We present an attempt to reconstruct the complete evolutionary path followed by cataclysmic variables ( CVs ) , based on the observed mass-radius relationship of their donor stars .
Along the way , we update the semi-empirical CV donor sequence presented in Knigge ( 2006 ) , present a comprehensive review of the connection between CV evolution and the secondary stars in these system , and reexamine most of the commonly used magnetic braking ( MB ) recipes , finding that even conceptually similar ones can differ greatly in both magnitude and functional form .

The great advantage of using donor radii to infer mass-transfer and angular-momentum-loss ( AML ) rates is that they sample the longest accessible time scales and are most likely to represent the true secular ( evolutionary average ) rates .
We show explicitly that if CVs exhibit long-term mass-transfer-rate fluctuations , as is often assumed , the expected variability time scales are so long that other tracers of the mass-transfer rate – including white dwarf ( WD ) temperatures – become unreliable .

We carefully explore how much of the radius difference between CV donors and models of isolated main-sequence stars may be due to mechanisms other than mass loss .
The tidal and rotational deformation of Roche-lobe-filling stars produces \simeq 4.5 \% radius inflation below the period gap , and \simeq 7.9 \% above .
A comparison of stellar models to mass-radius data for non-interacting stars suggests a real offset of \simeq 1.5 \% for fully convective stars ( i.e .
donors below the gap ) and \simeq 4.9 \% for partially radiative ones ( donors above the gap ) .
We also show that donor bloating due to irradiation is probably smaller than , and at most comparable to , these effects .

After calibrating our models to account for these issues , we fit self-consistent evolution sequences to our compilation of donor masses and radii .
In the standard model of CV evolution , AMLs below the period gap are assumed to be driven solely by gravitational radiation ( GR ) , while AMLs above the gap are usually described by a MB law first suggested by Rappaport , Verbunt & Joss ( 1983 ) .
We adopt simple scaled versions of these AML recipes and find that these are able to match the data quite well .
The optimal scaling factors turn out to be f _ { GR } = 2.47 \pm 0.22 below the gap and f _ { MB } = 0.66 \pm 0.05 above ( the errors here are purely statistical , and the standard model corresponds to f _ { GR } = f _ { MB } = 1 ) .
This revised model describes the mass-radius data significantly better than the standard model .

Some of the most important implications and applications of our results are as follows .
( 1 ) The revised evolution sequence yields correct locations for the minimum period and the upper edge of the period gap ; the standard sequence does not .
( 2 ) The observed spectral types of CV donors are compatible with both standard and revised models .
( 3 ) A direct comparison of predicted and observed WD temperatures suggests an even higher value for f _ { GR } , but this comparison is sensitive to the assumed mean WD mass and the possible existence of mass-transfer-rate fluctuations .
( 4 ) The predicted absolute magnitudes of donors stars in the near-infrared form a lower envelope around the observed absolute magnitudes for systems with parallax distances .
This is true for all of our sequences , so any of them can be used to set firm lower limits on ( or obtain rough estimates of ) the distance toward CVs based only on P _ { orb } and single-epoch near-IR measurements .
( 5 ) Both standard and revised sequences predict that short-period CVs should be susceptible to dwarf nova ( DN ) eruptions , consistent with observations .
However , both sequences also predict that the fraction of DNe among long-period CVs should decline with P _ { orb } above the period gap .
Observations suggest the opposite behaviour , and we discuss the possible explanations for this discrepancy .
( 6 ) Approximate orbital period distributions constructed from our evolution sequences suggest that the ratio of long-period CVs to short-period , pre-bounce CV is about 3 \times higher for the revised sequence than the standard one .
This may resolve a long-standing problem in CV evolution .

Tables describing our donor and evolution sequences are provided in electronically readable form .