Fossils were the first widely recognised evidence for extinction; it’s fairly obvious that nothing like a t-rex is alive today. Once the theory of evolution became established, people began to hypothesise now extinct missing links between similar looking species. Nowadays there are a host of other ways of inferring the existence of now extinct species; unoccupied ecological niches, survival adaptations for absent predators, seed dispersal mechanisms that rely on missing hosts, etc.
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