The underlying biology of spermatogenesis is also involved. As males age, the germ cells (~stem cells) that produce sperm are continuously dividing. One of the daughter cells from the division becomes sperm, the other continues on as a germ cell [0]. Over time and with aging, the germ cells accumulate new mutations (primarily single nucleotide changes), which are then also passed on in the newly created sperm. While it is also possible that a mother's eggs carries a new mutation, these do not increase in frequency with aging because her eggs are created in utero and do not undergo the lifetime of regeneration that the father's sperm do.
These "de novo" mutations can sometimes affect or "break" genes important for normal development, thus resulting in autism. They can be studied by sequencing father/mother/child families and comparing the genetic sequence of each. The de novo mutations show up in the child only. We can differentiate if they arose in the father's sperm or the mother's eggs by examining the "haplotype" around each of these mutations (basically, looking for other nearby mutations that were inherited by the child from either mom or dad).
These "de novo" mutations can sometimes affect or "break" genes important for normal development, thus resulting in autism. They can be studied by sequencing father/mother/child families and comparing the genetic sequence of each. The de novo mutations show up in the child only. We can differentiate if they arose in the father's sperm or the mother's eggs by examining the "haplotype" around each of these mutations (basically, looking for other nearby mutations that were inherited by the child from either mom or dad).
For more on this, see this paper: https://www.ncbi.nlm.nih.gov/pubmed/22495309
[0]: https://en.wikipedia.org/wiki/Spermatogenesis#/media/File:Sp...