The fossil record of ancient life forms provides scientific evidence for what?

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Fossil records provide evidence for the evolution of organisms over time. By comparing the bone structures of the same species from differing eras, paleontologist (scientists that study fossils) can provide evidence for the progression of that organism's anatomical features over time. For example, this fossil record of what is today's modern whale suggests that the whale once lived on land. In this way, the fossil record can help support the theory that all organisms share a common ancestry.

Likewise, the fossil record can show time periods that resulted in gradualism (slow periods of change) versus punctuated equilibrium (periods of rapid change) within species.

 Index fossils are fossils that are found within similar strata (layers) of different regions of the world. These fossils, such as trilobites, often had short life spans. They help in the process of relative dating. Relative dating is the science of finding the relative order of past events without finding the absolute age of a geological feature, such as through using the half-life of radioactive substances. 

For example, the layer within this picture that have the same type of fossils would be thought to have been formed during the same time period.