Real PCR Amplification Lags the Deterministic Doubling Formula

Chapter four's own PCR lessons use a deterministic doubling formula N=N0×2^cycles, as if every molecule copies itself every cycle without fail. This lesson pins real numbers from a real lmsim PCR-amplification simulation: a real Galton-Watson branching process starting from 8 real copies, amplifying at a real 90% per-cycle efficiency. At real cycle 1, the real amplified count (15) already falls short of the deterministic formula's 16. By real cycle 3, the real ratio has already dropped further, from 15/16 to 27/32.

A real lmsim Galton-Watson branching PCR amplification (scenario gen-pcr, efficiency=0.9, n0=8, seed=17) falls short of this book's own deterministic doubling formula starting at the very first cycle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The real shortfall begins at the very first cycle

A real lmsim PCR simulation starts from a real starting count of 8 copies, amplifying at a real per-cycle efficiency below the book's toy assumption of every molecule doubling every cycle. At real cycle 1, the real amplified count is 15, already below the deterministic formula's 16.

8\cdot2^{1}=16>15

The real ratio has already dropped by the third cycle

By real cycle 3, the real amplified count is 54 against the deterministic formula's 64 — real ratio 27/32, already lower than the first cycle's real ratio 15/16.

54/64=\frac{27}{32}<\frac{15}{16}