The so-called ‘vacuum effect’ in relation to feral cats is a reference to how feral cats repopulate an area which has been culled of feral cats because that particular area has a source of food which attracts the cats.
The whole situation turns on this fact: that feral cats occupy an area because there is a source of food. If you try to remove those cat through killing them and if the source of food remains then once again, over time, feral cats will repopulate the area because they are attracted by the food source. If you don’t kill all the feral cats then also the remaining cats will breed and repopulate the area.
The advantage of trap neuter return over simply killing cats is that it stabilises the population and indeed the population will decrease gradually if it is done comprehensively. And of course it is humane whereas the former method of simply killing cats can only be described as inhumane and ineffective.
Studies have demonstrated this. Alley Cat Allies refer to the removal of the entire population of feral cats from an island: Marion Island. It took 19 years of attrition against the feral cats using methods which would be unworkable in suburban areas. During the clearance cats from another area took their place thereby proving the point.
Cat haters, cat shooters and cat phobics (terrified of cats) hate the idea that the vacuum effect exists because they are very keen to see feral cats exterminated in any way possible and they hate TNR programs because for them it leaves cats on the ground where they can attack birds and other species of animal. Therefore cat haters will argue against the vacuum effect. They will say that it does not exist. They don’t substantiate their opinions with science. They are often ornithologists.
A more refined argument about killing feral cats would be to both kill them and remove the source of food at the same time. That would remove the cats from a particular area. But this is impractical and will never work. Sources of food are often businesses or indeed well-meaning people who voluntarily feed the cats. Other sources of food could be at harbours where there is fishing. You can’t remove businesses which is why the concept is impractical.