The diagnostic and prognostic power of the fractal complexity measure '' of detrended fluctuation analysis (DFA) has remained mysterious because there has been no explanation of its meaning, particularly in relation to spectral analysis. First, we present a mathematical analysis of the meaning of , in weighted power-spectral terms. Second, we test this hypothesis and observe correlations between DFA-based and weighted spectral methods of 0.97 (P < 0.0001) for ₁ and 0.98 (P < 0.0001) for ₂. Third, we predict mathematically that even in conventional (unweighted) spectral analysis there should be approximate counterparts to DFA, namely that ₁ and ₂ behave broadly in proportion to the conventional (unweighted) ratios LF/(HF + LF) and VLF/(LF + VLF), respectively. Fourth, we test this hypothesis by physiologically manipulating spectral ratios in healthy volunteers in two ways. The effect of 0.1 Hz controlled breathing on LF/(HF + LF) correlates markedly with the effect on ₁ (r = 0.73, P = 0.01); the effect on VLF/(LF + VLF) correlates markedly with that on ₂ (r = 0.76, P < 0.01). Likewise, with voluntary periodic breathing the reduction in ₂ correlates strongly with that in VLF/(LF + VLF) (r = 0.88, P < 0.001); effects on ₁ and LF/(HF + LF) again clearly correlate (r = 0.73, P = 0.01). Finally, we examine published literature to identify previously undiscussed evidence of the relationship between ₁ and LF/(HF + LF). We conclude that the ₁ and ₂ indices are simply frequency-weighted versions of the spectral ratios LF/(HF + LF) and VLF/(LF + VLF), respectively, multiplied by two (giving a range of 0-2). We can now understand fractal manifestations of physiological abnormalities: depressed baroreflex sensitivity -> low LF/HF -> low LF/(HF + LF) -> low ₁, while periodic breathing -> high VLF/LF -> high VLF/(LF + VLF) -> high ₂. Prognostic associations of are no longer mysterious.