Download Germline Selection: Population Genetic Aspects of the

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. 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 whosedynamics are
described by the genetics of the sexual/Mendelian life
cycle.
I thank W. G. HILLand colleagues for comments on the manuscript. This work was supported by a grant from the Agricultural
and Food Research Council.
LITERATURE CITED
ABRAHAMSON,
S., H. U. MEYER,E. HIMOEand G. DANIEL,
1966 Further evidence demonstrating germinal selection in
early premeiotic germ cells of Drosophila males. Genetics 5 4
687-696.
BARTON,
N. H., and M. TURELLI, 1989Evolutionary quantitative
genetics: how little do we know? Annu. Rev. Genet. 23: 337370.
BRAUN,
R. E., R. B. BEHRINGER,
J. J. PESCHON,
R. L. BRINSTER
and
R.D. PALMITER,1989 Genetically haploid spermatids are
phenotypically diploid. Nature 337: 373-376.
Buss, L., 1983 Evolution, development and the units of selection.
Proc. Natl. Acad. Sci. USA 8 0 1387-1 39 1.
CHARLESWORTH,
B., 1989 The evolution of sex and recombination. Trends Ecol. Evol. 4 264-267.
CROW,J. F., 1979 Genes that violate Mendel’s rules. Sci.Am.
240: 104-1 13.
and
CROW,J. F., 1986 BasicConceptsinPopulation,Quantitative,
Evolutionary Genetics. W. H. Freeman, New York.
CROW,J. F., 1988The importanceof recombination. In The
Evolution of Sex: An Examination of Current Ideas, edited by R.
E. MICHOD and B. R. LEVIN. SinauerAssociates, Sunderland,
Mass.
CROW, J.F., W. R. ENCELSand C. DENNISTON,
1990 Phase three
of Wright’s shifting balance theory. Evolution 44:233-247.
DAWKINS,
R., 1982 TheExtendedPhenotype. W. H. Freeman, Oxford.
DRYJA,T. P., S. MUKAI,R. PETERSEN,
J. M. RAPAPORT,
D. WALTON
and D. W. YANDELL,1989 Parental origin of mutations of
the retinoblastoma gene. Nature 3 3 9 556-558.
DYKHUIZEN,
D. E., and A. M. DEAN,1990 Enzymeactivity and
fitness. Trends Ecol. Evol. 5: 257-262.
FREIFELDER,
D., 1987 Molecular Biology. Johnes & Bartlet, Boston.
GETHMANN,
R. C., 1988 Crossing over in males of higher Diptera
(Brachycera).J. Hered. 7 9 344-350.
GILLESPIE,
J. H., 1976 A general method to account for enzyme
variation in natural populations. 11. Characterization of the
fitness functions. Am. Nat. 110: 809-821.
HARTL,D.L., 1989 The physiologyof weak selection. Genome
31: 183-189.
HARTL,D.L., and A. G. CLARK,1989 Principals of Population
Genetics, Ed. 2. Sinauer Associates, Sunderland, Mass.
HASTINGS,
I. M., 1989 Potential germline competition in animals
and its evolutionary implications. Genetics 123: 191-197.
JOHN, B., and G. L. MIKLOS,1988 The
Eukaryotic Genome in
Development and Evolution. Allen 8c Unwin, London
KACSER, H., and J. A. BURNS,1981 The molecular basis of dominance. Genetics 97:639-666.
KENNISON,
J. A., and P. RIPOLL,1981 Spontaneous mitotic recombination and evidence for an X-ray-inducible system for the
repair of DNA damage in Drosophila melanogaster.Genetics 98:
91-103.
LAMB,B. C., 1985 The relative importance of meiotic gene conversion, selection and mutational pressure, in population genetics and evolution. Genetica 67: 39-49.
LIGHTEN,M., and J. E. HABER,1989 Position effects in ectopic
and allelic mitotic recombination in Saccharomyces cereuisiae.
Genetics 123: 261-268.
LYON,M. F., 1981 Sensitivity of various germ-cell stages to environmental mutagens. Mutat. Res. 87: 323-345.
1176
I. M. Hastings
LYON,M. F., 1990 Search for differences among t haplotypes in
distorter and responder genes. Genet. Res. 55: 13-19.
MAYNARD
SMITH,J., 1978 The Evolution of Sex. Cambridge University Press, Cambridge, U.K.
MICHOD, R. E., and B. R. LEVIN,1988 TheEvolution of Sex: A n
Examination of Current Ideas. Sinauer Associates, Sunderland,
Mass.
MIYATA, T., H. HAYASHIDA,
K. KUMA and T . YASUNAGA,
1987a Male-drive molecular evolution demonstrated by different rates of silent substitutions between autosome- and sex
chromosome-linked genes. Proc. Jpn. Acad. B 63: 327-33 1.
K. KUMA,K. MITSUYASUand T.
MIYATA,T., H. HAYASHIDA,
YASUNAGA,
1987b Male-driven molecular evolution: a model
and nucleotide sequence analysis. Cold Spring Harbor Symp.
Quant. Biol. 52: 863-867.
H. H A Y A S H I D A YASUNAGA,
~~~T.
MIYATA,
T., K. KUMA,N. IWABE,
1990 Different rates of evolution of autosome-, X chromosome-, and Y chromosome-linked genes: hypothesis of maledriven molecular evolution, in Population Biology of Genes and
and J. F. CROW.Baifuken,
Molecules, edited by N. TAKAHATA
Chiyoda-ku, Tokyo.
PANTHIER,
J. J., J. GUENET,H. CONDAMINE
and F. JACOB,
1990 Evidence for mitotic recombination in We’/+ heterozygous mice. Genetics 1 2 5 175-182.
W. B., 1986 Selected Papers of Sewal Wright. University
PROVINE,
of Chicago Press, Chicago.
SLATKIN,
M., 1985 Somatic mutations as an evolutionary force,
P. H. HARVEY
and
in Evolution, edited by P.J. GREENWOOD,
M. SLATKIN.
Cambridge University Press, Cambridge, U.K.
S. C., 1987 TheEvolution of Sex and Its Consequences.
STEARNS,
Birkhauser Verlag, Basel.
J. M., and I. FARANA,1978Inheritance and linkage
SYZMURA,
analysis of five enzyme loci in interspecific hybrids of toadlets,
genus Bombina. Biochem. Genet. 16307-319.
J., K. ISHIZAKI,M. S. SASAKI,Y. NAKAMURA,
M.
TOCUCHIDA,
IKENAGA,
M. KATO, M. SUCIMOT,
Y. KOTOURAand T . YAMAMURO,1989 Preferential mutation of paternally derived RB
gene as the initial event in sporadic osteosarcoma. Nature 338:
156-158.
TURELLI,
M., 1984 Heritable genetic variation via mutation-selection balance: Lerch’s zeta meets the abdominal bristle. Theor.
Popul. Biol. 25: 138-193.
1987 Mammalian spermatoWILLISON,
W., and A. ASHWORTH,
genic gene expression. Trends Genet. 3: 351-355.
WINTER,R. M.,E.G.D.
TUDDENHAM,
E. GOLDMAN
and K.B.
MATTHEWS,
1983 A maximum likelyhood estimate of the sex
ratio of mutation rates in haemophilia A. Hum. Genet. 64:
156-159.
WRIGHT,S., 1934 Molecular and evolutionary theories of dominance. Am. Nat. 63:24-53.
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.
+