Evidence for a Mixed Timing and Counting Strategy in Mice Performing a Mechner Counting Task

Abstract

Numerosity, or the ability to understand and distinguish between discrete quantities, was first formalized for study in animals by Mechner ( 1958a ). Rats had to press one lever (the counting lever) n times to arm food release from pressing a second lever (the reward lever). The only cue that n presses had been made to the counting lever was the animal’s representation of how many times it had pressed it. In the years that have passed since, many researchers have modified the task in meaningful ways to attempt to tease apart timing-based and count-based strategies. Strong evidence has amassed that the two are fundamentally different and separable skills but, to date, no study has effectively examined the differential contributions of the two strategies in Mechner’s original task. By examining performance mid-trial and correlating it with whole-trial performance, we were able to identify patterns of correlation consistent with counting and timing strategies. Due to the independent nature of these correlation patterns, this technique was uniquely able to provide evidence for strategies that combined both timing and counting components. The results show that most mice demonstrated this combined strategy. This provides direct evidence that mice can and do use numerosity to complete Mechner’s original task. A rational agent with fallible estimates of both counts made and time elapsed in making them should use both estimates when deciding when to switch to the second lever.

Contingency, contiguity, and causality in conditioning: Applying information theory and Weber’s Law to the assignment of credit problem.

“…With a fixed interval schedule, subjects learn that reinforcement is contingent on the elapse of a fixed interval since the last reinforcement, which is why they pause after each reinforcement for an interval that is on average a fixed proportion of the fixed interval parameter (Church et al, 1994;Gibbon, 1977). With a fixed ratio schedule and a fixed number chain schedule with terminal choice links, they learn that reinforcement is contingent on making a fixed number of responses, which is why they respond in runs of more or less continuous very rapid responding, with well-marked run onsets (Berkay, Çavdarog ˘lu, & Balcı, 2016;Light et al, 2019;Rilling, 1967). This document is copyrighted by the American Psychological Association or one of its allied publishers.…”

Number and time in acquisition, extinction and recovery

“…Light et al (2019) devised an analysis of the sequence of presses on the prepare lever that enabled them to detect any of three possible strategies, a count strategy, a timing strategy or a mixed strategy. A hierarchically structured representation of the conditioning experience enables subjects to construe it in different ways for different purposes.…”

“…If a subject sometimes loses the count of the number of presses so far made while retaining a measure of the time elapsed since it began pressing the "prepare" lever, it may switch from a count target to a time target. Light et al (2019) devised an analysis of the sequence of presses on the prepare lever that enabled them to detect any of three possible strategies, a count strategy, a timing strategy or a mixed strategy. In a group of eight mice subjects, one mouse relied almost entirely on a count strategy, one relied almost entirely on a timing strategy, and the other six relied on a mixed strategy.…”

Symbolic quantitative cognition in wild zebrafish (Danio rerio)

“…Associative reward-based learning tasks that reward the choice of stimuli of a particular cardinality have been used successfully to elicit responses in a range of animals: chimpanzees 44– 54 , rhesus macaques 4,55–57 , dogs 58–62 , dolphins 63,64 , racoons 65 , rats 66–70 , mice 71–73 , horses 74 , bears 75 and birds like grey parrots 76–79 , crows, pigeons 80–87 , robins 7,88 , canaries 89 , and chicks 40,41,90–92 . Work on other vertebrate systems such as reptiles: tortoises 93 and lizards 94 and amphibians: frogs 95 , salamanders 96 has been scarce, but there has been a mushrooming of work on numerical cognition and associative learning in fish: zebrafish 31,97 , angelfish 98–100 , archerfish 101 , goldfish 102 , redtail splitfins 103 , mosquitofish 104 , guppies 105–107 , as well as some comparative work 108–110 .…”

“…Associative reward-based learning tasks that reward the choice of stimuli of a particular cardinality have been used successfully to elicit responses in a range of animals: chimpanzees [44][45][46][47][48][49][50][51][52][53][54] , rhesus macaques 4,[55][56][57] , dogs [58][59][60][61][62] , dolphins 63,64 , racoons 65 , rats [66][67][68][69][70] , mice [71][72][73] , horses 74 , bears 75 and birds like grey parrots [76][77][78][79] , crows, pigeons [80][81][82][83][84][85][86][87] , robins 7,88 , canaries 89 , and chicks 40,…”