An Attempt to Explain Oscillating Flies in Groups (Non-mathematically)

I was walking through Astbury Mere, a lake near my house, on a sunny clear day. There were many flies about, this may be due to the abundance of water, greenery and the general amount of good resources in that environment. I might have also witnessed these flies during their mating season, as many species conduct their mating over water or near water (especially the mayfly).

One particular feature of the flies (I did not know what species they were, but i found out after some time that many flies exhibit this) was that they seemed be arranged in a certain configuration in which each fly would oscillate in a confined region, then sporadically change its region or buzz off. I never really noticed this before. There was a geometrical neatness and efficiency about the group of flies oscillating.

I tried to think of reasons for this. I came up with a number of possibilities:

1) It is only a feature of flies in mating season, where male flies are scanning the group for potential mates or vice versa. The configuration is merely an evolved system which makes mating more efficient.

2) It is a general feature of many fly systems, but its specific configurations and behaviours vary from species to species. It is caused by the evolved need for the flies to communicate, through chemical emissions, either food resources, mating etc. (I do not know the limit of complexity of the communications, I can only hint that this feature could have a social function). This may have evolved as flies that carried genes which encouraged  communication between other flies in flight could help them gain food, more mates or find shelter which could help them survive hence pass on more genes etc..

3) It is only a coincidental phenomenon occuring randomly within that species or only a few species, the phenomenon occurs only due to spatial restrictions etc. (nothing programmed within their genetic code)

Hypothesis 3) can be ruled out quite easily. Why would flies waste energy in flying in oscillation within a group of flies randomly ?  Surely they would have evolved not to waste energy, they would instead spend it on gathering food, mating or finding shelter.

Then we come to another question. What if each fly tried to find food etc. but failed and kept on failing to find food and shelter but one fly found food and shelter. Now let's suppose that the fly who found the food and shelter had genetic relatives close by, it would be in his genes interest to communicate to them his new found prize.

It could be that this phenomenon (oscillating in groups) occurred already in some fly species due to mating (reason (1) ) what happens if some flies over a long period of time tried to continue this social oscillation process not just to mate but to communicate information about food etc. Obviously they would not make conscious decisions, the genes would instruct them. So this means over time a gene (or mutated gene from the same phenomenon for just mating) which encouraged flies to communicate in air in some manner about other resources, not just mating, became successful. Now we can understand, as biologists, why such a gene would spread as it would benefit an individuals genes to preserve his relatives which have some fractional amount of his genes, and it would benefit an outsider fly (of same species) who could listen in and make his own body survive (which in turn means his own genes survival).

Over time the geometry and mathematical efficiency of the phenomenon would become more complex, leading to flies finding the optimal position and group shape to pick up chemical signals from other flies.

The most common group shape I have witnessed is a sphere where flies would oscillate on the surface of the sphere.

From this information one could devise a mathematical algorithm which tells a fly where, how long and how often to oscillate, change position etc. within the group. (Energy expenditure would also play a role as a constraint).

I hope to think more on this problem and construct a sound mathematical algorithm to explain it.