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Modeling the interaction of numerosity and perceptual variables with the diffusion model.

ABSTRACT: Ratcliff and McKoon (2018) proposed integrated diffusion models for numerosity judgments in which a numerosity representation provides evidence used to drive the decision process. We extend this modeling framework to examine the interaction of non-numeric perceptual variables with numerosity by assuming that drift rate and non-decision time are functions of those variables. Four experiments were conducted with two different types of stimuli: a single array of intermingled blue and yellow dots in which both numerosity and dot area vary over trials and two side-by-side arrays of dots in which numerosity, dot area, and convex hull vary over trials. The tasks were to decide whether there were more blue or yellow dots (two experiments), more dots on which side, or which dots have a larger total area. Development of models started from the principled models in Ratcliff and McKoon (2018) and became somewhat ad hoc as we attempted to capture unexpected patterns induced by the conflict between numerosity and perceptual variables. In the three tasks involving numerosity judgments, the effects of the non-numeric variables were moderated by the number of dots. Under a high conflict, judgments were dominated by perceptual variables and produced an unexpected shift in the leading edge of the reaction time (RT) distributions. Although the resulting models were able to predict most of the accuracy and RT patterns, the models were not able to completely capture this shift in the RT distributions. However, when subjects judged area, numerosity affected perceptual judgments but there was no leading edge effect. Based on the results, it appears that the integrated diffusion models provide an effective framework to study the role of numerical and perceptual variables in numerosity tasks and their context-dependency.

SUBMITTER: Kang I

PROVIDER: S-EPMC7319178 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Neural representations of approximate numerical value, or numerosity, have been observed in the intraparietal sulcus (IPS) in monkeys and humans, including children. Using functional magnetic resonance imaging, we show that children as young as 3-4 years old exhibit neural tuning to cardinal numerosities in the IPS and that their neural responses are accounted for by a model of numerosity coding that has been used to explain neural responses in the adult IPS. We also found that the sensitivity of children's neural tuning to number in the right IPS was comparable to their numerical discrimination sensitivity observed behaviorally, outside of the scanner. Children's neural tuning curves in the right IPS were significantly sharper than in the left IPS, indicating that numerical representations are more precise and mature more rapidly in the right hemisphere than in the left. Further, we show that children's perceptual sensitivity to numerosity can be predicted by the development of their neural sensitivity to numerosity. This research provides novel evidence of developmental continuity in the neural code underlying numerical representation and demonstrates that children's neural sensitivity to numerosity is related to their cognitive development.Significance statementHere we test for the existence of neural tuning to numerosity in the developing brain in the youngest sample of children tested with fMRI to date. Although previous research shows evidence of numerical distance effects in the intraparietal sulcus of the developing brain, those effects could be explained by patterns of neural activity that do not represent neural tuning to numerosity. These data provide the first robust evidence that from as early as 3-4 years of age there is developmental continuity in how the intraparietal sulcus represents the values of numerosities. Moreover, the study goes beyond previous research by examining the relation between neural tuning and perceptual tuning in children.

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Modeling the interaction of numerosity and perceptual variables with the diffusion model.

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