Persistence of Tandem Arrays: Implications for Satellite and Simple-Sequence Dnas

Recombination processes acting on tandem arrays are suggested here to have probable intrinsic biases, producing an expected net decrease in array size following each event, in contrast to previous models which assume no net change in array size. We examine the implications of this by modeling copy number dynamics in a tandem array under the joint interactions of sister-strand unequal crossing over (rate gamma per generation per copy) and intrastrand recombination resulting in deletion (rate epsilon per generation per copy). Assuming no gene amplification or selection, the expected mean persistence time of an array starting with z excess copies (i.e., array size z + 1) is z(1 + gamma/epsilon) recombinational events. Nontrivial equilibrium distributions of array sizes exist when gene amplification or certain forms of selection are considered. We characterize the equilibrium distribution for both a simple model of gene amplification and under the assumption that selection imposes a minimal array size, n. For the latter case, n + 1/alpha is an upper bound for mean array size under fairly general conditions, where alpha(= 2 epsilon/gamma) is the scaled deletion rate. Further, the distribution of excess copies over n is bounded above by a geometric distribution with parameter alpha/(1 + alpha). Tandem arrays are unlikely to be greatly expanded by unequal crossing over unless alpha much less than 1, implying that other mechanisms, such as gene amplification, are likely important in the evolution of large arrays. Thus unequal crossing over, by itself, is likely insufficient to account for satellite DNA.