(2010) 104, 100–112 & 2010 Macmillan Publishers Limited All rights reserved 0018-067X/10 $32.00 www.nature.com/hdy ORIGINAL ARTICLE Segregation distortion and the evolution of sex-determining mechanisms

M Kozielska1,2, FJ Weissing2, LW Beukeboom1 and I Pen2 1Evolutionary , University of Groningen, Haren, The Netherlands and 2Theoretical , University of Groningen, Haren, The Netherlands

Segregation distorters are that distort normal segre- selection pressure, allowing novel sex-determining alleles to gation in their own favour. Sex chromosomal distorters lead spread. When distortion leads to -biased sex ratios, a to biased sex ratios, and the presence of such distorters, new masculinizing can invade, leading to a new male therefore, may induce selection for a change in the heterogametic system. When distortion leads to male-biased mechanism of sex determination. The evolutionary dynamics sex ratios, a feminizing factor can invade and cause a switch of distorter-induced changes in sex determination has only to female heterogamety. In many cases, the distorter- been studied in some specific systems. Here, we present a induced change in the sex-determining system eventually generic model for this process. We consider three scenarios: leads to loss of the distorter from the population. Hence, the a driving X , a driving and a presence of sex chromosomal distorters will often only be driving with a male-determining factor. We transient, and the distorters may remain unnoticed. The role investigate how the invasion prospects of a new sex- of segregation distortion in the evolution of sex determination determining factor are affected by the strength of distortion may, therefore, be underestimated. and the fitness effect of the distorting . Our models Heredity (2010) 104, 100–112; doi:10.1038/hdy.2009.104; show that in many cases, segregation distortion does create published online 12 August 2009

Keywords: segregation distortion; sex determination; meiotic drive; sex chromosome

Introduction Van Boven and Weissing, 1998; Jaenike, 1999; Mon- tchamp-Moreau et al., 2001; Atlan et al., 2003). Most follow ‘fair’ Mendelian segregation, The presence of a driving chromosome is usually not resulting in each of the homologues being present in neutral with respect to individual fitness, both in (approximately) 50% of the gametes. However, some heterozygous and homozygous condition (for example, genetic elements are recovered in more than half of the see Wallace, 1948; Curtsinger and Feldman, 1980; Jaenike, functional gametes of heterozygous individuals showing 1996; Taylor and Ingvarsson, 2003; Atlan et al., 2004). In so-called segregation distortion or meiotic drive. Segrega- some well-studied cases, homozygosity for a distorter tion distortion occurs in a number of taxa, ranging from allele causes sterility in males, or even lethality in males fungi to plants and animals (for reviews see, for example, and (for example, the t-complex of the house Jaenike, 2001; Burt and Trivers, 2006) with marked mouse and the segregation distorter of Drosophila melano- similarity between taxa (Taylor and Ingvarsson, 2003). gaster; see Lyttle, 1991; Burt and Trivers, 2006). Therefore, Segregation distortion is advantageous at the gene there will often be strong selection for suppressors of level, as distorter alleles have a transmission advantage segregation distortion (for example, see Hurst et al., 1996). and their frequency in the population will increase. Such suppressors have been indeed found in most of the Many distorters in nature show almost complete distor- species harbouring segregation distorters (for example, tion when unsuppressed (the distorter allele is present in see Jaenike, 2001; Burt and Trivers, 2006). more than 90% of functional gametes). However, When segregation distorters are located on sex considerable variation exists between populations and chromosomes, they not only have an effect on individual different distorters, and an effective distortion can range fitness but also lead to biased sex ratios in the population from just above 0.5 to almost 1 (for example, see (Jaenike, 2001). Biased sex ratios induce selection for Sturtevant and Dobzhansky, 1936; Hickey and Craig, increased production of the rarer sex. Unbiased sex ratios 1966; Gileva, 1987; Carvalho de et al., 1989; Jaenike, 1996; can either be restored through suppressors of drive or through a change in the mechanism of sex determination (Bull and Charnov, 1977; Cosmides and Tooby, 1981; Correspondence: Current address: Dr M Kozielska, Department of Werren and Beukeboom, 1998; Burt and Trivers, 2006). Pharmacokinetics, Toxicology and Targeting, University of Groningen, Segregation distortion has been proposed as the driving Antonius Deusinglaan 1, PO Box 196, Groningen 9700 AD, The force behind a change in the sex-determining mechanism Netherlands. of the wood lemming, Myopus schisticolor (Bengtsson, E-mail: [email protected] Received 8 March 2009; revised 1 July 2009; accepted 13 July 2009; 1977), the mole, Talpa occidentalis (McVean and Hurst, published online 12 August 2009 1996), the creeping vole, Microtus oregoni (Charlesworth Segregation distortion and sex-determining mechanisms M Kozielska et al 101 and Dempsey, 2001), the sciarid fly, Sciara coprophila mating and non-overlapping generations. We analyse (Haig, 1993b), the housefly, Musca domestica (Clark, 1999) three scenarios in an initial XY system: (1) a driving X and scale insects, Neococcoidea (Haig, 1993a). chromosome, (2) a driving Y chromosome and (3) a To our knowledge, there are only very few mathema- driving autosomal male-determining factor. First, we will tical models investigating the effect of sex chromosome present our general model assumptions and then segregation distortion on the evolution of sex determina- introduce modifications specific to the three scenarios. tion. Present models are tailored to a particular species, and aim to explain the observed sex-determining mechanism in that species (Bengtsson, 1977; Jayakar, and sex determination 1987; McVean and Hurst, 1996; Charlesworth and As the number of ways in which sex could be Dempsey, 2001). Therefore, there is currently still little determined is virtually unlimited, we decided to base understanding of the conditions under which sex our model on a relatively general mode of sex determi- chromosome segregation distortion can lead to changes nation. We consider a sex-determination system consist- in sex-determining mechanisms. We aim to fill this gap ing of three independent gene loci (on three different by means of a more generic model in which we analyse chromosomes). In the absence of segregation distortion, the conditions for the spread of a new sex-determining each has two basic alleles, but additional alleles can gene in a system with a distorting (driving) sex be present in specific models (see below). The first locus chromosome. corresponds to the standard XY system of sex determi- The best documented and probably most common case nation with two basic alleles: X and Y, in which Y is segregation distortion occurring during the production corresponds to a dominant male-determining factor. As of male gametes, wherein it is manifested by the X drive leads to female-biased sex ratios, one might dysfunction of (or pollen) lacking the driving expect selection in favour of male-determining factors. element, or, more precisely, loss of gametes carrying the Therefore, we also consider a second locus, which sensitive allele (for example, see Lyttle, 1993; Taylor and harbours a dominant male-determining M allele and a Ingvarsson, 2003). Sex chromosomal distortion is most standard m allele. We assume that this locus is autosomal common in systems with male heterogamety, and (not linked to the X or Y chromosome). Such autosomal usually, the drives against the Y chromo- male-determining factors have been found in a number some. Presumably, Y drive is less common, because it of species (Martin et al., 1980; Traut and Willhoeft, 1990; easily leads to population extinction (Hamilton, 1967; Du¨ bendorfer et al., 2002), and are a likely step in the Taylor and Ingvarsson, 2003). Therefore, we chose to evolution of sex-determining mechanisms (Bull, 1983). focus on the case in which the initial sex-determining Y chromosomal drive leads to male-biased sex ratios and mechanism is an XY system and in which segregation should favour feminizing . Therefore, we also distortion occurs only in males. consider a third locus, which has a female-determining We consider three scenarios: a driving X chromosome F allele and a standard f allele. There are many (scenario 1); a driving Y chromosome (scenario 2); and a possibilities of how female and male-determining factors driving autosome with a male-determining factor (sce- interact during sexual development. We consider the nario 3). Segregation distortion associated with all such simplest case, in which F is dominant over M and Y, chromosomes has been found in natural populations of meaning that the presence of F always leads to female various species (Clark, 1999; Jaenike, 2001; Burt and development, even if both Y and M are present in Trivers, 2006). The presence of driving chromosomes homozygous state. We assume that the lack of an X or Y leads to female-biased (scenario 1) or male-biased chromosome does not have negative effects on fitness (scenarios 2 and 3) sex ratios, presumably promoting (see Discussion). If F is absent, but Y and/or M are the spread of new masculinizing or feminizing factors, present, an individual becomes a male, otherwise respectively. Throughout, we assume that a distorting (neither Y nor M is present) it becomes a female. All allele has a detrimental effect on fitness in homozygous possible male and female genotypes are summarized in condition, either by reducing male fertility or by Table 1. This sex-determining system resembles that of reducing viability in males and/or females. the housefly (Du¨ bendorfer et al., 2002; Kozielska et al., By means of a dynamic model, we address the 2006), but we believe that the model is more generally following questions. Under which circumstances does applicable. sex chromosomal segregation distortion lead to changes in the mechanism of sex determination? More specifi- cally, how is the invasion prospect of a new sex- determining factor affected by the strength of distortion Table 1 All possible genotypes considered in the model (without and the fitness effect of a distorter present in the distinguishing between driving and non-driving alleles) population? When invasion is possible, will a new factor Females Males spread to fixation, leading to a switch to a different sex- determining mechanism? How is the frequency of the XX mm ff XY mm ff segregation distorter affected by the invasion of a new XX mm Ff XY Mm ff XX Mm Ff XY MM ff sex-determining factor? XX MM Ff XX Mm ff XY mm Ff XX MM ff XY Mm Ff YY mm ff The model XY MM Ff YY Mm ff We model the evolutionary dynamics of the sex- YY mm Ff YY MM ff determining system with a set of recurrence equations. YY Mm Ff YY MM Ff We assume an infinite diploid population with random

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 102 Drive denoted Yd and it is assumed to drive only against X. Segregation is random in females and in males that do Therefore, XYd males produce X gametes in frequency not possess a driving chromosome or are homozygous 1Àk and Yd gametes in frequency k. For all other for it. In males heterozygous for a driving chromosome male genotypes, segregation of alleles is Mendelian and sensitive chromosomes (also see below), k denotes (k ¼ 1/2). We start with the standard XY system, and the frequency of the driving allele in gametes and, hence, in step 1, introduce a driving Yd chromosome. This indicates the strength of distortion. causes male-biased sex ratios, and in step 2, an F allele is introduced. Fitness As described in the Introduction, the presence of Scenario 3: driving M distorter allele is often detrimental for fitness. Our In this scenario, segregation occurs at an autosomal invasion analysis (Appendix B) is based on quite general locus, in which M drives against m. The driving alleles assumptions on the fitness effects of a driving allele in will be denoted as Md. The frequency of Md in the homozygous condition: homozygous males have fertility gametes of Mdm males is equal to k, and the frequency of u (0pup1), and the viability of homozygous males and m gametes equals 1Àk. For all other male genotypes, females is given by nm and nf, respectively (0pnm, nfp1). segregation of alleles is Mendelian (k ¼ 1/2). We start For the numerical analysis, which allows us to study the with the standard XY system, and in step 1, introduce a full dynamics of the system, we considered three, more driving Md allele. This causes male-biased sex ratios, and specific, fitness schemes: (a) no cost of drive; (b) males in step 2, an F allele is introduced. homozygous for the driving allele (that is XdXd, YdYd or For each scenario, we run numerical iterations of the MdMd, depending on the scenario) are sterile; and recursion equations (Appendix A) to investigate the (c) homozygosity for the driving allele is lethal, both in effects of distortion strength k and various fitness males and females. schemes on the dynamics of the system. The results of the numerical analysis are fully in line with the (much Evolutionary dynamics more general) mathematical invasion analysis given in We assume random mating and discrete non-overlap- the Appendix B. ping generations. Under these conditions, the dynamics of the system can be easily expressed by a set of Results recursion equations for the frequency of each in each generation, depending on the frequency of all Scenario 1: driving X chromosome genotypes in the previous generation (see Appendix A). 1 d For any value of k42, the driving X chromosome (X ) Iteration of these equations allows studying the invades the population, leading to a female-biased sex dynamics of the system. ratio. When M is introduced, it increases the production In our numerical iterations, we started with the of males, and it is selected for, as long as selection against standard XY system (females: XX; mm; ff and males: biased sex ratios is not overcome by selection against XY; mm; ff), and at generation 0, introduced a distorter sterile genotypes. Once M invades, it causes the loss of Y allele (step 1) at a frequency of 0.001. We let the system from the population and restores the equal sex ratio. evolve and when the equilibrium was reached, a new Therefore, in most cases, there is a switch from an XY sex-determining factor was introduced (step 2) at a system to an XX system, in which sex is determined by frequency of 0.001. Again, frequencies of different M. Males are again the heterogametic sex, therefore, a genotypes were calculated at every generation until a new system can be seen as male heterogamety for M new equilibrium appeared to be reached. All simulation (Table 2). Interestingly, even though the presence of the results were confirmed by a mathematical invasion driving Xd chromosome is often responsible for the analysis (see Appendix B for details). switch from XY to an autosomal system, at equilibrium, The three scenarios for sex chromosomal distortion the Xd chromosome may be no longer present in the were implemented as follows: population (see below).

Scenario 1: driving X chromosome No cost of drive: Owing to its transmission advantage In this version of the model, three alleles segregate at and no fitness costs, Xd fixates in the population, the XY locus: standard Y, standard X and driving X. removing the standard X chromosome independently The latter will be denoted Xd, and it is assumed to of the value of k. This leads to a female-biased sex ratio drive only against Y. Therefore, the frequency of Xd with the proportion of females equal to the drive gametes produced by XdY males is equal to the drive strength k. This sex ratio bias facilitates the invasion of strength k and the frequency of Y gametes equal 1Àk. M, which very quickly spreads replacing Y as a sex- For all other male genotypes, segregation of alleles is determining factor, leading to male heterogamety for M Mendelian (k ¼ 1/2). We start with the standard XY (Figure 1a). Xd reaches fixation in both males and system, and in step 1 (see above), introduce a driving females. Although driving chromosomes are still Xd chromosome. This causes female-biased sex ratios, present in the population, the sex ratio is unbiased, as and in step 2, an M allele is introduced to regain equal the chromosomes sensitive to drive are absent. sex ratios. Sterility of XdXd males: The Xd invades the population Scenario 2: driving Y chromosome and replaces the standard X, as above, as males are In this version, three alleles segregate at the XY locus: always XdY and, therefore, do not have a fertility standard X, standard Y and driving Y. The later will be disadvantage. However, now the introduction of M

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 103 Table 2 Overview of changes in the sex-determining system induced by a driving X chromosome (Xd) No cost of drive Sterility of XdXd males Lethality of XdXd individuals

Initial state # XY; mm; ff ~ XX; mm; ff ^ 1 S ¼ 2

After introduction of Xd # XdY; mm; ff # XY; mm; ffa ~ XdXd; mm; ff ~ XX; mm; ffa ^ 2 ^ 1 S ¼ 1 À k 5oSo2

3 3 kp4 k44 # XdXd; Mm; ff # XdY; mm; ff # XX; Mm; ff # XX; Mm; ff After introduction of M ~ XdXd; mm; ff ~ XdXd; mm; ff ~ XX; mm; ff ~ XX; mm; ff ^ 1 ^ ^ 1 ^ 1 S ¼ 2 S ¼ 1 À k S ¼ 2 S ¼ 2

Resulting system Male heterogamety for M Male heterogamety for Y Male heterogamety for M Male heterogamety for M Male (#) and female (~) genotypes are given together with the equilibrium sex ratio (frequency of males; Sˆ). Columns correspond to the different fitness schemes considered (top row). When the outcome is the same for two fitness schemes, the corresponding columns are merged. Sometimes the outcome depends on the drive strength (k). In that case, different outcomes are listed separately; otherwise the outcome is independent of k. The rows correspond to the sequence of events, from the initial state to the equilibrium state after the introduction of driving Xd and the final equilibrium after the introduction of M. After the introduction of M, in some cases, the standard X chromosome has an advantage over Xd and it will invade the population when reintroduced. Therefore, at equilibrium it will be present in the population. See text for details. aX stands for either standard X or driving Xd, as is maintained in the population. leads to the production of sterile XdXd males and M high frequency, the decrease in fitness of M-bearing cannot invade the population. Only if the standard X is males through the production of rare lethal XdXd reintroduced into the population together with M can offspring is outweighed by the advantage from an they both invade, as some males produced by M possess increased production of males. Eventually Xd is the standard X and are fertile. These males have an removed from the population because of its detrimental advantage in strongly female-biased populations, and effect in the homozygous state, which is not both M and standard X increase in frequency. An counterbalanced by a transmission advantage, as XdY increase in the frequency of M leads to the production males are rare. A male heterogametic system for M gets of sterile XdXd males and selection against Xd. Xd is established (Table 2). eventually lost from the population and replaced by standard X (Figure 1b). Y is also removed from the Scenario 2: driving Y chromosome population, and a male heterogametic system for M Independent of the strength of drive k and the fitness of establishes. It should be noted that, although the homozygous YdYd individuals, Yd always spreads in the driving X chromosome induced changes in the sex- population replacing standard Y, as females never determining mechanism, it is no longer present in the harbour Yd and, therefore, males can never be homo- population. zygous for Yd. As all males are XYd, the sex ratio is 3 This happens only for strong drive k44, as this will biased with a proportion of males equal to the drive lead to the population sex ratio being very female biased strength, k. Whether F invades depends on the fitness and selection against the biased sex ratio is strong costs of homozygosity for Yd (Table 3). However, similar enough to overcome selection against infertile males. to scenario 1, a change in the sex-determining mechan- Therefore, even though the presence of M initially leads ism may lead to the complete removal of the driving to the production of many sterile XdXd males, if X is chromosome from the population. present in the population, this cost is compensated for by the increased production of males thanks to M. For No cost of drive: The feminizing F allele always spreads weaker drive, selection against biased sex ratio is not in the population, leading to fixation of Yd and a switch strong enough to overcome selection against sterile to a female heterogametic sex-determining system. genotypes and M cannot invade (Table 2). Although Yd is present in the population, the sex ratio equals 1:1, as the X chromosome sensitive to drive is lost. Lethality of XdXd genotypes: The Xd invades the population, but it cannot fixate, as homozygous Sterility of YdYd males: Selection against biased sex genotypes are lethal. Therefore, the sex ratio bias ratios facilitates the spread of F. It is present only in induced by Xd is less pronounced than that for the females, hence it does not have direct negative fitness scenarios presented above (Figure 1c). The frequency effects. However, F females produce some sterile YdYd d 1 1 1 1 of X is equal to 2 À 4k (that is, equals 2 for k ¼ 2, males, which prevent F from fixation. Polymorphism for 1 d and 4 for k ¼ 1). A female-biased sex ratio facilitates X and Y , and F and f is maintained, but the sex ratio in the invasion of the masculinizing factor M, which the population equals 0.5 (Figure 2). The frequencies of F in turn leads to a decrease in the frequency of Y and Yd increase with the strength of drive, k. At this state, and increased homozygosity for Xd; also in males. As reintroduction of the standard Y in the population will the standard X is present in the population at lead to its spread, as it does not cause a fitness cost in

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 104 Xd M fixation. X is removed, F is present in all females and a

1.0 female heterogametic system establishes (Figure 2). 0.9 Lethality of YdYd genotypes: If drive strength is low, F 0.8 does not invade the population, as selection against a 0.7 sex ratio (slightly) biased sex ratio is weaker than selection against 0.6 Y in males the lethal genotypes produced when F is present. 0.5 X in males Therefore, an XY system with the driving Yd d frequency 0.4 X in males chromosome (that is, no standard Y) and a biased sex 0.3 M in males 3 ratio is stable for ko5 (see Appendix B). For higher 0.2 values of k, the F factor invades the population. Initially, 0.1 a polymorphism on both the F and XY loci is maintained, 0.0 with a population sex ratio that is only slightly male 0 50100 150 200 biased, similar to the scheme with male sterility. For k generation 3 between 5 and 0.655 (see Appendix B), this polymorphic

d sex-determining system is stable and Y cannot reinvade X M+X the population. However, for k40.665, the reintroduction 1.0 of the standard Y also leads to an increase of F in 0.9 frequency and eventually to removal of Yd and X. 0.8 F reaches a frequency of 1 in females and female sex ratio 2 0.7 Y in males heterogamety with equal sex ratios is established. 0.6 X in males When F is present in the population, but before d 0.5 X in males fixation of standard Y, in some circumstances, autosomal M in males 0.4 frequency M can invade. However, it never reaches fixation, and 0.3 standard Y will fixate in the population once it is 0.2 reintroduced. Therefore, female heterogamety with the 0.1 frequency of standard Y equal to 1 is an equilibrium state 0.0 of this system, although polymorphism for M and m can 0 100 200 300 400 500 be present. generation

d Scenario 3. driving autosomal M X M Similar to the case with driving Yd, driving Md invades 1.0 the population regardless of drive strength and the 0.9 fitness of individuals homozygous for Md, as it is only 0.8 sex ratio present in males in heterozygous state. Y is removed 0.7 Y in males from the population and all individuals are XX. The 0.6 X in males population sex ratio is male biased and equal to drive 0.5 X d in males strength, k. Whether F invades depends on the fitness M in males d frequency 0.4 costs of homozygosity for M (Table 4). 0.3 0.2 No cost of drive: For any drive strength k, selection 0.1 against male-biased sex ratios facilitates the spread of the 0.0 feminizing F allele. The invasion of F leads to fixation of 0 100 200 300 400 500 600 Md, and a switch to a female heterogametic system with generation 1:1 sex ratio. Figure 1 Dynamics of the sex-determining system in the presence of a driving Xd chromosome. This is a representative example with Sterility of M dM d males: F always invades irrespective strength of drive k ¼ 0.8. Introduction of new alleles is indicated by of drive strength. However, fixation of F and Md is d arrows. The spread of X leads to biased sex ratios. When the impossible, as this will lead to all males being sterile. system appeared to reach equilibrium, an autosomal masculinizing Therefore, there is no full switch to female heterogamety, factor M was introduced, leading to a switch in sex-determining d mechanism to male heterogamety for M and restoration of equal sex but polymorphism for both M and m, and F and f is ratios. (a) No cost of drive. Standard X and Y are lost from the maintained in the population. The population sex ratio population. (b) Sterility of XdXd males. A driving Xd leads to the equals 0.5. With increasing k, the equilibrium frequency loss of standard X. In generation, 200 M and X are introduced of Md and F increases. If at any point Y is reintroduced d simultaneously, X and Y disappear from the population. Introdu- into this system, it will reinvade the population, as it cing M on its own has no effect (see Results). (c) Lethality of XdXd genotypes. Initially polymorphism for Xd and X is maintained. assures maleness without fitness costs. Eventually, Y Introduction of M leads to the removal of Xd and Y. spreads to fixation and all females become heterozygous for F. The frequency of Md decreases, but it is not removed from the population. Therefore, at the stable equilibrium, in effect, a female heterogametic system is males. The segregation advantage of Yd is low, as owing present, but with a polymorphism at the M locus to the low frequency of X, the frequency of YdX males is (Figure 3). low. Therefore, the segregation advantage is outweighed by selection against sterile YdYd males. The frequency of Lethality of M dM d genotypes: If the drive strength is d d 3 Y decreases, and standard Y replaces Y and spreads to weak (ko5), then the population sex ratio is only slightly

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 105 Table 3 Overview of changes in the sex-determining system induced by a driving Y chromosome (Yd) No cost of drive Sterility of YdYd males Lethality of YdYd individuals

Initial state # XY; mm; ff ~ XX; mm; ff ^ 1 S ¼ 2

# XYd; mm; ff After introduction of Yd ~ XX; mm; ff Sˆ ¼ k

3 3 k4 kp5 5okp0.655 0.665 After introduction of F # YdYd; mm; ff # YY; mm; ff # XYd; mm; ff # ZYd; mm; ff # YY; mm; ff ~ YdYd; mm; Ff ~ YY; mm; Ff ~ XX; mm; ff ~ ZZ; mm; Ff ~ YY; mm; Ff ^ 1 ^ 1 ^ 1 ^ ^ 1 S ¼ 2 S ¼ 2 S ¼ k 2oSok S ¼ 2

Resulting system Female heterogamety Female heterogamety Male heterogamety Polymorphism Female heterogamety Data are organized as in Table 2. F represents either F or f. Hence Ff indicates presence of both Ff or ff genotypes in females. Z represents either X or Yd. After the introduction of F, in some cases, the standard, non-driving Y chromosome has an advantage over Yd and it will invade the population when reintroduced. See text for details.

Y d F Y Discussion 1.0 0.9 Sex determination is a fundamental developmental 0.8 process and one might expect sex-determining mechan- sex ratio 0.7 isms to be highly stable. Yet, sex-determining mechan- X in males isms vary greatly between different taxonomic groups 0.6 Y in males 0.5 Y d in males and even between closely related species (Bull, 1983; F in females Kraak and Pen, 2002; Janzen and Phillips, 2006).

frequency 0.4 Although steady empirical progress is being made in 0.3 unravelling the genetics of sex-determining mechanisms, 0.2 there are still many unanswered questions about how 0.1 new sex-determining systems evolve. It has been 0.0 0100 200 300 400 500 600 proposed that ‘genetic conflict is the most likely general generation explanation for the diversity of sex-determining mechan- isms’ (Werren and Beukeboom, 1998). Recent theoretical Figure 2 Dynamics of the sex-determining system with a driving work has largely focused on maternal–offspring conflict d d d Y chromosome for the case in which Y Y males are sterile. over sex ratio (reviewed in Uller et al., 2007). Introduction of new alleles is indicated by arrows. Yd (with drive strength k ¼ 0.8) replaces standard Y and leads to a strongly male- Intragenomic conflict (between different genes within biased sex ratio. Introduction of F leads to a polymorphic system. an individual), in general, and segregation distortion, in If standard Y is reintroduced into this system, it invades the particular, is another selective force that can lead to population and fixates, replacing the driving Yd and leading to a changes in sex-determining systems (see Introduction). female heterogametic system. However, there is little theoretical understanding of the process. Most models considered thus far were tailored to one particular species and aimed at explaining the sex-determining mechanisms found in that species male-biased and F does not invade, because the (Bengtsson, 1977; McVean and Hurst, 1996). The more advantage of producing females by F is outweighed by general models make some unrealistic assumptions. For the disadvantage of producing lethal, homozygous Md example, Jayakar (1987) assumed that the driving individuals. Therefore, for weak drive, a system with chromosome shows the same segregation distortion male heterogamety for Md and a biased sex ratio is in males and females. Charlesworth and Dempsey (2001) stable. For higher k, F invades, leading to a system assumed that the distorter has a complete transmission polymorphic for F and f, and Md and m, with the advantage (present in 100% of gametes) in females and a equilibrium frequency of F and Md increasing with k complete transmission disadvantage in males. (as it does in the scheme with sterile males). The In this paper, we developed some general models to population sex ratio is slightly male biased. For k investigate the change in the mechanisms of sex 3 between 5 and 0.8 (see Appendix B), this polymorphic determination in systems in which a driving sex sex-determining system is stable and Y cannot reinvade chromosome is present. Although trying to be as general the population. For stronger drive (kX0.8), if Y is as possible, we had to make some assumptions concern- reintroduced it will spread to fixation, leading to ing sex determination and segregation distortion. female heterogamety. Although the frequency of Md Although we believe that our assumptions reflect the decreases, it is not removed from the population and most common patterns observed in natural systems (see polymorphism at the M locus is maintained (similar to the Introduction), we briefly discuss how our results the case with sterility of MdMd males). might be affected if these assumptions were not met.

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 106 Table 4 Overview of changes in the sex determining system induced by a driving autosomal factor Md No cost of drive Sterility of MdMd males Lethality of MdMd individuals

Initial state # XY; mm; ff ~ XX; mm; ff ^ 1 S ¼ 2

After introduction of Md # XX; Mdm; ff ~ XX; mm; ff S^ ¼ k

3 3 kX kp5 5oko0.8 0.8 After introduction of F # XX; MdMd; ff # YY; MM; ff # XX; Mdm; ff # XX; Mm; ff # YY; Mm; ff ~ XX; MdMd; Ff ~ YY; MM; Ff ~ XX; mm; ff ~ XX; Mm; Ff ~ YY; Mm; Ff ^ 1 ^ 1 ^ 1 ^ ^ 1 S ¼ 2 S ¼ 2 S ¼ k 2oSok S ¼ 2

Resulting s.d. system Female heterogamety Female heterogamety Male heterogamety Polymorphism Female heterogamety Data organized as in Table 2. M represents either m or driving Md. Hence MM indicates a polymorphism on this locus and the presence of mm, mMd and MdMd genotypes. F represents either F or f. Hence Ff indicates presence of both Ff or ff genotypes in the population.

M d F Y female heterogamety of an autosomal factor and removal 1.0 of the driving Z from the population. This is assuming 0.9 that the autosomal M in our model becomes a feminizing 0.8 factor and F becomes a masculinizing factor. Our sex ratio 0.7 scenario of sterility of males that are homozygous for M d in males 0.6 the driving allele would, by symmetry, apply to cases in Y in males which females that are homozygous for the driving allele 0.5 X in males are sterile. We do not know of such cases in nature, but frequency 0.4 F in females this scenario seems plausible, taking into account that a 0.3 driving chromosome disturbs meiosis. 0.2 We have performed a rather general invasion analysis 0.1 of new sex-determining genes for a broad range of fitness 0.0 0200 400 600 800 1000 schemes. The full dynamics of the system could only be generation studied numerically, and hence could only be performed for a few specific cases. To this end, we focused on Figure 3 Dynamics of the sex-determining system with a driving lethality and/or male sterility in individuals homozy- autosomal Md factor for the case of sterility in MdMd males. Introduction of new alleles is indicated by arrows. Spread of Md gous for the driving allele. However, our analytical (with drive strength k ¼ 0.8) leads to the removal of Y, the switch to results (Appendix B) suggest that the numerical analysis a male heterogametic system for Md, and male-biased sex ratios. can be extrapolated to other fitness schemes as well, as Introduction of F leads to a polymorphic system. When Y is the invasion prospects of a new sex-determining factor reintroduced, it leads to a switch to a female heterogametic system, do not often depend on the precise fitness values. but polymorphism on the M locus is maintained. Examples of reduced fitness of individuals possessing driving alleles, not only in homozygous but also in heterozygous state, or even increased fitness of hetero- zygous females, are known from nature (for example, In our model, we consider segregation distortion only Wallace, 1948; Curtsinger and Feldman, 1980; Jaenike, in males, the heterogametic sex. Male heterogamety is 1996; Atlan et al., 2004; Wilkinson et al., 2006). In general, the prevailing sex-determining mechanism in species fitness values of different genotypes will influence the with genetic sex determination, and most of the balance between sex ratio selection (favouring spread of described cases of segregation distortion affect sperm a new sex-determining factor) and viability selection or pollen production (Jaenike, 2001; Taylor and Ingvars- acting on new sex-determining factors. Strongly reduced son, 2003). However, meiotic drive has also been found viability may prevent the spread of a new factor. during female meiosis (for example, in maize; Buckler However, according to our results, once new factors et al., 1999), and sex ratio segregation distortion in XY invade, the equilibrium sex-determining mechanism is (ZW) females has been described in wood lemmings largely independent of the specific fitness effects. This (Bengtsson, 1977) and postulated in the butterfly Danaus may hold at least as long as segregation distorters have a chrysippus (Smith et al., 1998). For reasons of symmetry, negative effect on fitness. When distorter alleles show the results of our model immediately carry over to overdominance in females (Wallace, 1948; Curtsinger systems with female heterogamety and meiotic drive and Feldman, 1980; Wilkinson et al., 2006), the outcome occurring in females. For example, if females are ZW, of evolution may be different, as both fixation and and Z drives against W (symmetric to a driving X) and removal of the distorter allele may not be favoured. homozygosity for driving Z causes lethality, a driving Z In addition, one could imagine that a new sex- should invade but not reach fixation, and introduction of determining gene has fitness costs on its own (for an autosomal feminizing gene would lead to a switch to example, because of some genetic incompatibilities),

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 107 which would hamper its spread (Werren and Beuke- reproductive success). Once the sex-determining factor boom, 1998). Here again, results would probably depend does invade, however, the final state of the system (full on the balance between selection favouring spread of a switch to different sex-determining system) is usually new factor (sex ratio bias caused by drive) and selection independent of whether male or female fitness is affected against it (reduced fitness). A few simulations that we (at least for the numerical scenarios considered by us). did show was that if a new sex-determining factor has Therefore, our assumptions on the fertility or viability only a slightly reduced fitness (a reduction by 5%), the effects of segregation distorters do not seem to substan- resulting system is the same as that with no fitness costs, tially affect our predictions. The situation may be at least for the case with a driving Y chromosome. different if the population is structured into small local However, a complete switch may not occur if the mating groups or when different mating patterns occur M factor causes a fitness reduction. Interestingly, in case (Van Boven and Weissing, 1999; Pen, 2006). of lower fitness of F, we sometimes observed cycling In some of our simulations, a complete switch to a new behaviour. An increase in the frequency of F leads to a sex-determining system could only be achieved if the decrease in the frequency of Yd, which reduces sex ratio standard X or Y chromosome was reintroduced in the bias and selection favouring F, which in turn decreases population. This is more plausible than it may appear at F frequency, which allows an increase in the frequency of first sight. In our model, the standard X or Y chromo- Yd, which re-creates a biased sex ratio and increase in the some was completely driven out of the population. frequency of F and the repeats (results now shown). However, in natural systems, a population often consists In our model, we also assumed that the absence of a Y of many subpopulations with limited gene flow between or X chromosome does not have negative effects on them. Therefore, one can easily imagine that a driving fitness. This is probably not realistic in species with old, element will initially appear only in one subpopulation strongly differentiated sex chromosomes, in which Y and spread within it, and subsequently to other popula- usually lacks some of the genes that are present on the X tions. However, if a new sex-determining factor appears chromosome, or when Y possesses genes crucial for before the whole population is fixed for a driving allele, gametogenesis. In such cases, some of our results will not migration of standard chromosomes from other sub- hold, as a full switch to another sex-determining system populations will lead to spread of new sex-determining requires removal of one of the original sex chromosomes factor even in subpopulations in which the driving (either X or Y). However, absence of one of the sex element is fixed. Alternatively, even if the driving allele is chromosomes does not necessarily lead to (drastic) fixated in the whole population, any restoring reduction in fitness (Juchault and Rigaud, 1995). vitality or fertility of homozygotes will be favoured and Undifferentiated sex chromosomes have been found in spread in the population, even if it does not have a a number of animal and plant species (Charlesworth segregation advantage. et al., 2005; Fraser and Heitman, 2005), and even if the Perhaps the most interesting result of our simulations chromosomes are morphologically differentiated, they is that the segregation distorter, whose presence initiated may not possess any genes necessary for viability or the change in the sex-determination system, is often fertility (Hiroyoshi, 1977). More theoretical and empirical subsequently lost from the population. Perhaps surpris- work is needed to understand the effect of different ingly, such an effect has never been found in previous fitness values associated with different genotypes. models (Bengtsson, 1977; Jayakar, 1987; Haig, 1993a, b; The switch to a new sex-determining system is driven McVean and Hurst, 1996; Charlesworth and Dempsey, by selection against biased sex ratios. When there are no 2001). In these models, a change in the sex-determining fitness costs associated with homozygosity for the system usually neutralizes drive, for example, by distorter allele, even weak sex ratio selection leads to removing sensitive alleles, but never leads to the changes in sex-determining mechanism. However, often complete loss of the driving allele. However, our results sex ratio selection has to be sufficiently strong to show that the presence of a segregation distorter can only overcome selection against less-fit genotypes (Appendix B). be a transient state, the traces of which are no longer Therefore, in some cases, only strong segregation dis- visible once a new sex-determination system has become torters will lead to changes in sex-determining mechan- established. isms. This suggests that when segregation distortion is Loss of the driver would make it difficult to detect the weak, the evolution of suppressors may be the only way role of segregation distortion in the evolution of extant to decrease sex ratio bias. Interestingly, Lyttle (1981) in his sex-determining mechanisms, especially given that model on the evolution of new sex-determining mechan- changes to a new sex-determining mechanism are often ism through aneuploidy, also concluded that strong drive very rapid (Figures 1–3). Indication of the role of favours change in sex-determining mechanisms and weak segregation distortion in the evolution of sex-determin- drive favours the accumulation of suppressors. We ing mechanisms could be found indirectly, for example, suspect that this is a general phenomenon. Moreover, by looking at closely related species of a species in which once suppressors start accumulating in the population sex chromosome meiotic drive has been found, to check decreasing the effective drive, this may prevent changes in whether change in sex determination occurred and the sex-determining system, as long as suppressors are whether they are consistent with our results (for less costly than a new sex-determining mechanism. example, if X drives, invasion of a new male-determining According to our model, the invasion prospects of a factor is expected). Alternatively, in a species or a closely new sex-determining factor may depend on whether the related group of species in which sex-determining genes distorter has any effects on the fertility of males or on the are known to be located on different chromosomes (for viability of both sexes. Sometimes fitness of only one sex example, medaka fish, Takehana et al., 2007; the fly matters, that is, either viability of females or the product Megasela scalaris, Traut and Willhoeft, 1990), one could of viability and fertility in males (which is their lifetime investigate whether some of the populations (species)

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 108 possess driving sex chromosomes. If in such populations, Carvalho de AB, Peixoto AA, Klaczko LB (1989). Sex-ratio in the sex-determining mechanism is ancestral to other Drosophila mediopunctata. Heredity 62: 425–428. populations, this could suggest that segregation distortion Charlesworth B, Dempsey ND (2001). A model of the evolution was responsible for the change in sex-determining mechan- of the unusual sex chromosome system of Microtus oregoni. isms. However, this is only circumstantial evidence. Heredity 86: 387–394. A more direct test of the predictions of our model Charlesworth D, Charlesworth B, Marais G (2005). Steps in the evolution of heteromorphic sex chromosomes. Heredity 95: would probably demand laboratory experiments. They 118–128. could be set up using (closely related) species in which Clark ME (1999). The evolution of a neo-Y chromosome in the multiple sex-determining factors exist together with housefly, Musca domestica. PhD Thesis. University of segregation distorters. The housefly, Musca domestica, Houston, TX, USA. seems to be an especially good candidate. In this species, Cosmides LM, Tooby J (1981). Cytoplasmic inheritance and a variety of sex-determining mechanisms coexist in intragenomic conflict. J Theor Biol 89: 83–129. natural populations, such as a standard XY system, as Curtsinger JW, Feldman MW (1980). Experimental and theore- well as autosomal male and female-determining factors, tical analysis of the sex-ratio polymorphism in Drosophila with effects on sex determination, as described in our pseudoobscura. Genetics 94: 445–466. model (Du¨ bendorfer et al., 2002). In addition, in some Du¨ bendorfer A, Hediger M, Burghardt G, Bopp D (2002). Musca North American populations, autosomal M factors show domestica, a window on the evolution of sex-determining mechanisms in insects. Int J Dev Biol 46: 75–79. segregation distortion of 0.75–0.9 (Clark, 1999; although Feldmeyer B, Kozielska M, Weissing FJ, Beukeboom LW, Pen I driving M’s are probably absent in European popula- (2008). Temperature and the geographical distribution of sex tions; Kozielska, 2008). Unfortunately, changes in the determining mechanisms in the housefly. Evol Ecol Res 10: frequency of sex-determining factors in these North 797–809. American populations have not been studied. Even Fraser JA, Heitman J (2005). Chromosomal sex-determining though segregation distortion is probably not the main regions in animals, plants and fungi. Curr Opin Genet Dev 15: driving force for the evolution of sex determination in 645–651. natural populations of the housefly (Feldmeyer et al., Gileva EA (1987). Meiotic drive in the sex chromosome system 2008; Kozielska et al., 2008), experiments could be set up of the varying lemming, Dicrostonyx torquatus Pall. (Rodentia, to test predictions of our model. In addition, one could Microtinae). Heredity 59: 383–389. Haig D (1993a). The evolution of unusual chromosomal systems study frequencies of different factors in natural popula- in coccoids—extraordinary sex ratios revisited. J Evol Biol 6: tions with segregation distortion over long periods of 69–77. time. In addition, in other species with multiple sex- Haig D (1993b). The evolution of unusual chromosomal systems determining factors, segregation distortion could be in sciarid flies—intragenomic conflict and the sex ratio. J Evol induced with molecular techniques (Windbichler et al., Biol 6: 249–261. 2008) and subsequent dynamics of sex-determining Hamilton WD (1967). Extraordinary sex ratios. Science 156: mechanisms could be followed. 477–488. In summary, our simulations show that in many cases Hickey WA, Craig GB (1966). Genetic distortion of sex ratio in a segregation distortion creates selective pressure allowing mosquito Aedes aegypti. Genetics 53: 1177–1196. novel sex-determining alleles to spread and induce shifts Hiroyoshi T (1977). Some new mutants and revised linkage to a new sex-determining system. Interestingly, the maps of housefly, Musca domestica L. Jpn J Genet 52: 275–288. Hurst LD, Atlan A, Bengtsson BO (1996). Genetic conflicts. segregation distorter, the presence of which initiated this Quart Rev Biol 71: 317–364. shift, can be subsequently lost from the population. Jaenike J (1996). Sex-ratio meiotic drive in the Drosophila quinaria Therefore, the role of segregation distortion in the group. Am Nat 148: 237–254. evolution of sex-determining mechanisms may be under- Jaenike J (1999). Suppression of sex-ratio meiotic drive and the estimated. maintenance of Y-chromosome polymorphism in Drosophila. Evolution 53: 164–174. Jaenike J (2001). Sex chromosome meiotic drive. Annu Rev Ecol References Syst 32: 25–49. Janzen FJ, Phillips PC (2006). Exploring the evolution of Atlan A, Capillon C, Derome N, Couvet D, Montchamp-Moreau environmental sex determination, especially in reptiles. C (2003). The evolution of autosomal suppressors of sex-ratio J Evol Biol 19: 1775–1784. drive in Drosophila simulans. Genetica 117: 47–58. Jayakar SD (1987). Some two locus models for the evolution of Atlan A, Joly D, Capillon C, Montchamp-Moreau C (2004). Sex- sex-determining mechanisms. Theor Pop Biol 32: 188–215. ratio distorter of Drosophila simulans reduces male produc- Juchault P, Rigaud T (1995). Evidence for female heterogamety tivity and sperm competition ability. J Evol Biol 17: 744–751. in two terrestrial crustaceans and the problem of sex Bengtsson BO (1977). Evolution of the sex ratio in the wood chromosome evolution in isopods. Heredity 75: 466–471. lemming, Myopus schisticolor. In: Christiansen FB, Fenchel Kozielska M, Feldmeyer B, Pen I, Weissing FJ, Beukeboom LW TM (eds). Measuring Selection in Natural Populations. Springer: (2008). Are autosomal sex determining factors of the Berlin, pp 333–343. housefly (Musca domestica) spreading north? Genet Res 90: Buckler ES, Phelps-Durr TL, Keith Buckler CS, Dawe RK, 157–165. Doebley JF, Holtsford TP (1999). Meiotic drive of chromoso- Kozielska M, Pen I, Beukeboom LW, Weissing FJ (2006). Sex mal knobs reshaped the maize genome. Genetics 153: 415–426. ratio selection and multi-factorial sex determination in the Bull JJ (1983). The Evolution of Sex Determining Mechanisms. housefly: a dynamic model. J Evol Biol 19: 879–888. Benjamin/Cummings Publishing Co: Menlo Park, CA. Kozielska MA (2008). Evolutionary dynamics of sex determina- Bull JJ, Charnov EL (1977). Changes in the heterogametic tion. Mechanistic theory and empirical investigations. PhD mechanism of sex determination. Heredity 39: 1–14. Thesis. University of Groningen, Groningen, The Nether- Burt A, Trivers R (2006). Genes in Conflict. The Belknap Press lands. http://irs.ub.rug.nl/ppn/310130085. of Harvard University Press: Cambridge, Massachusetts/ Kraak SBM, Pen I (2002). Sex-determining mechanisms in London, England. vertebrates. In: Hardy ICW (ed). Sex Ratios Concepts and

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 109 Research Methods. Cambridge University Press: Cambridge, we encode genotypes by triplets i ¼ (i1,i2,i3), where in pp 158–177. corresponds to the genotype at locus n. At each locus, the Lyttle TW (1981). Experimental of meiotic genotypes are unordered, meaning that the heterozygous drive systems. III. Neutralization of sex ratio distortion in genotype AB is equivalent to BA. The sexual phenotype Drosophila through sex chromosome aneuploidy. Genetics 98: determined by genotype i is encoded as a binary 317–334. s ¼ s ¼ Lyttle TW (1991). Segregation distorters. Annu Rev Genet 25: variable: i 0 for females and i 1 for males. The 511–557. frequencies of genotype i among adult females Lyttle TW (1993). Cheaters sometimes prosper—distortion of andP malesP are written as xi and yi, respectively Mendelian segregation by meiotic drive. Trends Genet 9: ( i xi ¼ i yi ¼ 1 ). Note that for each i, either xi ¼ 0or 205–210. yi ¼ 0, because the genotype i uniquely determines sex. Martin J, Kuvangkadilok C, Peart DH, Lee BTO (1980). Multiple sex determining regions in a group of related Chironomus Fitness species (Diptera, Chironomidae). Heredity 44: 367–382. McVean G, Hurst LD (1996). Genetic conflicts and the paradox Each genotype has its specific viability v and fertility u. of sex determination: Three paths to the evolution of female In our model, all females have the same fertility, hence intersexuality in a mammal. J Theor Biol 179: 199–211. uf,i ¼ 1. Male fertility may depend on genotype and is Montchamp-Moreau C, Ginhoux V, Atlan A (2001). The Y denoted by um,i. For numerical examples in the main text, chromosomes of Drosophila simulans are highly polymorphic we considered three fitness schemes: (a) no cost of for their ability to suppress sex-ratio drive. Evolution 55: homozygosity for the driving allele, that is, vi ¼ um,i ¼ 1 728–737. for all i; (b) males homozygous for a driving allele are Otto SP, Day T (2007). A Biologist’s Guide to Mathematical completely sterile, that is, um,i ¼ 0 when i is homozygous Modeling in Ecology and Evolution. Princeton University Press: for a driving allele and um,i ¼ 1 otherwise; (c) homo- Princeton and Oxford. zygosity for a driving allele is lethal in both sexes, that is, Pen I (2006). When boys want to be girls: effects of mating system and dispersal on parent-offspring sex ratio conflict. vi ¼ 0ifi is homozygous for a driving allele and vi ¼ 1 Evol Ecol Res 8: 103–113. otherwise. Smith DAS, Gordon IJ, Depew LA, Owen DF (1998). Genetics of the butterfly Danaus chrysippus (L.) in a broad zone, Transmission with special reference to sex ratio, polymorphism and The frequency of genotype z among the offspring of a intergenomic conflict. Biol J Linn Soc 65: 1–40. cross between an i-female and a j-male is denoted by Sturtevant AH, Dobzhansky T (1936). Geographical distribution and cytology of ‘sex ratio’ in Drosophile pseudoobscura and Tz,ij, which can be decomposed into three per locus related species. Genetics 21: 473–490. components: Takehana Y, Demiyah D, Naruse K, Hamaguchi S, Sakaizumi M (2007). Evolution of different Y chromosomes in two Tz;ij ¼ Pðz1ji1j1ÞPðz2ji2j2ÞPðz3ji3j3Þ; ð1Þ medaka species, Oryzias dancena and O latipes. Genetics 175: 1335–1340. where PðznjinjnÞ is the probability that at locus n, the Taylor DR, Ingvarsson PK (2003). Common features of segregation offspring genotype will be zn given a maternal genotype distortion in plants and animals. Genetica 117: 27–35. in and paternal genotype jn. Traut W, Willhoeft U (1990). A jumping sex determining factor If offspring genotype at locus n is homozygous for in the fly Megaselia scalaris. Chromosoma 99: 407–412. allele A, then Uller T, Pen I, Wapstra E, Beukeboom LW, Komdeur J (2007). The evolution of sex ratios and sex-determining systems. ðz ¼ ji j Þ¼1 ; ð Þ P n AA n n 2qA;in kA;jn qA;jn 2a Trends Ecol Evol 22: 292–297. Van Boven M, Weissing FJ (1998). Evolution of segregation where qA;in and qA;jn are the frequencies of A alleles in

distortion: potential for a high degree of polymorphism. mother and father, and kA;jn is the segregation ratio J Theor Biol 192: 131–142. (proportion of gametes) of the A allele in jn-males. If jn is Van Boven M, Weissing FJ (1999). Segregation distortion in a heterozygous for a driving allele A and a non-driving deme structured population: opposing demands of gene, ¼ ¼ À ¼ 1 allele a, then kA;jn k and ka;jn 1 k, otherwise kA;jn 2 individual and group selection. J Evol Biol 12: 80–93. (‘honest segregation’). Wallace B (1948). Studies on ‘sex ratio’ in Drosophila pseudoobs- For heterozygous offspring with genotype AB at cura .1. Selection and ‘sex ratio’. Evolution 2: 189–217. locus n: Werren JH, Beukeboom LW (1998). Sex determination, sex ratios, and genetic conflict. Annu Rev Ecol Syst 29: 233–261. ð ¼ j Þ¼1 þ 1 : ð Þ P zn AB injn 2qA;in kB;jn qB;jn 2qB;in kA;jn qA;jn 2b Wilkinson GS, Johns PM, Kelleher ES, Muscedere ML, Lorsong A (2006). Fitness effects of X chromosome drive in the stalk-eyed fly, Cyrtodiopsis dalmanni. J Evol Biol 19: 1851–1860. Windbichler N, Papathanos PA, Crisanti A (2008). Targeting the Recurrence equations X chromosome during spermatogenesis induces Y chromo- Under random mating, a random mating pair consists of some transmission ratio distortion and early dominant an i-female and a j-male with probability given by the Anapheles gambiae PLoS Genetics 4 embryo lethality in . : x y e1000291 (doi:10.1371/journal.pgen.1000291). product of their frequencies, that is, i j. Allowing for fertility differences between males, the frequency of z-offspring before viability selection equals Appendix A X 1 T ¼ x y u T ; ð3Þ We model the evolutionary dynamics of the sex- z  i j m;j z;ij um ij determining system with a set of recurrence equations P similar to the one described by us earlier (Kozielska et al., where um ¼ j yjum;j is the mean fertility of males. 2006), although with slightly different notation. We Assuming discrete and non-overlapping generations, consider three independent sex-determining loci and the genotype frequencies after one round of reproduction

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 110 and selection are given by z^XY ¼ðx^1 ¼ 1; :::; y1 ¼ 1; :::Þ: 2 3   q 0 q 0 q 0 q 0 q 0 vzð1 À szÞTz vzszTz x1 x1 x1 x1 x1 x0 ¼ ; y0 ¼ ; ð4Þ 6 7 z vð1 À SÞ z vS 6 qx1 qx2 qx3 qy1 qy2 7 P 6 qx0 qx0 qx0 qx0 qx0 7   6 2 2 2 2 2 7 where v P¼ z vzTz is mean offspring viability and 6 qx1 qx2 qx3 qy1 qy2 7  6 0 0 0 0 0 7 S ¼ð1=vÞ vzTzsz is the sex ratio (proportion males) 6 qx qx qx qx qx 7 z J ¼ 6 3 3 3 3 3 7 after viability selection. 6 qx1 qx2 qx3 qy1 qy2 7 6 qy0 qy0 qy0 qy0 qy0 7 6 1 1 1 1 1 7 6 qx1 qx2 qx3 qy1 qy2 7 Appendix B 4 0 0 0 0 0 5 qy2 qy2 qy2 qy2 qy2 qx qx qx qy qy To support and generalize the numerical analysis in the 2 1 2 3 1 3 2 main text, we here perform an invasion analysis for 0 À1 À10À2k 6 2 7 driving alleles and new sex-determining factors. We 6 0 1 102k 7 follow the same sequence of scenarios, as in the main text. 6 2 7 ¼ 6 00 00 07 ð6Þ Scenario 1: driving X chromosome 4 1 5 0 À2 À10 0 We work with a two-locus model, with three alleles (X, Y, 0 1 10 0 Xd) at the XY locus and two alleles (m, M) at the unlinked 2 autosomal M locus. Therefore, there are three female genotypes (XXmm, XdXmm and XdXdmm)andsevenmale A rare Xd chromosome will spread if the leading genotypes (XYmm, XdYmm, XdYMm, XdXdMm, XYMm, eigenvalue of J is larger than 1 (for example, Otto and d XXMm and X XMm), with frequencies x1...x3 and y1...y7, Day, 2007).p Inffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi this case, the leading eigenvalue of J is 1 1 respectively. When paired with a Y chromosome in males, l1 ¼ 4ð1 þ 1 þ 16kÞ.Asl141 if and only if k42, a rare d 1 driving Xd chromosome can always invade an XY the driving allele X has a segregation ratio of k42, otherwise segregation is ‘honest’. We assume that males population, regardless of its effect on viability and male homozygous for Xd have relative fertility 0pup1(males fertility when in homozygous condition. d are sterile when u ¼ 0) and viability 0pvmp1, and females With X present and M (still) absent, there are at most d homozygous for X have viability vf. Then the full two equilibria in addition to the unstable equilibrium z^XY. dynamics is given by the recursions (4): One of these equilibria corresponds to fixation of d X ðx^3 ¼ 1; y^2 ¼ 1Þ . If female viability, vf, is sufficiently 1 1 0 v þ C x ¼y ð1x þ 1x Þþy ð1x þ 1x Þ large, this is the only equilibrium. For f o2 4k there is f 1 1 2 1 4 2 5 4 1 8 2 an additional equilibrium in which X and Xd coexist. 1 1 1 1 þ y6ð2x1 þ 4x2Þþy7ð4x1 þ 8x2Þ Specifically, in the sterility scenario of Table 2 (u ¼ 0, 0 1 1 1 v ¼ v ¼ 1), there is only an equilibrium with Xd fixed and Cfx2 ¼y1ð4x2 þ 2x3Þþky2ðx1 þ 2x2Þ f m 1 1 1 1 an adult sex ratio given by Sˆ ¼ 1Àk, whereas in the lethality þ ky3ð2x1 þ 4x2Þþuy4ð2x1 þ 4x2Þ scenario (u ¼ 1, vf ¼ vm ¼ 0), there is only a polymorphic 1 1 1 1 1 þ y5ð x2 þ x3Þþy6ð x2 þ x3Þþ y7 ^ 1 ^ 1 ^ 1 1 ^ 1 1  8 4 4 2 4 equilibrium (z1 ¼ 2k; z2 ¼ 1 À 2k; y1 ¼ 2 þ 4k; y2 ¼ 2 À 4k) 0 1 1 1 and the adult sex ratio is bounded by 2 from below (when Cfx3 ¼vf ky2ð x2 þ x3Þþky3ð x2 þ x3Þ 5 2 4 2 à k ¼ 1) and by 1 from above (k ¼ 1). If a polymorphic þ ð þ 1 Þþ ð1 þ 1 Þ 2 2 uy4 x2 2x3 y7 8x2 4x3 equilibrium exists, it is always locally stable and the fixation 0 1 1 1 Cmy1 ¼y1ð2x1 þ 4x2Þþð1 À kÞy2ðx1 þ 2x2Þ equilibrium is then unstable against invasion by X,whilethe 1 1 1 1 fixation equilibrium is stable against invasion by X if there is þð1 À kÞy3ð2x1 þ 4x2Þþy5ð4x1 þ 8x2Þ 0 1 1 1 no polymorphic equilibrium. Cmy2 ¼y1ð4x2 þ 2x3Þþð1 À kÞy2ð2x2 þ x3Þ ð5Þ 1 1 1 1 þð1 À kÞy3ð4x2 þ 2x3Þþy5ð8x2 þ 4x3Þ Invasion of M: Stability against invasion of M of the 0 1 1 1 1 equilibrium with Xd fixed is determined by the Jacobian Cmy3 ¼ð1 À kÞy3ð4x2 þ 2x3Þþy5ð8x2 þ 4x3Þ 0 1 1 1 1 restricted to the subspace without the X allele, evaluated Cmy4 ¼vm½ky3ð x2 þ x3Þþuy4ð x2 þ x3Þ 4 2 4 2 at z^Xd ¼ðx^3 ¼ 1; y^2 ¼ 1Þ: 1 1 þ y7ð8x2 þ 4x3ފ 2 3 0 00 0 0 C y ¼ð1 À kÞy ð1x þ 1x Þþy ð1x þ 1x Þ m 5 3 2 1 4 2 5 4 1 8 2 6 1Àkð1ÀvmÞ vmu 7 0 6 00À 2ð1ÀkÞ À 2ð1ÀkÞ 7 C y ¼y ð1x þ 1x Þþy ð1x þ 1x Þ J ¼ ð7Þ m 6 5 4 1 8 2 6 2 1 4 2 4 00 1=205 1 1 þ y7ð x1 þ x2Þ vmk vmu 4 8 00 2ð1ÀkÞ 2ð1ÀkÞ 0 1 1 1 1 Cmy7 ¼ky3ð2x1 þ 4x2Þþuy4ð2x1 þ 4x2Þ þ y ð1x þ 1x Þþy ð1x þ 1x Þþ1y 1 5 8 2 4 3 6 4 2 2 3 4 7 The leading eigenvalue of J is either l1 ¼ 2vmu=ð1 À kÞ 1 or l2 ¼ . Thus, if the driving allele in homozygous Here Cf ¼ umvð1 À SÞ and Cm ¼ umvS are normalization 2 factors, as defined in Appendix A. condition confers complete male sterility (u ¼ 0) or complete male lethality (vm ¼ 0), the M allele cannot invade a population with Xd fixed. Invasion will occur d 1 d Invasion of X into the standard XY system: To determine only if k41 À 2vmu, in other words, as long as X does not the stability of the XY system with respect to cause complete sterility or inviability, M can invade invasion of rare Xd chromosomes, we calculated the provided k is sufficiently large. Jacobian of system (B1), restricted to the subspace It is difficult to analyse invasion stability of the without the M allele, evaluated at the equilibrium point polymorphic equilibrium against invasion of M in full

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 111 d generality. For the special case of lethality (vf ¼ vm ¼ 0), with an X chromosome. Males homozygous for Y have the leading eigenvalue of the 10 Â 10 jacobian is fertility 0pup1 and viability 0pvmp1, whereas females independent of u and given by homozygous for Yd have viability 0 v 1. The twelve ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p fp p recursion equations are too bulky to reproduce here in 1 þ 4k þ 8k2 À 1 1 full. A Maple (version 11) code containing the algebra is l1 ¼ 41 , k42 2ð8k À 1 À 4k2Þ available upon request from the authors. Hence M can always invade. In the general case, we can 1 d approximate the leading eigenvalue near e ¼ k À 2: Invasion of Y into the standard XY system: The relevant 1 þ v u À 2v Jacobian matrix, restricted to the subspace without F and l m f e2 e3 1 ¼ 1 þ 2 þ Oð Þ evaluated at the XY equilibrium has leading eigenvalue 2k, ð1 À vf Þ d regardless of the values u, vm and vf.HenceY can always 1 invade provided k42. The equilibrium in which Y is lost and It can be seen that this expression may be smaller than all males are XYd is stable. unity, hence M cannot always invade. In particular, if d 2vf 41 þ vmu,thenM cannot invade for sufficiently small k. Invasion of F into the XY /ff system: The relevant 12 Â 12 Jacobian matrix has leading eigenvalue pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Simultaneous invasion of M and X when Xd is fixed: The 3 À 2kð1 À vf Þþ 1 þ 4kð1 À k À vf ð1 À vf ÞÞ situation is different when X and M are simultaneously l1 ¼ ð10Þ introduced at low frequency in a population otherwise 8ð1 À kÞ d fixed for X . Then the relevant Jacobian matrix is Hence l1 is independent of u and vm, and increases with given by vf. For full viability of homozygous females (vf ¼ 1),

2 3 0 0000 0 0 0 0 0 6 1 1 1 1 1 1 7 6 0 00 0 7 6 vf 2vf 2kvf 4kvf 2kvf 4kvf 7 6 À 1 À 1 0 À 1 00 0À 1 À 1 À 1 7 6 vf 2vf 2kvf 4kvf 2kvf 4kvf 7 6 7 6 1 1 000 0 0 0 0 07 6 2 7 6 À À1 À 1Àkð1ÀvmÞ vmu 1 1 À 1þvm 7 6 1 2 000 2ð1ÀkÞ 2ð1ÀkÞ 2ð1ÀkÞ 2ð1ÀkÞ 4ð1ÀkÞ 7 J ¼ 6 7 (8) 6 0 0000 1 0 1 007 6 2 4ð1ÀkÞ 7 6 kvm vmu vm 7 6 0 0000 2ð1ÀkÞ 2ð1ÀkÞ 004ð1ÀkÞ 7 6 7 6 0 0000 0 0 0 0 07 4 0 0000 0 0 0 0 05 1 1 1 0 0000 0 04ð1ÀkÞ 2ð1ÀkÞ 4ð1ÀkÞ

3 1 Three candidate leading eigenvalues are l141 k42, whereas for complete inviability (vf ¼ 0), pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 3 l141 k45. Thus, even for relatively weakly driving k þ kðk þ 4vf Þ d 1 3 l1 ¼ Y alleles (2pkp5), F can always invade, provided the 4kvf viability of YdYd females is sufficiently high (Table 3). v u l ¼ m ð9Þ 2 2ð1 À kÞ Re-invasion of Y: It is hard to calculate the equilibrium frequencies after invasion of F, except for some special 1 l ¼ cases. When YdYd males are fully sterile (u ¼ 0) and YdYd 3 4ð1 À kÞ females have full viability (vf ¼ 1), the stable equilibrium 3 d without Y is given by Since l341 , k44 , the equilibrium with X fixed is always unstable against simultaneous invasion of X and ð1 À kÞ2 M whenever k43. In case of complete male sterility ^ 4 x1 ¼ 2 (u ¼ 0) and full female viability (v ¼ 1) of XdXd geno- k f 2 types, l 41 , k41 and l ¼ 0, hence in this case, k43 is ð2k À 1Þð1 À kÞ 1 2 2 4 x^ ¼ necessary and sufficient for invasion of M (Table 2). In 2 k2 addition note that for sufficiently small vf, l141 for any 2ð2k À 1Þð1 À kÞ k41. Specifically, if XdXd females are lethal, then M can x^5 ¼ 2 k always invade together with X. 1 À k ^ y3 ¼ 1 1 À kð1 À vmÞÀ2vm Scenario 2: driving Y chromosome We study a two-locus system with seven female The leading eigenvalue of the (12 Â 12) Jacobian matrix genotypes (XXff, XXFf, XYFf, YYFf, XYdFf, YYdFf and evaluated at this equilibrium is YdYdFf) with frequencies x yx and five male genotypes pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 7 2 2 3 6 d d d d 1 À 2kð1 À kÞ þ ð2k À 1Þð2k À 1 þ 8k À 12k Þþ4k (XYff, YYff, XY ff, YY ff and Y Y ff) with frequencies l1 ¼ d 8ð1 À kÞk2 y1yy5.AnY chromosome only drives when paired

Heredity Segregation distortion and sex-determining mechanisms M Kozielska et al 112 3 1 d It can be shown that l141 k42, hence Y can always Invasion of M into the standard XY system: The invade when u ¼ 0 and vf ¼ 1 (Table 3). relevant 9 Â 9 Jacobian matrix restricted to the subspace For the scenario with lethality (u ¼ 1, vf ¼ vm ¼ 0), without the F allele has leading eigenvalue 3 1 d analytical results are not insightful. Numerical calcula- l ¼ 2k41 k42, hence a driving M allele can always tions of eigenvalues show that Y can invade when invade, regardless of its effects on fertility and viability k40.655. in homozygous condition. The new equilibrium, in which all males are heterozygous for Md and Y is lost, 1 is stable ( l1 ¼ 1=ð2kÞo1 , k42 ). Invasion of F into the XX/Mdm/ff system: The leading d Scenario 3: driving M eigenvalue of the full 18 Â 18 Jacobian matrix is again Now, we work with a three-locus system with 10 female given by (10). Hence l1 is independent of u and vm, and genotypes (XXmmff, XXmmFf, XYmmFf, YYmmFf, increases with vf. For full viability of homozygous XXmMdFf, XYmMdFf, YYmMdFf, XXMdMdFf, XYMdMdFf 3 1 females (vf ¼ 1), l141 k4 , whereas for complete d d y 2 and YYM M Ff) with frequencies x1 x10, and eight inviability (v ¼ 0), l 413k43. Thus, even for relatively d d f 1 5 male genotypes (XYmmff, YYmmff, XXmM ff, XYmM ff, weakly driving Md alleles (1pkp3), F can always invade d d d d d d d 2 5 YYmM ff, XXM M ff, XYM M ff and YYM M ff) with provided viability of MdMd females is sufficiently high. y d frequencies y1 y8. Males homozygous for M have Numerical iterations (Table 4) suggest that after fertility 0pup1 and viability 0pvmp1, whereas females invasion of F, for sufficiently high values of k, Y can d homozygous for M have viability 0pvfp1. Again, a once again invade and go to fixation (for lethality kX0.8, Maple 11 version of the system of 18 recursion equations sterility k40.5). Numerical calculations of eigenvalues is available for inspection upon request. confirm these invasion conditions.

Heredity