NO no, you have it backwards. Mutation is the only method by which you can bring about complexity from an evolutionary model.
Since I edited it late I will put it here too :
from wikepedia's article on natural selection:
The modern theory of natural selection is formulated in terms of
genetic differences between individuals, resulting in differences in the frequency of
alleles in a population over successive generations.
The genetic variation on which natural selection acts are now understood to arise from random mutations.
Natural selection only acts on genetic variation already present through mutation. The same with genetic drift etc. All change must happen on the gene level. From there selection and drift etc. act on the predominance of particular alleles in a given population.
Evolutionists must prove that there is the possibility of having that many positive mutations in the given time period. This has been particularly debated in the realm of human evolution due to the time allowed.
Every step from one cell, to two cells, to specialized cells, to integrated systems, to complex bio-chemical processes are all brought about through mutation. The probability of that many positive mutations , in this case positive leading to more complexity, seems remote since each time there is a mutation
a. it is usually negative or neutral (the idea that junk DNA is not junk is questioning the neutral idea)
b. it must be able to be passed on to young
c. it must actually be passed on through reproduction
d. it must then be passed on in sufficient numbers to establish a new species population that is selected for survival.
The rate at which mutations occur, are adopted, etc. is what is in question. In any case long periods are a definite must. You can't have complexity through mutations in a short time.