Non-coding DNA is known to account for a significant proportion of the genomes of many organisms. The discovery by the use of three statistical tests - the Zipf analysis, the fluctuation analysis and the Shannon entropy - of linguistic features and long-range correlations within non-coding DNA has given rise to the suggestion that this higher-order structure may form the basis of a biological language in non-coding DNA. This work describes the development of a model to explain the origin of these language-like features in DNA. The model is based on observed genome reshaping processes - namely, transposable element insertion/excision events and point mutations - and involves the repeated duplication of transposable element target sites to build up repetitive blocks of DNA. This model shows that the observed language-like features can be generated by known genetic rearrangements and therefore suggests that any function of non-coding DNA has been acquired opportunistically, through the use of these language-like features.