Chapter 5 Genetic Analysis of Apomixis - cimmyt

18 JI&.. lertIoaodheterozygous condition (Aa). Thehomozygous stage (AA) has been consideredlethal in some cases (Nogler 1984).Nevertheless, in discussing apomixis transfer,we will consider three models: (i) apomixis isactive as a dominant trait, either heterozygousor homozygous (Aa or AA) with the recessivehomozygote (aa) being sexual; (ii) apomixis isactive only as a heterozygote (Aa), with therecessive homozygote (an) being sexual; and(iii) apomixis is only expressed as a recessivehomozygote (ss), while sS and SS are sexual.We will also consider a residual rate ofsexuality, k, in apomictic plants, with 0 < k < 1.Simple models of population genetics predict,in the absence of selection, the diffusion of theapomixis gene (Pemes 1971; Marshall andBrown 1981). According to the models, it ispossible for the apomixis gene to transfer tolandraces, such as maize or pearl millet, andto inadvertently move to wild relatives (Pemes1971; van Dijk and van Damme 2000).In model 1, there is one dominant allele forapomixis and three categories of genotypes atgeneration n: AA (apomictic) at a frequency ofP n . Aa (apomictic) at a frequency of 2Qn, andaa (sexual) at a frequency of R n . Gametes forgeneration n+1 are distributed according to thefollowing frequencies: male gametes A have afrequency of P n + Q n and gametes a have afrequency of Q n + R ; female gametes A havena frequency of 0, gametes a, a frequency of R n ,gametes AA, a frequency of P n , and gametesAa a frequency of 2Qn'Three genotypes will appear at generation n +1 with the following frequencies (randommating of gametes): AA at a frequency ofP n+ I = P n , Aa at a frequency of2Q n+ 1 = 2Q n +Rn(Pn + Qn)' and nn at a frequency of R n+ 1=R (R + Q )·I1 n nWith Pn+ 2Q n + R n =1, we obtain Q =1/2(1­ nPn- R n ) and the recurrence relation:Equilibrium is reached for R = 1, thepopulation being entirely sexual, or for R = 0,the population being completely apomictic.This model is identical to the model proposedby Fisher (1941) for autogamy. In fact,apomictic plantsself-reproduce, however theysimultaneously release pollen with thedominant allele to the sexual plant forms;consequently, a portion of the progeny ofsexual forms becomes apomictic.If we take into account a rate of residualsexuality, k, the variation in frequency for Aallele becomes Pn + 1 + Q n + I = (Pn + Qn)(1 +1/2(l-k)R n ) (pemes 1971).The change in frequency of allele A fromgeneration n to generation n + 1 is a functionof Rn, the frequency of the recessive allele, anda function of k. A zero value for k (obligateapomixis) maximizes the frequency of A, whilehigher values of k reduce the frequency of A.This variation would be zero if k = 1, i.e., whenall plantsare sexual with either the A ora allele.In this model, we assume random mating ofgametes. Transfer would be favored if anapomictic variety, homozygous for A, wereinterplanted with the variety (landrace) to bemodified. In the case of maize, by detassellingand harvesting only the landrace, onlyheterozygous progeny would be produced.These new plants would be apomictic andgenetically fixed. Their ability to evolve wouldrely on'the rate of residual sexuality, k. Aproportion k of the apomictic forms can beferti lized by pollen from other sources.Moreover, pollen from the first generation ofapomictic forms can be used to pollinate thelandrace. After several cycles of suc!"1backcrossing, the new variety will be identicalto the land race except that it carries theapomixis gene. Evolution in these "new"landraces will depend on the rate of residualsexuality that is retained at the end of thetransfer process.