Hello Kariyanna; You might like to look up a particular extinct butterfly, Glaucopsyche xerces. It occurred in California near San Francisco. The last ones were seen in about 1942. Here is a link that will get you started. Best regards, Jim Des Lauriers.
The insect is found, and a type specimen is made, and identified and given a scientific name. And then, the range of the insect is determined. Then, for a period of time, if the insect is not seen, then it is presumed extinct.
Craig Carlton Dremann, Interesting answer. What about the insect displacement phenomenon? How we can consider this phenomenon before presuming insects got extinct.
You might find our IUCN UK Species Status review series of interest, and how we try and establish threat. The species accounts for some of the extinct species are worth reading.
The International Union for the Conservation of Nature (IUCN) ranks a species as extinct when there is no reasonable doubt that the last individual has died. This might sound like a simple definition, but it isn’t always easy to pinpoint exactly when a species has become extinct.
However, the definition could be extended as follows: a taxon is extinct in the wild when it only survives in culture, in captivity, or as a naturalized population (or populations) completely outside its original range. A taxon is presumed to be extinct in the wild when exhaustive surveys of its known and / or expected habitats at appropriate times (daily, seasonal, annual), and throughout its historical range, have not been carried out. been able to detect a single individual. The surveys must be carried out in periods times appropriate to the life cycle and life forms of the taxon.
I believe that several other replies here have added useful information for attempting to define this. Though I had some entomology courses and instruct a bit of this in my zoology teachings, I work largely with mammals. Extinction can be difficult, if not impossible, to verify for many species, so a consensus, such as the IUCN description is a useful working application.
In graduate school, a fellow researcher worked on a possible population census of wolverines in the state of Oregon. Though it was assumed that wolverines exist in Oregon, none were definitively sighted for several years. The research was based upon trace evidence - burrows, hair, tracks, and alleged sightings or predation of this species.
I myself assisted a colleague on trace evidence and reports of the thylacine (Thylacinus cynocephalus) in Tasmania. Largely considered to be extinct, but with continued reports, some from reputable sources. Is it extinct? Most mammalogists would say yes, but I am still uncertain with some of the reports and a large amount of suitable habitat that is difficult to access. On the other hand, species such as the Great auk, the passenger pigeon, and Steller's sea cow have no doubt that they are extinct and no sightings have been reported for a century or more.
Here is one reference for insect sampling and potential declines: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7069279/