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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 givesOnly 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.

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 $\sqrt{100(0.25)(0.75)}\approx 4.33$. 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: $5474/7324\approx 0.7474$ 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.^[ref] At several genetic loci, transmission patterns additionally depend on genetic linkage and genetic recombination.

Oogenesis is development of female gametes; the unequal divisions of human meiosis produce polar bodies alongside the developing ovum.

An ovum is a female gamete.

An angiosperm pollen grain is a small male gametophyte, not itself a seed or a single gamete. Its tube-forming biological cell supports delivery of sperm.^[ref]

A pollen tube germination assay makes tube emergence visible outside a flower. The published Practical Biology experiment, Observing the growth of pollen tubes (Practical Biology), Technical note 3, lists florist lilies among successful materials without specifying a species. Record the actual identification; success with one sample cannot establish a universal growth rate.^[ref]

Pearson's Core practical 4: Investigate the effect of sucrose concentration on pollen tube growth by Pearson Education Ltd, Teacher sheet, pp. 1–2, describes an inspectable experiment. Mix equal volumes of sucrose solution and mineral-salt medium on clean cavity slides. Dust in pollen from mature anthers with a mounted needle, record the addition time, and incubate without coverslips in covered dishes containing wet filter paper. The moist chamber reduces drying; the uncovered drops avoid oxygen limitation. Brief observations with an optical microscope at $100\times$, using an eyepiece graticule calibrated against a stage micrometer, reveal tube emergence and length. Return slides to the chambers and switch off the lamp between observations to reduce heating and drying. For comparisons of sucrose concentration, use the same flower across treatments to control maturity, then repeat with other flowers.^[ref]

An additional proposed experimental design check is a medium-only slide: it tests whether debris is being mistaken for pollen tubes. Compare matched pollen samples at different final sucrose concentrations, keeping temperature, elapsed time and observation rules fixed. A sample known to produce pollen tubes in a previously successful medium would test whether an apparent failure comes from handling or the tested condition. These controls are questions to test, not guaranteed outcomes. A negative result cannot distinguish dead pollen from an unsuitable medium without further comparisons.

Two original calculations clarify the readout. First, take $0.40\mathrm{mL}$ of $0.80\mathrm{mol}{\mathrm{L}}^{-1}$ sucrose solution and $0.40\mathrm{mL}$ of sucrose-free medium. Assuming additive volumes, conservation of the amount of substance givesThis dilution also halves the medium's original component concentrations. Label the final molar concentration, not the starting bottle.

Second, stipulate a toy field containing $40$ pollen grains, of which $12$ have emerged pollen tubes. Its emergence fraction is $12/40=0.30$. If those twelve pollen tubes have total measured length $960\mu \mathrm{m}$, their arithmetic mean length is $80\mu \mathrm{m}$. Assigning length zero to the other grains instead gives $960/40=24\mu \mathrm{m}$ per grain. These invented numbers show why emergence fraction and mean length among emerged tubes answer different questions. Specify the denominator and the emergence criterion before counting, and avoid selecting only conspicuous long pollen tubes.

Tube emergence in a drop demonstrates growth under that medium's conditions. It observes no stigma interaction, passage through a style, delivery into an ovule, gamete fusion, or seed development. Thus a positive pollen tube germination assay does not demonstrate successful fertilization in a living flower. Its beauty is making one otherwise hidden part of sexual reproduction directly observable.^[ref]

In angiosperms, pollination transfers pollen from an anther to a stigma. Fertilization is a later fusion of gametes; seed development follows. Pollination may use animals, wind or water, so an insect visit is neither required for every flower nor sufficient evidence of fertilization.^[ref]

The recombination fraction is the probability that a transmitted gamete carries a recombinant haplotype between two specified genetic loci, relative to the parent's known haplotype phase. Write it as $r$ here; the symbol $\theta$ is also common in genetic linkage analysis. In the ordinary symmetric two-locus model, $0\le r\le 1/2$, with $r=0$ for complete genetic linkage and $r=1/2$ for independent assortment.

For phase-known genotype $AB/ab$, fair Mendelian segregation and equal reciprocal gamete probabilities giveFor example, 1,000 independent informative transmissions with observed counts $400,400,100,100$ in this order have empirical recombination fraction $(100+100)/1000=0.2$. Those illustrative counts match the expected values in the toy model, but actual counts fluctuate. The genetic linkage diagram shows both the parental and recombinant classes, so their separate probabilities are not confused with the total $r$.

The recombination fraction measures the probability of an odd number of origin switches along the transmitted chromatid. It is neither the expected value of the exchange count nor the probability of at least one exchange: even positive counts can be invisible at the two endpoints. Converting an observed recombination fraction to a genetic map distance therefore needs an explicit model such as the Haldane mapping function. The distinction between transmitted-chromatid counts and four-chromatid exchange counts is discussed in Weeks, Tang and Kwon (2009), Casares' map function: No need for a 'corrected' Haldane's map function, Genetica 135, 305–307.

Reproductive isolation consists of barriers that reduce gene flow through sexual reproduction. Distinguish premating isolation from barriers after mating. Barriers before fertilization also include incompatible gametes; barriers after fertilization can reduce offspring survival or fertility. ^[ref]

An assay should state which step it measures. Observing fewer cross-group matings does not measure offspring fertility; observing fertilization does not demonstrate that the offspring will reproduce. These distinctions make a partial barrier informative without declaring completed speciation.

A male gamete.

A test cross crosses an individual with a homozygote for recessive alleles, allowing suitable offspring phenotypes to reveal transmitted gamete combinations.

The biological cell formed by fusion of gametes.