I live in the UK and have a free license to trap American Signal Crayfish, which are classified as an invasive species under the The Invasive Alien Species 2019. The law makes it illegal to release or allow to escape any American Signal Crayfish, or transport them. If you catch one in the UK, you are required to kill it.
If you ask a human whether they'd prefer to be boiled alive or have their skull split open, they'd probably almost all say the latter. However, I think applying that intuition to invertebrates isn't necessarily correct.
Why do burns hurt so badly?
Burns are some of the most painful types of wounds for humans. A large, second degree burn might easily be more acutely painful than a stab wound, even though the stab wound might be more life threatening. Why is this?
The answer is that free nerve endings, the nerve type that transmits pain in humans and other mammals, are densely packed on the surface of the skin. There are some internal nerve endings but they are far less dense. If you've ever had blood taken or a subcutaneous injection, you'll know that the needle hurts at the entry point, but once it goes under the skin, it doesn't hurt at all. That's because there's no free nerve endings directly below the skin in the fat layer.
Unlike some invertebrates, humans are covered with delicate, highly damageable skin. In order to avoid damage, we evolved densely packed nerve endings which allow us to detect even small areas of damage, like a pin prick. (Acupuncture needles are so thin it allows them to pass between nerve endings.) The larger the wound, the more pain; a cut hurts more than a pin prick because more nerve endings are activated. But a cut is still only 1 dimensional.
A burn is 2 dimensional, so the amount of nerve endings is squared relative to the cut. Thus, the amount of pain is squared, too. (Additionally, free nerve endings fire in response to both heat and mechanical damage. Since a burn is both, the nerve is pretty much guaranteed to fire.)
The peripheral nervous system of invertebrates
Invertebrates clearly demonstrate nociception. However, we can expect a priori a different nervous system arrangement due to a different risk profile than with soft bodied invertebrates or vertebrates. And indeed, that is the case.
Unlike mammals, there is no documentation of free nerve endings in decapods like lobsters, crayfish and crabs. This is likely because main cause of mechanical damage to an exoskeleton is going to involve deformation of the exoskeleton, i.e. the exoskeleton becoming inverted or crushed.
In particular, when an invertebrate molts, the new shell is very soft and they are particularly vulnerable to the shell becoming damaged at this time. So, they evolved to be sensitive to changes in vascular pressure. An increase in vascular pressure means the shell is in danger of being deformed or breached.
We should and do see a nociceptive response to increases in pressure on their exoskeleton that can cause deformation, i.e. crush injuries. Internally, the animal has mechanoreceptors, a different type of nerve ending, and these can detect these changes in vascular pressure. It's likely this nocireceptive response is elicited by these internal mechanoreceptors.
By contrast, a squeeze does not cause humans much discomfort, although of course we can also experience bruising and crush injuries. However we are not particularly sensitive to changes to pressure, relative to our response to burn injuries, because most mild pressure does not cause injury, whereas damage to the surface area of the skin leaves us very vulnerable to infection and consequently death.
The central nervous system of invertebrates
Given the option between boiling alive and cutting through the head, many people believe cutting through the head is the more human choice. Doing so involves taking a knife and essentially stabbing the crayfish or lobster through the main "brain", called the supraoesophageal ganglion.
Unlike humans and other animals, invertebrates like crustaceans and insects have a relatively distributed nervous system. Instead of having one main brain, they have several clusters of neurons called ganglia. This is why, for instance, you might have seen videos of insects moving without a head. It's alien to us, but ganglia in the thorax and abdomen can still operate independently of the supraoesphageal ganglion.
That said, I still think it's likely the animal cannot experience pain without the supraoesphaegal ganglion.
This is also the nature of being small and having an open circulatory system where neurological tissue is passively, rather than actively oxygenated. Loss of oxygen to a mammalian brain results in it ceasing functioning in a matter of seconds.
Brain size and complexity in invertebrates is limited by the ability of the innermost neurons to be passively oxygenated.
Meanwhile, invertebrate brains can remain operational for quite some time after the animal is dead. For instance, in my undergraduate neurophysiology class, we removed the brain of a slug and took electrical readings from individual neurons with a needle. The brain is small enough that the oxygen from the media it was in was enough to keep the neurons operational for an hour or more. (However, the individual neurons being operational doesn't mean the brain behaved normally or was conscious.)
Cold and the invertebrate
Placing a "cold-blooded" animal in the freezer for a period of time is often used to anaesthetise them (or in the case of freshwater inverts, an ice slurry). The reasoning is that at certain temperatures invertebrates become insensate. This means they don't respond to stimuli. However, I am not convinced this means this is a good form of anaesthesia. The inability to respond to stimuli is correlated with but not necessarily indicative of an inability to feel pain, though it is reasonable. There may be a window of time when the animal is insensate but can still feel pain.
So, too, may the process of cooling itself be unpleasant. The reasoning goes a cold blooded (ectotherm) is different from the warm blooded endotherm. Thus, needing to maintain internal homeostasis, we try to stay warm. But ectotherms also try to stay warm, and in fact, it's more important they do so as they lack the inborn furnace of metabolism that we have. They can tolerate a greater range of internal temperatures, but they clearly get "too cold" as well. And in fact there is evidence crayfish experience a transient increase in activity during cooling.
This is also another area where human intuition may also lead us astray. We experience cold as anaesthesia in part because of our free nerve endings, which again, crustaceans do not have. Free nerve endings fire in response to both skin damage and heat; because of this, if you apply a cold pack to i.e. a burn wound, it causes the free nerve endings to actually stop firing. Remove the cold pack and the free nerve endings start firing again. This does not work on crustaceans because they don't have free nerve endings, so this method of anaesthesia can't work through that pathway.
One of the ways that the invasive American Signal Crayfish damages the waterways in the UK is that during the winter they burrow into the mud to stay warm for the winter. At 10° C, they go to sleep. It may be popping a crayfish into the freezer without offering the behavioural comfort of digging into some mud to stay warm is unpleasant like it would be for a mammal. To go from conscious to insensate, too, is a relatively slow process relative to smaller invertebrates like insects because of their size; the larger the crustacean, the slower this process is.
The electric chair
It is possible to stun crayfish and lobsters with electric shock and this is estimated to be the quickest way of killing them according to the manufacturer. Electrical shock is still likely painful, however, so much relies on the manufacturer's estimates of time until death. Their claims about how long it takes for death to occur after boiling are almost certainly false (I go into more detail below). The device to do this is also expensive and is cost prohibitive for most individuals.
The options
When it comes to crayfish, I have personally done both common methods, boiling and destroying the brain.
The crayfish's response to destroying the brain was definitely nociceptive. I think it was likely experiencing the change in vascular pressure. However, fortunately it ceased moving relatively quickly after it was done, especially compared to my experience with dispatching insects. (So no, for instance, thrashing of the abdomen). I think the larger body size of the crayfish relative to the insect is the relevant factor. Loss of blood caused deoxygenation quite quickly, whereas passive oxygenation can keep neural tissue of smaller invertebrates alive for longer.
Boiling alive, if anything, seemed slightly faster. In both cases, though, cessation of movement was completed at about 3 seconds. (It is possible to do this in a relatively scientific way, though note such experimentation might require special permission from the UK government under the invasive species act.)
Observations of lobsters suggests that boiling a lobster takes longer to kill them than it does a crayfish. This suggests to me that for lobsters, stabbing the brain would be faster than boiling. However, it's surprisingly hard to get accurate information about this. The manufacturer of CrustaStun claims boiling takes 4-5 minutes to kill the lobster and this is almost certainly false. This review paper says "2 minutes" but tracing this claim to its origin only found work by Baker done in the 70s, i.e. this paper on crabs. According to the paper, cessation of movement for the crabs was done at sub- boiling temps (in order to avoid movement caused by boiling itself). Last movement did occur at 2.50 minutes on average, but the Baker himself concludes this is not deliberate movement but related to heat's effect on muscles and possibly air escaping from the brachia, writing that this measurement was "useless." Baker provides a rough estimate of 10 seconds for time of death.
This 10 second estimate for crabs puts boiling very much in line with CrustaStun's estimate, though plausibly lobsters take slightly longer.
Since this timing method wasn't useful, Baker looks instead to the loss of legs during boiling, since this requires a neurological response. More limbs were loss from boiling than piercing the brain and ventral nerve mass with an awl (similar to the splitting in lobsters and crabs). Unfortunately there are no timings listed for when the last leg loss occurs, only number of legs lost, so it's hard to estimate time of death. He concludes the awl is therefore the most humane, and I think it's not an unreasonable conclusion.
However piercing the brain alone did not prevent leg loss. He only did one trial where he pierced only the brain and the individual lost 5 legs (comparable to boiling) so he switched to destroying the ventral nerve mass as well. (This was apparently already known since 1882.) Both the brain and the ventral nerve ganglion needed to be destroyed. This is one area where not having a decentralised nervous does seem to impact things as the response occurs even in the absence of a brain.
If pain does require the supra esophageal ganglion, and leg loss occurs even without it, is it truly a good measure?
In crabs, the brain is positioned over the ventral nerve mass so both can be destroyed simultaneously with the awl; the body plan of the lobster is different. To get all ganglia, you must cut along the entire length of the lobster.
I also won't object to the idea that killing with the electric option is the most humane option available, though it is based on flawed claims about the duration of boiling to cause death. However, only large scale operations will likely have this as an option due to the expense.
I do think there is a good argument to be that stabbing the brain could be more painful than boiling, because of the differences in neuroanatomy, which include increased sensitivity to vascular pressure combined with decreased sensitivity to heat relative to mammals, as well as the fact that boiling destroys all the ganglia at once, whereas cutting through the head is unlikely to do so. It would also be nice practically speaking, because of how slow it is to split the number of crayfish you might get in a typical catch (~30-50), whereas for lobsters you're boiling maybe at most 4 at a time.
Even if boiling crayfish is better than stabbing, stabbing lobsters may still yet be better, because the larger size might mean lobsters could both lose consciousnesses when split more quickly and also die when boiled more slowly.
If you do choose boiling, I recommend letting the water return to boil between dropping in each crayfish, as having the temperature at maximum reduces the length of time until death.
Further research
It very strange to me this is a hotly contested issue complete with legislation in some countries, but no one has actually repeated Baker's experiments from the 70s and addressed some of these additional questions. It may be that the people most interested in this issue don't have the stomach for it, and CrustaStun's economic interest in promoting their product doesn't lend itself to fair comparison.
It's also unfortunate that the most important paper, the one on lobsters, has not been digitised at all. There seems to be only one copy of it in any library anywhere that I could find; it's listed amongst the papers collected by a scientist who donated his papers to the Bodleian upon his death. (This is a republication of the paper in a magazine, so it's possible the original had a different title, but if so I wasn't able to find what that title was as all the references to it I've found reference the republication in the magazine.)
Comment
This is a draft amnesty post so there may be factual errors! Please comment if you find one.