Wikipedia
Trap-neuter-return (TNR) is a program through which free-roaming cats (not belonging to particular humans) are humanely trapped; sterilized and medically treated; and returned to the outdoor locations where they were found. If those locations are deemed unsafe or otherwise inappropriate, feral cats (unsocialized to humans) are relocated to farmyard homes. Kittens still young enough to be socialized and friendly adult cats are typically placed in foster care for eventual adoption into homes as companion animals rather than returned to the outdoors. Cats found suffering with terminal or untreatable illnesses or injuries are humanely euthanized.
TNR is endorsed by the American Society for the Prevention of Cruelty to Animals (ASPCA) as "the most humane, effective and financially sustainable strategy for controlling free-roaming cat populations" and "the only proven humane and effective method to manage feral cat colonies." The Humane Society of the United States has also endorsed "community-based Trap-Neuter-Return (TNR) programs with on-going responsible management as the most viable, long-term approach available at this time to reduce feral cat populations." The American Humane Association is another supporter of TNR. In Canada, the Canadian Federation of Humane Societies supports TNR, stating that the care of feral cats "is society's responsibility" as their wild nature is the result of human neglect. The U.K.'s Royal Society for the Prevention of Cruelty to Animals (RSPCA) supports "trapping and neutering of feral cats where local charities have the capacity to do so." Worldwide supporters include the World Animal Foundation, based in Oneida, Kentucky, and the International Companion Animal Management Coalition.
North American wildlife organizations including the American Bird Conservancy and The Wildlife Society oppose TNR. They dispute its effectiveness at reducing feral cat populations, and claim that free-roaming cats are responsible for much of the decline in bird populations over the last number of years, killing 1.4 to 3.7 billion birds annually in the U.S. Rather than TNR, they recommend that free-roaming cats be taken to local animal shelters. The Wildlife Society "support[s] and encourage[s] the humane elimination of feral cat populations, including feral cat colonies, through adoption into indoor-only homes of eligible cats and humane euthanasia of unadoptable cats."
TNR advocates counter that cat predation is inflated. They argue that removing feral cats en masse can harm the environment and even birds; euthanizing healthy cats is inhumane, and even more expensive for public officials than TNR; and research and experience of TNR shows that community cat populations indeed decline. In the U.K., The Royal Society for the Protection of Birds states that there is no evidence that cat predation "is having any impact on bird populations UK-wide".
TNR is sometimes described as trap-neuter-release, changing the last word of the acronym. This wording appears to have been the first version of the TNR acronym. The word "return" emphasizes that most feral cats are returned to their original locations under this program, and is the word most in current use. Some programs also go by other acronyms: TNVR (trap-neuter-vaccinate-return) adds emphasis to the process of vaccinating the cats for diseases like rabies before their return to the outdoors. TNRM (trap-neuter-release-maintain) adds the word "maintain," emphasizing the final part of the program, where caregivers feed and monitor the feral cats after they are returned to their territories. TTVAR (trap-test-vaccinate-alter-release) adds details about testing undertaken for serious illnesses, but this acronym is not in wide usage.