Why do paleontologists count groups like genera instead of species?
It isn't easy for biologists to measure the number of extinctions that are happening in the modern world. We need a good estimate of the number of species that are currently alive in order to determine how many have become extinct in the future. We have a good idea of the number of species of animals and plants in developed countries like the United States, and historical records show that there have already been extinctions over the last 250 years. In more remote places, like the Amazon rainforests of South America, new species of animals (e.g., insects) are still being found. In these parts of the world, our estimates of extinction will be less accurate. Some species may literally go extinct before biologists are able to discover them. Rare species that have been discovered may seem to have become extinct because they are difficult to find again. Biologists have developed various mathematical methods to deal with these sampling problems.
It is even more difficult to study extinction in the remote past. We can never find fossils of every species that has ever lived. Many will not be preserved as fossils because they don't have a hard skeleton of shell and bone. Even if an individual animal has a hard shell, it will not be preserved if it is eaten by a predator, or if its shell is broken apart by waves after it dies. Common species are more likely to be discovered than rare species.
Paleontologists have a better chance of making an accurate estimate of what is called taxonomic diversity. Species are classified into a set of progressively larger groups called taxa (s. taxon). For example, several closely related species may be combined into a genus (pl. genera). A number of related genera form a family, and a set of related families are combined into a superfamily; and so on. To count a genus as having existed at a time in the past, you need find just one specimen of only one of the species that belong to that genus. We have a better chance of getting an accurate count of diversity if we consider taxa instead of species.
There are other sampling issues that must be accounted for in estimating taxonomic diversity. For example, the more specimens you count, the more taxa you find (also a problem when counting modern animals or plants). If there are large differences in counts between time periods, diversity will appear to change as a result of these sampling differences. Paleontologists use a variety of statistical methods to overcome these sorts of sampling problems.