Count On It

Far from being cold, mindless killing machines, in recent years, scientists have become increasingly aware of how intelligent and cognitively advanced sharks and rays are. Relative to the size of their bodies, sharks have very large brains and are surprisingly smart; capable of recognising individuals and forming friendships; forming mental maps to navigate around the world; and having unique personalities. Amazingly, we now know that sharks are rays are even capable of basic mathematics! But how on Earth do you test such a thing? What kind of arithmetic are sharks capable of? And why have they evolved this ability?

Put Two and Two Together
You might imagine it's impossible to figure out what sharks and rays are thinking. And it's true, we will probably never be able to fully understand how they perceive their worlds and what their internal experiences are like, but with very carefully designed experiments with strict controls in place, it is possible to ask scientific questions such as 'can a shark understand the concept of less-than and more-than?' and 'can sharks do maths?'. So how is this done?
In the lab scientists can train sharks and rays to recognise a visual stimulus - a picture or a drawing of a shape - and teach them to approach and touch these images in order to receive a reward. Once the animals have learnt to master this skill, researchers can then limit the supply of the reward under certain circumstances - when the animal has answered a posed question correctly (Fuss & Schluessel, 2015; Schluessel et al, 2022).

Out For The Count
The first scientific research to pose such a question focused on whether sharks could recognise an image that showed a higher number of shapes, including squares, dots, crosses and triangles, in differing quantities (Vila Pouca et al, 2019).
First, the scientists trained Port Jackson sharks (Heterodontus portusjacksoni) to swim towards the image that showed the greater number of shapes. This meant providing the sharks with two random images from their selection and only rewarding the shark with a tasty treat when they approached the image displaying greater quantity. This method is known as "operant conditioning" (Vila Pouca et al, 2019).
When presented with two images again under test conditions, the sharks consistently swam towards the tile showing the higher number, proving that these little sharks are capable of "quantity discrimination", that is to say, they understand when one quantity is larger than another, regardless of which shapes they are shown (Vila Pouca et al, 2019).

In a similar study, scientists trained grey bamboo sharks (Chiloscyllium griseum) and ocellate river stingrays (Potamotrygon motoro) to approach an image that either had a higher or a lower quantity of shapes shown. In addition to simple shapes, they also tested simple silhouettes of biologically relevant shapes, such as the outline of a crab or fish (Kreuter et al, 2021).
The data showed that both these species are capable of quantity discrimination, but individuals differ in their ability; with some being more accurate than others. This implies that the skill may not be critical to these animal's daily lives (Kreuter et al, 2021).
Taking it up a notch further, scientists recently studied whether freshwater stingrays are capable of basic arithmetic. To achieve this they presented the ray with an image displaying a number of shapes. The colours gave the stingray an instruction for how to answer; blue meant add one (+1) and yellow subtract one (-1) from the test stimulus. They would then be shown two possible answers - like a multiple choice test. The stingray would only be rewarded with a tasty treat if they selected the correct answer (Schluessel et al, 2022).
As these stingrays got the answers right, this proves that they have, not just a concept of quantities and "relative numerosity" (more-than and less-than), but they also understand what 'one' means. Thus they can identify a single shape and are able to add and subtract small quantities (Schluessel et al, 2022).

Do The Math
This probably all sounds completely bonkers - why on Earth would fish need to understand numbers!? Well, for many reasons, actually!

Firstly, being able to recognise a higher quantities of individuals in a large group versus few individuals in a group, can be vital for survival. Many prey items flock together - zebras, sheep, schooling fish - because, in a large group it is harder to pick out an individual. This is known as "the predator Dilution Effect" and it helps them to evade predation (Agrillo, 2015; Agrillo et al, 2011; Agrillo et al, 2015).
In addition, understanding amounts is vital for foraging. If you are able to grasp that there are more fish or other foodstuffs in one place versus another, this gives you the ability to visually identify good hunting grounds (Agrillo, 2015; Agrillo et al, 2011; Agrillo et al, 2015).

As these sharks and stingrays did not always get the answers right and there was noticable variation in their maths skills from one individual to the next, it seems likley that these abilities are not necessarily essential in their everyday lives; for foraging and avoiding predators. If they used their quantities estimation skills daily, we would expect the skill to be much more honed in every individual. Therefore, it seems more likely that these little sharks use their quantities estimation skills for finding a mate. If you are able to identify a larger group of individuals, this ups your chances of successfully finding a mating partner. Thus, the ability to recognise more-than and less-than is a critical evolutionary advantage that allows these sharks and rays to be able to breed (Agrillo, 2015; Agrillo et al, 2011; Agrillo et al, 2015; Brown & Schuessel, 2023).
Who knew strong maths skills could get you the girl!
To learn more about shark cognitive abilities check out Jaws and Brains.
References
Agrillo C (2015). Numerical and arithmetic abilities in non-primate species. In: Cadosh RC & Dowker A (Eds.). The Oxford Handbook of Numerical Cognition, pp 214–236.
Agrillo C, Piffer L & Bisazza A (2011). Number versus continuous quantity in numerosity judgments by fish. Cognition, 119. Access online.
Agrillo C, Petrazzini MEM & Bisazza A (2015). At the root of math: numerical abilities in fish. In: Geary DC, Berch DB & Koepke KM (Eds.). Mathematical Cognition and Learning. Elsevier, Amsterdam, vol 1, pp 3–33.
Brown C & Schluessel V (2023). Smart sharks: a review of chondrichthyan cognition. Animal Cognition, 26:1. Access online.
Fuss T & Schluessel V. (2015). Something worth remembering: visual discrimination in sharks. Animal Cognition, 18:2. Access online.
Kreuter N, Christophzik N, Niederbremer C, Bolle J & Schluessel V (2021). Counting on numbers—numerical abilities in grey bamboo sharks and ocellate river stingrays. Animals, 11:2634. Access online.
Schluessel V, Kreuter N, Gosemann I & Schmidt E (2022). Cichlids and stingrays can add and subtract ‘one’ in the number space from one to five. Scientific Reports, 12:3894. Access online.
Vila Pouca C, Gervais C, Reed J, Michard J & Brown C (2019). Quantity discrimination in Port Jackson sharks incubated under elevated temperatures. Behavioural Ecology & Sociobiology, 73:93. Access online.










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