The discrimination and representation of relative and absolute number in pigeons and humans.
Degree GrantorUniversity of Canterbury
The ability to discriminate relative and absolute number has been researched widely in both human and nonhuman species. However, the full extent of numerical ability in nonhuman animals, and the nature of the underlying numerical representation, on which discriminations are based, is still unclear. The aim of the current research was to examine the performance of pigeons and humans in tasks that require the discrimination of relative number (a bisection procedure), and absolute number (in a reproduction procedure). One of the main research questions was whether numerical control over responding could be obtained, above and beyond control by temporal cues in nonhuman animals, and if so, whether it was possible to quantify the relative influences of number and time on responding. Experiment 1 examines nonhuman performance in a numerical bisection task; subjects were presented with either 2 and 6, 4 and 12, or 8 and 24 keylight flashes across three different conditions, and were required to classify these flash sequences as either a “large” or “small” number, by pecking the blue or white key, respectively. Subjects were then tested with novel values within and 2 values higher and lower than the training values. Experiments 2-4 investigate responding in a novel numerical reproduction procedure, in which pigeons were trained to match the number of responses made during a production phase to the number of keylight flashes (2, 4, or 6) in a recently completed sample phase. Experiments 2 and 2A examined discrimination performance when the temporal variables, flash rate and sample phase duration, were perfectly correlated (Experiment 2) or only weakly correlated (Experiment 2a) with flash number. Acquisition of performance in the numerical reproduction procedure was investigated in Experiment 3. For Experiments 1-3, hierarchical regression analyses showed significant control by number over responding, after controlling for temporal cues. Additionally, positive transfer to novel values both within and outside the training range was obtained when the temporal organization of test sequences was similar to baseline training. Experiment 4 investigated the effects of increasing or decreasing the retention interval (RI) on performance in the reproduction procedure, and found this produced a response bias towards larger numbers, contrary to predictions based on previous RI research, and suggested responding was not affected by memorial decay processes. The structure of the representation of number developed by subjects in the bisection and reproduction procedures was investigated using analyses of responding and response variability in Chapters 2 and 6, respectively. Bisection points obtained in Experiment 1 were located at the arithmetic, not geometric mean of all three scales, and coefficients of variation (CVs) obtained in both the bisection and reproduction experiments tended to decrease as flash number increased. Additionally, analyses of the acquisition data found differences in average response number was better fit by a linear than logarithmic scale. These results show that responding did not conform to scalar variability and is largely inconsistent with previous nonhuman research. Together these results suggest responding appeared to be based on a linear scale of number with constant generalisation between values, similar to that associated with human verbal counting, rather than a logarithmic scale with constant generalisation or a linear scale with scalar generalisation between values. Experiment 5 compared pigeons’ and humans’ verbal and nonverbal discrimination performance with numbers 1-20 in analogous bisection, reproduction and report tasks. Human verbal and nonverbal performance in the three tasks was similar and resembled nonhuman performance, although verbal discriminations were more accurate and less variable. The main findings from Experiments 1 and 2A were replicated with humans; bisection points were located at the arithmetic mean, average response number increased linearly as sample number increased, though there was a tendency to underestimate sample number, and decreasing CVs were also obtained for values less than 8. An additional, interesting finding was that CVs showed scalar variability for values greater than 8, suggesting a less exact representation and discrimination process was being used for these values. Collectively, these five experiments provide new evidence for a nonverbal ability to discriminate relative and absolute number with increasing relative accuracy resembling human verbal counting in both human and nonhumans.