The chromosomes in meiosis are homologous because they have the same sequence of genes as each other but they are not identical because the alleles of some of the genes will be different.
Homologous chromosomes pair up at an early stage of meiosis.
Each chromosome consists of two chromatids after DNA replication, so there are four DNA molecules associated in each pair of homologous chromosomes.
A pair of homologous chromosomes is referred to as a bivalent and the pairing process is known as synapsis.
Crossing over takes place while the chromatids are still very elongated.
Two non-sister chromatids are brought together at the same point along their gene sequences.
The two strands of their DNA double helices are cut, one at a time, and are rejoined with the equivalent strand in the other chromatid.
This results in a mutual exchange of DNA and therefore genes between the two chromatids.
As non-sister chromatids are homologous but not identical, some alleles of the exchanged genes are likely to be different. Chromatids with new combinations of alleles are therefore produced.
Crossing over occurs at random positions anywhere along the chromosomes. At least one crossover occurs in each bivalent, but there is often more than one.
Each homologous pair of chromosomes forms a bivalent on the equator of the cell during first metaphase of meiosis.
Within each bivalent, the homologous chromosomes become attached to spindle microtubules from different poles.
The orientation of bivalents is random during first metaphase of meiosis, with a 50% chance of each of the two possible outcomes.
The orientation of bivalents has consequences, because the two homologous chromosomes have different alleles of some genes.
The inheritance of one particular allele by an individual depends only on which way a bivalent happened to be facing when spindle microtubules were attached.
The position of one bivalent does not affect other bivalents-their orientation is independent.
The number of possible combinations of chromosomes that a haploid cell produced by meiosis could contain as a consequence of the random orientation of bivalents is 2^n where n is the number of bivalents and also the haploid number for the species.
With two pairs of bivalents, as in the diagrams, there are four possible combinations, but most species have more chromosomes than this, so more possible outcomes.
In one human individual, random orientation of bivalents in meiosis can generate 2^23 possible outcomes-more than 8 million.
Combined with crossing over, this gives almost limitless numbers of possible combinations of alleles in cells produced by meiosis.