This is the first time I read that. That's fascinating. So they are very different then compared to what we have in humans? How do they work? Where can I read about this?
They aren't too different from human neurons. Non-spiking neurons also use nonlinear membrane dynamics to integrate inputs into a signal encoded by the voltage across the membrane. The cell then outputs a neurotransmitter in response to its voltage. In the case of a spiking cell and a spike dependent synapse, synaptic release is thought to be all or nothing. While in graded synapses, synaptic release is a more linear (modeled as a less steep sigmoid) function of voltage. Spiking cells can also have graded synapses (at least in crustaceans, I don't really know about vertebrates).
The idea is that spiking is one way to have a more robust signal over long distances: Crustaceans often have nonspiking local interneurons and spiking projection neurons and motor neurons. The problem of fast, reliable electrical signal transduction over long distances is also solved by having more insulation (particularly in vertebrates) or having thicker cables (particularly in invertebrates).
Humans also have non-spiking neurons with graded synapses in the retina.
I am not the best person to ask, since it's not my field. I heard this from the neuroscientists that I worked with. My understanding is that there are spiking and non-spiking neurons in most nervous systems, including human, but most of the ones in ours are spiking. The earliest-evolved animals, such as nematodes, do not have spiking neurons, or myelin, or some of the ion channels in neuron membranes that more evolved neurons have. Their neurons still have axons and dendrites, but the signals propagate much more slowly and in different ways. I am not sure how well they are understood.
As I said, this is possibly out-of-date information. If there is someone here from the neuroscience field, they can probably make a better comment.
Not all the cells of the nervous system produce the type of spike that define the scope of the spiking neuron models. For example, cochlear hair cells, retinal receptor cells, and retinal bipolar cells do not spike.
The idea is that spiking is one way to have a more robust signal over long distances: Crustaceans often have nonspiking local interneurons and spiking projection neurons and motor neurons. The problem of fast, reliable electrical signal transduction over long distances is also solved by having more insulation (particularly in vertebrates) or having thicker cables (particularly in invertebrates).
Humans also have non-spiking neurons with graded synapses in the retina.