Novel Population Genetics in Ciliates due to Life Cycle and Nuclear Dimorphism

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1 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: aroc@pomona.edu. Associate editor: Noah Rosenberg Article 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 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 Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please journals.permissions@oup.com 2084 Mol. Biol. Evol. 31(8): doi: /molbev/msu150 Advance Access publication April 30, 2014

2 Novel Population Genetics in Ciliates. doi: /molbev/msu150 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) andhasconsequences 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 q ¼ ð1þ S and for a dominant allele as 0 ¼ Sq 2 + Sð1 + MÞq S ð2þ where M ¼ 1 ð1 Þ n + 1 and S ¼ 1 ð1 sþ n + 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: rffiffiffi q ¼ ð3þ s and 0 ¼ sq 2 + 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. 2085

3 Morgens et al.. doi: /molbev/msu150 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: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ð1 Þ n + 1 rffiffiffi 1 ð1 sþ n + 1 > ð5þ s 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 ( ) 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 thesamelifecycleofciliates severalroundsofasexualgenerations 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;tableswiththe 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 ( =10 4 ) 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 ( =10 4 ) versus fitness (eq. 2). 2086

4 Novel Population Genetics in Ciliates. doi: /molbev/msu150 Table 1. Segregation Times for Neutral and Deleterious Alleles in Sexual Populations, and in Ciliate and Alternator Populations with Different Values of n. a Selection Coefficient Population Sexual Population Ciliate Population Alternator Population Neutral alleles n =5 n =25 n =50 n =75 n =5 n =25 n =50 n =75 s = (0.06) (0.21) (0.29) (0.10) (0.21) (0.11) (0.25) (0.82) (0.15) 10, (0.43) (0.35) (0.64) (0.48) (0.64) (0.86) (0.55) (0.13) (0.07) Recessive deleterious alleles s = (0.24) (0.29) (0.22) (0.36) (0.35) (0.32) (0.21) (0.21) (0.29) 10, (0.09) (0.12) (0.89) (0.62) (0.27) (0.47) (0.36) (0.45) (0.74) s = (0.18) (0.08) (0.09) (0.16) (0.41) (0.03) (0.03) (0.11) (0.12) 10, (0.50) (0.28) (0.35) (0.71) (0.48) (0.33) (0.70) (0.70) (1.29) Dominant deleterious alleles s = (0.03) (0.12) (0.02) (0.2) (0.22) (0.12) (0.22) (0.07) (0.22) 10, (0.00) (0.08) (0.26) (0.09) (0.06) (0.12) (0.1) (0.14) (0.07) s = (0.03) 9.44 (0.06) (0.06) (0.1) (0.09) 9.06 (0.02) 9.63 (0.01) 9.72 (0.05) 9.75 (0.08) 10, (0.04) 9.06 (0.09) (0.1) (0.05) (0.04) 8.72 (0.04) 9.31 (0.03) 9.39 (0.04) 9.43 (0.05) Partially dominant deleterious alleles s =0.05; h= (0.11) 17.3 (0.21) (0.11) (0.36) (0.43) 17 (0.18) (0.25) (0.15) (0.13) 10, (0.15) (0.15) (0.25) (0.21) (0.29) (0.13) 17.6 (0.27) (0.28) (0.04) 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). Table 2. Segregation Times for Beneficial Alleles in Sexual Populations and in Ciliate and Alternator Populations with Different Values of n. a Selection Coefficient Population Sexual Population Ciliate Population Alternator Population n =5 n =25 n =50 n =75 n =5 n =25 n =50 n =75 Recessive beneficial alleles s = (0.1) (0.22) (0.06) (0.28) (0.18) (0.14) (0.06) (0.24) (0.19) 10, (0.3) (0.46) (0.97) (0.16) 25.1 (0.35) (0.53) (0.19) (0.48) (0.7) Partial dominant beneficial alleles s = 0.05; h = (0.19) (0.17) (0.17) (0.34) (0.4) (0.25) (0.21) (0.06) (0.14) 10, (0.28) (0.84) (0.33) (0.3) (1.18) (1) (0.54) 43.1 (1.06) (1.11) Dominant beneficial alleles s = (0.15) (0.49) (0.4) (0.39) (0.7) (0.46) (0.62) (0.35) (0.52) 10, (0.06) (3.26) (3.79) (2.21) (2.13) (3.23) (2.15) (1.71) (7.09) 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). 2087

5 Morgens et al.. doi: /molbev/msu150 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 < 10 3, 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 < ; 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 < ). The segregation time of such mutations in ciliates increases as the number of asexual generations, n, increases (r > 0.9; P < ); 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 < ), 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 < ). For the beneficial dominant allele (s = 0.05), ciliates and alternators have larger segregation times than sexual organisms 2088 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.

6 Novel Population Genetics in Ciliates. doi: /molbev/msu150 (P < ). Alternators show an increasing segregation time with n for the beneficial dominant allele (r > 0.78; P < ), 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 < ), and the average allele frequency increases with n (r > 0.97; P < ), 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 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 (10 4 ) and back mutation (10 5 ). 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. 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 < ). 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 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 2089

7 Morgens et al.. doi: /molbev/msu150 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 removetheallelemoreslowlythansexualorganisms. 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,duetothealternatinglifecycleandtheinitial 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 confirmedbypreviouslypublishedstudiesandinturn,itsheds new light on previous observations regarding polymorphism levels and protein evolution in ciliates 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 andshowedthatit 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 SNPsaresupposedtobe(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).

8 Novel Population Genetics in Ciliates. doi: /molbev/msu150 Conclusions 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. 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 (Long et al. 2013). We use values of s between 0.01 and 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. Mutation Selection Balance 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 W 11,W 12, and W 22 respectively. We know that the relative genotype frequencies after one round of sexual reproduction are: AA sex ¼ p2 W 11 ; AB W sex ¼ 2pqW 12 ; BB W sex ¼ q2 W 22 ð6þ W where, W ¼ p 2 W pqW 12 + q 2 W 22 (Crow 1970). The change in genotype frequencies during n rounds of asexual reproduction is given by: ð Þ n AA n ¼ AA 0 W 11 ; AB W n ¼ AB 0 W 12 ; BB n W n ¼ BB 0 W 22 n where, W n ¼ AA 0 ðw 11 Þ n + AB 0 ðw 12 Þ n + BB 0 ðw 22 Þ n (Crow 1970). Therefore, we can calculate the allelic frequencies after a ciliatelifecyclebyusingthegenotypefrequencyafterone round of sexual reproduction as the initial genotype frequency for n rounds of asexual reproduction: p 0 ¼ p2 W 11 ð Þ n pqðw 12 Þ n + 1 W n + 1 ; q 0 ¼ q2 W 22 ð Þ n ð W n ð Þ n pqðw 12 Þ n + 1 W n + 1 where, W n + 1 ¼ p 2 ðw 11 Þ n pqðW 12 Þ n q 2 ðw 22 Þ n + 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: Þ n ð7þ ð8þ p 00 ¼ p 0 ð1 Þ n ; q 00 ¼ 1 ð1 q 0 Þð1 Þ n 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: p 00 ¼ p2 ðw 11 Þ n pqðw 12 Þ n + 1 ð1 Þ n + 1 ð10þ W n + 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 p 00. For the recessive case, we allow W 11,W 12, and W 22 to equal 1, 1, and W respectively, giving the relation: ð p ¼ p2 + pqþð1 Þ n + 1 p 2 + 2pq + q 2 W n + 1 which can be simplified to: rffiffiffiffi M q ¼ S ð11þ ð12þ 2091

9 Morgens et al.. doi: /molbev/msu150 where M ¼ 1 ð1 Þ n + 1 and S ¼ 1 ð1 sþ n + 1, where s, the selection coefficient, equals 1 W. For the dominant case, we allow W 11,W 12, and W 22 to equal 1, W, andw respectively. This gives us the equation: ð p ¼ p2 + pqw n + 1 Þð1 Þ n + 1 p 2 + 2pqW n q 2 W n + 1 which again, can be simplified: ð13þ 0 ¼ Sq 2 + Sð1 + MÞq M ð14þ where M ¼ 1 ð1 Þ n + 1 and S ¼ 1 ð1 sþ n + 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 generationsissetto0. 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 ands = 0.05, and for deleterious partial dominant alleles with s = 0.05 and degree of dominance of h =0.2(fitness 2092 of W 11, W 12, and W 22 equal to 1, 1 sh =0.99 and 1 s = 0.95). We also performed simulations of beneficial alleles: Recessive s = 0.05, W 11 = 0.95, W 12 = 0.95, W 22 =1; dominant s = 0.05, W 11 = 0.95, W 12 =1, W 22 = 1; and partial dominant s = 0.05, h =0.2,W 11 = 0.95, W 12 = 0.96, W 22 =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: (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 10 4 and a smaller back mutation rate of 10 5 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 (

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