Table 2.

Robustness of Tikhonov method to noise

Noise, %	Reproductive Statistics
	m	μ	σ	τ
0	4.00	2.00	1.20	0.500
1	4.11	1.92	0.95	0.497
10	5.09	2.22	1.08	0.470

Reproductive statistics showing that the Tikhonov method is robust against noise in simulated experimental data. The table lists true and numerically derived values for m, μ, σ, and τ. The true values are derived from the solid lines in Fig. 2 C and D, which are precisely the same. The values for 1% and 10% noise are numerically derived from ▴ in Fig. 2 C and D, respectively. As expected, the errors in the numerically derived reproductive statistics increase as the experimental noise increases. A level of 10% random noise is a reasonable estimate for typical laboratory data based on flow cytometry. With such levels of noise, the table illustrates that our methods generate useful estimates of the true reproductive statistics. Based on many numerical simulations, we have found that τ is least sensitive to random noise, m and μ are immediate in sensitivity, and σ is most sensitive. These sensitivities are reflected in the results of Table 2. 

 Deriving Table Quantities. The solid line in Fig. 2 C and D represents the true age-specific fertility curve that was selected for this particular simulation. The four true reproductive statistics were derived by applying Eqs. 1–4 in the Methods to this solid line. The Tikhonov method generates discrete points for the age-specific fertility curve and, in order to derive the reproductive statistics from such points, Eqs. 1–4 were used in conjunction with the trapezoidal rule.