Do cuttlefish have fraction number sense?

Number sense is a key cognitive function in animals. The biological functions of number discrimination have a wide range, including the selection of prey and social interaction. In a previous study, we have shown that cuttlefish are able to distinguish numerical differences among various integers, including 1 vs. 2, 2 vs. 3, 3 vs. 4, and 4 vs. 5. However, it is not known whether cuttlefish are able to discriminate various fractions, that is, various non-integer numbers. In addition, no study on invertebrates has examined fraction number sense. Using the active preying behavior of cuttlefish (Sepia pharaonis), we investigated the spontaneous preference for larger quantity by presenting two-alternative choice between 1 vs. 1.5, 1.5 vs. 2, 2 vs. 2.5, and 2.5 vs. 3. In this context, the quantity1.5 is composed of one large shrimp and one small shrimp, in which the size of the small shrimp is one-half of that of the large shrimp. The result shows that the cuttlefish chose larger quantity in the first three pairs, but they could not distinguish the pair 2.5 vs. 3. Despite that the absolute differences in these pairs are the same (0.5), the relative differences in these pairs decrease (0.5, 0.33, 0.25, and 0.2, respectively). This implies that the perceived difference in quantity is proportional to the initial quantity (Weber's law). Although the present study does not truly differentiate the number difference from the quantity difference, this result does raise the possibility that cuttlefish may be equipped with the primitive concept of fractions, and if so, the perceived just noticeable difference is similar for both integer and fraction number discrimination.