Eeny, meeny, miny, mice: counting and numeric meta skills in animals

All aspects of animal behaviour are the result of a choice. By choosing to do one thing an animal is therefore not doing something else. These decisions need to be made in a manner that maximizes the likelihood of survival. Because of this emphasis on survival, decisions are generally studied from an ecological perspective; however, likelihood of survival is also essential in the cognitive domain.

One way in which animals measure aspects of their environment is through the use of number.

Humans use numbers in all aspects of our daily lives. How much change do we get after buying a cinema ticket (sadly not much anymore)? How tall am I (again, sadly not very)? Did he get more than me (probably)? Non-human animals need to be able to assess similar things, for example to assess quantity of food or the size of group.

It turns out that animals have a sense of number that enables them to perform those tasks.

Impressive mathematical abilities have been shown in a number of species. Ayuma the chimp is able to order numbers even after only seeing them very briefly and totally outperforms humans in this sort of task. See for yourself: Watch the movie below and see if you could perform as well or better:

Animals can discriminate numerical values, count and even do simple arithmetic. Most of the research in this area has focused on number discriminations. This is clearly important in and of itself; however, number judgments are also interesting because it is apparently related to other judgments of quantities or extents, such as timing.

It has therefore frequently been claimed that the ability to count is likely to be controlled by similar mechanisms in the brain as the ability to judge time. This hypothesis has been supported by the fact that they have similar psychophysical properties. Both numerosity judgments and timing judgments follow Weber’s law which, in this context, suggests that the amount of error is proportional to the size of the target number, or, the length of the target delay. More errors occur when these are large, so you are less accurate, and therefore decisions on the basis of those judgments are riskier. So, if you need to press a button 100 times to earn a reward, you are more likely to get lost or make more errors than if you need to press it 3 times. Thus, responding is riskier with the higher number.

The relationship between optimal decision making and numerical perception has been explored by Bilgehan Çavdaroğlu and Fuat Balcı (Koç University) in a recent paper published in Psychonomic Bulletin and Review. They investigated whether mice were able to count and, if so, whether uncertainty impacted upon their decisions when counting.

The researchers did this by using a really interesting setup in which the mice had to press a lever a certain number of times. After pressing it 10, 20 or 40 times (depending on the stage of the experiment) the mice then had to press another lever. If the animals pressed the second lever too early then it reset the count and the mice had to start over again with another 10, 20, or 40 taps. Thus, there was a penalty for under-shooting the required number of presses.

However, pressing the first lever too many times was also costly, albeit only in terms of effort. Thus the rats needed to count the number of lever presses accurately before making the decision to press the second lever, but there was a crucial asymmetry in the penalty—a little bit of effort for over-shooting and a lot of wasted effort for under-shooting—that turns out to be crucial.

By increasing the number of lever presses required to get rewarded the experimenters manipulated the size of the target number. They predicted, on the basis of Weber’s law, that the greater the number required, the greater the error. Error, in turn, leads to uncertainty in outcome, which should affect the optimality of the animals’ decision making.

The optimal strategy was for animals to respond more than the minimum requirement before pressing the second lever, because the penalty of “wasted effort” was far smaller than the penalty of having to start over again from the beginning. But how much more? How much should the animals overshoot?

The optimal size of the overshoot depends on how certain the animals are: if they are very certain, as they might be with smaller numbers, they would respond shortly after 10 presses. By contrast, if they are not very certain, for example if they are required to make 40 lever presses, then we would expect greater overshoot. That is exactly what was observed. Animals were able to take into account uncertainty about their own numerical judgment when making a decision about when to press the second lever, and were thus able to optimize their decision making.

Not only do mice know how to count, they also seemingly have “meta” knowledge of the accuracy of their counting.

These findings reveal that optimal risk assessment is a general phenomenon that crosses species boundaries. The data also support the idea that counting appears to be susceptible to similar psychophysical properties to timing. So, when cooking a beautiful fillet steak, then counting the seconds until you take it off will be equally as risky as estimating the time taken. Unless, of course, you have it blue.

Article discussed in this post: Çavdaroğlu, B. & Balcı, F. (2015). Mice can count and optimize count-based decisions. Psychonomic Bulletin & Review.

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