Biologically speaking, is it true that there are no parasites in Parasyte? Watching the anime "Parasyte - the maxim" I can't really see any of the organisms shown as real parasites, from a biological/ecological viewpoint.

Can any of the different kinds of alien parasytes shown be classified as a bona fide parasite?
I will use "parasite" (lower case, with an "i") to refer to the ecological relationship, and "Parasyte" (upper case, with an "y") to refer to the manga creatures.



From Wikipedia on parasitism:


  Parasitism is a non-mutual symbiotic relationship between species, where one species, the parasite, benefits at the expense of the other, the host. (...) Unlike predators, parasites typically do not kill their host (...)


Then, on decapitation:


  This form of injury invariably results in death (...)




So, on the three kinds of Parasytes:


The ones that "eat" the brain and take over the head, they already killed their hosts upon infection. So they are not parasites because they first kill the host, then inhabit the corpse. Parasitism is a kind of symbiosis, meaning that both organisms must be alive.


From Livescience:


  A person is considered brain-dead when he or she no longer has any neurological activity in the brain or brain stem — meaning no electrical impulses are being sent between brain cells.


The head of those bodies is the Parasyte, the original human head long gone, consumed by the Parasyte larvae. So there is no ecological relationship between living organisms. The Parasyte simply took over the corpse of the human they killed. Such is the case when a Parasyte changes bodies too, like when


   Shinichi's mom is beheaded by the car crash Parasyte, because it needed a female body to inhabit.


We can then infer that these head-Parasytes are not parasites. The relationship between them is called Metabiosis.


The co-inhabiting Parasytes, like Migi and Joe, they are really either mutualist symbiotes because the Parasyte provides his host with augmented abilities and protection from a predator (other Parasytes), and even if we think of a co-inhabiting Parasyte that stays dormant on his host, it would still be a case of phoresis or inquilinism commensalism. 


The human in the case of a commensalist symbiote would not be harmed or hindered, because the Parasyte emulates the body part it "ate" and the commensalist Parasytes are not too eager to kill their host since their primary drive is survival, and as Migi states, without eating the brain they do not know how to control a whole human body.


The colony Parasytes, like



   Miki and Gotou


are a colony of same-species organisms mimicking a human body. They are also not parasites.



From the bullet points above, we can say that none of the Parasytes shown in the manga or the anime (so far) are not really parasites.