A crossover between homologous nonsister chromatids can change which alleles are carried together on one chromatid. For two linked loci, whether a crossover produces a recombinant gamete depends on whether the crossover lies between those loci.

Consider a heterozygote in coupling phase:

$$AB/ab.$$

Before crossover, the parental chromatid combinations are $AB$ and $ab$.

A crossover outside the interval does not recombine the two loci

If a crossover occurs to the left of both $A$ and $B$, or to the right of both, the exchanged DNA lies outside the interval separating the loci. The $A$ allele remains associated with $B$, and $a$ remains associated with $b$ for the two-locus comparison.

A single crossover between the loci creates two recombinant chromatids

Suppose one nonsister chromatid from each homolog crosses over between $A$ and $B$:

before:
A -------- B

a -------- b

crossover between loci

products include:
A -------- b

a -------- B

The four chromatids in the meiotic cell then include two parental types and two recombinant types:

$$AB,\quad ab,\quad Ab,\quad aB.$$

If those four chromatids contribute equally to gametes, this particular meiosis produces two recombinant gametes out of four.

A crossover event and a recombinant gamete are not the same thing

A crossover occurs between two chromatids, not all four chromatids of a homolog pair. Therefore one single crossover between the loci does not make every gamete recombinant.

Likewise, observing a recombinant gamete tells us that the chromatid's allele combination differs from the parental phase, but it does not by itself reveal the exact number or positions of all crossover events that occurred in that meiosis.

Distance affects the chance of recombination

Two loci that are close together define a short chromosomal interval, giving fewer opportunities for a crossover to occur between them. More distant loci define a longer interval and are more likely to have one or more crossovers between them.

This creates the basic mapping principle:

larger chromosomal interval
        ↓
more opportunities for crossover
        ↓
more recombinant gametes, up to a limit

Recombination therefore connects a physical event during meiotic prophase I to a statistical pattern in gametes and offspring.