You'll notice right away that choosing the correct side without counting the fish individually is pretty tough. This difficulty stems from the fact that humans can only assess relative quantities by snap judgment under certain conditions. Take away six fish from the right-hand side, for example, and this task becomes noticeably easier.
Previous studies have shown that other primates handle numerical exercises like this one about as well as we do — but now, new research has revealed that the fish in this image are just as capable of this kind of task as humans and chimps. Find out how, when it comes to approximation, a guppy's math sense is every bit as good as yours.
We'll get to the fish in a minute — for now let's take a quick look at the numerical systems that humans use to perceive relative quantities.
For those of you who haven't counted yet, the guppies on the left outnumber those on the right 19 to 18 (or 22 to 20 if you're counting fins, as well). But remember, you weren't asked to count the fish one-by-one; you were asked to extract meaningful numerical information from the image you were presented with as quickly as possible — i.e. without counting the fish individually.
Your capacity for performing this task is subject to something called Weber's law, which roughly states that your ability to accurately discriminate between two quantities improves as the ratio between them increases. Psychologists believe that your ability to approximate relative quantities in accordance with Weber's law is based on something called your "analog magnitude system."
Interestingly, the principles of Weber's law — and your reliance upon your analog magnitude system — crumble when you start comparing smaller quantities. Most people, for example, have a more difficult time discriminating 15 objects from 20 than they do discriminating 5 from 20 (this is to be expected under Weber's law); ask them to discriminate 3 objects from 4, however, and you'll find they perform just as well as if you'd asked them to distinguish just one object from four. Psychologists call the numerical system that helps you track small numbers of individual objects your "object-file system." (Psychologists believe that our object-file system is dependent upon the ability to subitize — i.e. our ability to know right away, without counting them serially, that there are three blue stars in the image on the left. For more on subitizing, see here.)
Alright, are you still with me? Remember: Your first numerical system — your analog magnitude system — applies to large numbers and relies on the ratio between the quantities you are comparing; your second numerical system — your object-file system — applies to small numbers and is dependent upon your inborn ability to track small quantities without counting them individually.
Which brings us back to the fish. In a study published in the latest issue of PLoS ONE, a team of researchers led by psychologist Christian Agrillo has revealed that human subjects and guppies show almost identical performance patterns in experiments designed to test both the analog magnitude system and the object-file system.
The researchers accomplished this by having both the fish and human test subjects determine which of two collections of objects was larger. The students played a computerized game in which they were sequentially presented with two groups of dots and asked to estimate — without verbally counting the dots — which group was more numerous.
The guppies were placed in a tank and given the chance to join either of two groups containing different numbers of fish. (According to the researchers, previous work has shown that guppies strongly prefer to join larger groups.) The researchers describe their findings:
When tested in the same numerical tasks, the students and guppies showed almost identical performance patterns. In both species, the ability to discriminate between large numbers (>4) was approximate and strongly dependent on the ratio between the numerosities. In contrast, in both fish and students, discrimination in the small number range was not dependent on ratio and discriminating 3 from 4 was as easy as discriminating 1 from 4. Likelihood ratio analyses indicate that the lack of ratio effect is 3.68 times more likely than the alternative hypothesis in fish and 3.67 times in students. As a consequence, the discrimination of larger numerical ratios, 0.67 and 0.75, is easy in the small number range for both species, but becomes relatively more difficult (among students) or even impossible (among fish) when confronted with large numbers.
Translation? For all intents and purposes, these fish are every bit as good at evaluating numerical ratios as we are, and they may even do it via the same two mechanisms of numerical representation — with one system responsible for evaluating numbers 1—4, and another responsible for larger quantities.
"The results of this comparative study admits the possibility of common mechanisms between primates and basal vertebrates," explain the researchers, "suggesting that the evolutionary emergence of numerical abilities may be very ancient, possibly dating back to before the [evolutionary divergence of triassic-period fish and tetrapods]."
The researchers' findings are published in the latest issue of PLoS ONE (no subscription required).
Top image via; Subitization image via Wikimedia Commons; Test figures via PLoS ONE