Quantity discrimination in Tenebrio molitor: evidence of numerosity discrimination in an invertebrate?

Numerosity discrimination, the ability to distinguish between sets with more and less items, is recognised as the foundation for higher numerical abilities. Understanding numerosity discrimination from a comparative perspective is hence pivotal in tracing the evolution of numerical representation systems. However, numerosity discrimination has been well studied only in vertebrates, where two innate systems of number representation have been described: an ‘analog magnitude system’ used to discriminate among numerosities by representing them as cardinal magnitudes and a ‘parallel individualisation system’ that allows precise discrimination among small arrays of items (≤4) by representing objects individually. We investigated the existence of quantity discrimination in an insect species (Tenebrio molitor) by using a spontaneous two-choice procedure in which males were exposed to substrates bearing odours from different numbers of females (≤4) in increasing numerosity ratios (1:4, 1:3 and 1:2). We show that males can discriminate sources of odours reflecting 1 versus 4 and 1 versus 3 females, but not 2 versus 4 or 1 versus 2, indicating that T. molitor males exhibit a marked preference for sources reflecting more female donors only when numerosity ratios are below 1:2. We discuss the functional significance of this finding and whether our pattern of results could be best explained by summation of a non-numerical continuous variable or by the existence of a numerosity discrimination mechanism with an operational signature ratio of 1:2.     

Number estimation relies on a set of segmented objects

How do we estimate the number of objects in a set? Two types of visual representations might underlie this ability - an unsegmented visual image or a segmented collection of discrete objects. We manipulated whether individual objects were isolated from each other or grouped into pairs by irrelevant lines. If number estimation operates over an unsegmented image, then this manipulation should not affect estimates. But if number estimation relies on a segmented image, then grouping pairs of objects into single units should lead to lower estimates. In Experiment 1 participants underestimated the number of grouped objects, relative to disconnected objects in which the connecting lines were ‘broken’. Experiment 2 presents evidence that this segmentation process occurred broadly across the entire set of objects. In Experiment 3, a staircase procedure provides a quantitative measure of the underestimation effect. Experiment 4 shows that the strength of the grouping effect was equally strong for a single thin line, and the effect can be eliminated by a small break in the line. These results provide direct evidence that number estimation relies on a segmented input.     

Enumeration of small and large numerosities: The effect of element visibility

Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1–8) or by tens (10–80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.     

Number sense and quantifier interpretation

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

Quantity discrimination in female mosquitofish

The ability in animals to count and represent different numbers of objects has received a great deal of attention in the past few decades. Cumulative evidence from comparative studies on number discriminations report obvious analogies among human babies, non-human primates and birds and are consistent with the hypothesis of two distinct and widespread mechanisms, one for counting small numbers (<4) precisely, and one for quantifying large numbers approximately. We investigated the ability to discriminate among different numerosities, in a distantly related species, the mosquitofish, by using the spontaneous choice of a gravid female to join large groups of females as protection from a sexually harassing male. In one experiment, we found that females were able to discriminate between two shoals with a 1:2 numerosity ratio (2 vs. 4, 4 vs. 8 and 8 vs. 16 fish) but failed to discriminate a 2:3 ratio (8 vs. 12 fish). In the second experiment, we studied the ability to discriminate between shoals that differed by one element; females were able to select the larger shoal when the paired numbers were 2 vs. 3 or 3 vs. 4 but not 4 vs. 5 or 5 vs. 6. Our study indicates that numerical abilities in fish are comparable with those of other non-verbal creatures studied; results are in agreement with the hypothesis of the existence of two distinct systems for quantity discrimination in vertebrates.     

Symbolic magnitude modulates perceptual strength in binocular rivalry

Basic aspects of magnitude (such as luminance contrast) are directly represented by sensory representations in early visual areas. However, it is unclear how symbolic magnitudes (such as Arabic numerals) are represented in the brain. Here we show that symbolic magnitude affects binocular rivalry: perceptual dominance of numbers and objects of known size increases with their magnitude. Importantly, variations in symbolic magnitude acted like variations in luminance contrast: we found that an increase in numerical magnitude of adding one lead to an equivalent increase in perceptual dominance as a contrast increment of 0.32%. Our results support the claim that magnitude is extracted automatically, since the increase in perceptual dominance came about in the absence of a magnitude-related task. Our findings show that symbolic, acculturated knowledge about magnitude interacts with visual perception and affects perception in a manner similar to lower-level aspects of magnitude such as luminance contrast.     

Find the picture of eight turtles: a link between children's counting and their knowledge of number word semantics

An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before realizing that all number words refer to numerosity. Alternatively, knowledge of this general principle may form relatively early and proceed to guide and constrain the acquisition of individual number word meanings. The current article describes two experiments in which 116 children (2½- to 4-year-olds) were given a Word Extension task as well as a standard Give-N task. Results show that only children who understood the cardinality principle of counting successfully extended number words from one set to another based on numerosity—with evidence that a developing understanding of this concept emerges as children approach the cardinality principle induction. These findings support the view that children do not use a broad understanding of number words to initially connect number words to numerosity but rather make this connection around the time that they figure out the cardinality principle of counting.     

Number bias for the discrimination of large visual sets in infancy

This brief report attempts to resolve the claim that infants preferentially attend to continuous variables over number [e.g. Psychol. Sci. 10 (1999) 408; Cognit. Psychol.44 (2002) 33] with the finding that when continuous variables are controlled, infants as young as 6-months of age discriminate large numerical values [e.g. Psychol. Sci. 14 (2003) 396; Cognition 89 (2003) B15; Cognition 74 (2000) B1]. In two parallel experiments, we compare 6-month-old infants' ability to discriminate number and ignore continuous variables with their ability to form a representation of a cumulative surface area and ignore number. We find that infants discriminate a 2-fold change in number but fail to discriminate a 2-fold change in cumulative surface area. The results point to a more complicated relationship between discrete and continuous dimensions than implied by previous literature.     

Local rather than global processing of visual arrays in numerosity discrimination by pigeons (Columba livia)

A series of experiments investigated which stimulus properties pigeons use when they discriminate pairs of visual arrays that differ in numerosity. Transfer tests with novel stimuli confirmed that the birds’ choices were based on relative differences in numerosity. However, pigeons differed from other species in the non-numerical cues that affected their choices. In human and non-human primates, numerical discrimination is often influenced by continuous variables such as surface area or overall stimulus brightness. Pigeons showed little evidence of using those cues, even when summed area and brightness had been correlated with numerosity differences and reward outcome. But when array-element sizes were asymmetrically distributed across numerosities, the birds readily utilized information about item sizes as an additional discriminative cue. These novel results are discussed in relation to pigeons’ tendency to focus on local, rather than global dimensions when they process other non-numerical complex visual stimuli. The findings suggest there may be inter-specific differences in the type of perceptual information that provides the input stage for mechanisms underlying numerical processing. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.