Subitizing endures in sequential rather than simultaneous comparison tasks

Subitizing is the ability to appraise a number of small quantities (up to four) rapidly and precisely. This system, however, can be impaired by distractors presented along with targets to be enumerated. To better understand whether this limitation arises in perceptual circuits or in the response selection stage, we investigated whether subitizing can endure in simultaneous comparison tasks. Participants were asked to compare the number of dots in two sets on the left and right sides of the screen, presented either simultaneously or sequentially. For comparing within the numerosity range (6-32 dots), both the error rate and reaction time increased steadily as the ratio between the two numbers compared approached "1." Namely, a phenomenon labeled the ratio effect was revealed. For comparison with small numbers (<5), the sequential comparison task was errorless despite the ratio, suggesting the feature of subitizing. Individual efficiency (measured by the inverse efficiency score [IES]) did not correlate between number ranges in sequential comparison, suggesting that distinct mechanisms were involved. However, we found that in simultaneous tasks, error rate and efficiency showed an increase as the ratios of the two numbers compared approached "1." This is similar to the ratio effect revealed in the comparison for moderate numbers. Individual efficiency within these two ranges correlated, indicating that the enumeration within these two ranges was based on a single mechanism. These results suggest that subitizing cannot process sets in parallel, and numerosity takes the job whenever subitizing fails.

A critical review of risk-sensitive foraging

Foraging is risk sensitive if choices depend on the variability of returns from the options as well as their mean return. Risk-sensitive foraging is important in behavioural ecology, psychology and neurophysiology. It has been explained both in terms of mechanisms and in terms of evolutionary advantage. We provide a critical review, evaluating both mechanistic and evolutionary accounts. Some derivations of risk sensitivity from mechanistic models based on psychophysics are not convincing because they depend on an inappropriate use of Jensen's inequality. Attempts have been made to link risk sensitivity to the ecology of a species, but again these are not convincing. The field of risk-sensitive foraging has provided a focus for theoretical and empirical work and has yielded important insights, but we lack a simple and empirically defendable general account of it in either mechanistic or evolutionary terms. However, empirical analysis of choice sequences under theoretically motivated experimental designs and environmental settings appears a promising avenue for mapping the scope and relative merits of existing theories. Simply put, the devil is in the sequence.

Visual complexity of egg patterns predicts egg rejection according to Weber's law

Visual complexity is ubiquitous in nature. Drivers of complexity include selection in coevolutionary arms races between antagonists. However, the causes and consequences of biological complexity and its perception are largely understudied, partly because complexity is difficult to quantify. Here, we address this by studying egg pattern complexity and its perception in hosts (tawny-flanked prinia Prinia subflava), which visually recognize and reject mimetic eggs of their virulent brood parasite (cuckoo finch Anomalospiza imberbis). Using field data and an optimization algorithm, we compute a complexity metric which predicts rejection of experimentally placed conspecific eggs in prinia nests. Real cuckoo finch eggs exhibit significantly lower pattern complexity than prinia eggs, suggesting that high complexity benefits hosts because it distinguishes host eggs from parasitic eggs. We show that prinias perceive complexity differences according to Weber's law of proportional processing (i.e. relative, rather than absolute, differences between stimuli are processed in discrimination, such that two eggs with simple patterns are more easily discriminable than two with complex patterns). This may influence coevolutionary trajectories of hosts and parasites. The new methods presented for quantifying complexity and its perception can help us to understand selection pressures driving the evolution of complexity and its consequences for species interactions.

Prior Expectations in Visual Speed Perception Predict Encoding Characteristics of Neurons in Area MT

Bayesian inference provides an elegant theoretical framework for understanding the characteristic biases and discrimination thresholds in visual speed perception. However, the framework is difficult to validate because of its flexibility and the fact that suitable constraints on the structure of the sensory uncertainty have been missing. Here, we demonstrate that a Bayesian observer model constrained by efficient coding not only well explains human visual speed perception but also provides an accurate quantitative account of the tuning characteristics of neurons known for representing visual speed. Specifically, we found that the population coding accuracy for visual speed in area MT ("neural prior") is precisely predicted by the power-law, slow-speed prior extracted from fitting the Bayesian observer model to psychophysical data ("behavioral prior") to the point that the two priors are indistinguishable in a cross-validation model comparison. Our results demonstrate a quantitative validation of the Bayesian observer model constrained by efficient coding at both the behavioral and neural levels.SIGNIFICANCE STATEMENT Statistical regularities of the environment play an important role in shaping both neural representations and perceptual behavior. Most previous work addressed these two aspects independently. Here we present a quantitative validation of a theoretical framework that makes joint predictions for neural coding and behavior, based on the assumption that neural representations of sensory information are efficient but also optimally used in generating a percept. Specifically, we demonstrate that the neural tuning characteristics for visual speed in brain area MT are precisely predicted by the statistical prior expectations extracted from psychophysical data. As such, our results provide a normative link between perceptual behavior and the neural representation of sensory information in the brain.

Precision in grasping: Consistent with Weber's law, but constrained by "safety margins"

Whether the visuomotor coding of size in grasping obeys Weber's law is currently debated. Following up on previous work from our laboratory, here we investigated the precision associated with the maximum in-flight index-thumb aperture (MGA) in grasping small-to-medium sized objects. We report three main findings. First, grasp preparation was longer with 5 mm objects and became increasingly faster as object size increased from 10 to 20-40 mm. Second, MGA variable errors increased as sizes increased from 5 to 10-20 mm, whereas they decreased as size reached 40 mm. Third, MGA distributions were symmetrical with 5 mm objects, but became increasingly right-skewed as size increased. These results, as well as a re-analysis of previous findings, suggest that the precision of visuomotor representations varies as a function of size, consistent with the key principle underlying Weber's law. However, a fundamental constraint on precision grips (the MGA must always exceed physical size) changes the skew of the distribution and reduces the variability of MGAs as size increases from very small to medium.

Beyond the classic sensory systems: Characteristics of the sense of time of harbor seals (Phoca vitulina) assessed in a visual temporal discrimination and a bisection task

Beyond the classic sensory systems, the sense of time is most likely involved from foraging to navigation. As a prerequisite for assessing the role time is playing in different behavioral contexts, we further characterized the sense of time of a harbor seal in this study. Supra-second time intervals were presented to the seal in a temporal discrimination and a temporal bisection task. During temporal discrimination, the seal needed to discriminate between a standard time interval (STI) and a longer comparison interval. In the bisection task, the seal learnt to discriminate two STIs. Subsequently, it indicated its subjective perception of test time intervals as resembling either the short or long STI more. The seal, although unexperienced regarding timing experiments, learnt both tasks fast. Depending on task, time interval or duration ratio, it achieved a high temporal sensitivity with Weber fractions ranging from 0.11 to 0.26. In the bisection task, the prerequisites for the Scalar Expectancy Theory including a constant Weber fraction, the bisection point lying close to the geometric mean of the STIs, and no significant influence of the STI pair condition on the probability of a long response were met for STIs with a ratio of 1:2, but not with a ratio of 1:4. In conclusion, the harbor seal's sense of time allows precise and complex judgments of time intervals. Cross-species comparisons suggest that principles commonly found to govern timing performance can also be discerned in harbor seals.

Perception in autism does not adhere to Weber's law

Perceptual atypicalities are a widely acknowledged but poorly understood feature of autism. We demonstrate here a striking violation of one of the most adaptive psychophysical computations - Weber's law - in high-functioning individuals with autism. JNDs based on the best-fitting psychometric functions were measured for size visual judgments (Exp. 1), weight haptic discrimination (Exp. 2), and illusive perception of weight (brightness-weight illusion; Exp. 3). Results for the typically developed group confirmed Weber's law, demonstrating a linear increase in JNDs with intensity, resulting in constant fractions across intensities. The results for the ASD, in contrast, showed no scaling of JNDs with intensity; instead, fractions decreased linearly with intensity. In striking contrast to its consistency in typical perception, Weber's law does not hold for visual and haptic perception in autism. These robust modulations in psychophysical computations, demonstrated for different domains of perception, suggest a modality-independent, low-level mechanism driving altered perception in autism.

A Simplified Model of Communication Between Time Cells: Accounting for the Linearly Increasing Timing Imprecision

Many organisms can time intervals flexibly on average with high accuracy but substantial variability between the trials. One of the core psychophysical features of interval timing functions relates to the signatures of this timing variability; for a given individual, the standard deviation of timed responses/time estimates is nearly proportional to their central tendency (scalar property). Many studies have aimed at elucidating the neural basis of interval timing based on the neurocomputational principles in a fashion that would explain the scalar property. Recent experimental evidence shows that there is indeed a specialized neural system for timekeeping. This system, referred to as the “time cells,” is composed of a group of neurons that fire sequentially as a function of elapsed time. Importantly, the time interval between consecutively firing time cell ensembles has been shown to increase with more elapsed time. However, when the subjective time is calculated by adding the distributions of time intervals between these sequentially firing time cell ensembles, the standard deviation would be compressed by the square root function. In light of this information the question becomes, “How should the signaling between the sequentially firing time cell ensembles be for the resulting variability to increase linearly with time as required by the scalar property?” We developed a simplified model of time cells that offers a mechanism for the synaptic communication of the sequentially firing neurons to address this ubiquitous property of interval timing. The model is composed of a single layer of time cells formulated in the form of integrate-and-fire neurons with feed-forward excitatory connections. The resulting behavior is simple neural wave activity. When this model is simulated with noisy conductances, the standard deviation of the time cell spike times increases proportionally to the mean of the spike-times. We demonstrate that this statistical property of the model outcomes is robustly observed even when the values of the key model parameters are varied.

Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects

HIGHLIGHTS

We test whether symbolic number comparison is handled by an analog noisy system.

Analog system model has systematic biases in describing symbolic number comparison.

This suggests that symbolic and non-symbolic numbers are processed by different systems.

Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog Number System (ANS) working according to Weber's law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and non-symbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times, and diffusion model drift rates were systematically analyzed in both non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

Tactile-Based Pantomime Grasping: Knowledge of Results is Not Enough to Support an Absolute Calibration

Tactile-based pantomime-grasping requires that a performer use their right hand to 'grasp' a target previously held in the palm of their opposite hand - a task examining how mechanoreceptive (i.e., tactile) feedback informs the motor system about an object property (i.e., size). Here, we contrasted pantomime-grasps performed with (H+) and without (H-) haptic feedback (i.e., thumb and forefinger position information derived from the grasping hand touching the object) with a condition providing visual KR (VKR) related to absolute target object size. Just-noticeable-difference (JND) scores were computed to determine whether responses adhered to - or violated - Weber's law. JNDs for H+ trials violated the law, whereas H- and VKR trials adhered to the law. Accordingly, results demonstrate that haptic feedback - and not KR - supports an absolute tactile-haptic calibration.

The statistics of the vestibular input experienced during natural self-motion differ between rodents and primates

KEY POINTS

In order to understand how the brain's coding strategies are adapted to the statistics of the sensory stimuli experienced during everyday life, the use of animal models is essential. Mice and non-human primates have become common models for furthering our knowledge of the neuronal coding of natural stimuli, but differences in their natural environments and behavioural repertoire may impact optimal coding strategies. Here we investigated the structure and statistics of the vestibular input experienced by mice versus non-human primates during natural behaviours, and found important differences. Our data establish that the structure and statistics of natural signals in non-human primates more closely resemble those observed previously in humans, suggesting similar coding strategies for incoming vestibular input. These results help us understand how the effects of active sensing and biomechanics will differentially shape the statistics of vestibular stimuli across species, and have important implications for sensory coding in other systems.

ABSTRACT

It is widely believed that sensory systems are adapted to the statistical structure of natural stimuli, thereby optimizing coding. Recent evidence suggests that this is also the case for the vestibular system, which senses self-motion and in turn contributes to essential brain functions ranging from the most automatic reflexes to spatial perception and motor coordination. However, little is known about the statistics of self-motion stimuli actually experienced by freely moving animals in their natural environments. Accordingly, here we examined the natural self-motion signals experienced by mice and monkeys: two species commonly used to study vestibular neural coding. First, we found that probability distributions for all six dimensions of motion (three rotations, three translations) in both species deviated from normality due to long tails. Interestingly, the power spectra of natural rotational stimuli displayed similar structure for both species and were not well fitted by power laws. This result contrasts with reports that the natural spectra of other sensory modalities (i.e. vision, auditory and tactile) instead show a power-law relationship with frequency, which indicates scale invariance. Analysis of natural translational stimuli revealed important species differences as power spectra deviated from scale invariance for monkeys but not for mice. By comparing our results to previously published data for humans, we found the statistical structure of natural self-motion stimuli in monkeys and humans more closely resemble one another. Our results thus predict that, overall, neural coding strategies used by vestibular pathways to encode natural self-motion stimuli are fundamentally different in rodents and primates.

Multiple sites of adaptation lead to contrast encoding in the Drosophila olfactory system

Animals often encounter large increases in odor intensity that can persist for many seconds. These increases in the background odor are often accompanied by increases in the variance of the odor stimulus. Previous studies have shown that a persistent odor stimulus (odor background) results in a decrease in the response to brief odor pulses in the olfactory receptor neurons (ORNs). However, the contribution of adapting mechanisms beyond the ORNs is not clear. Thus, it is unclear how adaptive mechanisms are distributed within the olfactory circuit and what impact downstream adaptation may have on the encoding of odor stimuli. In this study, adaptation to the same odor stimulus is examined at multiple levels in the well studied and accessible Drosophila olfactory system. The responses of the ORNs are compared to the responses of the second order, projection neurons (PNs), directly connected to them. Adaptation in PN spike rate was found to be much greater than adaptation in the ORN spike rate. This greater adaptation allows PNs to encode odor contrast (ratio of pulse intensity to background intensity) with little ambiguity. Moreover, distinct neural mechanisms contribute to different aspects of adaptation; adaptation to the background odor is dominated by adaptation in spike generation in both ORNs and PNs, while adaptation to the odor pulse is dominated by changes within olfactory transduction and the glomerulus. These observations suggest that the olfactory system adapts at multiple sites to better match its response gain to stimulus statistics.

Scalar utility theory and proportional processing: What does it actually imply?

Scalar Utility Theory (SUT) is a model used to predict animal and human choice behaviour in the context of reward amount, delay to reward, and variability in these quantities (risk preferences). This article reviews and extends SUT, deriving novel predictions. We show that, contrary to what has been implied in the literature, (1) SUT can predict both risk averse and risk prone behaviour for both reward amounts and delays to reward depending on experimental parameters, (2) SUT implies violations of several concepts of rational behaviour (e.g. it violates strong stochastic transitivity and its equivalents, and leads to probability matching) and (3) SUT can predict, but does not always predict, a linear relationship between risk sensitivity in choices and coefficient of variation in the decision-making experiment. SUT derives from Scalar Expectancy Theory which models uncertainty in behavioural timing using a normal distribution. We show that the above conclusions also hold for other distributions, such as the inverse Gaussian distribution derived from drift-diffusion models. A straightforward way to test the key assumptions of SUT is suggested and possible extensions, future prospects and mechanistic underpinnings are discussed.

The entropic basis of collective behaviour

We identify a unique viewpoint on the collective behaviour of intelligent agents. We first develop a highly general abstract model for the possible future lives these agents may encounter as a result of their decisions. In the context of these possibilities, we show that the causal entropic principle, whereby agents follow behavioural rules that maximize their entropy over all paths through the future, predicts many of the observed features of social interactions among both human and animal groups. Our results indicate that agents are often able to maximize their future path entropy by remaining cohesive as a group and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of possible future paths. We derive social interaction rules that are consistent with maximum entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber's law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus–response mechanism and providing a novel basis for the common assumption of linearly additive ‘social forces’ in simulation studies of collective behaviour.

Visual biases in judging body weight

OBJECTIVES

There has been a steady rise in obesity levels in Western countries, and a contributory factor is people's failure to recognize weight gain. Two important visual perceptual biases, contraction bias and Weber's law, that have hitherto been ignored in the obesity literature could contribute to this problem. Contraction bias predicts that the weight of obese bodies will be underestimated and the degree of underestimation will increase as body mass index (BMI) increases. Weber's law predicts that change in the body size will become progressively harder to detect as their BMI increases.

METHODS

In Experiment 1, 29 women participants estimated the weight of 120 women varying in their body mass. In Experiment 2, 28 women participants judged which body was the heavier in a 2-alternative forced choice paradigm.

RESULTS

In Experiment 1, as predicted the participants showed a progressive underestimation of overweight and obese bodies, β1  = 0.71, t = 26.96, p < .0001. For Experiment 2, there was a significant effect of the BMI of the bodies being judged on the just noticeable difference needed to discriminate between them: F(1, 196) = 89.39, p < .0001 for 3D bodies and F(1, 86.5) = 44.57, p < .0001 for digital photographs.

CONCLUSIONS

Normal visual perceptual biases influence our ability to determine body size: contraction bias and Weber's law mean that as bodies become overweight and obese, it is harder to judge their weight and detect any increase in size. These effects may therefore compromise people's ability to recognize weight gain and undertake compensatory weight control behaviours. Statement of contribution What is already known on this subject? It is common knowledge that obesity levels in the West are rapidly rising and that people fail to recognize weight gain. What has not been widely recognized before is that there are sound perceptual reasons for this failure. Here, we identify two such perceptual biases. What does this study add? Weber's law and contraction bias compromise people's ability to recognize weight gain. It becomes progressively harder to discriminate the size of bodies as their body mass index increases. This compromises the ability to recognize weight gain and undertake compensatory behaviours.

A temporal basis for Weber's law in value perception

Weber's law—the observation that the ability to perceive changes in magnitudes of stimuli is proportional to the magnitude—is a widely observed psychophysical phenomenon. It is also believed to underlie the perception of reward magnitudes and the passage of time. Since many ecological theories state that animals attempt to maximize reward rates, errors in the perception of reward magnitudes and delays must affect decision-making. Using an ecological theory of decision-making (TIMERR), we analyze the effect of multiple sources of noise (sensory noise, time estimation noise, and integration noise) on reward magnitude and subjective value perception. We show that the precision of reward magnitude perception is correlated with the precision of time perception and that Weber's law in time estimation can lead to Weber's law in value perception. The strength of this correlation is predicted to depend on the reward history of the animal. Subsequently, we show that sensory integration noise (either alone or in combination with time estimation noise) also leads to Weber's law in reward magnitude perception in an accumulator model, if it has balanced Poisson feedback. We then demonstrate that the noise in subjective value of a delayed reward, due to the combined effect of noise in both the perception of reward magnitude and delay, also abides by Weber's law. Thus, in our theory we prove analytically that the perception of reward magnitude, time, and subjective value change all approximately obey Weber's law.

What does scalar timing tell us about neural dynamics?

The “Scalar Timing Law,” which is a temporal domain generalization of the well known Weber Law, states that the errors estimating temporal intervals scale linearly with the durations of the intervals. Linear scaling has been studied extensively in human and animal models and holds over several orders of magnitude, though to date there is no agreed upon explanation for its physiological basis. Starting from the assumption that behavioral variability stems from neural variability, this work shows how to derive firing rate functions that are consistent with scalar timing. We show that firing rate functions with a log-power form, and a set of parameters that depend on spike count statistics, can account for scalar timing. Our derivation depends on a linear approximation, but we use simulations to validate the theory and show that log-power firing rate functions result in scalar timing over a large range of times and parameters. Simulation results match the predictions of our model, though our initial formulation results in a slight bias toward overestimation that can be corrected using a simple iterative approach to learn a decision threshold.

Psychophysics and the evolution of behavior

Sensory information allows animals to interpret their environment and make decisions. The ways in which animals perceive and measure stimuli from the social and physical environment guide nearly every decision they make. Thus, sensory perception and associated cognitive processing have a strong impact on behavioral evolution. Research in this area often focuses on the unique properties of the sensory system of an individual species, yet certain relevant features of perception and cognition generally hold across taxa. One such general feature is the proportionally based translation of physical stimulus magnitude into perceived stimulus magnitude. This process has been recognized for over a century, but recent studies have begun to consider how a law of proportional psychophysics, Weber's law, exerts selective force in behavioral evolution.

The importance of being relevant: modulation of magnitude representations

The current study aims to answer two main questions. First, is there a difference between the representations of the numerical and the physical properties of visually presented numbers? Second, can the relevancy of the dimension change its representation? In a numerical Stroop task, participants were asked to indicate either the physically or the numerically larger value of two digits. The ratio between the physical sizes and the numerical values changed orthogonally from 0.1 (the largest difference) to 0.8. Reaction times (RT) were plotted as a function of both physical and numerical ratios. Trend analysis revealed that while the numerical dimension followed Weber's law regardless of task demands, the physical ratio deviated from linearity. Our results suggest that discrete and continuous magnitudes are represented by different yet interactive systems rather than by a shared representation.

Grasping time does not influence the early adherence of aperture shaping to Weber's law

The “just noticeable difference” (JND) represents the minimum amount by which a stimulus must change to produce a noticeable variation in one's perceptual experience (i.e., Weber's law). Recent work has shown that within-participant standard deviations of grip aperture (i.e., JNDs) increase linearly with increasing object size during the early, but not the late, stages of goal-directed grasping. A visually based explanation for this finding is that the early and late stages of grasping are respectively mediated by relative and absolute visual information and therefore render a time-dependent adherence to Weber's law. Alternatively, a motor-based explanation contends that the larger aperture shaping impulses required for larger objects gives rise to a stochastic increase in the variability of motor output (i.e., impulse-variability hypothesis). To test the second explanation, we had participants grasp differently sized objects in grasping time criteria of 400 and 800 ms. Thus, the 400 ms condition required larger aperture shaping impulses than the 800 ms condition. In line with previous work, JNDs during early aperture shaping (i.e., at the time of peak aperture acceleration and peak aperture velocity) for both the 400 and 800 ms conditions scaled linearly with object size, whereas JNDs later in the response (i.e., at the time of peak grip aperture) did not. Moreover, the 400 and 800 ms conditions produced comparable slopes relating JNDs to object size. In other words, larger aperture shaping impulses did not give rise to a stochastic increase in aperture variability at each object size. As such, the theoretical tenets of the impulse-variability hypothesis do not provide a viable framework for the time-dependent scaling of JNDs to object size. Instead, we propose that a dynamic interplay between relative and absolute visual information gives rise to grasp trajectories that exhibit an early adherence and late violation to Weber's law.