= Mendelian segregation
{c}
{title2=$Aa\times Aa:\quad\tfrac14AA,\ \tfrac12Aa,\ \tfrac14aa$}
In ordinary <diploid> <meiosis>, the two copies at a <genetic locus> separate: each <gamete> receives one copy. With fair transmission, a <heterozygote> $Aa$ produces <gametes> carrying $A$ or $a$ with <probability> $1/2$ each. This is a transmission mechanism conditional on a parental <genotype>, rather than a statement about how common either <allele> is in a population.
For the one-locus cross $Aa\times Aa$, assume independent parental transmissions, no new <mutation>, and no differences in <fertilization> or survival between the resulting <genotypes>. Multiplying the two <gamete> <probabilities> gives four equally likely ordered outcomes: $AA,Aa,aA,aa$, each with <probability> $1/4$. Combining the two orders of the <heterozygote> gives
$$
P(AA)=0.25,\qquad P(Aa)=0.50,\qquad P(aa)=0.25.
$$
Only under the additional ideal model of <complete dominance> of $A$, complete <penetrance>, and no environmental changes to the scored characteristic do $AA$ and $Aa$ share the dominant <phenotype>. Its <probability> is then $0.25+0.50=0.75$. The inheritance calculation alone does not determine a <phenotype> or predict a generic <disease> risk.
\Image[/mendelian-segregation.png]
{title=Fair Mendelian transmission in an Aa × Aa cross, with phenotype grouping under complete dominance and penetrance}
These are <probabilities>, not a requirement that every four offspring contain one $AA$, two $Aa$ and one $aa$. For 100 independent offspring under the ideal model, the <expected values> of the three counts are $25,50,25$; the $aa$ count has a <binomial distribution> with <standard deviation> $\sqrt{100(0.25)(0.75)}\approx4.33$. Each new transmission keeps the same <conditional probabilities> given the parental <genotypes>.
In his paper published in 1866, Mendel reported 5,474 round and 1,850 wrinkled pea seeds: $5474/7324\approx0.7474$ round, close to the ideal $0.75$. Following descendants also distinguished two inherited classes within the round <phenotype>, illustrating why <genotype> cannot always be read from appearance.<Experiments in Plant Hybridization by Gregor Mendel>[sections 5–6]{ref} At several <genetic loci>, transmission patterns additionally depend on <genetic linkage> and <genetic recombination>.
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