The Importance of Replication in Comparative Psychology: The Lesson of Elephant Quantity Judgments

for the existence of an approximate system of numerical representation. Such a system, commonly referred to as the “analog magnitude system,” seems to have no upper limit but is subject to a ratio limit in accordance with Weber’s Law, which states that the capacity to discriminate between two quantities becomes more accurate as the ratio between the smaller and the larger quantity increases (Beran, 2007). The mechanism is supposed to operate as an accumulator, with numerical magnitudes represented by distance along the accumulator. Some researchers have also hypothesized the existence of a precise mechanism devoted to the processing of small numbers. This mechanism often is called subitization, defined as the ability to immediately perceive the quantity of small sets without serial counting (see, for example, Bonanni et al., 2011; Agrillo et al., 2012). However, while researchers still debate the existence of this small number system, they generally accept the analog magnitude system and use it to explain the full range of numerical competence in non-human animals. Indeed, how easily an animal can discriminate between two quantities has been found to depend upon the ratio in mammals (e.g., Beran, 2007; Ward and Smuts, 2007), birds (e.g., Al Aïn et al., 2009), amphibians (e.g., Krusche et al., 2010), and fish (e.g., GòmezLaplaza and Gerlai, 2011). A recent paper by Irie and Hasegawa (2012) has now opened a wide-ranging debate in the scientific community regarding the performance of three elephants (Elephas maximus) that undertook a summation task. The authors adopted a modification of the method that Beran (2004) used with chimpanzees: different numbers of food items were sequentially inserted into two opaque boxes so that the subjects could never acquire a global view of the entire contents of the sets and could only use represented quantity information. In The importance of replication in comparative psychology: the lesson of elephant quantity judgments