Transposable element copy number and stable polymorphisms

We consider a simple and analytically solvable model for the spread of a transposable element which has deleterious effects on fitness. Two possible modes are treated, one in which transposition occurs in the newly fertilized zygote, and another in which transposition takes place only in the germ line. In effect, transposition precedes selection in the first case and follows it in the second. This has different long-term consequences depending on the rate of transposition and the values of the selection coefficients. Conditions are derived for the existence of a stable polymorphism with respect to element copy number; the conditions are more stringent in the first case than in the second. It is proved that a polymorphism is impossible unless the copy number decreases fitness in a more-than-muitiplicative fashion.