Models of the spread of non-autonomous selfish transposable elements when transposition and fitness are coupled

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Abstract
Summary: I investigate models of the spread of transposable elements, such as theDrosophila melanogasterP elements, that can exist in autonomous and non-autonomous forms. Elements which have their major impact on host fitness in the process of transposition can, under certain conditions, come to a stable balance between transposition and selection. This stable balance for autonomous elements can be disrupted by the invasion of further elements, which do not produce a transposase enzyme, and may produce a repressor of transposition. I examine this secondary invasion process, and show that a stable equilibrium copy number for intact elements is neither a necessary nor a sufficient condition for non-autonomous elements to invade. Nevertheless, invasion occurs under a broad range of models and conditions. This requires neither that the non-autonomous elements produce atrans-acting repressor of transposition, nor that they titrate transposase. The elimination of autonomous elements follows the increase in non-autonomous elements unless the latter encode powerful repressors of transposition. Approximate solutions for the equilibrium copy number of autonomous elements and rate of invasion of non-autonomous elements can be found under some models for transposition and selection. The predictions of the model are compared with recent empirical studies of theD. melanogasterP system