Hi SHEKINAH, and welcome to the fray.
Let me add something that has not been covered in the other responses.
... If animals of a given species mate and produce an abnormal offspring (i.e. a mutant), it also is sterile. Therefore, how could the macro evolutionary process advance? ...
This is not how new species are formed.
This is not how macroevolution occurs.
Wherever you got this information from, it is wrong, you have not been given correct information on how evolution works. I suggest that you discard all you think you know about evolution and start over, using sources from science, such as
An introduction to evolution - Understanding Evolution
Evolution is a process that occurs continuously in all known species of living organisms, and it is the change in proportions of the hereditary traits in breeding populations from generation to generation in response to ecological opportunities.
Mutations are differences in genes produced during reproduction within breeding populations, and these can harm the new organism, have no effect on it, or improve it's ability to survive and breed. You have many mutations that your parents did not have in their original DNA used in the process of reproduction to create you.
Natural selection means that those organisms that are better able to survive and breed within a breeding population pass on more hereditary traits than organisms that do not do so well at survival or breeding. Over time this will cause a shift in the proportion of hereditary traits available within the population.
If a part of a species (defined as a breeding population) moves into a new habitat, leaving the remaining members of the species population in the previous habitat, then there will be different ecological opportunities due to:
(1) the habitat is different in it's ability to provide nourishment,
(2) the predators\prey relationships of the ecosystem will be different,
(3) the mutations that occur in the breeding members of the sub-population in the new habitat will be different from the mutations that occur in the breeding members of the sub-population in the old habitat,
(4) these mutations may, or may not, provide a benefit to the organisms in the habitat they inhabit, and
(5) the mutations in the sub-populations may not be shared with the other sub-populations due to isolation mechanisms.
If the reproductive isolation is complete enough, the different sub-populations will evolve in different ways, and can reach the point where they are not able to breed with the other sub-population.
This is what has occurred with horses, donkeys and zebras -- they all are descendants of an ancestor equine population, but have evolved in slightly different ways to the point where hybrid offspring are usually sterile.
This is the point at which new species are formed: when the daughter populations can no longer interbreed and produce fertile offspring. After this point has been reached, each daughter species is free to evolve in different ways and become more divergent from the other daughter species over time.
This is macroevolution. Evolution plus time.
Enjoy.
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