Belief in the afterlife is not compatible with belief in natural selection.

Is belief in the afterlife compatible with the belief that evolution is due solely to natural selection?

No, it isn't. There are three reasons.

1. Since the spirit can influence the behavior of an individual, the characteristics of that spirit can influence the fitness of the individual. Therefore fitness is not determined solely by the genetic content of the organism.
   
   
2. The ease with which the organism may be controlled by the spirit also affects it's fitness. Species may evolve to more readily respond to the intentions of the spirit. They will develop characteristics that are not a response to environmental factors but are determined by the mechanism by which the spirit interacts with the physical body.
   
   
3. Spirit scientists might influence the evolution of the the human species to make it a better vehicle for incarnation. They might do this directly through genetic manipulations in which case mutations would not occur by chance but be inserted by an intelligent entity. Or, spirits might incarnate only into those organisms that have desirable characteristics. In this case fitness might be determined not by nature but by spirits.
   

There is a lot of controversy in our society about the whether natural selection really explains the evolution of life on earth. The strongest evidence against natural selection is the evidence for the afterlife. Given the vast amount of evidence for the afterlife, Darwinists have a lot to be worried about. Their theory is incomplete because it does not consider the effects spirits may have on the fitness of the individual.