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tokens: migration rate is removed, the bumps are smoothed out. The 100-d population between 50 and 60 R ⊙ is negligible, due to the small number of such planets in the observed WJ period distribution. 7 COMPARISON TO OBSERVATIONS The model described here is motivated by the claimed deficit of WJs around moderately evolved stars (Johnson et al. 2007 , 2011 ), as seen in Fig. 1 and Section 2 . We postulate that the reason for this deficit is that the observed eccentricity distribution of WJs around main-sequence stars is really a snapshot of a population whose eccentricities are oscillating via the KL mechanism while they migrate inwards due to tidal friction. The fact that the oscillation time-scale is short compared to the characteristic time-scale for the stellar evolution means that planets are removed from the observed sample when their periapsides oscillate to the minimum value and interact with the host star. Fig. 15 shows the result of such a model and demonstrates that, under these conditions, a pre-existing WJ population will be largely removed by the time the stars evolve to 4 R ⊙ , in contrast to the case where the eccentricities of the observed population do not oscillate. The exact location of WJ removal depends on the details of tidal forces and the perturber, but the general behaviour is well described by Fig. 16 . However, our results do not match all observations. Figs 17 and 18 show the distribution of eccentricities for our simulated systems and observed WJs (from the Exoplanet Orbit Database), respectively, with our simulated population drawn from the same period distribution. In both cases, the systems are restricted to the Jupiter mass range (0.3–3) and the period range of 10–100 d. Comparison of these two populations using the Kolmogorov–Smirnov (KS) test gives a p -value of 1 × 10 −4 , indicating they are unlikely to be drawn from the same underlying population. The discrepancy is primarily due to the significant fraction (15 per cent) of simulated WJs with high eccentricity ( e > 0.8), while no observed WJs have such high values. The lack of high-eccentricity WJs has also been noted by Dawson, Murray-Clay Johnson ( 2015 ). Figure 18. The eccentricity distribution for observed WJs, taken from the Exoplanet Orbit Database. The small number of highly eccentric planets differs significantly from the oscillating distribution, but that may be a result of low DE. The observed population also includes an excess number of low-eccentricity planets, which is difficult to reconcile with the orbital behaviour of our planets. Many of the simulated planets, even those started with eccentricity of 0.05, had a minimum eccentricity peak above 0.1, similar to the eccentricity distribution shown in Fig. 7 . This figure also shows the cumulative distribution of eccentricity values; blue, green, and red dashed lines indicate the cumulative observed distribution at 75, 90, and 98 per cent of WJs, respectively, for the simulated planet (dotted lines)