The effect of augmented insertional mutagenesis

The question is, what form of negative selection occurs if the number of nonproductive inserts formed by L1 is enough to become a serious constraint on the system. The treatment of Charlesworth and Langley (1986) of sterile/lethal defects does not model this, because they only accounted for the loss of productive inserts because they happened to be sterile/lethal inserts. They did not account for the loss of the parental locus that occurs when one of its progeny inserts kills a host progeny. For LINE-1, the likelihood of an insert being a sterile/lethal is probably between 1%-0.1%, based on the number of genes exposed on the sex chromosomes. There would also be some likelihood of an autosomal insert being paired to a defect coming from the other parent, or being very deleterious in the heterozygous state. The likelihood of a productive LINE-1 insert being a sterile/lethal itself is too small to worry about. But because of the burden of nonproductive inserts produced, there is an exaggerated likelihood that a host carrying an active LINE-1 element will lose fitness because of sterile/lethal nonproductive inserts in its progeny.

Let the factor (a) represent the relative likelihood of producing a sterile/lethal insert to producing an active LINE-1 insert. So whereas un represents the total production of active inserts per generation (u being the rate of production of active inserts only; n being the existing copy number), aun will represent the total production of sterile/lethal progeny per generation. (a) will be a product of the likelihood of an insert being a sterile/lethal mutation (around 1%-0.1%) with the total number of nonproductive inserts per active insert (at least 20, and maybe in the thousands). So (a) could be greater than 1.

The negative selection will be incorporated in equation 19 of Charlesworth & Charlesworth (1983).

delta_n = n(1-n/T)@ln(w)/@n + n(u-v)
[Read @ as "partial derivative of"]

• delta_n is the expected change in copy number per generation, on which we want to see the effect.
• (v) is the excision rate which is too low for LINE-1 to worry about, so I will drop it out.
• (w) (potentially a function of n) is the fitness function into which we need to incorporate the (a) factor. The fitness will just be the likelihood of not getting any sterile/lethal mutations in any generation at a given value of a; so from the Poisson equation w(n) is exp(-aun).

Making all these substitutions, and dividing by n (which is always positive) yields:

delta_n/n = -au + u = u(1-a)

So above a=1, the transposon shouldn't be able to exist. At a=1, there is very peculiar behavior: n is stable, now matter what it is, and jumping faster doesn't increase n. Of course, a real system will have other sources of loss, so a=1 won't really be stable. But it shows the limit behavior approached by lower values of a. The advantage of jumping faster will be dimished and n will change more slowly in systems with a substantial value of a.