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The term stellar evolution refers to a star's changing stellar structure over its own lifetime. Astrophysics' use of the term evolution is not analogous to biological evolution: stellar evolution it is used for the changes in individual stars as they age rather than the differences in stars with those born in subsequent eras. Stars' lives go through phases and the length of time in each phase is of interest.
Stellar evolution models of main sequence stars take into account the change in the constituents of stars as fusion reduces the hydrogen, i.e., a gradual change in a star's stellar structure model. Essentially, they work through stellar structure at a given time, take into account the ongoing changes in composition implied by the model as well as with any structural "movement" that it triggers, work out what the structure should be after some time-step, and repeat the whole process at that later point in time. Such models can be checked somewhat through star counts and the resulting H-R diagrams, to identify the counts of stars in different phases and see if the counts are consistent with the stellar evolution models and what's known of the galaxy's star formation. Among the general phases in the life of a main sequence star according to well-established models:
(MS stars with the lowest mass are all still within their extremely long MS phase, and in the far future when their MS finishes, they are expected to grow hotter from a collapse, then slowly cool.)
Among the factors that have to be taken into account when modeling a star's evolution are the star's mass, its changing composition due to fusion, diffusion, settling due to gravity, mixing/homogenization (e.g., due to convection), the effects of stellar rotation, mass gain and loss (e.g., accretion and stellar wind), and interactions among binary stars. The initial mass of the star is a major factor (see Vogt-Russell theorem), particularly in determining the luminosity and the lengths of time in each phase, the more massive stars being more luminous, the greater luminosity more than making up for their greater mass, giving them shorter lives and less time in each phase.