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Equation 6 · Human Evolution Did Not Stop, and Medicine Is Now Steering It

What does this equation mean?

qn+1=qn/(1+qn)≈0.009901q_{n+1} = q_n/(1+q_n) \approx 0.009901

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Inputs and operationsq_n/(1+q_n) ≈ 0.009901
Result or conditionq_n+1
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This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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qn+1q_{n+1}

Symbol q_n+1

qnq_n+1 is part of the quantity the equation computes from the expression on the right.

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qnq_n

Symbol q_n

qnq_n is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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≈

≈

Approximately equal to; the equality is not exact.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

Its accuracy depends on the assumptions and range of use described in the article. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Set s = 1 , the theoretical maximum in which every affected embryo is detected and never implanted: for q = 0.01 , this gives qn+1q_{n+1} = qnq_n/(1+qnq_n) ≈\approx 0.009901 , a reduction of under one-tenth of one percent of the allele’s frequency in a single generation, even at total, universal, perfectly effective screening. The reason the effect is so small is structural, not a modeling artifact: for a rare recessive allele, the overwhelming majority of copies are carried silently in heterozygous carriers, invisible to any selection that acts only on homozygotes, and embryo selection — like natural selection against recessive disease before it — can only ever act on the small fraction of matings…
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Set s = 1 , the theoretical maximum in which every affected embryo is detected and never implanted: for q = 0.01 , this gives qn+1q_{n+1} = qnq_n/(1+qnq_n) ≈\approx 0.009901 , a reduction of under one-tenth of one percent of the allele’s frequency in a single generation, even at total, universal, perfectly effective screening. The reason the effect is so small is structural, not a modeling artifact: for a rare recessive allele, the overwhelming majority of copies are carried silently in heterozygous carriers, invisible to any selection that acts only on homozygotes, and embryo selection — like natural selection against recessive disease before it — can only ever act on the small fraction of matings where two carriers happen to pair up. Layered on top of that structural limit is the fact that PGT operates only within IVF, itself a minority pathway to conception worldwide, so the realized value of the effective screening fraction f across all human conception is far below the illustrative s=1 ceiling used above. Screening’s population-genetic footprint, in other words, is real, directionally opposite to the tiny drift toward higher mutation load discussed earlier, and — on the arithmetic above — slower than either.

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