Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn abstract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli, covarying with number. Here we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for co-varying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs. 6 elements; Exp. 2: 2 vs. 3 elements); these were controlled for several combinations of physical variables (elements’ size, overall area, overall perimeter, density and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs. 3, 5 vs. 8 and 6 vs. 9 in Exp. 1; 3 vs. 4, 3 vs. 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence that archerfish spontaneously use abstract relative numerical information for both small and large numbers when only numerical cues are available.

Nonsymbolic numerosity in sets with illusory-contours exploits a context-sensitive, but contrast-insensitive, visual boundary formation process

The visual mechanisms underlying approximate numerical representation are still intensely debated because numerosity information is often confounded with continuous sensory cues (e.g., texture density, area, convex hull). However, numerosity is underestimated when a few items are connected by illusory contours (ICs) lines without changing other physical cues, suggesting in turn that numerosity processing may rely on discrete visual input. Yet, in these previous works, ICs were generated by black-on-gray inducers producing an illusory brightness enhancement, which could represent a further continuous sensory confound. To rule out this possibility, we tested participants in a numerical discrimination task in which we manipulated the alignment of 0, 2, or 4 pairs of open/closed inducers and their contrast polarity. In Experiment 1, aligned open inducers had only one polarity (all black or all white) generating ICs lines brighter or darker than the gray background. In Experiment 2, open inducers had always opposite contrast polarity (one black and one white inducer) generating ICs without strong brightness enhancement. In Experiment 3, reverse-contrast inducers were aligned but closed with a line preventing ICs completion. Results showed that underestimation triggered by ICs lines was independent of inducer contrast polarity in both Experiment 1 and Experiment 2, whereas no underestimation was found in Experiment 3. Taken together, these results suggest that mere brightness enhancement is not the primary cause of the numerosity underestimation induced by ICs lines. Rather, a boundary formation mechanism insensitive to contrast polarity may drive the effect, providing further support to the idea that numerosity processing exploits discrete inputs.

Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn astract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli covarying with number. Here we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for co-varying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs. 6 elements; Exp. 2: 2 vs. 3 elements); these were controlled for several combinations of physical variables (elements' size, overall area, overall perimeter, density and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs. 3, 5 vs. 8 and 6 vs. 9 in Exp. 1; 3 vs. 4, 3 vs. 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence of the spontaneous use of abstract relative numerical information in archerfish for both small and large numbers.

A robust electrophysiological marker of spontaneous numerical discrimination

Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability—especially in children—but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During 1-min sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.

Application of an abstract concept across magnitude dimensions by fish

Mastering relational concepts and applying them to different contexts presupposes abstraction capacities and implies a high level of cognitive sophistication. One way to investigate extrapolative abilities is to assess cross-dimensional application of an abstract relational magnitude rule to new domains. Here we show that angelfish initially trained to choose either the shorter of two lines in a spatial task (line-length discrimination task) or the array with “fewer” items (numerical discrimination task) spontaneously transferred the learnt rule to novel stimuli belonging to the previously unseen dimension demonstrating knowledge of the abstract concept of “smaller”. Our finding challenges the idea that the ability to master abstract magnitude concepts across domains is unique to humans and suggests that the circuits involved in rule learning and magnitude processing might be evolutionary conserved.

Individually distinctive features facilitate numerical discrimination of sets of objects in domestic chicks

Day-old domestic chicks approach the larger of two groups of identical objects, but in a 3 vs 4 comparison, their performance is random. Here we investigated whether adding individually distinctive features to each object would facilitate such discrimination. Chicks reared with 7 objects were presented with the operation 1 + 1 + 1 vs 1 + 1 + 1 + 1. When objects were all identical, chicks performed randomly, as expected (Experiment 1). In the remaining experiments, objects differed from one another due to additional features. Chicks succeeded when those features were differently oriented segments (Experiment 2) but failed when the features were arranged to depict individually different face-like displays (Experiment 3). Discrimination was restored if the face-like stimuli were presented upside-down, disrupting global processing (Experiment 4). Our results support the claim that numerical discrimination in 3 vs 4 comparison benefits from the presence of distinctive features that enhance object individuation due to individual processing. Interestingly, when the distinctive features are arranged into upright face-like displays, the process is susceptible to global over local interference due to configural processing. This study was aimed at assessing whether individual object processing affects numerical discrimination. We hypothesise that in humans similar strategies aimed at improving performance at the non-symbolic level may have positive effects on symbolic mathematical abilities.

A robust electrophysiological marker of spontaneous numerical discrimination

Humans have a Number Sense that enables them to represent and manipulate numerical quantities. Behavioral data suggest that the acuity of numerical discrimination is predictively associated with math ability – especially in children – but some authors argued that its assessment is problematic. In the present study, we used frequency-tagged electroencephalography to objectively measure spontaneous numerical discrimination during passive viewing of dot or picture arrays in healthy adults. During one-minute sequences, we introduced periodic numerosity changes and we progressively increased the magnitude of such changes every ten seconds. We found significant brain synchronization to the periodic numerosity changes from the 1.2 ratio over medial occipital regions, and amplitude strength increased with the numerical ratio. Brain responses were reliable across both stimulus formats. Interestingly, electrophysiological responses also mirrored performances on a number comparison task and seemed to be linked to math fluency. In sum, we present a neural marker of numerical acuity that is passively evaluated in short sequences, independent of stimulus format and that reflects behavioural performances on explicit number comparison tasks.

Effectiveness of Entropy Weight Method in Decision-Making

Entropy weight method (EWM) is a commonly used weighting method that measures value dispersion in decision-making. The greater the degree of dispersion, the greater the degree of differentiation, and more information can be derived. Meanwhile, higher weight should be given to the index, and vice versa. This study shows that the rationality of the EWM in decision-making is questionable. One example is water source site selection, which is generated by Monte Carlo Simulation. First, too many zero values result in the standardization result of the EWM being prone to distortion. Subsequently, this outcome will lead to immense index weight with low actual differentiation degree. Second, in multi-index decision-making involving classification, the classification degree can accurately reflect the information amount of the index. However, the EWM only considers the numerical discrimination degree of the index and ignores rank discrimination. These two shortcomings indicate that the EWM cannot correctly reflect the importance of the index weight, thus resulting in distorted decision-making results.

Sex differences in cognitive performance, style and domain relationships in mosquitofish (Gambusia affinis)

Given that the sexes often differ in their ecological and sexual selection pressures, sex differences in cognitive properties are likely. While research on sexually dimorphic cognitionoften focuses on performance, it commonly overlooks how sexes diverge across multiple cognitive tasks (cognitive domains) and in behaviors associated with cognitive performance (cognitive style). We tested male and female western mosquitofish (Gambusia affinis) in three cognitive tasks: associative learning (numerical discrimination), cognitive flexibility (detour task), and spatio-temporal learning (shuttlebox). We characterized statistical relationships between cognitive performances and cognitive style during the associative learning task with measures of anxiety, boldness, exploration, reaction time, and activity. We found sex differences in performance, cognitive style, and the relationships between cognitive domains. Females outperformed males in spatio-temporal learning task, while the sexes performed equally in associate learning and cognitive flexibility assays. Females (but not males) exhibited a ‘fast-exploratory’ cognitive style during associative learning trials. Meanwhile, only males showed a significant positive relationship between domains (associative learning and cognitive flexibility). We propose that these sexually dimorphic cognitive traits result from strong sexual conflict in this taxon; and emphasize the need to explore suites of sex-specific cognitive traits and broader comparative work examining sexual selection and cognition.HighlightsMales and females perform at similar levels in associative learning and cognitive flexibility assays, but females tend to outperform males on a spatio-temporal learning task.Female performance in associative learning trials (numerical discrimination task) can be predicted by cognitive style behaviors (exploration, reaction time, and activity); whereas male performance cannot.Males, but not females, show a predictive relationship between associative learning and cognitive flexibility performance.Our results demonstrate that sex differences in cognition extend beyond performance into cognitive style and domain relationships, suggesting that investigations into animal personality and cognition require more comprehensive characterization.