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20 25 30 Generation

Figure 2.19 The decay of gametic disequilibrium (D) over time for four recombination rates. Initially, there are only coupling (Pn = P22 = V 2) and no repulsion gametes (P12 = P21 = 0). Gametic disequilibrium decays as a function of time and the recombination rate (Dtn = Dt0(1 - r)n) assuming a single large population, random mating, and no counteracting genetic processes. If all gametes were initially repulsion, gametic disequilibrium would initially equal -0.25 and decay to 0 in an identical fashion.

20 25 30 Generation

Figure 2.19 The decay of gametic disequilibrium (D) over time for four recombination rates. Initially, there are only coupling (Pn = P22 = V 2) and no repulsion gametes (P12 = P21 = 0). Gametic disequilibrium decays as a function of time and the recombination rate (Dtn = Dt0(1 - r)n) assuming a single large population, random mating, and no counteracting genetic processes. If all gametes were initially repulsion, gametic disequilibrium would initially equal -0.25 and decay to 0 in an identical fashion.

in allele frequency so that the maximum value of D in each population is also different. If all alleles are not at equal frequencies in a population, then the frequencies of the two coupling or the two repulsion gametes are also not equal. When D < 0, Dmax is the larger of -p1q1 or -p2q2, whereas when D > 0, Dmax is the smaller ofp1q2 or p2q1.

A way to avoid these problems is to express D as the percentage of its largest value:

This gives a measure of gametic disequilibrium that is normalized by the maximum or minimum value D can assume given population allele frequencies. Even though a given value of D may seem small in the absolute, it may be large relative to Dmax given the population allele frequencies.

Measures of gametic disequilibrium can be used to test fundamental hypotheses regarding the processes that shape genotype frequencies in natural populations. In epidemiology, pathogens are often considered to reproduce predominantly clonally even if capable of sex and recombination. This assumption has implications for clinical treatment of infections, the emergence of new virulent strains, and vaccine development strategies. Clonal reproduction would accompany high levels of gametic disequilibrium since recombination would not occur, a hypothesis that can be tested with genetic marker data. The protozoan parasite Toxoplasma gondii is one such example. It infects all mammals and birds and causes toxoplasmosis, an illness in humans, and was considered clonal despite sexual reproduction that occurs in cats. To test this hypothesis, Lehmann et al. (2004) sampled T. gondii from pigs, chickens, and cats, and then genotyped the protozoa at seven loci. The results revealed normalized gametic disequilibrium (| D'|) between pairs of loci that ranged from 0.35 to 0.96. The two loci known to be physically linked showed the highest values of D' while all others have less gametic disequilibrium. This pattern is inconsistent with clonal reproduction, which would maintain gametic disequilibrium at all loci regardless of the physical distance between loci.

D is frequently called the linkage disequilibrium parameter rather than the gametic disequilibrium parameter. This is a misnomer, since physical linkage only dictates the rate at which allelic combinations approach independent assortment. Recombination, determined by the degree of linkage, only causes a reduction in gametic disequilibrium over time, but it cannot cause an increase in gametic disequilibrium. Processes other than linkage are responsible for the production of deviations from independent assortment of alleles at multiple loci in gametes. Using the term gametic disequilibrium reminds us that the deviation from random association of alleles at two loci is a pattern seen in gametes or haplotypes. Although linkage can certainly contribute to this pattern, so can a number of other population genetic processes. It is even possible that several processes operating simultaneously produce a given pattern of gametic disequilibrium. Processes that maintain or increase gametic disequilibrium include those discussed in the following sections.

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