I'd like to teach the bee to count

From the Discworld :

In fact, trolls traditionally count like this: one, two, three, many, and people assume this means they can have no grasp of higher numbers. They don’t realise that many can BE a number. As in: one, two, three, many, many-one, many-two, many-three, many many, many-many-one, many-many-two, many-many-three, many many many, many-many-many-one, many-many-many-two, many-many-three, LOTS.

Remember how bees can supposedly count up to four and understand zero ? Well this new study says it's more subtle than that.

We found the bees could tell the difference between groups of one vs. four flowers—but not between, say, four vs. five. Basically, they couldn't differentiate between groups of two or more flowers. 

Our honeybees were shown pairs of flower quantities ranging from easier number comparisons (such as one flower vs 12 flowers) to more challenging scenarios (such as four flowers vs five flowers). Interestingly, despite previous findings that trained honeybees can discriminate between challenging quantities and can also learn to add and subtract, the bees performed poorly in our spontaneous number task. 

We found they were only able to discriminate between one vs 3, one vs 4, and one vs 12 flowers—wherein they preferred the larger quantity. When one flower was an option they succeeded, but confused any comparisons between groups of two flowers or more.

But this leaves so many questions. Only 1 vs 12 ? Why not 1 vs 6 ?

Suppose I'm a bee. My job is to collect as much nectar as possible, but I have limited visual information on which to judge this. Flower size being equal, I'll need to maximise nectar collection by visiting as many different flowers as possible, but if flower size is not equal then I might prefer one big flower to two smaller ones. And I'm going to want to minimise nectar collection time, so one big flower is going to be preferable to lots of widely-separated flowers. Furthermore, I might not have great visual resolution to distinguish between lots of small flowers crammed together.

This is going to make testing the bee's ability to count somewhat tricky : a bee might prefer one big flower to three small ones not because it's an idiot, but because it knows that choosing one big flower is more sensible. On the other hand, bees might be able to learn that the experimental reward given is based purely on the number of flowers, not their size.

So my guess would be that if you want to see if bees can count you would start by giving them a reward in response to choosing a patch containing one "flower" of varying different sizes, always while keeping the size of the patch constant. Then you add a second flower, and this patch should contain twice the reward. If the bees can distinguish between one and two, then they should surely always choose a patch containing two simulated flowers, no matter the size or size ratio of the two (again always keeping the patch size - i.e. flower number density - constant), within the limits of their visual acuity.

Those are my pre-emptive caveats. So does the paper give anything more informative than the press release ?

Yes and no. The authors do carefully set out their control conditions, e.g. testing whether the background colour of the patch makes any difference, randomly moving the different patches around the testing area etc.; they also account for the "flowers" being able to have the same total area or have fixed individual sizes. But they were only trained in response to a single "flower" with the same reward. So, surely, the bee then has to make its own judgement about whether it would be better to go for more flowers or bigger flowers. How is it to know how much nectar each contains ?

Another thought occurs : smell. There's nothing mentioned about it, but in the wild bees will also be able to smell greater amounts of sugar. So how did they control for this ? Retroactively, I'd say in the training phase you have the bees exposed to different quantities of sugar in proportion to the number of flowers regardless of their size or number density. And why not go the whole hog and do the entire thing by scent ? If they can distinguish 2 vs 6 in terms of scent alone, that's still counting in my book.

The way they chose the numbers of flowers also seems a bit odd to me and it's not at all clear how they chose it. The obvious thing to me would have been 1v2, 1v3, 1v4 etc. But they don't have 1v5 or 6 or 7. This is a shame, because while there's no numerical preference between 1vs2, there is for 1vs3 and a stronger one for 1vs4. Maybe this would have increased further, presumably reaching some limit when the density becomes so high it just looks like one giant flower or is indistinguishable from the previous case.

All that said, their discussion section is very nice, and contains some additional self-criticism :

It may not be important for bees to differentiate between two or more flowers as they may simply classify these quantities as ‘many’ [YAY TROLLS !]. When foraging, perhaps there is little difference between visiting a flower patch which provides two flowers to visit as opposed to three or four. However, when conditions are not optimal and few flowers are present in an environment, it may be vitally important to find a patch with more than one flower. 

Perhaps the number of elements contained within the alternative stimuli during tests was too high for bees to process the visual task efficiently, leading to errors and/or a tendency to choose at random. 

Honeybees have evolved in tropical environments, which host scarce but clustered sources of nutrition. Thus, honeybees may have acquired a fast but inaccurate visual search strategy when compared with bumblebees, which have evolved in sparse but evenly distributed resource environments in temperate zones. Consequently, bumblebees use a slow but careful foraging strategy. The fast but error-prone strategy of honeybees is useful for environments where accuracy provides no benefit.

In short, bees might think a bit like trolls, but it's very hard to tell for sure.

One, then some: How to count like a bee

If you were a honeybee, how would you choose where to find flowers? Imagine your first flight out of the hive searching for food. What would you do if you saw flower patches with one flower, or three, or twelve, or twenty?