Hi Allister,
Twins can be classified in to two varieties:
1) IDENTICAL - such caused by an "accident" of nature.
The development process (mitosis) hiccups at a very early stage, producing two embryos from one egg.
Each contains an identical set of genes, though such may then develop (slightly) differently.
There is NO tendency for this to happen down family lines.
So, as such, it is NOT a genealogical trait.
2) NON-IDENTICAL - such caused by the release of multiple eggs immediately prior to the time of fertilisation.
This can result in multiple quite-different embryos.
Such IS a genealogical trend, carried down the female line (obviously).
[Some women are very prone to it, and pass such down to their female offspring.]
N.B. Female children are born with their full (finite) life's-complement of eggs (for "their" creation of the next generation) already aboard.
Such eggs are "created" while the (yet to be born) "future mother" is still within the womb of her own mother (aka "future granny").
There have been studies conducted on such, particularly in the context of the Irish Famine.
[How did Granny's experience of deprivation during such, affect the future bodies/lives/life-expectancy of her grandchildren. Interesting /scary stuff!]
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Identical siblings are much less common than non-identical ones.
The upshot for your research is therefore that, if you reckon there were many "twins" within your family's descent chain, they are much more likely to have been non-identical ones.
As such, they will follow the female lines of descent.
Such will thus be more likely to NOT having WILSON as their surname.
[Unless there was an element of cousins marrying ...]
Capt Jock (an accident of nature, yet still "beloved of God"!)