Evidence for Two Numerical Systems That Are Similar in Humans and Guppies

Abstract

BackgroundHumans and non-human animals share an approximate non-verbal system for representing and comparing numerosities that has no upper limit and for which accuracy is dependent on the numerical ratio. Current evidence indicates that the mechanism for keeping track of individual objects can also be used for numerical purposes; if so, its accuracy will be independent of numerical ratio, but its capacity is limited to the number of items that can be tracked, about four. There is, however, growing controversy as to whether two separate number systems are present in other vertebrate species.Methodology/Principal FindingsIn this study, we compared the ability of undergraduate students and guppies to discriminate the same numerical ratios, both within and beyond the small number range. In both students and fish the performance was ratio-independent for the numbers 1–4, while it steadily increased with numerical distance when larger numbers were presented.Conclusions/SignificanceOur results suggest that two distinct systems underlie quantity discrimination in both humans and fish, implying that the building blocks of uniquely human mathematical abilities may be evolutionarily ancient, dating back to before the divergence of bony fish and tetrapod lineages.

Impaired Numerical Ability Affects Supra-Second Time Estimation

“…An alternative hypothesis to explain the supra-second time estimation impairment in DDs that we observed may be that sub-and supra-second distinctions in the time domain parallel small (up to 3-4) and bigger numerosity (bigger than 4) processing in the numerical domain (Agrillo et al, 2012;Buhusi & Cordes, 2011;Butterworth, 2010;Trick & Pylyshyn, 1993). This suggestion is based on the proposal that smaller numbers rely on similar mechanisms as sub-sec time perception, while bigger numbers rely on joint mechanisms as supra-second time estimation (Buhusi & Cordes, 2011).…”

“…This idea is consistent with the proposition that dyscalculics would be more impaired when bigger numbers are involved (but see But-terworth, 2010), and also with the fact that DDs are not significantly impaired in sub-sec timings (Cappelletti et al, 2011a). Furthermore, the transition between sub-second ('automatic' or 'sensory-motor' timing, Bueti et al, 2012;Buhusi & Meck, 2005;Buonomano, 2007;Lewis & Miall, 2003;Macar et al, 2006;Naatanen et al, 2004;Wiener et al, 2010) and supra-second ('cognitive') timing mechanisms occurs at around 3 s (Gilaie-Dotan et al, 2011;Poppel, 1997), which might parallel the transition between mechanisms supporting small and larger numerosities (Agrillo et al, 2012;Buhusi & Cordes, 2011;Cordes & Brannon, 2009), although there is no consensus about this idea (see Buhusi & Cordes, 2011 for review). While a distinction between 'small' and 'large' numerosities can be dichotomised, one might also consider it on a magnitude continuum.…”

Numerosity representation is encoded in human subcortex

“…If the computation supported by human subcortex is related to that performed by other species, one would expect facilitation for both larger and smaller numbers because other nonprimate species do evince ratio-dependent effects for both small and large numbers (38,40,42). In this experiment, participants performed the same task as in experiment 2, but with arrays with small numbers (one to four) of dots.…”

“…Several studies have documented ratio effects in the subitizing range (55-59), but others have found ratio effects only with larger numbers (22,42) and the emergence of these effects may be experiment-or task-dependent (54). Our findings corroborate previous research showing that ratio effects exist for numerosities both within and beyond the subitizing range, and, in the context of this particular experimental approach, the subcortex appears to represent ratio-dependent numerosity for the evaluation of both small and large numbers.…”

“…Mosquitofish can perform various numerical tasks including picking larger shoals (38), choosing more companions (39) or mates (40), or discriminating larger quantities (41), and guppies have been shown to differentiate ratios with levels of precision similar to that of undergraduate college students (42). Moreover, number processing is not restricted to vertebrates as both honeybees (43) and spiders (44) possess some ability to process number, as well.…”