Final answer:
The concept described in the question, which parallels natural selection but operates on a higher taxonomic level and involves species persisting, speciating, or going extinct, is called species selection.
Step-by-step explanation:
The process referred to in the question, which can help in analyzing evolutionary trends where higher taxa see some species persist and speciate while others go extinct, is known as species selection. This process is similar to natural selection but occurs at a higher taxonomic level. In natural selection, individuals with traits better suited to their environment are more likely to survive and reproduce. Similarly, in species selection, certain species within a higher taxonomic group (taxa), due to their collective heritable characteristics, may be more successful in persisting and diversifying, while others may not and thus go extinct.
Species selection is thought of as operating on entire species (or other higher taxa) rather than on individual organisms within a population. It suggests a level of selection that can contribute to broad patterns in macroevolution - the evolution of taxonomic groups larger than a single species.