How do pigeons represent numbers?

Pigeons' bisection of two number scales, 1-16 and 2-32, was examined in two experiments. In Experiment 1, pigeons learned to choose different comparison keys following 1 or 16 key pecks and 2 or 32 key pecks and then were tested with intermediate numbers of key pecks on nonreinforced probe trials. Psychophysical curves that plotted choice of the large number key against number of pecks showed superposition of the two number scales and indifference between the two keys at the geometric means of each scale. The same procedures were used in Experiment 2, but pigeons were trained to bisect each scale at its arithmetic mean. Two asymmetries appeared in curves that plotted discrimination performance against number: near the midpoints of the scales, accuracy was higher for high numbers than for low numbers, but this relationship reversed at the ends of the scales, with low numbers discriminated more accurately than high numbers. An associative model that assumed stimulus generalization between numbers was used to predict the findings of these two experiments. The model showed a good qualitative fit to the obtained data when it was assumed that number was represented on a log scale and generalization was constant at all numbers but not when it was assumed that number was represented on a linear scale and generalization was scalar.