← Mathematical compendium

Published equation contexts

qn+1=qn(1−sqn)1−sqn2q_{n+1} = \frac{q_n(1 - s q_n)}{1 - s q_n^2}

Why this formula appears here

It is worth working through what that channel can and cannot do to a population’s allele frequencies, because the arithmetic is genuinely calculable and genuinely modest. Consider a recessive disease allele at population frequency q , and suppose that in some fraction of pregnancies where both parents are identified carriers, embryo testing prevents the birth of an affected (homozygous) child while parents still have the same number of children overall, drawn from the surviving unaffected and carrier embryos. The standard discrete-generation recursion for selection with coefficient s against a fully recessive genotype is: qn+1=qn(1−sqn)1−sqn2q_{n+1} = \frac{q_n(1 - s q_n)}{1 - s q_n^2}. Set s = 1 , the theoretical maximum in which…

Read the full article-specific guide →

Read the representative guide

qn2q_n^2

Symbol q_n^2

qn2q_n^2 occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Read this term in its guide →
1−sqn21 - s q_n^2

Denominator: 1 - s q_n^2

The complete quantity below the fraction bar; it must be nonzero for this division.

Read this term in its guide →

How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

Research cited beside this formula

Learn the mathematics behind it

Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

qn+1=qn(1−sqn)1−sqn2q_{n+1} = \frac{q_n(1 - s q_n)}{1 - s q_n^2}

Equation 3 · Technological Evolution

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

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

It is worth working through what that channel can and cannot do to a population’s allele frequencies, because the arithmetic is genuinely calculable and genuinely modest. Consider a recessive disease allele at population frequency q , and suppose that in some fraction of pregnancies where both parents are identified carriers, embryo testing prevents the birth of an affected (homozygous) child while parents still have the same number of children overall, drawn from the surviving unaffected and carrier embryos. The standard discrete-generation recursion for selection with coefficient s against a fully recessive genotype is: qn+1=qn(1−sqn)1−sqn2q_{n+1} = \frac{q_n(1 - s q_n)}{1 - s q_n^2}. Set s = 1 , the theoretical maximum in which…

Equation guide → · Article →