Copyright 0 1991 by the Genetics Society of 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 EH9 3JT, Scotland Manuscript received January 15, 1991

Accepted for publication August 12, 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 divisions in the germline prior to meiosis and sexual recombi- nation. The processes of mitotic mutation, mitotic crossing over, and mitotic gene conversion create genotypic diversity between diploid cells in the germline. Genes expressed in the germline whose products affect cell viability (such as many “housekeeping” enzymes) may be subjected to natural selection acting on this variability resulting in a non-Mendelian output of gametes. Such genes will 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. When appropriate parameter values were included in 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 to a genotype of higher fitness despite intervening genotypes of lower fitness, reducing the problems of underdominance and Wright’s adaptive landscape encoun- tered by purely sexual populations. As might be expected this ability is chiefly determined by the number of asexual mitotic cell divisions within the germline. The evolutionary consequences of “housekeeping” loci being governed by the dynamics of the sexual/asexual life cycle are considered.

T HE relative merits of sexual and asexual modes of reproduction have been the subject of ex-

tended debate in the literature (e.g., MAYNARD SMITH 1978; STEARNS 1987; MICHOD and LEVIN 1988) and arguments as to their evolution and maintenance re- main unresolved. Sexual reproduction occurs when individuals inherit genes from two parents resulting in the production of new combinations of alleles. Individuals fortunate enough to inherit 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 each generation. This has drawbacks for a sexual population’s ability to overcome underdominance or undergo coevolution. An example of underdomi- nance occurs when three genotypes aa, Aa and AA have fitnesses such that Aa << aa < AA (as may occur if, for example, the gene products interact to form a dimeric or polymeric enzyme molecule). A large sex- ual population cannot evolve from being predomi- nantly 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 ad- vantage when homozygous is outweighed by the selec- tive disadvantage when heterozygous and allele A cannot invade a sexual population of genotype 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 ran- dom drift to occur. A similar problem was considered in WRIGHT’S model of an adaptive landscape. This is an analogous problem to underdominance but de- scribes 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 on one hill cannot traverse a valley of reduced fitness (CROW 1986, 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 be of the less fit intermediate genotypes.

Asexual reproduction has opposite properties to those of sexual reproduction. Only the relatively slow processes of mutation and gene conversion create new combinations of alleles, making asexual populations less responsive to changing selection pressures. One advantage is that favorable combinations of alleles are not destroyed so any individual containing a genotype of higher fitness will leave offspring of the same genotype and the population will move to a higher fitness.

The advantages and disadvantages of sexual and asexual modes of reproduction were briefly reviewed here as an understanding of the effects of recombi- nation is critical to the arguments which follow. A

1168 I. M. Hastings

more extended discussion is given by CROW (1988) and CHARLFSWORTH (1 989).

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 con- cerned with the fate of individual alleles within pop- ulations; 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. Indi- vidual 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 germline and is usually regarded as a “black box” producing a Mendelian output of gametes. How- ever, mutation, crossing over and gene conversion are known to occur during mitosis (JOHN and MIKLOS 1988) and have been demonstrated in yeast (LICHTEN and HABER 1989; YUAN and KEIL 1990; references therein), Drosophila (KENNISON and RIPOLL 1981; GETHMANN 1988) and mice (PANTHIER et 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 synthe- sizing apparatus) will be subject to selection.

Many organisms such as plants, fungi and “lower” animals do not have a specialized germline (BUSS 1983). Gametes in these organisms arise from somatic tissue and the potential for somatic mutation and selection is more obvious (Buss 1983; SLATKIN 1985). The model developed here is equally applicable to both systems as it makes no distinction between mu- tations accumulating during mitosis in a specialized germline and those accumulating in a totipotent so- matic 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 ga- metes. Such alleles have population dynamics de- scribed 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 recom- bination and stability of favorable combinations of alleles. It allows loci subjected to selection in the germline to overcome underdominance, and allows coevolution between loci to a greater extent than 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 neu- tral: in this case selection acts retrospectively on germ- line diploid genotypes by the differential survival of gametes formed at meiosis (the haploid genotypes appear not to be expressed in animals so the gametes are effectively metabolic copies of their diploid pro- genitors, BRAUN et al. 1989). A familiar example of gamete competition occurs in mammals where the fitness of sperm depends on their ability to convert stored and environmental energy sources into motil- ity, thus creating selection pressures on their basic metabolic pathways. Gamete selection has been inves- tigated previously (HASTINGS 1989) although at the time a formal distinction was not made between ga- metic and germline competition. The 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 two- locus, two-allele model to investigate coevolution be- tween two loci. Transition matrices T can be con- structed whose elements i,j hold the probability of genotype i producing genotype j during a single cell division due to the actions of mutation and gene conversion (Table 1). These matrices were generated on the assumption that mutation and conversion rates per cell division are sufficiently small that double 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. The same values of mutation and conversion are assumed to occur in mitosis and meiosis (see later) so T de- scribes 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, and i = 1 to 9 in the two-locus, two- allele model of coevolution); the columns of these vectors correspond to the same genotypes as the T matrices. Fio represents the fertilized egg of genotype 2, z.e., the single cell present at germline generation zero, and Fin holds 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); it has the same structure as the T

. .

Germline Selection: Genetic Aspects 1169

TABLE I

Transition matrices (T) whose elements i, j hold the probability of parental cell genotype i producing daughter cell genotype j during a single cell division

(i ) One-locus, two-allele model ~ ~

Daughter genotype Parental genotype aa Aa AA

aa 1 -2p, 2Pr 0 Aa p + x 1-p-pr2x p, + x AA 0 2 r 1 -2p

(ii) Two-locus, two-allele model

Parental genotype aabb aaBb aaBB Aabb AaBb AaBB AAbb AABb AABB

Daughter genotype

aabb 1 -4p % 0 2/1 0 0 0 0 0 aaBb P + X 1 -4p-2X P + X 0 2P 0 0 0 0 aaBB 0 2P 1 -4p 0 0 2 r 0 0 0 Aabb P + X 0 0 1 -4p-2X 2P 0 P + X 0 0 AaBb 0 P + X 0 P + X 1 -4p-4x P + X 0 @ + X 0 AaBB 0 0 P + X 0 2 r 1 -4p-2X 0 0 P + X AAbb 0 0 0 2P 0 0 1 -4p 2 a 0 AABb 0 0 0 0 2P 0 /L + X 1-4p-2X p + X AABB 0 0 0 0 0 2P 0 2P 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 allele. This matrix differs slightly from that presented in HASTINCS (1989) as X is the rate of conversion per allele rather than per locus; this 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 gen- otype i.

Assuming n germline divisions, the relative germline genotype frequencies at gametogenesis will be given

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 corre- spond to the same genotypes as the T matrices). The G matrix records the consequencies of germline selec- tion in the form of gametic output, and will conse- quently be used when modelling the complete sexual/ asexual life cycle. If differences exist between the germlines of the two sexes, one G matrix will be required for each sex.

A row vector At is used to hold the relative fre- quencies of adult genotypes prior to reproduction at generation t and is ordered as F. The relative fre- quencies of gametes produced by each sex in each adult generation are obtained from the product AtG, where G is the matrix obtained from the male or

by

female germline as appropriate. The diploid genotype frequencies in the following generation are calculated assuming random fertilization of male and female gametes and stored in the row vector A,, (Hardy- Weinburg frequencies cannot be assumed if the sexes produce different frequencies of gametes). The ma- trix 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 stages are there- fore combined to model the entire life cycle. In the models of underdominance and coevolution, the fre- quencies 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 re- quired to produce a constant output of large numbers of sperm (e.g., 40-80 in mice, 200-500 in humans, LYON 1981) but such estimates are sensitive to un- quantified factors such as cell senescence and the extent to which later cell cycles occur within a syncy- tium (WILLISON and ASHWORTH 1987; BRAUN et al. 1989). The range 100 to 500 was chosen as probably within the right order of magnitude for most mam- malian 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, or on different chromosomes (LICHTEN and HABER 1989; YUAN and KEIL 1990; references therein). In male Drosophila mitotic cross- ing over is approximately IO-’ to 1 0 - ~ per gamete (GETHMANN 1988). These estimates from yeast and Drosophila are compatible given the likely number of mitotic divisions prior to Drosophila spermatogenesis, so the values of 1 O-’and 1 0-4 were investigated (which allows comparison with the model of gamete compe- tition described by HASTINCS 1989). 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 “con- version.’’

Mutation rates per gamete are typically estimated as to 10”j per locus per gamete for structural loci, although estimates of mutations at loci affecting quantitative traits are usually around (TURELLI 1984). Both and were used to investigate the model. I t is also necessary to determine the pro- portion of mutations which arise during mitosis as only they will be exposed to germline selection. Indi- rect evidence that most mutations arise during mitosis comes from the relative mutation rates in males and females of higher organisms. Male gametes are the product of a much greater number of 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 mutation rates should be similar. Investigations of deleterious mutations in humans suggest that most arise paternally (e.g. , WINTER et al. 1983; DRYJA et al. 1989; TOCUCHIDA et al. 1989; ZHU et al. 1989) and the molecular evolution of X-linked and autosomal genes (which should reflect differences in their mu- tation rates) was also consistent with the hypothesis that most mutations arise in the male germline (MI- YATA et al. 1987a,b, 1990). This suggests that esti- mates of total mutation rates per gamete of and

are likely to be reasonable estimates of the total mitotic mutation rate per gamete. The “back muta- tion” rate restoring activity to an allele 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 1 0-3 of 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 1 0-3) than those creating inactive alleles. The mutation rates of 1 0-4 and 1 0-6 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 rate per gamete, no back mutation was allowed from the deleterious a allele to the wild-type A allele. This would be rare (approximately lo-’ of the forward rate), and a pro- portion of such reversions would arise through a compensatory mutation distal to the original mutation thereby producing a different allele (HARTL 1989). 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 ob- tained by dividing this figure by the selected number of cell divisions; for example, the model examining a mutation rate of 1 0-4 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 iden- tical in meiosis and mitosis (if require separate T matrices can be generated for mitosis and meiosis and substituted in Equation 1). The 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 life cycle to cross fitness barriers may have been underestimated.

The models of underdominance and coevolution investigated the following parameter values and all combinations thereof: 100, 200 and 500 germline divisions; mutation rates between favorable alleles of lo-’ and 1 O-’ per gamete; gene conversion rates of 1 0-3 and 1 0-4 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 germ- line which is represented by the first model and as- sumes 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, respec- tively, where h is a dominance index. In the one locus, two allele model used to investigate underdominance, the relative fitnesses of genotypes AA, Aa, and aa are fAA, fAa , and faa , respectively. f A A is set to unity and

Germline Selection: Genetic Aspects 1171

TABLE 2

Combinations of parameters used to investigate the models of underdominance and coevolution

n X P Reference

100 1 o - ~ 10-7 ( 9 10-9 (ii)

1 0 - 4 1 o - ~ (iii) 10-9 (iv)

200 1 o-J 10-7 ( 4 10-9 (vi)

1 o - ~ 10” (vii) 1 o - ~ (viii)

10-9 (x) 1 o - ~ 1 o - ~ (xi)

1 o - ~ (xii)

500 10-3 10-7 (ix)

Where n is the number of germline generations, X is the conver- sion 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 from the “activity of interaction” between the two gene products (such as tRNA/rRNA, hormone/cell receptor, protein kinase/target protein, etc). For example, 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. The values of f A / b , f a / B and f a / b were varied between 0 and 1 .O in increments of 0.1. The results presented later 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-dimen- sional 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 (WRIGHT 1934; KACSER and BURNS 198 1 ; GILLESPIE 1976; DYKHUIZEN and DEAN 1990). A suit- able transformation may be performed if 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 per locus per gamete which would occur in the absence of

germline selectioh. Table 3 shows the mutation rate per gamete arising from an underlying mutation rate of 1 O-4. Gene conversion rates of lo-’ and 1 0-4 were used to investigate the model and gave identical re- sults. The results indicate that the mutation rate per locus per gamete may vary 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 under the same sets of parameters: the results were precisely lo-’ those given on Table 3. These results suggest that under plausible assumptions of germline molec- ular biology, the mutation rate per gamete may 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 right preclude invasion. The same parameter combinations in sexual popula- tions (modelled by setting n = 1 in Equation 1) all failed to fix allele A when faa - fAa 2 0.1. All combinations of parameters where selection was re- stricted 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 germ- lines 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 underdomi- nant 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 ini- tially consisting solely of alleles a and b; all values to the upper left of a line result in fixation, all combina- tions to the lower right preclude invasion. These results are similar to those obtained for underdomi- nance (Figure 1): invasion occurs if the fitness of the original combination is less than 0.6, thereafter suc- cessful invasion is dependent on the number of germ- line cell generations and, to a lesser extent, the gene conversion rate. Identical results are obtained when selection is assumed to act solely in the male germline.

The results show that for the parameter values investigated the number of asexual germline genera- tions 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-

1172 I. M. Hastings

TABLE 3

Mutation rates per locus per gamete in germline lineages with an underlying mutation rate of lo”

s = 1 s = 0.5 s = 0.1

n h = 0.01 h = 0.2 h = 0.01 h = 0.2 h = 0.01 h = 0.2

100 6.4 X 1 0 - ~ 5.0 X lo-‘ 7.9 x 10-5 1.0 X 10-5 9.6 X 10 -~ 4.3 x 1 0 - ~ 200 4.3 X 10-5 2.5 X lo-‘ 6.3 X 1 0 - ~ 5.0 X lo-‘ 9 .1 x 1 0 - ~ 2.5 X 500 2.0 x 1 0 - ~ 1.0 x lo-‘ 3.7 x 1 0 - ~ 2.0 x lo-‘ 7.9 X 10-5 1.0 X 10-5

Gene conversion rates of lo-’ and Rave the same results. An underlying mutation rate of gave the same results reduced by a factor of lo-‘. The parameters n, s and h a; defined in the text.

0.9

n (4 0.0

d ?i

9 :

v 0.7

g 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

Fitness of aa genotype ( f a a ) FIGURE 1 .-Underdominance between two alleles A and a pres-

ent 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 values to the lower right preclude successful invasion. These results were obtained when selection occurred on adults and germlines of both sexes. When selection was restricted to the male germline, all parameter values resulted in successful invasion ie., all lines lay along the x-axis. Also shown is the line “sex” representing a purely sexual life cycle, ie., when n = 1, X = lO-’or 1 OT4, and p = or 1 o+.

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 compe- tition is considered (HASTINGS 1989): mutation is nec- essary 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 flex- ible as most of its assumptions (for example that mu- tation and conversion rates are identical in mitosis and meiosis, or that selection is of equal intensity in adults and germline and in each sex, or that conver- sion between alleles was unbiased) were made solely

0

FIGURE 2.-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 the male germline or was assumed to act on adults and 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 invasion of alleles A and E into a population initially of genotype aabb while all values to the lower right preclude successful invasion.

on the grounds of 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 (LAMB 1985), or meiotic drive (HARTL and CLARK 1989); it is presently being ex- tended to investigate the (non-Mendelian) population genetics of cytoplasmic organelles such as mitochon- dria. However, its use in the present study was re- stricted to an investigation of the properties of the sexual/asexual life cycle. A critical question in assess- ing its significance is therefore to identify the type of gene products subject to germline selection and which are likely to be governed by the dynamics of the sexual/asexual life cycle.

A gene product which affects a cell’s ability to survive or reproduce (by mitotic division) within the germline will, by definition, be subjected to germline

Germline Selection: Genetic Aspects 1173

0.0 h

t 0.8 d W

0.7

0.6 2 $ 0.5 Y

.d 0.4 G (0

h 0.3 +4 0

h

+ 0.1

4 n n

:: 4 Y u . I.”

0.1 0.2 0.3 0.4 0.5 0.0 0.7 0.8 0.0 Activity of a / a interaction ( f a / a )

FIGURE 3.-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 combina- tions 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 invasion of alleleA into a population 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).

FIGURE 4.-Underdominance between alleles A and a in genes present as five copies in the diploid genotype. Selection was re- stricted to the male germline. Parameter combinations are as enu- merated 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 suppose that this includes genes concerned with DNA replication, RNA transcription and translation, protein synthesis, cell cycle regulation, and the mechanics of cell division. It is also likely to include the large number of “house- keeping” loci encoding the 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 )

FIGURE 5.-Coevolution between two types of genes, which may encode alleles A or a and B or b, respectively; each gene is present as five copies 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 while all values to the lower right preclude successful invasion. The line “sex” represents a purely sexual life cycle (details in the caption of Figure 1).

for the viability of any cell in any tissue and which will therefore, by definition, be subjected to selection within the germline. Germline selection cannot act on genes whose expression is restricted to the soma, such as many regulatory, developmental and tissue-specific genes. It is interesting to note that 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 “that occur mostly in vertebrates or are expressed only in specific cells.”

Evidence that germline selection may occur in Dro- sophila has been obtained experimentally (ABRAHAM- SON et al. 1966, and references therein). These studies scored the frequency of recessive lethals arising on each chromosome of irradiated males. Male Drosoph- ila contain only a single copy of the X chromosome so any “recessive lethal” mutations occurring on 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 fol- lowing meiosis; the data from this and previous ex- periments suggested that about 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-spe- cific genes which are not expressed premeiotically and which would therefore not be exposed to germline selection. Exclusion of this class of genes would in- crease the estimate of premeiotic loss of mutations at

1174 I . M. Hastings

housekeeping loci, but to what extent was not deter- mined.

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 out- put 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 geno- types are not observed producing non-Mendelian ra- tios of gametes in natural populations is that the process is so rapid that the chances of observing a “driven” allele are remote. Alternatively, if the process is relatively slow (perhaps due to extremely small fitness differences among germline genotypes) the degree of non-Mendelian behavior is likely to be im- perceptible in most experimental protocols. For ex- ample, if f a a = 0.98 and fAa = 0.96 under parameter combination (iii) in Table 2 (i.e., n = 100, X = = lo-’), the frequency of A gametes produced by genotype Aa is 0.504. Thus non-Mendelian behavior in natural populations is likely to be either too tran- sient or too small to observe. One situation worth investigating is where distinct strains or subspecies occur within a species; if the separate genotypes have undergone significant coevolution then germline com- petition in hybrids may result in non-Mendelian be- havior. SYZMURA and FARANA (1978) investigated seg- regation at five enzyme loci in hybrids of the toad species Bombina bombina and Bombina variegata; no consistent non-Mendelian segregation was observed at individual loci although significant gametic disequi- librium 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 (TURELLI 1984; BARTON and TURELLI 1989); esti- mates of mutation rates at single loci are generally in the region of to 1 0-6 per gamete 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 incom- patible if the actions of germline selection are consid- ered. Estimates at single loci typically investigate housekeeping loci, while mutations affecting quanti- tative traits are more likely to be developmental, 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 substitu- tions.

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 be reassessed. 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 a favorable reces- sive 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 geno- types 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 germline need not affect the viability nor fertility of adults. The effects of germline selection may therefore be largely invisi- ble in the adult phenotype. In some circumstances, alleles favored in the germline may be disadvanta- geous in the adult; in those cases where positive selec- tion 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 sys- tems have been observed 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 deleteri- ous effects on the adult are likely to be noticed (DAWK- INS 1982). Germline competition therefore has three consequences for selection on housekeeping loci: first, it allows recessive alleles to spread more rapidly; sec- ond, genetic load in the form of reduced adult fertility or viability is not the sole mechanism of selective changes in gene frequency; third, stable “meiotic drive” (or more appropriately “mitotic drive”) systems may arise from conflicting selection pressures acting in different stages of the life cycle.

The possible effects of germline competition may also warrant consideration in discussions of the rela-

Germline Selection: Genetic Aspects 1175

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 cycle may be advan- tageous for evolution at housekeeping loci, as it ap- pears 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 me- tabolism may provide at least a partial repayment of the twofold cost of anisogamous sexual reproduction. This may only be a partial answer for when non- housekeeping genes (e.g., developmental, regulatory, or tissue-specific) are considered, the distinction is still between purely sexual and asexual alternatives.

The model provides an indication of the properties of the sexual/asexual life cycle but needs to be further developed to investigate the effects of drift and link- age. 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 of interactions between different alleles. How- ever, 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 success- fully cross a “valley” of reduced fitness was clearly realized by WRIGHT (PROVINE 1986, p. 328) who stated that:

The combination of prevailing uniparental 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 multipli- cation under favorable conditions. The situation is closely similar to that of subdivision of a population into local inbreeding races with occasional intermigration. A rich field of variability is provided even by infrequent crossbreeding, while interclone selection provides for the effective selection of types which have adaptive genotypes 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 cross fitness “valleys” may therefore be determined by the genes under consid- eration. The sexual/asexual life cycle of housekeeping genes may enable them to coevolve despite interven- ing genotypes of reduced fitness, while genes whose expression is restricted to the soma may coevolve by a process of local differentiation and migration (WRIGHT 1977, Chapter 13; CROW, ENGELS and DEN- NISTON 1990). It therefore seems possible that two types of gene are present in populations of sexual metazoa. The housekeeping genes whose population dynamics are governed by the genetics of the sexual/ asexual life cycle, and those genes whose expression

is restricted to the soma and whose dynamics are described by the genetics of the sexual/Mendelian life cycle.

I thank W. G. HILL and colleagues for comments on the manu- script. This work was supported by a grant from the Agricultural and Food Research Council.

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APPENDIX

Many genes exist in multiple copies and it is possible to extend the model to investigate underdominance and coevolution between such genes. Analogous models are constructed, all loci are assumed to be unlinked and no account is kept of the relative posi- tions of the alleles. For example, genotypes AAAAAAAAaa are all regarded as identical irrespective of whether the a alleles are on homologous or non- homologous chromosomes (this assumption may be justified as, in yeast, the rate of mitotic recombination appears insensitive to the relative positions of alleles, LICHTEN and HABER 1989). 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 type A 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 prod- ucts 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 incre- ments of 0.1. For example, if f a / a = 0.6 and f A / a = 0.2, genotype AAaa would have fitness (0.25 X 0.6) + (0.5 x 0.2) + (0.25 x 1.0) = 0.5.

The models of underdominance and coevolution investigated genes present as five copies in the diploid genotype; as before it was assumed there were two alleles of each type of 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 genes are present in multiple copies as a greater number of deleterious intermediate genotypes are present. The results support the previous findings that, for the parameter values investigated, the num- ber of germline generations is the single most impor- tant factor determining whether a sexual/asexual pop- ulation can evolve across genotypes of reduced fitness. The rate of gene conversion is of lesser importance while the two mutation rates investigated had no effect on the final outcome.