I was walking home from work, having mysteriously cycled in that morning without my bike, whereupon I noticed a rather large dragonfly on the side of the road. Huge, thick, green and blue.
Anax imperator, the Emperor Dragonfly, largest UK species. I was quite overjoyed to see one, especially so close, though it seemed very odd that it was standing on the floor like that. Resolving to investigate, and leant down and put my finger under its front, mindful of its predatory mandibles. It crawled onto my finger and I lifted it up to examine it more closely.
I was able to diagnose the problem readily and with not a little surprise. It had no head.
And yet it was still alive. It adjusted the position of its legs and gripped my finger tightly as it's abdomen pulsated, curled and uncurled. It's wings flickered restlessly.
I don't deny that it instilled in me a certain unease. It had lost its vital front end and hadn't noticed. In retrospect, I would not expect any living being to notice such a gruesome injury without the benefit of a working brain. As I peered into the dry, black wound at the front of the thorax I was startled further when the animal very suddenly took flight. It quickly flipped upside down and crashed into the grass about two feet away. Well, what would you expect? Poor thing couldn't see where it was going.
I picked it up again and finished my examination, it's abdomen coiling about itself vigorously now as though shamed by its aerial performance and indignant at the injustice of its unenviable circumstances. I then began a brief inspection of the surrounding area, which yielded no sign as to the whereabouts of the dragonfly's head. Fearing that this specimen may have been beyond my aid, I put it back down on the grass and completed my journey home. There I began my research.
To understand how an insect can survive losing its head it helps to understand why a person does not. Firstly, the human circulatory system is highly pressurised. Decapitation represents a substantial breach of containment, leading to catastrophic loss of blood pressure. Secondly, the brain is essential for controlling both heart and lungs. Decapitation therefore also causes suffocation and cardiac arrest, though these will be the least of your worries.
In insects, neither of these are true, which means that death by decapitation is not necessarily instantly fatal. The circulatory system, such as there is one, is not pressurised, so there will only be a little leakage that will quickly clot. There are no lungs, gaseous exchange happens across a network of trachea through which air passes by diffusion alone. These trachea are connected to the atmosphere by way of spiracles, of which there are several alone the side of the insect's body. As for the heart, it is a very simple muscular tube connected to the insect's open circulator system (ours is closed) and is controlled by the relevant segment's nerve ganglion.
Arthropods are segmented organisms. In insects many of these segments are extremely derived and highly specialised, but they are segments just the same. Each segment contains a ganglion that serves all organs and appendages like a remote pseudo-brain. An insect's actual brain is a fusion of three such ganglions. It is primarily responsible for the animal's behaviour and general coordination.
A headless insect's days are indeed numbered, and there are numerous ways in which headlessness can hasten the arrival of death.
1: Infection. The loss of the head represents a major injury and leaves a rather large open wound. This breach in the insect's outer defences leaves it especially vulnerable to infection by bacteria, viruses, fungi and protists. As usual.
2: Drying out. Another major function of an insect's dermis is to keep moisture in. The sheer effectiveness of insect moisture-retention is one of many factors that contribute to the superlative success of Classis Insecta. Depending on the climate, headlessness can lead to a rapid loss of water.
3: Predation. An insect's senses are not quite as localised as our own, but the head is still the sole location of sight, and also the brain that directs its actions. While all the reflexes are still live and literally kicking, predator evasion takes a major hit which the loss of the head.
4. Starvation. The head contains the mouth. While the digestive system remains oh-so open after decapitation, insects cannot deliver food into it without the mouth, which is usually quite specialised for the diet. At least a human would be dexterous enough to employ a funnel were hand-eye coordination not such an issue. Neither can an insect easily locate food without its eyes and antennae, or a brain to make use of such sensory input.
Fortunately, if that word is applicable to such a situation, insects are poikilothermic, (the technical and more accurate term for "cold blooded") and thus require substantially less sustenance per gram than we exotherms. So assuming that a headless insect stays hydrated, uneaten and mould-free, it could last a number of weeks before it ignominiously starves to death.
Which, it seems, is the best my dragonfly can hope for. If it were in any condition to hope anything at all.