During which phases of the cell cycle are chromosomes composed of two chromatids?

The correct phases are S phase, prophase, anaphase.  

Explanation:

The cell cycle, the sequence of events spanning the period from the completion of one cell division to the end of the next division, involves both the division of the cell nucleus (karyokinesis) and the division of the cytoplasm (cytokinesis). S phase, the next section of the interface, is marked by a dramatic increase in DNA synthesis and the synthesis of histones which are major cellular proteins bound to DNA. The cell is preparing for the start of mitosis. Chromosomes duplicate lengthwise, and each chromosome consists of two identical "chromatids."During prophase, the degree of packing of the chromatin increases, so the chromosomes become shorter and thicker and the centromeres begin to become visible. Each of the chromosomes, due to its duplication in S phase, is made up of two identical chromatids, called sister chromatids. Anaphase is the short phase, the sister chromatids begin to separate and migrate to the poles. Once the two chromatids separate, each is called a chromosome.

the fossil record provides evidence of a common ancestor to many species.