and pl and a decreased frequency of pl and pl (see table below). bateson and punnett experiment phenotype and genotypeobservedexpected from 9:3:3:1 ratio purple, long (p_l_)284216 purple, round (p_ll)2172 red, long (ppl_)2172 red, round (ppll)5524 unlinked genes vs. linked genes their experiment revealed linkage between the p and l alleles and the p and l alleles. the frequency of p occurring together with l and with p occurring together with l is greater than that of the recombinant pl and pl. the recombination frequency is more difficult to compute in an f2 cross than a backcross, but the lack of fit between observed and expected numbers of progeny in the above table indicate it is less than 50%. the progeny in this case received two dominant alleles linked on one chromosome (referred to as coupling or cis arrangement). however, after crossover, some progeny could have received one parental chromosome with a dominant allele for one trait (e.g. purple) linked to a recessive allele for a second trait (e.g. round) with the opposite being true for the other parental chromosome (e.g. red and long). this is referred to as repulsion or a trans arrangement. the phenotype here would still be purple and long but a test cross of this individual with the recessive parent would produce progeny with much greater proportion of the two crossover phenotypes. while such a problem may not seem likely from this example, unfavourable repulsion linkages do appear when breeding for disease resistance in some crops. the two possible arrangements, cis and trans, of alleles in a double heterozygote are referred to as gametic phases, and phasing is the process of determining which of the two is present in a given individual. when two genes are located on the same chromosome, the chance of a crossover producing recombination between the genes is related to the distance between the two genes. thus, the use of recombination frequencies has been used to develop linkage maps or genetic maps. however, it is important to note that recombination frequency tends to underestimate the distance between two linked genes. this is because as the two genes are located farther apart, the chance of double or even number of crossovers between them also increases. double or even number of crossovers between the two genes results in them being cosegregated to the same gamete, yielding a parental progeny instead of the expected recombinant progeny. as mentioned above, the kosambi and haldane transformations attempt to correct for multiple crossovers. linkage of genetic sites within a gene in the early 1950s the prevailing view was that the genes in a chromosome are discrete entities, indivisible by genetic recombination and arranged like beads on a string. during 1955 to 1959, benzer performed genetic recombination experiments using rii mutants of bacteriophage t4. he found that, on the basis of recombination tests, the sites of mutation could be mapped in a linear order. this result provided evidence for the key idea that the gene has a linear structure equivalent to a length of dna with many sites that can independently mutate. edgar et al. performed mapping experiments with r mutants of bacteriophage t4 showing that recombination frequencies between rii mutants are not strictly additive. the recombination frequency from a cross of two rii mutants (a x d) is usually less than the sum of recombination frequencies for adjacent internal sub-intervals (a x b) + (b x c) + (c x d). although not strictly additive, a systematic relationship was observed that likely reflects the underlying molecular mechanism of genetic recombination. variation of recombination frequency while recombination of chromosomes is an essential process during meiosis, there is a large range of frequency of cross overs across organisms and within species. sexually dimorphic rates of recombination are termed heterochiasmy, and are observed more often than a common rate between male and females. in mammals, females often have a higher rate of recombination compared to males. it is theorised that there are unique selections acting or meiotic drivers which influence the difference in rates. the difference in rates may also reflect the vastly different environments and conditions of meiosis in oogenesis and spermatogenesis. genes affecting recombination frequency mutations in genes that encode proteins involved in the processing of dna often affect recombination frequency. in bacteriophage t4, mutations that reduce expression of the replicative dna polymerase increase recombination (decrease linkage) several fold. the increase in recombination may be due to replication errors by the defective dna polymerase that are themselves recombination events such as template switches, i.e. copy choice recombination events. recombination is also increased by mutations that reduce the expression of dna ligase (gp30) and dcmp hydroxymethylase (gp42), two enzymes employed in dna synthesis. recombination is reduced (linkage increased) by mutations in genes that encode proteins with nuclease functions (gp46 and gp47) and a dna-binding protein (gp32) mutation in the bacteriophage uvsx gene also substantially reduces recombination. the uvsx gene is analogous to the well studied reca gene of escherichia coli that plays a central role in recombination. meiosis indicators with very large pedigrees or with very dense genetic marker data, such as from whole-genome sequencing, it is possible to precisely locate recombinations. with this type of genetic analysis, a meiosis indicator is assigned to each position of the genome for each meiosis in a pedigree. the indicator indicates which copy of the parental chromosome contributes to the transmitted gamete at that position. for example, if the allele from the 'first' copy of the parental chromosome is transmitted, a '0' might be assigned to that meiosis. if the allele from the 'second' copy of the parental chromosome is transmitted, a '1' would be assigned to that meiosis. the two alleles in the parent came, one each, from two grandparents. these indicators are then used to determine identical-by-descent (ibd) states or inheritance states, which are in turn used to identify genes responsible for diseases.