The interactions between transposable elements (TEs) and their hosts constitute one of the most profound co-evolutionary processes found in nature. The population dynamics of TEs depends on factors specific to each TE families, such as the rate of transposition and insertional preference, the demographic history of the host and the genomic landscape. How these factors interact has yet to be investigated holistically. Here we are addressing this question in the green anole (Anolis carolinensis) whose genome contains an extraordinary diversity of TEs (including non-LTR retrotransposons, SINEs, LTR-retrotransposons and DNA transposons). We observed a positive correlation between recombination rate and frequency of TEs and densities for LINEs, SINEs and DNA transposons. For these elements, there was a clear impact of demography on TE frequency and abundance, with a loss of polymorphic elements and skewed frequency spectra in recently expanded populations. On the other hand, some LTR-retrotransposons displayed patterns consistent with a very recent phase of intense amplification. To determine how demography, genomic features and intrinsic properties of TEs interact we ran simulations using SLiM3. We determined that i) short TE insertions are not strongly counter-selected, but long ones are, ii) neutral demographic processes, linked selection and preferential insertion may explain positive correlations between average TE frequency and recombination, iii) TE insertions are unlikely to have been massively recruited in recent adaptation. We demonstrate that deterministic and stochastic processes have different effects on categories of TEs and that a combination of empirical analyses and simulations can disentangle these mechanisms.