Quantifying memetic linkage in nursery rhymes

I created my pages about memetic linkage and memetic hitchhiking way back in 2011. However, I haven't seen much in the way of attempts to quantify memetic linkage. To help rectify this I performed a quick study of linkage between lines within nursery rhymes. The aim was to see how the distance between lines altered the chance of them being inherited together. Some results (obtained via Google searches):

Doe a deer

Reference line	Target line	Document count
Doe, a deer, a female deer	Ray, a drop of golden sun	394,000
Doe, a deer, a female deer	Me, a name I call myself	353,000
Doe, a deer, a female deer	Far, a long, long way to run	296,000
Doe, a deer, a female deer	Sew, a needle pulling thread	180,000
Doe, a deer, a female deer	La, a note to follow Sew	116,000
Doe, a deer, a female deer	Tea, a drink with jam and bread	121,000

This old man

Reference line	Target line	Document count
He played knick-knack on my thumb	He played knick-knack on my shoe	3,290
He played knick-knack on my thumb	He played knick-knack on my knee	2,670
He played knick-knack on my thumb	He played knick-knack on my door	2,550
He played knick-knack on my thumb	He played knick-knack on my hive	2,130
He played knick-knack on my thumb	He played knick-knack on my sticks	2,030
He played knick-knack on my thumb	He played knick-knack up in heaven	1,630
He played knick-knack on my thumb	He played knick-knack on my gate	1,930
He played knick-knack on my thumb	He played knick-knack on my spine	1,670

The first thing to say about this data is that memetic linkage is clearly evident, and its effect is quite large.

With genetic linkage, the probability of two genes being separated is roughly proportional to the distance between them, at least for small distances. This is a consequence of the logic of meiosis. However, with memetic linkage, much less linear relationships could be possible - because selection by humans for brevity is involved, and the shape of the linkage curve depends to some extent on how much humans like brevity.

While the data here suggests a fairly linear relationship, we should not expect that result to hold in general. It seems likely that some sets of adjacent memes will have natural "fracture points" where the probability of memes on either side getting unlinked during transmission is high.

A science of memetic linkage is important in advertising and marketing. Many want to attach memetic payloads to existing highly viral memes, in order to spread their content around. That means engineering high memetic linkage. At the risk of stating the obvious, sound engineering ought to be based on good science.