When I was a child I completely accepted the premise of evolution. Random mutations occur, and some mutations have a greater likelihood of getting passed on to further generations. Eventually, new traits develop.
How does this work though? Surely life is complicated enough that one mutation isn't likely to change much. Has there been a mathematical analysis done of evolutionary processes which demonstrate that given enough time and individuals, indeed changes as you expect occur?
Surely there's also the tradeoff between how big the variations between the offsprings phenotype and how much evolution can occur. For example, if the variations are too big, the new advantageous traits should be cancelled out, because only a small part was advantageous and mutations completely eliminate it. But too little variability is also bad, because there's no space for exploration of new traits.
Did we evolve to have exactly the right amount of variation among offspring, or is it simpler than that?
In general, does anyone know a book on explanation of evolution preferably from a somewhat mathematical perspective