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Copyright 0 1991 by the Genetics Societyof America Germline Selection: Population Genetic Aspects of the Sexual/Asexual Life Cycle Ian M. Hastings Institute of Cell, Animal and Population Biology, University of Edinburgh, Edinburgh EH93JT, Scotland Manuscript received January15, 1991 Accepted for publication August12, 199 1 ABSTRACT Population geneticists make a distinction between sexual and asexual organisms depending on whether individuals inherit genes from one or two parents. When individual genes are considered, this distinction becomes less satisfactory for multicellular sexual organisms. Individual genes pass through numerous asexual mitotic cell divisionsin the germline prior tomeiosis and sexual recombination. The processes of mitotic mutation, mitotic crossingover, and mitotic gene conversion create genotypic diversity between diploid cells in the germline. Genes expressed in the germline whose products affect cellviability(suchasmany “housekeeping” enzymes) maybe subjected to natural selection acting on this variability resulting ainnon-Mendelian output of gametes. Such geneswill be governed by the population genetics of the sexual/asexual life cycle rather than the conventional sexual/Mendelian life cycle. A model is developed to investigate some properties of the sexual/asexual life cycle. Whenappropriate parametervalues were includedin the model,it was found that mutation rates per locus per gamete may vary by a factor of up to 100 if selection acts in the germline. Sexual/ asexual populations appear able to evolve a genotype to of higher fitness despite intervening genotypes of lower fitness, reducing the problems of underdominance and Wright’s adaptive landscape encountered by purely sexual populations. As might be expected this ability is chiefly determined by the number ofasexualmitoticcelldivisions within the germline. The evolutionaryconsequencesof “housekeeping”loci being governed by the dynamics of the sexual/asexual life cycle are considered. HE relative merits of sexual and asexual modes T of reproduction have been the subject of extended debatein the literature(e.g., MAYNARDSMITH 1978; STEARNS 1987; MICHODand LEVIN1988) and arguments as to theirevolution and maintenance remain unresolved. Sexual reproduction occurs when individuals inherit genes from two parents resulting in theproduction of new combinationsof alleles. Individuals fortunateenoughtoinherit favorable combinations will flourish, leave numerous offspring, and sexual reproduction will persist. However, an inevitable consequence of sexual recombination is that advantageous combinations of alleles are broken up eachgeneration.This has drawbacks for a sexual population’s ability to overcome underdominance or undergo coevolution. An exampleofunderdominance occurs when three genotypes aa, A a and AA have fitnesses such that A a << aa < AA (as may occur if, for example, the gene products interact to form a dimeric or polymeric enzyme molecule). A large sexual populationcannot evolve from beingpredominantly aa to the fitter A A genotype since most alleles of type A will occur in heterozygotes and will therefore be at a selective disadvantage. Thus the selective advantage when homozygous is outweighed by the selective disadvantage when heterozygous and allele A cannotinvadea sexual populationofgenotype aa (CROW 1986, pp. 95-96; HARTL and CLARKE 1989, Genetics 129: 1167-1176 (December, 1991) p. 163) without either a very high mutation rate or a population size sufficiently small for significant random drift tooccur. A similar problem was considered in WRIGHT’Smodel of an adaptive landscape. This is an analogousproblem to underdominancebutdescribes coevolution in two (or more) dimensions using the analogy of a geological “landscape” consisting of “hills” of high fitness separated by “valleys” of lower fitness. A sexual population situated onone hill cannot traverse a valley of reduced fitness (CROW1986, pp. 106-1 08 and 198-200) for the same reasons cited above: genotypes represented as a higher peak will be at an immediate advantage but their offspring will tend to beof the less fit intermediate genotypes. Asexual reproduction has oppositepropertiesto those of sexual reproduction. Only the relatively slow processes of mutation and gene conversion createnew combinations of alleles, making asexual populations less responsive to changing selection pressures. One advantage is that favorable combinationsof alleles are not destroyedso any individual containing a genotype ofhigher fitness will leave offspring of the same genotype and the population will move to a higher fitness. T h e advantages and disadvantages of sexual and asexual modes of reproduction were briefly reviewed here as an understanding of the effects of recombination is critical to the arguments which follow. A 1168 I. M. Hastings more extended discussion is given by CROW(1988) and CHARLFSWORTH(1989). Species are classified as sexual or asexual depending on whether recombination takes place between genes of separate individuals. This classification is useful but may be limited in population genetics which is concerned with the fate of individual alleles within populations; in this case the description of any metazoan species as “sexual” appears to be an oversimplification. This is best illustrated by reviewing the life cycle of a sexual metazoan from the viewpoint of an individual allele: one generation consists of numerous asexual mitotic cell divisions within the germline followed by meiosis, fertilization and sexual recombination. Individual alleles are therefore involved in a alternating sexual/asexual life cycle rather than a simple sexual life cycle. The asexual stage of the life cycle occurs within the germlineand is usually regarded as a “black box” producing Mendelian a output of gametes. However, mutation, crossing over and geneconversion are known to occur during mitosis (JOHN and MIKLOS 1988) andhave been demonstrated in yeast (LICHTEN and HABER1989; YUAN and KEIL 1990; references therein), Drosophila (KENNISONand RIPOLL 1981; GETHMANN1988) and mice (PANTHIERet al. 1990). These processes create genotypic variability within the germline and alleles which affect the cells’ ability to survive or reproduce in this asexual stage(for example DNA translating enzymes or protein synthesizing apparatus) will be subject to selection. Many organisms such as plants, fungi and “lower” animals do not have a specialized germline (BUSS 1983). Gametesin these organisms arise from somatic tissue andthe potentialfor somatic mutation and selection is more obvious (Buss 1983; SLATKIN1985). T h e model developed here is equally applicable to both systems as it makes no distinction between mutations accumulating during mitosis in a specialized germline and those accumulating in a totipotent somatic cell lineage such as plant meristem tissue. The presence of genotypic variability and selection pressures within the asexual germline or soma may therefore result in a non-Mendelian output of gametes. Such alleles have population dynamics described by the sexual/asexual model of the life cycle. A description and consideration of the properties of the sexual/asexual life cycle forms the subject of this investigation. It appears to have advantages of both sexual and asexual reproduction in terms of recombination and stability of favorablecombinations of alleles. It allowsloci subjected to selection in the germline to overcome underdominance, and allows coevolution between loci to a greaterextentthan predicted under the sexual/Mendelian model. At this stage a distinction should be made between the two types of selection acting in the asexual stage of the life cycle. First, germline competition in which the genotypic diversity created by mitotic mutation, mitotic crossing over and mitotic gene conversion forms the basis for selection to favor or eliminate cell lineages containing certain genes or combinations of genes; this is the type of selection considered here. Second, gamete competition in which the genotypic diversity generated during mitosis is selectively neutral: in this case selection acts retrospectively on germline diploid genotypes by the differential survival of gametesformed at meiosis (the haploid genotypes appear not to be expressed in animals so the gametes are effectively metabolic copies of their diploid progenitors, BRAUNet al. 1989). A familiar example of gametecompetitionoccurs in mammals where the fitness of sperm depends on their ability to convert stored and environmental energy sources into motility, thus creating selection pressures on their basic metabolic pathways. Gamete selection has been investigated previously (HASTINGS1989) although at the time a formal distinction was not made between gametic and germline competition. T h e present study is designed to complement the first by investigating the properties of germline competition within the sexual/ asexual life cycle. METHODS Principle of the model: Two models will be used in the following studies: a single locus, two allele model to investigate the effects of germline selection on mutation rates and underdominance, and a twolocus, two-allele model to investigate coevolution between two loci. Transition matrices T can be constructed whose elements i,j hold the probability of genotype i producing genotype j during a single cell division duetothe actions of mutation andgene conversion (Table 1). These matrices were generated on theassumption that mutation and conversion rates per cell division are sufficiently small thatdouble events can be ignored. In the two-locus model it is further assumed, for simplicity, that mutation and conversion rates are the same for each allele. T h e same values of mutation and conversion are assumed to occur in mitosis and meiosis (see later) so T describes both types of division. A row vector Fi holds the relative frequency of each germline genotype within an adult of genotype i (i = 1, 2 or 3 in the single locus, two-allele model of underdominance, andi = 1 to 9in the two-locus, twoallele model of coevolution); the columns of these vectors correspond to the same genotypes as the T matrices. Fiorepresents the fertilized egg of genotype . . 2, z.e., the single cell present at germline generation zero, and Finholds the relative frequencies of germline genotypes after n cell divisions. A fitness matrix W holds the relative fitnesses of the genotypes (assumed to the same in both adult and germline stages of the life cycle, see later); ithas the same structure as the T Germline Selection: Genetic Aspects 1169 TABLE I Transition matrices(T)whose elements i,j hold the probabilityof parental cell genotype iproducing daughtercell genotype j during a single cell division (i) One-locus, two-allele model ~ ~ Daughter genotype Parental genotype Aa aa AA aa 1-2p, 2Pr Aa p x 1-p-pr2x AA 0 2r (ii) Two-locus, two-allele model + 0 p, +x 1-2p Daughter genotype Parental aaBb AABb aabb genotype aabb aaBb aaBB Aabb AaBb AaBB AAbb AABb AABB 1-4p P+X 0 P+X 0 0 0 0 0 AAbb AaBB % 1-4p-2X 2P 0 P+X 0 0 0 0 aaBB AaBb 0 P+X 1-4p 0 0 P+X 0 0 0 AABB Aabb 2/1 0 0 1-4p-2X P+X 0 2P 0 0 0 2P 0 2P 1-4p-4x 2r 0 2P 0 0 0 0 0 0 0 0 0 2r 0 P+X 1-4p-2X 0 0 2P 0 P+X 0 0 1 -4p /L + X 0 0 0 @+X 0 2a 1-4p-2X 2P 0 0 0 P+X 0 p + X 1-4p In (i) p is the mutation rate from A to a per allele, p, is the “reverse” mutation rate from a to A and X is the rate of gene conversion per (1989) as X is the rate of conversion per allele rather than per locus; this allele. This matrix differs slightly from that presented in HASTINCS facilitates extension of the model to the case of multiple gene copies (see APPENDIX). In (ii) p is the mutation rate per allele (assumed to be equal for each allele) and X is the rate of conversion per allele. matrices but all off-diagonal elements are zero and the diagonal elements hold the relative fitness of genotype i. Assuming n germline divisions, the relative germline genotype frequencies at gametogenesis will be given by Fin = Fio(TW)””T (1) It is assumed that no selection occurs during meiosis so the nth division is not multiplied by W. Each adult genotype i must be investigated in turn by setting its relative frequency in the FiO matrix to unity. The relative frequencies of each type of gamete produced from each adult genotype i can then be calculated from Fin. These frequencies are scaled to sum to unity and stored in a matrix G whose elements i,j hold the frequency with which gamete genotype j is produced from zygote genotype i (the rows correspond to the same genotypes as the T matrices). The G matrix records the consequencies ofgermline selection in the form of gametic output, and will consequently be used when modellingthe complete sexual/ asexuallifecycle.If differences existbetween the germlines of the twosexes, one G matrix will be required for each sex. A row vector At isused to hold the relative frequencies of adult genotypes prior to reproduction at generation t and is ordered as F. The relative frequencies of gametes produced by each sexin each adult generation are obtained from the product AtG, where G is the matrix obtained from the male or female germline as appropriate. The diploid genotype frequencies in the following generation are calculated assuming random fertilization ofmale and female gametes and stored in the rowvector A,, (HardyWeinburg frequencies cannot be assumed if the sexes produce different frequencies of gametes). The matrix A,, may then be multiplied by W to represent selection in the adult stage of the life cycle so that A,+1 = AtjW (2) after which the elements of A,+1 should be scaled to sum to unity. The sexual and asexual stagesare therefore combined to model the entire life cycle. In the models of underdominance and coevolution, the frequencies of adult genotypes aa and aabb respectively are set to unity in A0 and the adult stage of the life cycle iterated until the relative genotype frequencies reach a steady state. Choice of parameters for the model: It is possible to calculate the minimum number of cell cycles required to produce a constant output of large numbers humans, of sperm (e.g., 40-80 in mice, 200-500 in LYON 1981) but such estimates are sensitive to unquantified factors suchascellsenescence and the extent to which later cell cycles occur within a syncytium (WILLISONand ASHWORTH1987; BRAUNet al. 1989). The range 100 to 500 was chosen as probably within the right order of magnitude for most mammalian species. Mitotic gene recombination has been estimated as to 1O”per locus per cell generation in yeast, but 1170 I. M. Hastings may be influenced by the relative positions of the genes i.e., at the same locus, at different loci on the same chromosome, orondifferent chromosomes (LICHTENand HABER1989; YUAN and KEIL 1990; references therein). In male Drosophila mitotic crossing over is approximately IO-’ to 1 0 - ~per gamete 1988). These estimates from yeast and (GETHMANN Drosophila are compatible given the likely number of mitotic divisions prior to Drosophila spermatogenesis, so the values of 1O-’and 10-4 were investigated (which allows comparison with the model of gamete competition described by HASTINCS1989). Mitotic crossing over and mitotic gene conversion differ in the amount of genetic material exchanged:a whole section of chromosome in crossing over or a small section in gene conversion. When unlinked loci are considered, as in these models, the processes are identical in effect and for convenience are referred to simply as “conversion.’’ Mutation rates per gamete are typically estimated asto 10”j per locus per gameteforstructural loci, although estimates of mutations at loci affecting quantitative traits are usually around (TURELLI 1984). Both and were used to investigate the model. It is also necessary to determine the proportion of mutations which arise during mitosis as only they will be exposed to germline selection. Indirect evidence that most mutations ariseduring mitosis comes from the relative mutation rates in males and females of higher organisms. Male gametes are the product of a muchgreater numberof mitotic divisions than female gametes and should have a much higher mutation rate if most arise during mitosis; conversely, if most mutations occur during meiosis, the relative be similar. Investigations of mutationratesshould deleterious mutations in humans suggest that most arise paternally (e.g., WINTERet al. 1983; DRYJAet al. 1989; TOCUCHIDA et al. 1989; ZHU et al. 1989) and the molecular evolution ofX-linked and autosomal genes (which should reflect differences in their mutation rates) was also consistent with the hypothesis that most mutations arise in the male germline (MIYATA et al. 1987a,b, 1990). This suggests that estimates of total mutationrates pergamete of and are likely to be reasonable estimates of the total mitotic mutation rate per gamete. The “back mutation” rate restoring activity to anallele inactivated by a previous structural mutation is approximately of the forward mutation rate (FREIFELDER 1987): the mutation rate between active alleles was estimated in the same manner, i.e., as 10-3of the forward mutation rate. Mutations are assumed to occur between active alleles in models of underdominance or coevolution and are therefore much less frequent (by a factor of around 10-3)than those creating inactive alleles. T h e mutation rates of 10-4 and 10-6 per locus per gamete were therefore replaced by 10” and lo-’ per locus per gamete when investigating underdominance or coevolution. In models used to investigate the effects of germline selection in altering the mutation rateper gamete, no a back mutation was allowed fromthedeleterious allele to the wild-type A allele. This would be rare (approximately lo-’ of the forward rate), and a proportion of such reversions would arise througha compensatory mutationdistal to theoriginal mutation thereby producing a different allele (HARTL1989). The low rate of back mutation in relation to forward mutation and gene conversion rates meant that its omission had no significant effects for the parameter values investigated. These mutation and gene conversion rates are the rates per gamete. The rate per cell division was obtained by dividing this figure by the selected number of cell divisions; for example, the model examining a mutation rate of 10-4 per gamete with, 99 mitotic and 1 meiotic division assumes a rate of per cell division. This assumes for simplicity that the mutation and gene conversion rates per cell division are identical in meiosis and mitosis (if requireseparate T matrices can be generated for mitosis and meiosis and substituted in Equation 1). T h e model is deterministic and assumes infinite population sizes of both adults and germline cells. The effects of random drift were not investigated. Drift generally facilitates evolution across a fitness barrier of the type investigated in the models of underdominance and coevolution, and its absence means that the ability of the sexual/asexual lifecycle to cross fitness barriers may have been underestimated. T h e models of underdominance and coevolution investigated the following parameter values and all combinationsthereof: 100, 200 and 500 germline divisions; mutation rates between favorable alleles of lo-’ and 1O-’ per gamete; gene conversion rates of 10-3 and 10-4 per gamete (see Table 2). Selection was assumed to act either (i) in the male germline alone, or (ii) in both male and female germlines and in the adult. Selection on housekeeping metabolism may be most intense in rapidly dividing tissue. In mammals this rapid division occurs principally in the male germline which is represented by the first model and assumes negligible selection in the female germline and adult stages of the life cycle. Calculation of the fitnesses of each genotype: In the one locus, two allele model used to investigate differences in mutation rates the relative fitnesses of the three genotypes AA, Aa, and aa are represented in the conventional way as 1, l-hs, and 1-s, respectively, where h is a dominance index.In the onelocus, two allele model used to investigate underdominance, the relative fitnesses of genotypes AA, Aa,and aa are f A A , f A aand , f a a , respectively.f A A is set to unity and Aspects Genetic Selection: Germline TABLE 2 Combinations of parameters used to investigate the models of underdominance and coevolution X n 1 o-~ 100 Reference P 10-7 10-9 1o - ~ 10-4 10-9 1o-J 200 1o 10-7 500 10-7 10-9 10” 1o - -~ ~ 10-3 1o 10-9 1o - ~ 1o - ~ -~ (9 (ii) (iii) (iv) (4 (vi) (vii) (viii) (ix) (x) (xi) (xii) Where n is the number of germline generations, X is the conversion rate per gamete, and /.t is the mutation rate per gamete. The combinations are enumerated to allow easy reference in Figures 1 and 2. f A a and f a a varied between 0 and 1.0 in increments of 0.1. In the two locus, two allele model of coevolution, fitness was estimated fromthe “activity of interaction” between the two gene products(such as tRNA/rRNA, hormone/cell receptor, protein kinase/target protein, etc).Forexample, the two locus, two allele model codes for products A , a , B , and b; the biochemical activity of interaction between alleles A and B can be represented as f A / B = 1, similarly f A / b = 0.2 (if this type of interaction has 20% of A / B activity), f a / B = 0.3 (30%of A / B activity) and f a / b = 0.7 (70% of A / B activity). In this example genotype AaBb will result in a frequency of 0.25 of each combination of type A/B, A / b , a/B and a/b giving a mean activity of (0.25 X 1) (0.25 X 0.2) (0.25 X 0.3) (0.25 X 0.7) = 0.55; similarly the activity of genotype aaBb is given by (0.5 X 0.3) (0.5 X 0.7) = 0.50. T h e values of f A / b , f a / B andf a / b were varied between 0 and 1.O in increments of0.1. The results presentedlater were obtained when f A / b = f a / B ; this meant that only two variables were altered, i.e., f a / b and f A / b = f a / B , enabling the results to be presented in the standard two-dimensional form. Fitness is assumed to be proportional to activity. This may be an oversimplification as the relationship between activity and fitness appears to be a convex function (WRIGHT1934; KACSERand BURNS1981; GILLESPIE 1976; DYKHUIZEN and DEAN1990). A suitable transformation may be performedif desired (e.g., fitness = 2 * activity/(l activity)) but was omitted here for simplicity. + + + + + RESULTS The “underlying mutation rate” used to investigate the model of mutation is defined as the rate perlocus per gamete which would occur in the absence of 1171 germline selectioh. Table 3 shows the mutation rate per gamete arising from an underlying mutation rate of 1O-4. Gene conversion rates of lo-’ and 10-4 were used to investigate the model and gave identical results. The results indicate that the mutation rate per locus per gamete mayvary from in the absence of germline selection, to when s = 1, h = 0.2 and 500 cell cycles occur in the germline. An underlying mutation rate of was also investigated underthe same sets of parameters: the results were precisely lo-’ those given on Table 3. These results suggest that under plausible assumptions of germline molecular biology, the mutation rate per gametemay differ up to 100-fold between loci due to selection within the germline. The results obtained from a one locus, two allele model of underdominance are shown on Figure 1. The lines join values of f A / a and f a l a which result in the successful invasion of allele A into a population initially of genotype aa; all combinations of f A / a and f a / a to the upper left of a line result in fixation, all combinations to the lower rightpreclude invasion. T h e same parameter combinations in sexual populations (modelled by setting n = 1 in Equation 1) all failed to fix allele A when f a a - fAa 2 0.1. All combinations of parameters where selection was restricted to the male germline resulted in fixation of allele A up to and including the maximum degree of underdominance investigated, i.e., when the fitness of genotype aa = 0.9 and the fitness of genotype Aa = 0.1. When selection was assumed to act in both germlines and adult the ability of parameter combinations to fix allele A was reduced when values of f a a exceeds 0.6. In these circumstances, the ability of the sexual/ asexual population to evolve through an underdominant genotype appears to be principally determined by the number of cell generations occurring in the germline. The results obtained from a two locus, two allele model of coevolution are shown on Figure 2. The lines join values of f a / b and f A / b = f a / B which allow favorable alleles A and B to invade a population initially consisting solely of alleles a and b; all values to the upper left of a line result in fixation, all combinations tothe lower rightpreclude invasion. These results are similar to those obtained for underdominance (Figure 1): invasion occurs if the fitness of the original combination is less than 0.6, thereafter successful invasion is dependent on the numberof germline cell generations and, to a lesser extent, the gene conversion rate. Identical results are obtained when selection is assumed to act solely inthe male germline. The results show thatfortheparameter values investigated the number of asexual germline generations is the most important factor determining the ability of a sexual/asexual life cycle to evolve through a genotype of lesser fitness. The rate of mitotic con- I. M. Hastings 1172 TABLE 3 Mutation ratesper locus per gamete in germline lineages with an underlying mutation rate of s= 1 h = 0.01 h = 0.2 100 200 6.4 X 1 0 - ~ 4.3 X 10-5 2.0 x 1 0 - ~ 5.0 X lo-‘ 2.5 X lo-‘ 1.0 x lo-‘ 500 s = 0.1 s = 0.5 n h = 0.01 7.9 x 10-5 6.3 X 1 0 - ~ 3.7 x 1 0 - ~ lo” h = 0.2 h = 0.01 1.0 X 10-5 5.0 X lo-‘ 2.0 x lo-‘ 9.6 X 1 0 - ~ 9.1x 10-~ 7.9 X 10-5 Gene conversion rates of lo-’ and Rave the same results. An underlying mutation rate of factor of lo-‘. The parameters n, s and h a; defined in the text. h = 0.2 4.3 x 1 0 - ~ 2.5 X 1.0 X 10-5 gave the same results reduced by a 0.9 n (4 0.0 d v 0.7 ?i g 9 0.6 0.5 : 0.4 0 a a 0.3 2 E +) 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.8 0.7 0.8 0.9 0 Fitness of a a genotype ( f a a ) FIGURE1.-Underdominance between two alleles A and a present at a single locus. Parameter combinations were as enumerated on Table 2. Line “a” corresponds to parameter combination (iv), line “ b to combinations (i), (ii) and (iii),and line “c”to combinations (v) to (viii);combinations (ix) to (xii) lie along the x-axis. All values to the upper left of any line correspond to successful invasion of allele A into a population initially of genotype aa while all valuesto the lower right preclude successful invasion. These results were obtained when selection occurred on adultsand germlines of both sexes. When selection was restricted tothe male germline, all parameter values resulted insuccessfulinvasion ie., alllines lay along the x-axis. Also shown is the line “sex” representing a purely sexual life cycle, ie., when n = 1, X = lO-’or 1OT4, and p = or 1o+. version is of lesser importance while the two mutation rates investigated has no effect. Similar results are obtained when genes present in multiple copies are investigated (see APPENDIX) or when gamete competition is considered (HASTINGS 1989): mutation is necessary to create the initial diversity in the germline, thereafter it is the mitotic conversion rate (which is orders of magnitudes higher than the mutation rate) which is the chief source of genotypic diversity. DISCUSSION This model of population genetics is extremely flexible as most of its assumptions (for example that mutation and conversion rates are identical inmitosis and meiosis, or that selection is of equal intensity in adults and germline and in each sex, or that conversion between alleles was unbiased) were made solely FIGURE2.-Coevolution between two genes, which may encode alleles A or a and B or b, respectively. Parameter combinations investigated were as enumerated on Table 2. Line “a” corresponds to combinations (iii) and (iv), and line “b” to combinations (i) and (ii); the lines corresponding to combinations (v) to (xii) lay along the x-axis. The same results were obtained when selection was restricted to themale germline or was assumed to act on adultsand germlines of both sexes. The line “sex” represents a purely sexual life cycle (details in the caption of Figure 1). All values to the upper left of any line correspond to successful invasionof alleles A and E into a population initially of genotype aabb while all values to the lower right preclude successful invasion. on the groundsof convenience and can be eliminated by generating separate matrices of type T or W and substituting into Equations 1 and 2. The ease with which it incorporates such processes makes it a useful general model of non-Mendelian behavior such as biased gene conversion (LAMB1985), or meiotic drive (HARTLand CLARK1989); it is presently being extended to investigate the (non-Mendelian) population genetics of cytoplasmic organelles such as mitochondria. However, its usein the present study was restricted to an investigation of the properties of the sexual/asexual life cycle. A critical question in assessing its significance is therefore to identify the type of gene productssubject to germline selection and which are likely to be governed by the dynamics of the sexual/asexual life cycle. A geneproduct which affects a cell’s ability to survive or reproduce (by mitotic division) within the germline will, by definition, be subjected to germline Aspects Genetic Selection:Germline 1173 0.0 h t d 0.8 W 0.7 2 $ 0.6 0.5 Y G .d (0 0.4 h 0.3 +4 0 h :+: 0.1 4 Y u 4. n n I.” 0.1 0.2 0.3 0.4 0.5 0.7 0.0 0.8 0.0 Activity of a / a interaction ( f a / a ) FIGURE3.-Underdominance between alleles A and a in genes present as five copies in the diploid genotype. Selection was assumed to act on adults and germlines of both sexes. Parameter combinations are as enumerated on Table 2; combinations (ix) to (xii) lie along the x-axis. All values to the upper left of any line correspond to successful invasionof alleleA into apopulation initially containing only allele a while all values to the lower right preclude successful invasion. Also shown is the line “sexn representing a purely sexual life cycle (details in the caption of Figure 1). FIGURE4.-Underdominance between alleles A and a in genes present as five copies in the diploid genotype. Selection was restricted to the male germline. Parameter combinations are as enumerated on Table 2; combinations (ix) and (x) lie along the x-axis. All values to the upper left of any line correspond to successful invasion of allele A into a population initially containing only allele a while all values to the lower right preclude successful invasion. Also shown is the line “sex” representing a purely sexual life cycle (details in the caption of Figure 1). selection. It seems reasonable to supposethat this includes genes concernedwith DNA replication, RNA transcription and translation,protein synthesis, cell cycle regulation, and themechanics of cell division. It is also likely to include the large number of “housekeeping” loci encodingthe enzymes necessary for efficient metabolism such as sugar, lipid and amino acid metabolism. The term “housekeeping loci” used here is defined as a gene whose product is essential Activity of a / b interaction ( f a / b ) FIGURE5.-Coevolution between two types of genes, which may encode alleles A or a and B or b, respectively; each gene is present as fivecopies in the diploid genotype. Parameter combinations investigated are as enumerated on Table 2. The same results were obtained when selection was restricted to the male germline or was assumed to act on adults and germlines of both sexes. All values to the upper left of any line correspond to successful invasion of alleles A and B into a population initially containing only alleles of type a stand b whileallvalues to the lower right preclude successful invasion. The line “sex” represents apurely sexual life cycle (details in the caption of Figure 1). for theviability of anycell in any tissue and which will therefore, by definition,besubjected to selection within the germline. Germline selection cannot act on genes whose expression is restricted to thesoma, such as many regulatory, developmental and tissue-specific genes.It is interesting tonotethat MIYATA et al. (1987a,b, 1990) reported differences in the rate of molecular evolution of enzymes depending on whether they were genes “which might be vital for most organisms and cells” (ie., “housekeeping” genes) or genes “thatoccur mostlyin vertebrates or are expressed only in specific cells.” Evidence that germline selection may occur in Drosophila has been obtained experimentally (ABRAHAMSON et al. 1966, andreferences therein). Thesestudies scored the frequency of recessive lethals arising on each chromosome of irradiated males. Male Drosophila contain only a single copy of the X chromosome so any “recessive lethal”mutationsoccurringon this chromosome will be effectively dominant. Selection acting in the germline will be revealed as an unequal ratio of sex-linked to autosomal recessive lethals following meiosis; the data from this and previous experiments suggested thatabout 50% of sex-linked recessive lethals were lost prior to meiosis. This may be an underestimate for“housekeeping” genes as the scored lethals included developmental and tissue-specific genes which are not expressedpremeiotically and which would therefore not be exposed to germline selection. Exclusion of this class of genes would increase the estimate of premeiotic loss of mutations at 1174 I. M. Hastings housekeeping loci, but to what extent was not determined. The reason why germline selection may occur in natural populations yet non-Mendelian segregation is generally not observed may lie in the dynamics of the process. Alleles in a sexual/asexual life cycle are able to evolve across genotypes of reduced fitness as these deleterious genotypes produce a non-Mendelian output of gametes, making the process analogous to a “meiotic drive” system (discussed later). Meiotic drive systems are transient phenomena in which the favored allele is rapidly driven to fixation (unless balanced by an extremely deleterious effect on the adult, CROW 1979). One plausible reason why coevolving genotypes are not observed producing non-Mendelian ratios of gametes in naturalpopulations is thatthe process is so rapid that the chances of observing a “driven”allele are remote.Alternatively, if the process is relatively slow (perhaps dueto extremely small fitness differencesamonggermline genotypes) the degree of non-Mendelian behavior is likely to be imperceptible in most experimental protocols. For example, if f a a = 0.98 and f A a = 0.96 under parameter combination (iii) in Table 2 (i.e., n = 100, X = = lo-’), the frequency of A gametesproduced by genotype Aa is 0.504. Thus non-Mendelian behavior in natural populations is likely to be either too transient or too small to observe. One situationworth investigating is where distinct strains or subspecies occur within a species; if the separate genotypes have undergone significant coevolution then germlinecompetition in hybrids may result in non-Mendelian behavior. SYZMURA and FARANA (1978)investigated segregation at five enzyme lociin hybrids of the toad species Bombinabombina and Bombina variegata; no consistent non-Mendelian segregation was observed at individual loci although significant gametic disequilibrium between loci was noted in several matings. The effects of germline selection may partly explain the anomaly previously noted between mutation rates at single loci and those affecting quantitative traits (TURELLI1984; BARTONand TURELLI 1989); estimates of mutation rates at single loci are generally in the region of to 10-6 pergamete while those at loci affecting quantitative traits are typically in excess of lo-’. Even allowing for the large number of loci affecting quantitative traits, there still appear to be underlying differences in mutation rates. The results of Table 3 suggest the two estimates are not incompatible if the actions of germline selection are considered. Estimates at single locitypically investigate housekeeping loci, while mutations affecting quantitative traits aremore likely to bedevelopmental, regulatory, or tissue-specific genes of the type not subjected to selection within the germline. A further implication of these results is that mutation rates per gamete may differ even within the same gene: “silent” substitutions of base pairs being more frequent per gamete than substitutions causing amino acid substitutions. One drawback of reviewing evidence to support a theoretical prediction is that a post hoc assessment is less satisfactory than direct observation. Despite this drawback, the evidence reviewed above demonstrates that a consideration of germline selection enables the results of some experiments to bereassessed. It seems difficult to objectively ignore the effects of germline selection in natural populations. An allele can persist only by surviving from zygote to gamete to zygote and so on ad injnitum. Any mutation which alters the viability of the germline cell in which it is expressed will be selected or eliminated by natural selection in the same way as mutations which affect the viability or fertility of the entire animal. Thus genes whose expression affect cellular viability within the germline must be governed by the dynamics of the sexual/ asexual life cycle Selection in the germline enables afavorable recessive allele to spread more rapidly in a population than would occur in a sexual/Mendelian life cycle. Mitotic gene conversion and crossing over in the germline of heterozygotes produces homozygous recessive genotypes which will proliferate and contribute a higher, non-Mendelian, proportion of recessive alleles to the following generation; this situation is similar to that of meiotic drive discussed below. Germline selection avoids the “genetic load” incurred in other models of selection as competition in the germlineneednot affect the viability nor fertility of adults. The effects of germline selection may therefore be largely invisible in the adult phenotype. In some circumstances, alleles favored in the germline may be disadvantageous in the adult;in those cases where positive selection in the germline is exactly balanced by negative selection in the adult, no allele will predominate and a “meiotic drive” system will be observed. Such systems havebeenobserved in several species (e.g., HARTL and CLARK 1989; LYON 1990;references therein) although most appear following meiosis, i.e., arise through gametic selection rather than germline selection. Meiotic drive may also be more common than realized as only those alleles with large deleterious effects on the adult are likely to be noticed(DAWKINS 1982). Germline competition therefore has three consequences for selection on housekeeping loci: first, it allows recessive alleles to spread more rapidly; second, genetic loadin the formof reduced adultfertility or viability is notthe sole mechanism of selective changes in genefrequency;third, stable “meiotic drive” (or more appropriately “mitotic drive”) systems may arise from conflicting selection pressures acting in different stages of the life cycle. T h e possible effects of germline competition may also warrant consideration in discussions of the rela- 1175 Germline Selection: Genetic Aspects tive merits of sexual and asexual reproduction (e.g., STEARNS 1987; MICHOD and LEVIN 1988). From a genetic viewpoint,it appears more appropriate to regard the sexual life cycle as sexual/asexual and to compare its properties with those of a purely asexual life cycle. The sexual/asexual life cyclemay be advantageous for evolution at housekeeping loci, as it appears to combine favorable properties of each system. The advantages of this system cannot be quantified but the merits of a sexual/asexual life cycle in the maintenance and evolution of basic housekeeping metabolism may provide at least a partial repayment of the twofold cost of anisogamous sexual reproduction. This mayonly be a partial answer for when nonhousekeeping genes (e.g., developmental, regulatory, or tissue-specific)are considered, the distinction is still between purely sexual and asexual alternatives. The model providesan indication of the properties of the sexual/asexual life cycle but needs to be further developed to investigate the effects of drift and linkage. A quantitative investigation of real genes in real populations is precluded by the absence of molecular data on mitotic mutation and conversion rates, the number of germline generations in each sex, and the activity ofinteractions between different alleles. However, it appears that the sexual/asexual life cycle has properties markedly different from either the purely sexual or asexual cycle. The ability of sexual/asexual organisms to successfullycross a “valley”of reduced fitness was clearly realized by WRIGHT(PROVINE1986, p. 328) who stated that: The combination of prevailinguniparental reproduction with occasional cross breeding gives results with favorable properties of both systems (clonal vs. sexual), especially in cases in which there is the possibiIity of very rapid multiplication under favorable conditions. The situation is closely similar to that of subdivision of a population into local inbreeding races with occasionalintermigration. A rich field of variability is provided even by infrequent crossbreeding, while interclone selection provides for the effective selection of types which have adaptivegenotypes as wholes. The opportunity for such rapid multiplication is provided in the germline where the lifetime of a cell is much shorter than that of the adult.The mechanism enabling populations to crossfitness“valleys” may therefore be determined by the genes under consideration. The sexual/asexual life cycle of housekeeping genes may enable them to coevolve despite intervening genotypes of reduced fitness, while genes whose expression is restricted to the soma may coevolve by a process of local differentiation and migration (WRIGHT1977, Chapter 13; CROW,ENGELSand DENNISTON 1990). It therefore seemspossible that two typesof gene are present in populations of sexual metazoa. 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WRIGHT,S., 1977 Evolution and the Genetics of Populations, V O ~ . 3. University of Chicago Press, Chicago. YUAN, L-W, and R. L. KEIL, 1990 Distance-independence of mitotic intrachromosomal recombination in Saccharomyces cerevisiae. Genetics 124: 263-273. A. D. GODDARD, K. E. PATON, ZHU,X.,J. M. DUNN,R. A. PHILLIPS, A. BECKERand B. L. GALLIE,1989 Preferential germline mutation of the paternal allele in retinoblastoma. Nature 3 4 0 312-313. Communicating editor: D. CHARLESWORTH APPENDIX Many genes existin multiple copiesand it is possible to extend the model to investigate underdominance and coevolutionbetweensuchgenes.Analogous models are constructed, allloci are assumed to be unlinked and no account is kept of the relative positions of the alleles. For example, genotypes AAAAAAAAaa are all regarded as identical irrespective of whether the a alleles are on homologous or nonhomologous chromosomes (this assumption may be justified as, in yeast, the rateof mitotic recombination appears insensitive to the relative positions of alleles, LICHTENand HABER1989). The conversion rate per allele is weighted by the frequency of the alternative type of allele in the other loci of the genome so that “conversions” of typeA to A , a to a, B to B and b to b are ignored. For example in the genotype AAAAAAAAaa the frequency of conversion of an allele A to a is (2/9)X, and of a to A is (8/9)X. In the case of underdominance, the fitness of individual genotypes are calculated from the “activity of interaction” method described for coevolution:f a / a is the activity of interactions of products from alleles a, f A / a is the activity of products from A and a, and f A / A of products from A . As before, f A / A = 1, and the values of f A / a and f a / a are varied between 0 and 1.0 in increments of 0.1. For example, if f a / a = 0.6 and f A / a = 0.2, genotype AAaa would have fitness (0.25X 0.6) + (0.5 x 0.2) (0.25 x 1.0) = 0.5. The models of underdominance and coevolution investigated genespresent as five copies inthe diploid genotype; as before it was assumed there were two alleles of each typeof gene. The results are presented on Figures 3, 4 and 5. Sexual/asexual populations are less able to evolve to the genotype of higher fitness when genesare present in multiple copies as a greater number of deleterious intermediate genotypes are present. The results support the previousfindings that, for the parameter values investigated, the number of germline generations is the single most important factor determining whether a sexual/asexual population can evolve across genotypes of reduced fitness. The rate of gene conversion is of lesser importance while the two mutation rates investigated hadno effect on the final outcome. +