Novel Population Genetics in Ciliates due to Life Cycle and
Nuclear Dimorphism
David W. Morgens,1 Timothy C. Stutz,1 and Andre R.O. Cavalcanti*,1
1
Biology Department, Pomona College, Claremont, CA
*Corresponding author: E-mail: [email protected].
Associate editor: Noah Rosenberg
Abstract
Our understanding of population genetics comes primarily from studies of organisms with canonical life cycles and
nuclear organization, either haploid or diploid, sexual, or asexual. Although this template yields satisfactory results for
the study of animals and plants, the wide variety of genomic organizations and life cycles of unicellular eukaryotes can
make these organisms behave differently in response to mutation, selection, and drift than predicted by traditional
population genetic models. In this study, we show how each of these unique features of ciliates affects their evolutionary
parameters in mutation–selection, selection–drift, and mutation–selection–drift situations. In general, ciliates are less
efficient in eliminating deleterious mutations—these mutations linger longer and at higher frequencies in ciliate populations than in sexual populations—and more efficient in selecting beneficial mutations. Approaching this problem via
analytical techniques and simulation allows us to make specific predictions about the nature of ciliate evolution, and we
discuss the implications of these results with respect to the high levels of polymorphism and high rate of protein
evolution reported for ciliates.
Key words: segregation times, selection–drift, mutation–selection balance, mutation–selection–drift.
Introduction
Article
Ciliates are unicellular eukaryotes characterized by the presence of cilia and nuclear dimorphism. This last characteristic
allows ciliates to separate soma and germline functions in
different types of nuclei. The transcriptionally silent, germline
micronucleus is used to transfer genetic material after sexual
conjugation and to form the transcriptionally active, somatic
macronucleus. Ciliate cells alternate between periods of vegetative growth, when they divide by binary fission, and sexual
conjugation, when two cells exchange haploid nuclei to form
zygotes (Prescott 1994).
In addition to serving distinct functions, the two types of
nuclei divide via distinct mechanisms. During vegetative
growth, the germline micronucleus divides by mitosis, and
each daughter cell receives an identical copy of this nucleus.
The somatic macronucleus, on the other hand, divides by a
process called amitosis, in which the nuclear material duplicates, and the nucleus divides roughly in half (Prescott 1994).
After several rounds of vegetative growth, ciliate cells undergo sexual conjugation. During conjugation, the macronucleus is destroyed, whereas the micronucleus undergoes
meiosis, forming haploid nuclei that are exchanged between
conjugating partners. Two haploid nuclei, one from the donor
cell, one from the recipient cell, then fuse to form a diploid zygotic micronucleus. This nucleus then divides by mitosis without cell division, and one of the resulting copies
becomes the macronucleus of the new cells (fig. 1; Prescott
1994).
Thus, two factors make the evolutionary dynamics of
ciliates distinct from that of other sexual eukaryotes,
who may fall under the standard Wright–Fisher model
(Fisher 1930; Wright 1931). First, the ciliate life cycle—
several rounds of asexual growth followed by sexual
conjugation—should affect the propagation of mutations
(neutral [Balloux et al. 2003], deleterious, or beneficial).
One reason for this is that sex allows the formation of
homozygous individuals. Thus, the paucity of sex in the ciliate
life cycle results in fewer homozygous individuals, altering
how alleles are selected.
Second, during vegetative growth, mutations can accumulate in both the macronucleus and the micronucleus. As the
old macronucleus is destroyed during conjugation, any mutations accumulated in this nucleus during vegetative growth
are eliminated following sexual conjugation. Because the
micronucleus is transcriptionally silent, mutations occurring
in this nucleus during vegetative growth are not expressed
and thus are effectively neutral, until conjugation. Following
conjugation, a new macronucleus is formed from the new
zygotic micronucleus, and all mutations accumulated in the
micronucleus during vegetative growth will be expressed in
this new macronucleus (fig. 1).
Thus, if a ciliate gained a deleterious mutation in the
micronucleus during vegetative growth, the mutation
would be silent, as no proteins are expressed from the
micronucleus, and this ciliate’s line could flourish by drift
unchecked by selection. However, when any of these
ciliates enters conjugation, the mutation can be expressed
and might affect the fitness of all their daughter cells
(fig. 1). In this way, a cell line whose fitness, in the
long term, is very low can survive to represent a large
fraction of the population, creating a disconnect between
the evolutionary forces of selection and mutation. This
ß The Author 2014. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please
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Mol. Biol. Evol. 31(8):2084–2093 doi:10.1093/molbev/msu150 Advance Access publication April 30, 2014
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FIG. 1. The ciliate life cycle showing the masking of mutations during vegetative growth. The larger nucleus in each cell is the macronucleus and
the smaller the micronucleus. Nuclei with mutant alleles are represented in black. The lightning bolt represents a mutational event in the
micronucleus. During vegetative growth, the cells divide asexually by binary fission, and the micronucleus is transcriptionally silent. Any mutation occurring in the micronucleus during this period is not expressed and can propagate neutrally in the population until the next sexual
conjugation. During sexual conjugation, the micronucleus divide by meiosis, and haploid copies are exchanged between conjugating partners,
to form a new zygotic micronucleus, which then divides mitotically without cell division. The old macronucleus is eliminated, represented
by gray dotted lines, and a new one is generated from one of the copies of the new micronucleus. Any mutation present in the zygotic
micronucleus will be expressed in the new macronucleus. Alternator organisms present the same life cycle as ciliates, except that mutations are
not initially masked.
nuclear dimorphism has been predicted to have varying and
far-reaching effects on the evolution (Zufall et al. 2006;
Morgens et al. 2013) and population dynamics of ciliates
(Lynch and Gabriel 1990; Sung et al. 2012) and has consequences for the dynamics of both deleterious and beneficial
mutations.
Plasmodium, another unicellular eukaryote and the causative agent of malaria, also has a unique life cycle, distinct
from that of ciliates. Recently, this has been shown to alter
this organism’s population genetics, enhancing both selection
and drift with respect to the Wright–Fisher model (Chang
et al. 2013). On the basis of their results for Plasmodium,
Chang et al. (2013) show that the existing population genetics
tools are not robust to unique and complex life cycles, that is,
the standard population models can lead to incomplete or
erroneous conclusions when applied indiscriminately to organisms that do not follow the assumptions of the Wright–
Fisher model.
Here, we describe another example of novel population
genetics, brought on not only by the life cycle but also by the
unique genomic organization of ciliates. On the basis of these
two factors, we will derive an analytical equation for the mutation–selection balance in infinite ciliate populations and
use simulations to calculate the segregation time and fixation
probabilities of mutations in a finite ciliate population under
selection. We will show that for an infinite population, a deleterious allele under mutation–selection has a higher equilibrium frequency in ciliates than in other eukaryotes. In finite
populations, the segregation times of mutant alleles are
higher in ciliates than expected for sexual organisms. We
will tease apart the two factors and show how both the ciliate
life cycle and nuclear dimorphism affect the segregation
time of mutations in ciliates. We will also present the results
of a mutation–selection–drift simulation, validating our
analysis.
Results
Mutation–Selection Balance
We derive the equilibrium frequency, q, of a deleterious allele (selection coefficient = s; fitness = W; s = 1 W) for
an infinite ciliate population with mutation rate, , and
n asexual generations between conjugations for a recessive
allele as
rffiffiffiffi
M
ð1Þ
q¼
S
and for a dominant allele as
0 ¼ Sq2 + Sð1 + MÞq S
ð2Þ
where M ¼ 1 ð1 Þn + 1 and S ¼ 1 ð1 sÞn + 1 .
Note that in these equations, if we let n = 0, which corresponds to an exclusively sexually reproducing organism, then
L = and S = s, and our equations reduce to:
rffiffiffiffi
q¼
ð3Þ
s
and
0 ¼ sq2 + sð1 + Þq ð4Þ
which describe the equilibrium frequencies for a recessive
and a dominant allele in a sexual organism (Crow 1970;
Chasnov 2000). In these equations, we are assuming that
back mutation to the wild-type allele is negligible.
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Comparing the ciliate equations with those of sexual organisms in the recessive case, it is easy to see that ciliates have
a higher equilibrium frequency of deleterious alleles for any
value of n > 0, as long as < s, because in these cases:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffi
1 ð1 Þn + 1
ð5Þ
n+1 >
s
1 ð1 sÞ
Note that for s, the allele becomes fixed in both ciliate
and exclusively sexual populations. Unfortunately, it is not so
easy to show analytically that ciliates always have higher or
equal equilibrium values than sexual populations in the dominant case. However, if we assume that q is low ( << s), the
equilibrium frequency of a dominant allele in sexual organisms can be approximated by q ¼ =s. Under the same assumption, the ciliate equation becomes q ¼ M=S. Thus, when
<< s, ciliates always have a higher equilibrium frequency
than sexual organisms. Using the derived equations, we
can show numerically that as n increases, the difference
between ciliates and sexual organisms becomes more dramatic (fig. 2). We also performed a wide numerical search
of several combinations of fitness effects (0–1) and mutation
rates (106–103) and confirmed that the equilibrium frequency of a deleterious dominant allele remains higher in
ciliates throughout the parameter space for n = 75 (supplementary materials, Supplementary Material online).
Selection–Drift Simulations
To calculate how long the mutant allele persists in finite
populations, that is, the segregation time, we used simulations
of ciliate populations and compared the results with those of
simulations of exclusively sexual organisms. To separate the
effects of nuclear dimorphism from those of life cycle, we
performed simulations of populations of organisms with
the same life cycle of ciliates—several rounds of asexual generations followed by sexual conjugation—but with no nuclear
dimorphism—mutations are expressed as soon as they occur.
We will use the term “alternators" to refer to these organisms
and the term “alternating life cycle" to describe this aspect of
the ciliate life cycle.
We performed simulations with a wide range of population sizes but only report here the segregation times for populations of size 100 and 10,000 (tables 1 and 2; tables with the
results for all simulated population sizes are available in the
supplementary materials, Supplementary Material online). To
directly compare the segregation times of ciliates and alternators to those of sexual organisms, we show graphs of the
ratios of the segregation time of ciliates versus sexual
FIG. 2. Equilibrium frequency of deleterious alleles for ciliates with different numbers of generations between conjugation (n) and for ideal sexual
organisms. In all cases, the equilibrium frequency of the deleterious allele increases with n. Note that n = 0 corresponds to a sexually reproducing
organism. (A) Equilibrium frequency for a deleterious recessive allele (s = 0.05) versus mutation rate (eq. 1). (B) Equilibrium frequency for a deleterious
recessive allele ( = 104) versus fitness (eq. 1). (C) Equilibrium frequency for a deleterious dominant allele (s = 0.05) versus mutation rate (eq. 2). (D)
Equilibrium frequency for a deleterious dominant allele ( = 104) versus fitness (eq. 2).
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100
10,000
100
10,000
100
10,000
100
10,000
100
10,000
100
10,000
Population
10.68 (0.11)
10.73 (0.15)
10.12 (0.03)
9.26 (0.00)
6.64 (0.03)
6.28 (0.04)
10.60 (0.18)
14.44 (0.50)
11.70 (0.24)
15.26 (0.09)
11.85 (0.06)
15.57 (0.43)
Sexual Population
17.3 (0.21)
15.98 (0.15)
15.27 (0.12)
13.89 (0.08)
9.44 (0.06)
9.06 (0.09)
16.91 (0.08)
23.07 (0.28)
19.48 (0.29)
24.03 (0.12)
19.59 (0.21)
24.48 (0.35)
n=5
19.31 (0.11)
18.04 (0.25)
17.48 (0.02)
15.56 (0.26)
11.21 (0.06)
10.76 (0.1)
19.39 (0.09)
25.44 (0.35)
22.37 (0.22)
27.19 (0.89)
22.79 (0.29)
27.18 (0.64)
20.47 (0.36)
18.47 (0.21)
18.21 (0.2)
16.07 (0.09)
12.32 (0.1)
11.68 (0.05)
20.76 (0.16)
26.39 (0.71)
23.47 (0.36)
27.77 (0.62)
23.42 (0.10)
27.50 (0.48)
n = 50
Ciliate Population
n = 25
(0.22)
(0.06)
(0.09)
(0.04)
20.62 (0.43)
18.69 (0.29)
18.98
16.63
12.86
12.48
21.61 (0.41)
26.44 (0.48)
24.00 (0.35)
27.05 (0.27)
23.85 (0.21)
27.43 (0.64)
n = 75
17 (0.18)
16.32 (0.13)
15.33 (0.12)
13.75 (0.12)
9.06 (0.02)
8.72 (0.04)
16.93 (0.03)
23.31 (0.33)
19.70 (0.32)
23.69 (0.47)
19.60 (0.11)
25.02 (0.86)
n=5
19.07 (0.25)
17.6 (0.27)
16.55 (0.22)
14.82 (0.1)
9.63 (0.01)
9.31 (0.03)
19.40 (0.03)
25.06 (0.70)
22.21 (0.21)
27.01 (0.36)
22.51 (0.25)
27.25 (0.55)
19.66 (0.15)
17.83 (0.28)
17.05 (0.07)
15.02 (0.14)
9.72 (0.05)
9.39 (0.04)
20.74 (0.11)
26.56 (0.70)
23.49 (0.21)
27.22 (0.45)
23.17 (0.82)
28.32 (0.13)
n = 50
Alternator Population
n = 25
19.79 (0.13)
17.84 (0.04)
17.07 (0.22)
15.23 (0.07)
9.75 (0.08)
9.43 (0.05)
21.50 (0.12)
26.48 (1.29)
24.00 (0.29)
26.96 (0.74)
23.89 (0.15)
27.81 (0.07)
n = 75
100
10,000
100
10,000
100
10,000
Population
22.61 (0.15)
143.0 (0.06)
12.49 (0.19)
22.69 (0.28)
10.99 (0.1)
14.75 (0.3)
Sexual Population
45.47 (0.49)
286.4 (3.26)
20.73 (0.17)
37.91 (0.84)
17.63 (0.22)
23.69 (0.46)
n=5
49.07 (0.4)
291.3 (3.79)
22.67 (0.17)
40.59 (0.33)
19.13 (0.06)
25.56 (0.97)
n = 25
47.56 (0.39)
266.5 (2.21)
22.63 (0.34)
39.33 (0.3)
19.58 (0.28)
25.76 (0.16)
n = 50
Ciliate Population
46.50 (0.7)
242.9 (2.13)
22.11 (0.4)
36.97 (1.18)
19.57 (0.18)
25.1 (0.35)
n = 75
48.00 (0.46)
303.1 (3.23)
21.02 (0.25)
38.57 (1)
17.58 (0.14)
23.22 (0.53)
n=5
61.04 (0.62)
372.2 (2.15)
23.68 (0.21)
42.86 (0.54)
19.29 (0.06)
25.58 (0.19)
n = 25
67.84 (0.35)
405.5 (1.71)
23.86 (0.06)
43.1 (1.06)
19.53 (0.24)
25.54 (0.48)
n = 50
Alternator Population
73.13 (0.52)
427.8 (7.09)
24.46 (0.14)
42.86 (1.11)
19.84 (0.19)
25.32 (0.7)
n = 75
Results based on three sets of simulations. Each set consisted of 100,000 replicates. The average segregation time was calculated for the replicates. To estimate the variance of the average segregation times, we repeated each set of simulation three
times and calculated the average and standard deviation (given in parentheses).
a
Dominant beneficial
alleles
s = 0.05
Partial dominant
beneficial alleles
s = 0.05; h = 0.2
Recessive beneficial
alleles
s = 0.05
Selection Coefficient
Table 2. Segregation Times for Beneficial Alleles in Sexual Populations and in Ciliate and Alternator Populations with Different Values of n.a
a
Results based on three sets of simulations. Each set consisted of 100,000 replicates. The average segregation time was calculated for the replicates. To estimate the variance of the average segregation times, we repeated each set of simulation three
times and calculated the average and standard deviation (given in parentheses).
Partially dominant deleterious
alleles
s = 0.05; h = 0.2
s = 0.05
Dominant deleterious alleles
s = 0.01
s = 0.05
Recessive deleterious alleles
s = 0.01
s=0
Neutral alleles
Selection Coefficient
Table 1. Segregation Times for Neutral and Deleterious Alleles in Sexual Populations, and in Ciliate and Alternator Populations with Different Values of n.a
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organisms and of alternators versus sexual organisms for populations of size 10,000 and different values of n, the number of
asexual generations between conjugations (fig. 3; graphs for
the other simulated population sizes are similar to these and
are available in the supplementary materials, Supplementary
Material online). We also investigate recessive, partial dominant, and dominant alleles, which function by the standard
definitions in sexual and alternating populations, whereas in
ciliates, the fitness is determined by the alleles present in the
macronucleus, as alleles in the micronucleus are not
expressed.
In the case of neutral or deleterious recessive alleles, nuclear dimorphism seems to have no effect on the segregation
time of mutations, as alternators remain indistinguishable
from ciliates with a similar life cycle. In the case of neutral
alleles, this happens because there is no difference in fitness
whether the allele is expressed or not. For recessive alleles, the
fitness of an individual is only affected after the formation of
homozygotes through conjugation, thus the effect of such
alleles remains masked in both ciliate and alternator populations until conjugation, regardless of nuclear dimorphism.
For all values of n tested, the mutant allele persists longer in
both ciliates and alternators than in sexual organisms
(P < 103, table 1). The number of generations till either
fixation or elimination of the mutant allele, that is, the segregation time, increases as we increase the number of asexual
generations between conjugations for all population sizes
and for neutral and recessive alleles (r > 0.67; P < 3 103;
table 1; fig. 3A). Recessive deleterious mutations appear to
have a lower fixation probability in ciliates and alternators
than in sexual organisms (supplementary materials,
Supplementary Material online).
A dominant or partially dominant deleterious allele persists in ciliate and alternator populations longer than in purely
sexual organisms for all population sizes and values of n tested
(P < 3 104). The segregation time of such mutations
in ciliates increases as the number of asexual generations,
n, increases (r > 0.9; P < 3 106); varying from 40% higher
than that of sexual organisms for n = 5 to 100% higher for
n = 75 (table 1; fig. 3B). For alternators, there is a similar effect
as that for ciliates. When n is small, alternators and ciliates are
almost indistinguishable, but as n increases, the ciliate segregation time increases at a higher rate than that of alternators
(fig. 3B). Dominant and partial dominant deleterious mutations appear to have a lower fixation probability in ciliates and
alternators than in sexual organisms (supplementary materials, Supplementary Material online).
The effects become more varied for beneficial alleles (table
2; fig. 3C). For the recessive case (s = 0.05), alternators and
ciliates are indistinguishable for the same reasons discussed
above. They both have an increased segregation time over
sexual organisms (P < 7 104), an effect which seems to
increase with n for some population sizes (table 2; fig. 3C).
For the case of partial dominant alleles (s = 0.05; h = 0.2), the
segregation times for both ciliates and alternators are again
larger than that of sexual organisms (P < 1 103). For the
beneficial dominant allele (s = 0.05), ciliates and alternators
have larger segregation times than sexual organisms
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FIG. 3. Ratio of segregation times for different alleles in ciliate and alternator populations versus sexual populations for various n. n is the
number of asexual generations between sexual conjugations (population size = 10,000). n = 0 corresponds to sexual organisms, and all points
are normalized to this. (A) Neutral allele (s = 0) and recessive deleterious
alleles (s = 0.01 and s = 0.05). (B) Dominant (s = 0.01 and s = 0.05) and
partial dominant (s = 0.05; h = 0.2) deleterious alleles. (C) Dominant
(s = 0.05), partial dominant (s = 0.05; h = 0.2), and recessive (s = 0.05)
beneficial alleles. The average of 100,000 simulations is reported.
The simulation was performed in triplicate, and the error bars represent
the standard deviation of the average.
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(P < 2 104). Alternators show an increasing segregation
time with n for the beneficial dominant allele (r > 0.78;
P < 3 104), whereas ciliate segregation times do not
show significant increase with n (and indeed seem to decrease
with n for several population values). Beneficial mutations
appear in some cases to have a higher fixation probability
in ciliates and alternators than in sexual organisms (supplementary materials, Supplementary Material online).
Selection–Drift–Mutation Simulations
When we allow recurrent and back mutations, we can
measure the average mutant allele frequencies in a population (fig. 4). As we include back mutations in our simulations,
true fixation of the mutant allele is impossible, but transient
fixations do occur and can bias the results. Thus, the data,
especially for smaller populations, is quite noisy and many
of the comparisons nonsignificant. Here, we present the
statistics only for the largest population (10,000), to illustrate
that the results of the other analyses are valid in a mutation–
selection–drift situation. Note that the results for smaller
population sizes are typically nonsignificant. They are,
however, consistent with the results for the larger population
(supplementary materials, Supplementary Material online).
For the population of size 10,000 and recessive deleterious
alleles (s = 0.05), both alternators and ciliates follow a similar
pattern to the mutation–selection results, where a larger
average allele frequency is observed than for sexual
organisms (P < 2 107), and the average allele frequency increases with n (r > 0.97; P < 1015), the number
of asexual generations between conjugations. For dominant and partial dominant alleles (s = 0.05), alternators
do not appear to have a larger average allelic frequency
than sexual organisms, whereas ciliates do (P < 0.01).
The relative frequency of the allele in ciliates compared
with that of sexual organisms increases with n (r > 0.96;
P < 5 1015).
Discussion
Mutation–Selection
By deriving the mutation–selection balance equations
for ciliate populations, we showed that in an infinite population, for both the recessive and dominant cases and a
given mutation rate and fitness cost, an individual deleterious allele exists at a higher equilibrium frequency in ciliates than in purely sexual organisms (fig. 2). The nuclear
dimorphism of ciliates allows deleterious mutations that
arise in the micronucleus during vegetative growth to
remain selectively neutral until a new macronucleus is
formed following conjugation. Mutations occurring in
the macronucleus during vegetative growth can be subjected to selection immediately, but as the macronucleus is
eliminated following conjugation, these mutations do not
persist in the population. The infinite population model
confirms our basic hypothesis that ciliates have different
evolutionary dynamics and are less efficient in removing
deleterious alleles than sexual organisms due to nuclear
dimorphism. These analytical results provide an estimate of
the magnitude of this effect in the case of extremely
large effective population sizes. Although the conclusions
based on this model are limited as it assumes infinite populations and no back mutations, the analytical nature and
simplicity of the results suggest the validity of the main
hypothesis presented: Ciliates respond to selection differently than sexual organisms and thus have a different population genetics dynamic.
Selection–Drift
FIG. 4. Ratio of the average allelic frequency in ciliate and alternator
populations versus sexual populations for various n, under mutation–
selection–drift (population size = 10,000). Values generated via finite
population simulations with both forward (104) and back mutation
(105). The simulation is run for 100,000 generations, and the average
allele frequency is calculated for the last 90,000 generations. This was
repeated 32 times to estimate the variance. Error bars represent a single
standard deviation as calculated from the 32 averages.
Our model of mutation–selection balance does not consider
all the possible effects of the ciliate life cycle. In our selection–
drift simulations, we can separate the effects of nuclear dimorphism and the alternating life cycle by considering a hypothetical alternator. These organisms have the same life
cycle as ciliates but do not mask novel alleles in a germline
nucleus. The inclusion of drift in a finite population allows the
observation of the interplay between the effects of life cycle
and nuclear dimorphism in the population genetics of ciliates.
Additionally, selection–drift simulations allow us to directly
estimate the persistence of an allele in a population.
When a deleterious allele appears in the micronucleus of a
ciliate, it is initially masked. This allows the allele to spread
neutrally until the next sexual division. This decreased selection after the initial mutation causes a deleterious allele to
persist longer in a ciliate population than in a purely sexual
organism. Some of this effect can also be attributed to the
drift process of the alternating life cycle. Although we might
expect reduced selection to translate into a higher fixation
probability, the life cycle opposes this effect, likely due to the
reduced creation of homozygotes (Balloux et al. 2003). In the
case of a deleterious dominant allele, this allows for more
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efficient selection as more alleles are present in heterozygous
individuals (fig. 3B). The opposing effects of genetic drift and
lower formation of homozygotes due to the alternating life
cycle can be seen in the results for neutral and recessive alleles
(fig. 3A).
A similar, though reduced, effect is seen in partial dominant deleterious alleles (fig. 3B). Again, the initial neutrality of
the allele allows it to propagate until conjugation.
Additionally, the alternating life cycle reduces the creation
of homozygotes, causing less efficient selection. These separate effects can be seen by noting that ciliates remove the
allele more slowly than alternating organisms, which in turn
remove the allele more slowly than sexual organisms.
For beneficial, dominant alleles, the effects of nuclear dimorphism and life cycle are opposed (fig. 3C). A dominant
advantageous allele introduced to a ciliate population will be
initially neutral, thus giving it the opportunity to be eliminated by drift before selection can occur. However, the life
cycle limits the creation of homozygotes, allowing for more
effective selection. As more positive alleles are present in
heterozygous individuals, once unmasked, the allele is more
effectively preserved. Despite the opposing effects of life cycle
and nuclear dimorphism, ciliates can still, in many cases,
retain and fix novel positive alleles more effectively than
sexual organisms.
We have shown that the persistence of a mixed allele
population state (i.e., the segregation time) is generally
higher in ciliate populations than in populations of sexual
organisms, due to the alternating life cycle and the initial
masking of alleles in ciliate populations.
Mutation–Selection–Drift
When we consider finite populations with recurring mutations and include back mutations, we see results similar to
those of the analytically derived mutation–selection balance
equation. Ciliates will retain, on average, a higher frequency of
a deleterious mutant allele than sexual organisms. The extent
of the parameter space, namely the rates of forward and back
mutations, and the large number of generations necessary to
calculate the average allelic frequency, prevents a thorough
search of the parameter space like that performed for the
mutation–selection model in a reasonable amount of time.
The purpose of presenting these limited results is simply to
strengthen our confidence in the selection–drift and mutation–selection results, that is, that ciliates are less capable of
removing deleterious mutations than sexual organisms and
that deleterious mutations are retained longer and in higher
frequencies in ciliate populations.
Ciliate Evolution
Our results support a novel view of ciliate population genetics, whereby nuclear dimorphism and the ciliate life cycle
cause ciliates to retain deleterious alleles in the population
for longer than expected. The hypothesis tested here is confirmed by previously published studies and in turn, it sheds
new light on previous observations regarding polymorphism
levels and protein evolution in ciliates.
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The Oxytricha genome project paper (Swart et al. 2013)
proposed that based on the large number of silent polymorphisms in its genome, this ciliate might have the largest
effective population size of any eukaryote. Other articles
have suggested that ciliate genomes have higher than
expected levels of polymorphism, although there has been
some debate in the literature whether this could be an artifact
(Lynch and Conery 2003; Katz et al. 2006; Snoke et al. 2006;
Catania et al. 2009). According to the standard Wright–Fisher
model, the frequency of silent polymorphisms should be
proportional to the effective population size and to the
mutation rate.
Mutations rates have been measured for two commonly
studied ciliates, Tetrahymena and Paramecium. Long et al.
(2013) studied the mutation rate in Tetrahymena and
showed that it is average for a eukaryote. Sung et al. (2012)
studied the mutation rate in Paramecium and showed that it
is the lowest ever observed for a eukaryote. However, the
authors propose that the ciliate life cycle might bring this
observed mutation rate in line with that of other eukaryotes
if one considers a ciliate generation to be the time between
sexual conjugations (Sung et al. 2012). Without a high mutation rate, the only traditional explanation for the high levels of
polymorphism observed in ciliate genomes is that they have
enormous effective population sizes.
Our model proposes an alternate explanation. Namely,
that neutral or weakly deleterious mutations—as most
SNPs are supposed to be (Lynch 2007; Sung et al. 2012)—
are preserved for longer and at higher levels in ciliates due to
the life cycle and nuclear dimorphism of these organisms.
A consequence of this model is that even with a low or an
average mutation rate, each individual mutation introduced
in a ciliate population is eliminated at a much slower rate,
allowing them to accumulate in the genomes. Thus, because
of these unique features of ciliates, an exceptionally large
population size is not necessary to explain the higher than
expected heterozygosity of ciliates. Our analytical results also
show that the approach of Sung et al. (2012), which is simply
to redefine a generation to fit better with canonical population genetics models, is oversimplistic. Mutation rate is
adjusted, but in an exponential fashion, and selection is also
different.
In addition to high levels of silent site polymorphism, several articles showed that proteins tend to evolve faster than
expected in ciliates compared to other eukaryotes (Katz et al.
2006; Zufall et al. 2006). Several hypotheses were invoked to
explain this observation, including the division of labor
between the nuclei. A mildly deleterious mutation will persist
longer in a ciliate population, which in turn allows the population to more effectively explore sequence space toward
more advantageous phenotypes. This is because the persistence of mildly deleterious mutations might allow ciliates to
find novel compensatory mutations that lead to better fitness. This mechanism was proposed by Katz et al. (2006)
based on the high levels of diversity of histone H4 in ciliates;
here we quantify the effect and confirm the plausibility of the
proposal by Katz et al. (2006).
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Novel Population Genetics in Ciliates . doi:10.1093/molbev/msu150
Conclusions
Mutation–Selection Balance
We have derived an analytical solution to the mutation–
selection balance in ciliates which is distinct, though similar,
to the canonical population models. Examining both selection–drift and mutation–selection–drift simulations further
confirms that ciliate population genetics are novel. They join
malaria (Chang et al. 2013) as counter examples to the idea
that one size fits all. Other ciliates features, which we have not
considered here, may also affect the population genetics.
For example, it is known that the number of copies of
different alleles in the macronucleus can fluctuate during
vegetative growth in ciliates, possibly leading to phenotypic
assortment, the complete loss of one of the alleles in the
macronucleus. Phenotypic assortment can allow a heterozygous ciliate cell to express a homozygous phenotype, further
insulating the genetic micronucleus from selection (Merriam
and Bruns 1988; Doerder et al. 1992; Katz et al. 2006). If this
does occur, it lends further explanation to high levels of diversity observed in ciliate genomes by preventing selection
against deleterious alleles. As we uncover greater diversity in
life cycles, genomic organization, and other features among
eukaryotes, we need to carefully consider how they can affect
the basic processes of evolution in these organisms.
Consider an infinite and randomly mating diploid ciliate population, with a single gene locus with two alleles, the wild-type
A and a deleterious mutant B, with frequencies p and q. Let
the genotypes AA, AB, and BB have relative fitness W11, W12,
and W22 respectively. We know that the relative genotype
frequencies after one round of sexual reproduction are:
Materials and Methods
We will first derive an equation for the equilibrium frequency
of an allele under mutation–selection balance in an infinite
ciliate population, and then we will describe simulations to
calculate the segregation time of mutations in finite ciliate
populations. The simulations depend on a number of parameters, and for each of these, the ranges were chosen to be
consistent with the limited experimental data available. The
number of asexual generations between sexual conjugations,
n, has been estimated to be lower than 75 generations in
Paramecium (Sung et al. 2012); in Sterkiella histriomuscorum,
Adl and Berger (2000) found that the ciliates were only able to
conjugate after at least 20 asexual duplications and became
unable to do so after 80 asexual generations. Consistent with
these results, we perform simulations for a series of n values in
the range of 5–75 generations. Estimates of the average fitness
effect of deleterious mutations in Tetrahymena give a range of
0.044–0.27 (Long et al. 2013). We use values of s between 0.01
and 0.05.
Note that there is an implicit assumption in all calculations
that fitness during sexual reproduction and during asexual
reproduction is the same. Although this may, biologically, not
be the case, this assumption is necessary for a direct comparison of exclusively sexually reproducing organisms with
ciliates. An additional assumption is that we do not consider
the possible effects of amitosis on ciliate phenotype. This
mechanism could potentially allow the phenotypic effect of
an allele to vary during vegetative growth in ciliates, either
through changes of dosage or complete silencing of an allele.
This last factor makes our calculations conservative, as any
effect of phenotypic assortment would tend to decrease
the fitness effects of deleterious alleles as these might be
eliminated by assortment.
2
W11
AAsex ¼ p W
;
2
W22
BBsex ¼ q W
12
ABsex ¼ 2pqW
;
W
ð6Þ
where, W ¼ p2 W11 + 2pqW12 + q2 W22 (Crow 1970). The
change in genotype frequencies during n rounds of asexual
reproduction is given by:
n
n
AAn ¼ AA0WðW11 Þ ;
ðW12 Þ
ABn ¼ AB0W
;
n
n
n
ðW22 Þ
BBn ¼ BB0W
n
ð7Þ
n
n
n
where, W n ¼ AA0 ðW11 Þ + AB0 ðW12 Þ + BB0 ðW22 Þ (Crow
1970).
Therefore, we can calculate the allelic frequencies after a
ciliate life cycle by using the genotype frequency after one
round of sexual reproduction as the initial genotype frequency for n rounds of asexual reproduction:
2
n+1
p0 ¼ p ðW11 Þ
+ pqðW12 Þn + 1
Wn + 1
2
; q0 ¼ q ðW22 Þ
n+1
+ pqðW12 Þn + 1
Wn + 1
ð8Þ
where, Wn + 1 ¼ p2 ðW11 Þn + 1 + 2pqðW12 Þn + 1 + q2 ðW22 Þn + 1 .
To calculate the change in allelic frequencies due to mutation, we assume that mutations from A to B are unidirectional, that is, back mutations are negligible. For a given
mutation rate m, the allelic frequencies after n generations,
sexual or asexual, are:
p00 ¼ p0 ð1 Þn ;
q00 ¼ 1 ð1 q0 Þð1 Þn
ð9Þ
where p’ is the allele frequency after selection. This can be
derived via simple recursion. Substituting the changes due to
selection for p’ gives the allelic frequency in the next life cycle
due to both mutation and selection:
2
p ðW11 Þn + 1 + pqðW12 Þn + 1 ð1 Þn + 1
00
p ¼
ð10Þ
Wn + 1
We can then consider the allelic frequency after one ciliate
life cycle, adjusted for mutation, and calculate when the allelic
frequency equals that of the next life cycle. This is the equilibrium frequency, obtained when these two forces—selection, driving out deleterious alleles, and mutation, generating
new deleterious alleles—are equal: p ¼ p00 .
For the recessive case, we allow W11, W12, and W22 to equal
1, 1, and W respectively, giving the relation:
p¼
ðp2 + pqÞð1 Þn + 1
p2 + 2pq + q2 Wn + 1
ð11Þ
which can be simplified to:
rffiffiffiffi
M
q¼
S
ð12Þ
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MBE
Morgens et al. . doi:10.1093/molbev/msu150
where M ¼ 1 ð1 Þn + 1 and S ¼ 1 ð1 sÞn + 1 ,
where s, the selection coefficient, equals 1 W. For the dominant case, we allow W11, W12, and W22 to equal 1, W, and W
respectively. This gives us the equation:
p¼
ðp2 + pqWn + 1 Þð1 Þn + 1
p2 + 2pqWn + 1 + q2 W n + 1
ð13Þ
which again, can be simplified:
0 ¼ Sq2 + Sð1 + MÞq M
ð14Þ
where M ¼ 1 ð1 Þn + 1 and S ¼ 1 ð1 sÞn + 1 .
Selection–Drift Simulations
We performed simulations of the ciliate life cycle. Starting
with a population of size N, the simulation goes through
n asexual generations, where in each generation a ciliate
divides with probability equal to its fitness. N ciliates are
then selected randomly (without consideration of fitness)
to continue to the next generation. After the n asexual
generations, the ciliate population mates randomly, then
divides based on fitness, and N ciliates are chosen randomly
for the next generation. During mating, two parents are
selected randomly, then two offspring are created by
randomly sampling the parental alleles.
Beginning with a population of wild-type ciliates, we introduce a single mutant allele into the micronucleus at a random
point in the life cycle. As this allele arises in the micronucleus,
it does not affect the fitness of the individual until mating
occurs. The simulation continues until the mutant allele is
either eliminated or fixed. Each simulation is performed
100,000 times, and the average segregation time and
fixation probability are calculated. Results on fixation
probabilities are available as supplementary materials,
Supplementary Material online. This process is repeated
three times to give an estimate of the precision of the
values calculated.
To separate the effects of life cycle from those of nuclear
dimorphism, all the simulations were repeated for organisms
that alternate between sexual and asexual generations without nuclear dimorphism. We will refer to these organisms
throughout the rest of the paper as alternators. For alternators, the only difference in the simulations is that as soon as a
mutant allele is introduced in the population, it could be
expressed and affect the fitness of the individual cell. As a
control and for comparison, the same experiment was performed for sexual organisms. For these, the number of asexual
generations is set to 0.
We performed the simulations with a variety of population
sizes—100, 500, 1,000, 3,000, and 10,000. For each population
size, we performed simulations for ciliates with different n (5,
25, 50, and 75), alternators with different n (5, 25, 50, and 75),
and sexual organisms (n = 0).
Each of these simulations was performed for neutral alleles,
for deleterious recessive alleles with selection coefficients of
s = 0.01 and s = 0.05, for deleterious dominant alleles with
s = 0.01 and s = 0.05, and for deleterious partial dominant alleles with s = 0.05 and degree of dominance of h = 0.2 (fitness
2092
of W11, W12, and W22 equal to 1, 1 sh = 0.99 and
1 s = 0.95).
We also performed simulations of beneficial alleles:
Recessive s = 0.05, W11 = 0.95, W12 = 0.95, W22 = 1; dominant s = 0.05, W11 = 0.95, W12 = 1, W22 = 1; and partial
dominant s = 0.05, h = 0.2, W11 = 0.95, W12 = 0.96, W22 = 1.
All results are consistent with our conclusions. Here, we
present the results for two population sizes: 100 and 10,000 in
tabular format. To facilitate a comparison between the ciliate
and alternator segregation times with those for sexual
organisms, we plot the ratio of the segregation times of
ciliates/sexual organisms and of alternators/sexual organisms
for the population size of 10,000. Tables and graphs for the
other population sizes are available in the supplementary
materials, Supplementary Material online.
For each parameter combination, we calculate the average
segregation time and standard deviation for three sets of
100,000 simulations and use single-tailed, unpaired t-tests to
determine whether each average segregation time calculated
for ciliates and alternators is significantly larger than those
calculated for sexual organisms (total of 360 t-tests).
To determine whether ciliates and alternators have different
segregation times for a certain combination of parameters, we
pool the values for all n and perform paired sample, singletailed t-tests (45 tests). To test how the values change with n,
the number of asexual generations, Pearson correlations were
calculated for ciliates and for alternators in each parameter
combination (90 tests). Note that the sexual organism point is
excluded from this test. The least significant P values, that is,
an upper bound, of each set of tests are presented, avoiding
issues with multiple testing. The complete set of tests is available in the supplementary materials, Supplementary Material
online.
Simulations are written in Python and the scripts are available in a public repository at: https://bitbucket.org/dmorgens/novel-population-genetics-in-ciliates/ (last accessed
May 15, 2014).
Mutation–Selection–Drift
The ciliate life cycle is simulated as above. For a given simulation, the ciliate population is initiated with a per-allele,
per-generation mutation rate of 104 and a smaller back
mutation rate of 105 to prevent fixation. The simulation is
run for 100,000 generations, the first 10,000 generations are
not included in the analysis to allow for the allele frequencies
to reach a dynamic equilibrium. The mutant allele frequency
is then averaged for the last 90,000 generations. This is repeated 32 times to estimate the variance. As above, we performed the simulations with a variety of population sizes,
patterns of inheritance, and strength of fitness effects.
However, because of the noise in the data, our analysis only
includes the largest population.
Supplementary Material
Supplementary materials are available at Molecular Biology
and Evolution online (http://www.mbe.oxfordjournals.org/).
Novel Population Genetics in Ciliates . doi:10.1093/molbev/msu150
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