One Fish, Two Fish

Counting is an ability that humans use every day, often without thinking about it: paying for purchases, measuring out sugar for your coffee, and calculating just how much longer until lunch. But do animals possess this ability too?

It would make sense for animals to have a ratio-based ability to determine amounts; that is, given two different amounts of an item (such as food), it would be evolutionarily advantageous if they could determine which amount is largest.

Humans and other animals actually do use a ratio-based system, and there’s an intuitive rule about how it works: Weber’s Law states that as the ratio between quantities gets smaller, discrimination becomes more difficult. Which makes sense, since it’s more difficult to discriminate between 7 items and 8 items than between 7 items and 20 items.

7 vs. 8 dots

7 vs. 20 dots





It turns out that for small amounts (less than 4 items), some animals (including humans) can accurately discriminate between them regardless of their ratio (they discriminate between 1 and 2 items just as accurately as between 1 and 3 items). This indicates that another, number-specific system may be used when discriminating between small numbers of objects.

Some interesting research has been done on how humans use these two number systems, and it appears that the systems are independent of each other (one or the other system is used while making a numerical judgment, but not both).

Researchers discovered this by assessing how well human infants could discriminate between different quantities of objects. They found that infants can accurately discriminate between large quantities, as long as the ratio between those quantities is sufficiently large. But when quantities are small (less than 4 items), infants can accurately discriminate between them, even if the ratio between those quantities is small (i.e. 2 items vs. 3 items).

Here’s the result that really clinches the independence of these two number systems: infants cannot discriminate between quantities that span the small quantity – large quantity boundary. So while they can discriminate between 1 and 2 items, or 1 and 3 items, or 2 and 3 items, they cannot accurately discriminate between 1 and 4 items, or 3 and 6 items (remember that the number-specific system is only used for quantities less than 4). This indicates that the two number systems can’t be used together – they’re independent.

[An important feature of these two systems is that they’re nonverbal (don’t involve the use of language). Having verbal numerical labels obviously makes numerical discrimination easier, and it helps explain why older humans can easily discriminate between quantities that span the small quantity – large quantity boundary.]

The research on these two number systems in non-human animals has yielded conflicting results, so I’m just going to discuss one really interesting recent study. Why this particular study? Because (spoiler alert) it suggests that FISH CAN COUNT. I don’t know about you, but I’ve always assumed that there’s not too much going on in the brain of a fish, so the results of this study really surprised me.


Xenotoca eiseni

Stancher et al. (2013) investigated whether redtail splitfin fish (Xenotoca eiseni) could discriminate between small quantities. Since redtail splitfin males compete for access to females for mating, the researchers studied whether a male could discriminate between two different quantities of females. They assumed that the male would swim toward the area of a fish tank containing the greater quantity of females.

They found that the males were able to discriminate between 1 and 2 females, and 2 and 3 females, but not 3 and 4 females. First of all, these results show that FISH CAN COUNT. Which is incredible, and suggests that some sort of counting ability developed really, really early in evolution.

Second, this pattern of results matches what we see in infants, where the number-specific system only works for quantities less than 4. However, unlike human infants, the fish were able to discriminate between 1 and 4 females, and between 2 and 4 females.

The fact that the fish were able to discriminate across the so-called small quantity – large quantity boundary indicates that they may use only one number system, rather than two independent number systems. The researchers suggest that the fish possibly use a ratio-based number system for all quantities, not just larger ones. This is supported by the fact that the fish were unable to discriminate between the quantities with the smallest ratio (3 vs. 4).

*A note about the two number systems described above: the actual terms used for these systems are the Object File System (what I called the “number-specific system”) and the Analog Magnitude System (what I called the “ratio-based system”). These terms are based on the theories of how these systems actually operate in the brain, which I didn’t have the space to detail here.


Feigenson, Lisa, Susan Carey, and Marc Hauser. “The representations underlying infants’ choice of more: Object files versus analog magnitudes.” Psychological Science 13.2 (2002): 150-156.
Stancher, Gionata, et al. “Discrimination of small quantities by fish (redtail splitfin, Xenotoca eiseni).” Animal cognition 16.2 (2013): 307-312.

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