement in complete darkness without a fixation point. In the case of fixation of a stationary point with one eye and of illumination of the other, the effect was also manifest, but it was less pronounced. During illumination of the eye with diffused light (through spectacles with frosted glasses) the effect of diminution of the saccade amplitude was smaller, though the brightness remained unchanged. A decrease in the saccade amplitude was practically not observed when the point was fixed at diffuse illumination. It has also been shown that with greater brightness of the fixation point (0.3; 25; 92 and 1000 nit), the amplitude and frequency of involuntary saccades diminish. The results attest that in choosing the conditions of work of the saccadic system two factors should be taken into consideration: the presence of the contours of the visible object and its brightness, the latter by itself having a lesser effect than the former.     

The three-loop model: a neural network for the generation of saccadic reaction times

This paper presents a computer simulation of the three-loop model for the temporal aspects of the generation of visually guided saccadic eye movements. The intention is to reproduce complex experimental reaction time distributions by a simple neural network. The operating elements are artificial but realistic neurones. Four modules are constructed, each consisting of 16 neural elements. Within each module, the elements are connected in an all-to-all manner. The modules are working parallel and serial according to the anatomically and physiologically identified visuomotor pathways including the superior colliculus, the frontal eye fields, and the parietal cortex. Two transient-sustained input lines drive the network: one represents the visual activity produced by the onset of the saccade target, the other represents a central activity controlling the preparation of saccades, e.g. the end of active fixation. The model works completely deterministically; its stochastic output is a consequence of the stochastic properties of the input only. Simulations show how multimodal distributions of saccadic reaction times are produced as a natural consequence of the model structure. The gap effect on saccadic reaction times is correctly produced by the model: depending only on the gap duration (all model parameters unchanged) express, fast-regular, and slow-regular saccades are obtained in different numbers. In agreement with the experiments, bi- or trimodal distributions are produced only for medium gap durations (around 200 ms), while for shorter or longer gaps the express mode disappears and the distributions turn bi- or even unimodal. The effect of varying the strength of the transient-sustained components and the ongoing activity driving the hierarchically highest module are considered to account for the interindividual variability of the latency distributions obtained from different subjects, effects of different instructions to the same subject, and the observation of express makers (subjects who produce exclusively express saccades). How the model can be extended to describe the spatial aspects of the saccade system will be discussed as well as the effects of training and/or rapid adaptation to experimental conditions.     

Distinct control of initiation and metrics of memory-guided saccades and vergence by the FEF: a TMS study

Background

The initiation of memory guided saccades is known to be controlled by the frontal eye field (FEF). Recent physiological studies showed the existence of an area close to FEF that controls also vergence initiation and execution. This study is to explore the effect of transcranial magnetic simulation (TMS) over FEF on the control of memory-guided saccade-vergence eye movements.

Methodology/Principal Findings

Subjects had to make an eye movement in dark towards a target flashed 1 sec earlier (memory delay); the location of the target relative to fixation point was such as to require either a vergence along the median plane, or a saccade, or a saccade with vergence; trials were interleaved. Single pulse TMS was applied on the left or right FEF; it was delivered at 100 ms after the end of memory delay, i.e. extinction of fixation LED that was the “go” signal. Twelve healthy subjects participated in the study. TMS of left or right FEF prolonged the latency of all types of eye movements; the increase varied from 21 to 56 ms and was particularly strong for the divergence movements. This indicates that FEF is involved in the initiation of all types of memory guided movement in the 3D space. TMS of the FEF also altered the accuracy but only for leftward saccades combined with either convergence or divergence; intrasaccadic vergence also increased after TMS of the FEF.

Conclusions/Significance

The results suggest anisotropy in the quality of space memory and are discussed in the context of other known perceptual motor anisotropies.     

Some stochastic features of bacterial constant growth apparatus

Stochastic models for bacterial constant growth apparatus such as the chemostat are posed and studied. Approximations are given for the mean and variance of the size of the bacterial population when the population is in steady state. Procedures for stimulating a chemostat are developed and the approximate moments are compared with simulated values. The distribution is derived for the waiting time until the occurrence of a population change-over to a faster growing strain. Research supported by National Institutes of Health Grant 5-R01-GM21214.     

Isozyme variability in species of the genus Drosophila. I. A multiple allelic isozyme system in Drosophila busckii: Inheritance and general considerations

Starch gel electrophoretic analysis of a triallelic leucine aminopeptidase polymorphism in a laboratory population of Drosophila busckii is described. The three alleles involved are expressed without dominance. A series of single-pair matings revealed an excess of heterozygous types in most segregating families, suggesting selection against the homozygous genotypes. A few cases of heterogeneity among progeny extracted from a single family were the result of matings that produced Mendelian ratios. These few cases had no clear genetic explanation, but there is a suggestion of two isoalleles for the electrophoretically intermediate enzyme.The research reported here was begun at the University of Hawaii and completed at the University of Texas and was supported (in part) by Public Health Service Research Grant No. GM 11609 to W. S. Stone and M. R. Wheeler and by Training Grant No. 2 T1-GM-337-06 and GM 00337-07 to R. P. Wagner et al., from the National Institutes of Health.