I have noticed that when insects are placed on their backs, they tend to turn themselves over quickly or else appear to be in distress. Is there a physiologic, anatomic, or adaptive reason why supine positioning might be unfavorable in insects?
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Insects don't "like" being on their back because they can't get back on their legs and they therefore get stuck somewhere where they can gently wait for death to come.
Not all insects are unable to switch back on their legs but some can't do that (or can hardly do that). The reasons for which many insects are not able to get back on their legs (while mammals for example usually can do that) is that they have a exoskeleton. Their exoskeleton limits drastically their movements.
I'd guess that this varies quite a lot among different insects; in some, lying on their backs was a sign of their impending death, while others will flip over onto their backs to play dead. This isn't really surprising --- there's over a million described insect species, so some amount of variety is to be expected! Here's a video of a bunch of insects exhibiting different strategies for turning themselves over.