Difference in flowering time can initiate speciation of nocturnally flowering species.

Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Difference in flowering time can initiate speciation of nocturnally flowering species Tomotaka Matsumoto a,n, Akiko A Yasumoto b, Kozue Nitta b, Shun K Hirota c, Tetsukazu Yahara b, Hidenori Tachida b a

Graduate School of Systems Life Sciences, Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan Department of Biology, Faculty of Sciences, Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan c Graduate School of Systems Life Sciences, Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan b

H I G H L I G H T S

We simulated the evolution of the nocturnally flowering species. We included genetic model which is estimated from empirical studies. We examined the probability of the evolution under several parameter sets. As the result, the evolution occurred in relatively wide parameter range. Our result suggested the effect of the flowering time as a magic trait of speciation.

art ic l e i nf o

a b s t r a c t

Article history: Received 31 May 2014 Received in revised form 25 January 2015 Accepted 28 January 2015

Isolation mechanisms that prevent gene flow between populations prezygotically play important roles in achieving speciation. In flowering plants, the nighttime flowering system provides a mechanism for isolation from diurnally flowering species. Although this system has long been of interest in evolutionary biology, the evolutionary process leading to this system has yet to be elucidated because of the lack of good model species. However, the genetic mechanisms underlying the differences in flowering times and the traits that attract pollinators between a pair of diurnally and nocturnally flowering species have recently been identified in a few cases. This identification enables us to build a realistic model for theoretically studying the evolution of a nocturnally flowering species. In this study, based on previous experimental data, we assumed a model in which two loci control the flowering time and one locus determines a trait that attracts pollinators. Using this model, we evaluated the possibility of the evolution of a nocturnally flowering species from a diurnally flowering ancestor through simulations. We found that a newly emerging nighttime flowering flower exhibited a sufficiently high fitness, and the evolution of a nocturnally flowering species from a diurnally flowering species could be achieved when hybrid viability was intermediate to low, even in a completely sympatric situation. Our results suggest that the difference in flowering time can act as a magic trait that induces both natural selection and assortative mating and would play an important role in speciation between diurnally and nocturnally flowering species pairs. & 2015 Published by Elsevier Ltd.

Keywords: Reproductive isolation Flowering time Magic trait Theoretical study

1. Introduction Reproductive isolation is critical for preventing gene flow and leads to speciation. Many ecological and non-ecological factors cause such isolation, including geographic distance, mate choice and host differences; determining which factor triggered reproductive isolation

n Corresponding author. Pressent address: Department of Population Genetics, National Institute of Genetics, Shizuoka, Japan. Tel.: þ 81 55 981 6793. E-mail address: [email protected] (T. Matsumoto).

is important for understanding the mechanism of speciation (Coyne and Orr, 2004; Schluter, 2009). In flowering plants, the evolution of a nocturnally flowering species from a diurnally flowering ancestor species has been of continued interest since it was discussed by Darwin (Darwin, 1862; Baker, 1961; Grant, 1983; Nilsson, 1988; Grant, 1993; Fenster et al., 2004). Previous studies of some diurnally and nocturnally flowering species pairs have reported that nocturnally flowering species flower at nighttime, usually showing a lighter flower color, such as white or pale yellow, and emitting a sweet fragrance to attract nocturnal pollinators. In contrast, the diurnal flowering species of the pairs flower at daytime

http://dx.doi.org/10.1016/j.jtbi.2015.01.036 0022-5193/& 2015 Published by Elsevier Ltd.

Please cite this article as: Matsumoto, T., et al., Difference in flowering time can initiate speciation of nocturnally flowering species. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.01.036i

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T. Matsumoto et al. / Journal of Theoretical Biology ∎ (∎∎∎∎) ∎∎∎–∎∎∎

and are adapted to diurnal pollinators, showing a darker color, such as pink or red, with a weaker fragrance (Dudareva et al., 1996 for Clarkia species; Stuurman, 2004; Hoballah, 2007 for Petunia species; Hirota et al. 2012; for Hemerocallis species). Therefore, there are at least two types of premating isolation between a nocturnally flowering species and its diurnally flowering ancestor: differences in flowering time and pollinator preference to the attractive trait (flower color or fragrance). Intuitively, a switch of the flowering time from daytime to nighttime also causes a switch of the pollinator from diurnal to nocturnal. Thus, the initial divergence of the flowering time would cause the subsequent adaptation of attractive traits and be important for the establishment of strong premating isolation as the initial stage of speciation. Nevertheless, the evolutionary process leading from diurnally flowering species to nocturnally flowering species remains poorly understood because of the lack of good model species for studying this phenomenon (Hasegawa et al., 2006). Recently, however, a series of genetic studies has revealed that a few major genes or even a single gene can cause differences between diurnally and nocturnally flowering species pairs in terms of flower morphology (Stuurman et al., 2004), flower color (Hoballah et al., 2007), flower fragrance (Dudareva et al., 1996; Verdonk et al., 2005) and flowering time (Haesgawa et al., 2006; Nitta et al., 2010). These studies allow us to build a realistic genetic model for traits that cause premating isolation between a diurnally and nocturnally flowering species and theoretically address the evolutionary mechanism of a nocturnally flowering species using computer simulation. In particular, Hemerocallis species are good model taxa for this topic. Previously, Hasegawa et al. (2006) revealed a bimodal flowering time distribution in a natural population of hybrids between Hemerocallis fulva (diurnally flowering species with a reddish flower) and H. citrina (nocturnally flowering species with a yellowish flower) and suggested that speciation arising from one or a few mutations might have taken place in these two species. Subsequently, Nitta et al. (2010) showed that the flowering times of H. fulva and H. citrina were regulated primarily by two loci, one regulating flower opening time and the other regulating flower closing time, supporting the suggestion that was previously made by Hasegawa et al. (2006). Because nocturnally flowering species have evolved multiple times from the ancestral diurnally flowering species within the genus Hemerocallis (Noguchi and Hong, 2004), the same genetic system may have yielded multiple occasions of such evolution. Previously, many theoretical studies have been conducted on the evolution of different flowering periods. First, Weis et al. (2005) employed a single-locus model and analyzed the effect of a different flowering period as an isolating barrier. Second, Devaux and Lande (2008, 2009, 2010) assumed a one-locus, or quantitative, genetic model for flowering period and showed that two flowering periods can evolve and be maintained. In the models that were studied by Stam (1983) and Gavrilets and Vose (2007), environmental differences initially induced differences in the flowering periods. In particular, Gavrilets and Vose (2007) focused on two palm species with different flowering periods on an oceanic island and showed that speciation between these two species could occur in a relatively wide parameter range based on individual-based simulation that was tailored to the palm species. Another study by Van Dijk and Bijlsma (1994) considered a case in which two species have different flowering periods and their hybrids are unviable, both of which prevent gene flow between these species. Although the above studies provided important insight into the effect of the flowering period on speciation, they did not consider one important pollination process that would occur between diurnally and nocturnally flowering species: pollen export from early- to late-flowering flowers. If two flower species have different flowering times in one day, pollinators that visited the early flowering flowers can fertilize the late-flowering flowers using pollen from the early-flowering flowers. Recently,

Matsumoto et al. (2013) theoretically examined the effectiveness of the difference in one-day flowering time as a reproductive isolation mechanism. Their results strongly suggested that pollen export from early- to late-flowering flowers greatly increases the fitness of early flowering and makes the maintenance of the two different flowering times more difficult. Considering that the pollen export from early- to late-flowering flowers occurs in natural populations, we incorporate this fertilization process to accurately evaluate the possibility of the evolution of a nocturnally flowering species. In this study, we theoretically examine under what conditions the evolution of a nocturnally flowering species from a diurnally flowering ancestor can occur. We introduce a model incorporating pollen flow from early to late flowering flowers and four isolating barriers: difference in flowering time, difference in pollinator preference to the attractive trait, geographic separation and reduced hybrid viability. Geographic separation and reduced hybrid viability have been thought to be important reproductive isolation mechanisms that cause speciation (Coyne and Orr, 2004; Gavrilets, 2004) and therefore can have significant effects on the probability of the evolution of a nocturnally flowering species. Moreover, because two loci primarily determine the flowering time in Hemerocallis (Nitta et al., 2010), we also incorporated this genetic feature into the model. To simplify our model, we assumed fertilization always succeeds when pollination occurs. As a result, our model does not include postmating, prezygotic isolation barriers (e.g., difference in pollen tube growth). We also assume that only one attractive trait is regulated by one locus based on the study of Petunia species (Hoballah et al., 2007). Under this model, we carried out individual-based simulations and investigated the conditions under which a nocturnally flowering species evolves from a diurnally flowering species by varying the intensities of these four isolating barriers. Then, we discuss the possibility of the evolution of a nocturnally flowering species, such as H. citrina, from a diurnally flowering species, such as H. fulva, as a special case of this model. We focus on the evolution of phenotypes that are specific to nocturnally flowering species, which causes premating isolation as observed during the initial stage of speciation rather than on the establishment of subsequent postmating isolation. Therefore, we do not use the term “speciation”, and if these phenotypes evolved, we state that the evolution of a nocturnally flowering species has occurred.

2. Model for simulation To evaluate the effects of the four isolating factors (difference in flowering time, difference in pollinator preference to the attractive trait, geographic separation and reduced hybrid viability) on the evolution of the nocturnally flowering species, we consider two populations, population 1 and population 2, initially consisting of only diurnally flowering species. Some geographic distance, which determines the migration rate defined later, separates the two populations. Two types of pollinators (diurnal pollinators, such as butterflies or bees, and nocturnal pollinators, such as moths or bats) visit each population. The two plant species are annual and diploid with discrete generations. Each individual plant has one flower. In the following sections, we explain the details of the model that was used in this study. 2.1. Major assumptions In this section, we explain two important assumptions concerning the genetic models of the two traits, flowering time and an attractive trait that causes the preferential visitation of pollinators. The first assumption concerns the number of loci regulating each trait. We assume that two loci, each with two alleles, control


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the flowering time (duration between flower opening time and flower closing time) based on the results of Nitta et al. (2010). We also assume that another locus with two alleles determines the phenotype of the attractive trait. Such a single-locus control of an attractive trait is found in diurnally and nocturnally flowering species in Petunia (Hoballah et al., 2007). Levels of pollinator preference may vary among pollinators and plant species (Hoballah et al., 2007; Hirota et al., 2012). For example, in the case of H. fulva and H. citrina, butterflies strongly prefer a reddish flower, but hawkmoths weakly prefer a yellowish flower (Hirota et al., 2012). We parameterize this feature into the model, as described later. We assume that there is free recombination between any pair of the three loci. The second assumption concerns the phenotypes of flowering time. We divide a day into three phases: phase 1, phase 2 and phase 3, representing daytime, evening and nighttime, respectively. The lengths of phases 1, 2 and 3 are t1, t2 and t3, respectively, and the sum of these lengths is assumed to be 24 h based on observations of Nitta et al. (2010) that H. fulva, H. citrina and their hybrids exhibit three phenotypes concerning flowering time. The phenotype OmCe (an acronym of Open morning Close evening) opens at the beginning of phase 1 and closes at the end of phase 2, phenotype OeCm opens at the beginning of phase 2 and closes at the end of phase 3, and phenotype OeCe opens at the beginning of phase 2 and closes at the end of phase 2 of the following day (Fig. 1). Thus, the plants of the last phenotype flower during all three phases. In phase 2, all of the flowers are flowering; thus, as the length of phase 2 (t2) decreases, isolation by the flowering time becomes stronger. Nitta et al. (2010) also reported differences in the flowering time among F1 hybrid plants even though these plants have the same genotype, as well as among flowers within an F1 or F2 hybrid plant. The ratio of the three phenotypes in the F1 population differs from that in the F2 population. Although the underlying mechanism for such phenotypic plasticity is currently unknown, this plasticity needs to be considered in the modeling. To incorporate phenotypic plasticity, we assume that the diurnally and nocturnally flowering species have phenotypes OmCe and OeCm, respectively, and that each individual with the hybrid genotype exhibits one of the three phenotypes with a fixed probability. Under this model, both diurnally and nocturnally flowering species flower during phase 2 and produce hybrids as in the case of H. fulva and H. citrina.

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Table 1 Relationship between 9 genotypes and 3 phenotypes for flowering time.

O1O1C1C1 O1O1C1C2 O1O1C2C2 O1O2C1C1 O1O2C1C2 O1O2C2C2 O2O2C1C1 O2O2C1C2 O2O2C2C2

OmCe

OeCm

OeCe

1 p2 p2 p2 p1 p2 p2 p2 0

0 q2 q2 q2 q1 q2 q2 q2 1

0 1 (p2 þq2) 1 (p2 þq2) 1 (p2 þq2) 1 (p1 þq1) 1 (p2 þq2) 1 (p2 þq2) 1 (p2 þq2) 0

O2O2C2C2 and O1O2C1C2 exhibit flowers with an OmCe, OeCm or OeCe phenotype with probabilities of p2, q2 and 1 (p2 þ q2), respectively. The flowering times of all of the genotypes are shown in Table 1.

2.3. Genetics of an attractive trait and pollinator preference Assume that the diurnally flowering species has the genotype A1A1 and that the nocturnally flowering species has the genotype A2A2. Each genotype produces an alternative phenotype of the attractive trait, and two types of pollinators exhibit different preferences for each phenotype. We assume that diurnal pollinators prefer flowers with genotypes A1A1, A1A2 and A2A2 with preferences 1, 1 h1X1 and 1 X1, respectively, and that nocturnal pollinators prefer flowers with genotypes A1A1, A1A2 and A2A2 with preferences 1 X2, 1 h2X2 and 1, respectively. The parameters X1 and X2 determine the level of the preference (0 r X1, X2 r 1) to a specific phenotype of the attractive trait, and h1 and h2 represent the degrees of dominance (0 rh1, h2 r1). Thus, as X1 and X2 increase, pollinators become more selective to a specific phenotype (the level of pollinator preference becomes stronger), and as h1 and h2 increase, heterozygotes becomes less preferred. In our simulation, pollinators do not change their preference in each run, and only the genotype of the flower's attractive trait determines how strongly diurnal and nocturnal pollinators prefer the flower.

2.2. Genetics of flowering time

2.4. Viability of each genotype

Assume that the diurnally flowering species has genotype O1O1C1C1 exhibiting phenotype OmCe and that the nocturnally flowering species has genotype O2O2C2C2 exhibiting phenotype OeCm. The F1 hybrids therefore have genotype O1O2C1C2, and we assume that their flowers exhibit the OmCe, OeCm or OeCe phenotype with probabilities of p1, q1 and 1 (p1 þq1), respectively. We assume that the F2 genotypes excluding O1O1C1C1,

Although the viability of adult plants has not been systematically measured in Hemerocallis or its hybrids, hybrid seeds have reduced germination rates (Yasumoto, personal communication). Previously, Zhang et al. (2007) reported that the increased expression of genes that are involved in the circadian clock decreased the germination rate of seeds in Arabidopsis. In addition, De Montaigu et al. (2010) reported that the genes that are involved in the circadian clock affect many aspects of the life cycle, including reproduction and susceptibility to disease. Therefore, in this study, we assume that unstable flowering times of hybrids reduce their viability and set the viability v of hybrid genotypes of the flowering time as r1 and that of the other genotypes as 1. As the hybrid viability is reduced, the levels of gene flow between the diurnally and nocturnally flowering species decreased.

phase1 daytime

phase2

phenotype OmCe phenotype OeCm phase3 nighttime

phenotype OeCe

Fig. 1. Flowering times of three phenotypes within one day. Phenotype OmCe flowers from the beginning of phase 1 to the end of phase 2. OeCm flowers from the beginning of phase 2 to the end of phase 3. OeCe flowers from the beginning of phase 2 on one day to the end of phase 2 on the following day.

2.5. Mutation model We assume a reversible mutation model at the three loci O, C and A. The mutation rate is the same in both directions at all three loci and is designated with u.


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2.6. Pollinator behavior and geographic isolation At the beginning of a generation, there are Ndi diurnal and Nni nocturnal pollinators in population i (i¼ 1, 2). The diurnal pollinator initiates its activity in the morning (beginning of phase 1) and ends it in the evening (end of phase 2), whereas the nocturnal pollinator initiates its activity in the evening (beginning of phase 2) and ends it in the morning (end of phase 3). We assume that each pollinator moves independently to another flower at the fixed rate a per hour. In the simulation, we divide the time into short intervals (1/100 h) so that the probability of more than one pollinator moving in the same interval is very small. Thus, each pollinator moves at a fixed rate, a/100 per time step. The migration rate m measures the level of geographic separation. When a move occurs, it is to the same population or to the other population with a probability of 1–m or m, respectively. If m ¼0.5, the two populations become completely sympatric, and as m decreases, the geographic separation becomes stronger. The flower to which a pollinator moves depends on the attractive trait phenotype that is expressed by the flower and that is determined by its genotype as explained in Genetics of an attractive trait and pollinator preference. In a move, each pollinator is assumed to encounter the flowers in the population in a random order without replacement. A pollinator visits an encountered flower with a probability that is equal to the absolute value of the pollinator preference to the attractive trait of the flower. For example, when a nocturnal pollinator encounters an A1A1 flower, the probability of a visitation is 1 X2, and when a nocturnal pollinator encounters an A2A2 flower, a visitation always occurs with a probability of 1. This encountering process within a move is continued until the pollinator visits a flower or until the pollinator encounters all of the flowers in the populations without any visitation. Thus, if pollinator preference is less than 1 for all of the flowers in the population, the pollinator may be unable to visit any flower. Considering the observation by Hobbalah et al. (2007) that hawkmoths never visited non-preferred reddish Petunia integrifolia during the period when only this flower was flowering, this assumption would be more realistic than employing the relative value of pollinator preference as the visitation probability. 2.7. Pollen deposition and fertilization process in a day As explained in the Introduction, we equate a success of pollination (pollen deposition into the stigma) with a success of fertilization. Thus, flowers are always fertilized by the pollen that is carried and deposited by the first pollinator. During a visitation, pollen removal always occurs, and the visiting pollinator completely replaces the attached pollen to new pollen of the present flower. Therefore, a flower can experience pollen deposition only once, but its pollen can be carried by pollinators multiple times. The deposited (fertilized) flower produces b seeds. The genotype of a seed is determined by the random sampling of one gamete each from its mother plant (pollen recipient) and father plant (pollen donor). 2.8. Fertilization process in one generation Let g be the number of days in the flowering period per generation. Each flower of the plants flowers for only one day, as shown in Fig. 1, and its flowering day is determined randomly within the flowering period. On each flowering day, the one-day fertilization process that is explained in the previous section occurs. Note that the time span separating two consecutive flowering periods is long (approximately one year if g is short). Previously, Dafni and Firmage (2000) reported that the pollen of many flowering plants can survive only for several days. Thus, we

assume discrete generation and that pollen grains can survive within one generation but cannot survive across generations. Therefore, at the beginning of each generation, no pollinator carries any surviving pollen grain, and only pollen removal occurs on the first visitation. We assume that the pollen that is attached to a pollinator at the last visitation of a day is not removed at the beginning of the next day. Therefore, in our model, the pollen export from nighttime-flowering flowers to daytime-flowering flowers in later days also occurs. However, daytime-flowering flowers would still have an advantage as discussed by Matsumoto et al. (2013) because on the first day of each generation, only pollen export from daytime-flowering flowers to nighttime-flowering flowers occurs. After the fertilization process in one generation, all of the seeds are subject to natural selection. If a seed has a hybrid genotype of the flowering time, its viability after germination is reduced (reduced hybrid viability (v)), and the surviving seeds form the parental populations of the next generation (we assume discrete generations). Exactly following the model explained above, we conducted individual-based simulation to evaluate the effects of four isolating barriers on the probability of the evolution of the nocturnally flowering species. We begin the simulation from two initial plant populations consisting of only the diurnal flowering species and two initial pollinator populations, whose constituent proportions will be described later. All of the parameters that are used in the model are listed in Table 2. The program is written in C and is available from TM upon request.

3. Results In the simulations, we observed the number of each genotype after 10,000 generations, and if the numbers of diurnally flowering species (O1O1C1C1A1A1) and nocturnally flowering species (O2O2C2C2A2A2) genotypes were both greater than the total number of hybrid genotypes, we considered the evolution of the nocturnally flowering species to have been achieved. Because of the large number of parameters, we first investigated the effects of four isolating factors (difference in flowering time, difference in pollinator preference to the attractive trait, geographic separation and reduced hybrid viability) that would have important effects on the probability of the evolution of the nocturnally flowering species using fixed values for the other parameters. The effects of the other parameters were examined later. The parameters whose values were fixed are degrees of dominance for the attractive traits (h1 ¼ h2 ¼0.5); the numbers of diurnal and nocturnal pollinators (Nd1 ¼ Nn1 ¼Nd2 ¼Nn2 ¼ 5); the pollinator movement rate (a¼ 0.1, as estimated from the results of Hirota et al. (2012)); the number of seeds per flower (b¼ 10, K. Table 2 Parameters used in this study. v m p1, q1 p2, q2 X1 X2 h1, h2 Nd1 Nn1 Nd2 Nn2 a N g

Hybrid viability Migration rate Phenotypic proportion of F1 hybrids Phenotypic proportion of F2 hybrids Strength of the preference of the diurnal pollinator Strength of the preference of the nocturnal pollinator Degree of dominance for the attractive trait Number of diurnal pollinators in population 1 Number of nocturnal pollinators in population 1 Number of diurnal pollinators in population 2 Number of nocturnal moths in population 2 Moving rate of a pollinator per unit time Number of flowers in one population Flowering period per one generation


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Table 3 Estimates of the average probability of the evolution of the nocturnally flowering species with their standard errors when lengths of phase1, phase2, phase3 (t1, t2, t3) and phenotypic proportion of hybrids (p1, p2, q1, q2) are changed. t1, t2, t3

Phenotypic proportion of hybrids

Probability of the evolution

8, 8, 8

p1 ¼ p2 ¼ 1, q1 ¼q2 ¼0 p1 ¼ p2 ¼ 0.9, q1 ¼ q2 ¼ 0.05 p1 ¼ p2 ¼ 0.33, q1 ¼ q2 ¼ 0.33 p1 ¼ p2 ¼ 0.05, q1 ¼ q2 ¼ 0.99 p1 ¼ p2 ¼ 0, q1 ¼ q2 ¼1

0.00027 0.0001 0.0081 7 0.0001 0.01897 0.0002 0.0226 7 0.0002 0.0226 7 0.0001

11, 2, 11


0.00017 0.0001 0.00057 0.0001 0.0328 7 0.0002 0.07857 0.0005 0.0905 7 0.0005

12, 0, 12


0.00017 0.0001 0.0023 7 0.0002 0.06787 0.0.0005 0.20067 0.0.0008 0.24247 0.0.0006

Nitta, personal observation) and the mutation rate (u¼ 10 5). Hotta et al. (1984) suggested that the flowering season of H. fulva and H. citrine peaks in early and middle July. Thus, we set the flowering period as one week (g ¼7). We calculated the probability of the evolution of the nocturnally flowering species by changing the values of t1, t2, and t3 (the length of each phase); p1, p2, q1, and q2 (the phenotypic proportions of hybrids); v (hybrid viability); m (the migration rate); X1 (preference of the diurnal pollinator); and X2 (preference of the nocturnal pollinator). 3.1. Effect of flowering time Table 3 shows the probability of the evolution of the nocturnally flowering species under three parameter sets for the length of the overlapping time (t2)—(1) t1 ¼t2 ¼t3 ¼8; (2) t1 ¼t3 ¼11 and t2 ¼2; and (3) t1 ¼t3 ¼12 and t2 ¼0—and five sets for the phenotypic proportions of hybrids—(1) p1 ¼p2 ¼1 and q1 ¼q2 ¼0; (2) p1 ¼p2 ¼ 0.9 and q1 ¼q2 ¼0.05; (3) p1 ¼ p2 ¼ 0.33 and q1 ¼q2 ¼0.33; (4) p1 ¼ p2 ¼0.05 and q1 ¼q2 ¼0.9; and (5) p1 ¼ p2 ¼0 and q1 ¼ q2 ¼1. For each combination of the parameter values, we changed the values of v (hybrid viability, 0–1 incremented by 0.1), m (the migration rate, 0, 0.001, 0.01, 0.1 and 0.5), and X1 and X2 (the levels of pollinator preferences, 0–1 incremented by 0.2). We replicated the simulation 10 times for each parameter set and averaged the probabilities of the evolution of the nocturnally flowering species for different values of the parameters v, m, X1 and X2. A decrease in the length of phase 2 increased the probability of the evolution of the nocturnally flowering species (Table 3), most likely because a reduction of the overlap of the flowering time decreased the gene flow between species. The probability of the evolution of the nocturnally flowering species also increased as the probabilities (q1 and q2) of the hybrids having nighttime flowering increased. 3.2. Effects of reduced hybrid viability, migration rates and pollinator preference Next, we examined the effects of reduced hybrid viability, migration rates and levels of pollinator preferences. Fig. 2 shows the probability of the evolution of the nocturnally flowering species as associated with different hybrid viabilities and migration rates in (A) m ¼ 0 and (B) m ¼ 0.5 with t1 ¼t3 ¼ 12 and t2 ¼0, and p1 ¼p2 ¼ 0 and q1 ¼q2 ¼1. First, the evolution of the nocturnally flowering species occurred with a high probability under intermediate hybrid viability conditions (v¼ 0.3 and 0.5). As noted above, if hybrid viability is sufficiently high,

Fig. 2. Effects of hybrid viability (v), migration rate (m) and the preferences of the diurnal pollinator (X1) and nocturnal pollinator (X2) on the evolution of the nocturnally flowering species that are associated with t1 ¼t3 ¼ 12, t2 ¼ 0. We assumed that Nd1 ¼ Nn1 ¼ Nd2 ¼Nn2 ¼5, h1 ¼h2 ¼ 0.5 and u ¼10 5. (A) and (B) show the results with m¼ 0 and 0.5, respectively. For each parameter set, the simulation was replicated 10 times, and the probability of the evolution of the nocturnally flowering species in each parameter set is shown in grayscale.

hybrids may have a higher fitness than nocturnally flowering species because their flowers may exhibit a longer flowering time (phenotype OeCe). In that case, hybrid genotypes increase in the population. However, as the hybrid viability decreases, the fitness difference between the hybrids and the nocturnally flowering species becomes smaller and even negative. Then, the frequency of the nocturnally flowering species in the hybrid population increases, and the probability of the evolution of the nocturnally flowering species also increases. Nevertheless, if hybrid viability is too low, the reduction of fitness in hybrids makes it difficult for the initial increase in hybrids to occur, and the probability of the evolution of the nocturnally flowering species consequently decreases. Second, the effect of migration was smaller than that of hybrid viability, although the probability of the evolution of nocturnally flowering species increased slightly when the migration rate was high. This result was somewhat counterintuitive but may be explained as follows: for the evolution of the nocturnally flowering species to occur, their frequency needs to be sufficiently high in one population or intermediate in both populations. Although a low migration rate would increase the probability of the former scenario, it impedes the invasion of the nocturnally flowering species to the other population and reduces the probability of the latter scenario. In supplementary Fig. 1, we show the results when m ¼0.001 and m ¼0.01. These results also suggest the weak effects of the migration rate on the evolution of the nocturnally flowering


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species. When m ¼0.1, the result was almost the same as that in m ¼0.5 (data not shown). The importance of intermediate hybrid viability and weak effects of the migration rate on the evolution of the nocturnally flowering species was similarly observed in the cases with other values of the flowering times (t1, t2 and t3) and phenotypic proportions of hybrids (p1, p2, q1 and q2) (data not shown). Third, a stronger pollinator preference (high X2 and X2) increased the probability of the evolution of the nocturnally flowering species by promoting the maintenance of both species. However, if the preference of the nocturnal pollinators (X2) is too strong, their probability of visiting flowers with genotype A1A1 becomes very low, and thus hybrid flowers exhibiting nighttime flowering but without the attractive trait that is preferred by the nocturnal pollinators may not be visited by these pollinators until the allele A2 emerges in these hybrids. Therefore, the evolution of the nocturnally flowering species becomes difficult, which explains why the probability of the evolution of the nocturnally flowering species decreased when X2 ¼0.8 and 1. However, as the length of phase 2 increased, the number of visits to hybrids with phenotype OeCm by the diurnal pollinator increased during phase 2. Thus, the probability of the evolution of the nocturnally flowering species was not small, even when X2 approached 1 when t1 ¼t3 ¼ 11, t2 ¼2 and t1 ¼t2 ¼ t3 ¼8. An example of the effect of the level of pollinator preference with overlapping flowering times will be shown later for Hemerocallis. As shown in Fig. 2, there was an interaction between the effect of hybrid viability and the level of pollinator preference on the evolution of a nocturnally flowering species. If the hybrid viability was low (vr 0.5), the probability of the evolution of a nocturnally flowering species largely depended on the preference of the nocturnal pollinator (X2). If the preference of the nocturnal pollinator was not too strong (X2 ¼0.2 0.6 in Fig. 2), the evolution of the nocturnally flowering species was possible with a high probability, regardless of the diurnal pollinator preference (X1). If the hybrid viability was high (v 40.5), strong preferences of diurnal and nocturnal pollinators were required for the evolution of the nocturnally flowering species. 3.3. Effect of the degree of dominance in the attractive trait Thus far, we assumed no dominance for the attractive trait (h1 ¼ h2 ¼0.5). Next, we examine the effects of relaxing this assumption. Table 4 shows the probability of the evolution of a nocturnally flowering species in three cases of the degree of dominance. The difference between the probabilities of the evolution of a nocturnally flowering species in the two extreme cases h1 ¼h2 ¼ 0 and h1 ¼h2 ¼1 was small (Table 4). We also found that effects of other parameters, such as v, X1 and X2, on the evolution of a nocturnally flowering species were almost the same in all three cases of the degree of dominance (data not shown). From these results, the degree of dominance of the attractive trait appears to have only a small effect on the evolution of the nocturnally flowering species compared to the other factors that were examined above. 3.4. Timing of the evolution of new traits The evolution of a nocturnally flowering species requires the evolution of two traits, nighttime flowering and the new attractive trait. We investigated which trait, nighttime flowering or the new attractive trait that is preferred by nocturnal pollinators, evolved first. We calculated the average frequencies of the corresponding genotypes among 10 cases in which the evolution of a nocturnally flowering species was achieved. In most of the cases, the evolution of a nocturnally flowering species was initiated by the evolution of

Table 4 Estimates of the average probability of the evolution of the nocturnally flowering species with their standard errors with different phenotypic proportions of hybrids (p1, p2, q1, q2) and degrees of dominance in the attractive trait (h1 and h2) when t1 ¼ t3 ¼12, t2 ¼ 0. Phenotypic proportions of hybrids

Degree of dominance


p1 ¼ p2 ¼1, q1 ¼ q2 ¼0

h1 ¼ h2 ¼ 0 h1 ¼ h2 ¼ 0.5 h1 ¼ h2 ¼ 1

0.00017 0.0001 0.00017 0.0001 0.00047 0.0001

p1 ¼ p2 ¼0.9, q1 ¼ q2 ¼ 0.05

h1 ¼ h2 ¼ 0 h1 ¼ h2 ¼ 0.5 h1 ¼ h2 ¼ 1

0.00017 0.0001 0.0022 7 0.0002 0.01167 0.0001

p1 ¼ p2 ¼0.33, q1 ¼q2 ¼ 0.33

h1 ¼ h2 ¼ 0 h1 ¼ h2 ¼ 0.5 h1 ¼ h2 ¼ 1 h1 ¼ h2 ¼ 0 h1 ¼ h2 ¼ 0.5 h1 ¼ h2 ¼ 1

0.04817 0.0005 0.06787 0.0005 0.07067 0.0003 0.1939 7 0.0006 0.20067 0.0008 0.20707 0.0006

h1 ¼ h2 ¼ 0 h1 ¼ h2 ¼ 0.5 h1 ¼ h2 ¼ 1

0.24177 0.0004 0.24247 0.0006 0.24547 0.0007

p1 ¼ p2 ¼0.05, q1 ¼ q2 ¼ 0.9

p1 ¼ p2 ¼0, q1 ¼ q2 ¼ 1

nighttime flowering, suggesting the importance of this trait (Fig. 3). However, in the t1 ¼ t2 ¼t3 ¼ 8 case, the new attractive trait evolved earlier (Supplementary Fig. 2). In summary, four traits were important for the evolution of a nocturnally flowering species: a short overlap of the flowering times of the diurnally and nocturnally flowering species (small t2), a high probability of hybrid genotypes flowering at night (large q1 and q2), intermediate hybrid viability (v), intermediate preference of the nocturnal pollinator (X2) when hybrid viability is low, and strong preference of diurnal and nocturnal pollinators (X1 and X2) when hybrid viability is high. Next, we applied our model to a pair of diurnally and nocturnally flowering species, Hemerocallis fulva and H. citrina. As previously mentioned, the flowering time is controlled by two loci in H. fulva and H. citrina (Nitta et al., 2010). Thus, we can apply our model to study the evolution of the nocturnally flowering species H. citrina using the estimates of some of the parameters that were obtained in the species pair. 3.5. Parameter values in Hemerocallis In Hemerocallis, we set the lengths of the three phases as t1 ¼12, t2 ¼ 2 and t3 ¼10 based on the data from Hasegawa et al. (2006). The phenotypic proportions of the F1 and F2 hybrids were also estimated from the data of Nitta et al. (2010) as well as unpublished data (Supplementary Table 1). Using the data that are shown in Supplementary Table 1, we estimated that p1 ¼0.65 and q1 ¼0.25, and p2 ¼0.38 and q2 ¼ 0.2, assuming free recombination between loci O and C. The pollinator movement rate (a ¼0.1), the number of seeds per flower (b¼ 10) and the flowering period (g ¼7) were estimated from these Hemerocallis species (see above). As the dominance of the attractive trait did not have much effect, we set h1 ¼h2 ¼0.5. With this set of known parameter values, we examined the conditions under which the evolution of the nocturnal H. citrina was possible. 3.6. Effects of the mutation rate and the number of pollinators in Hemerocallis Tables 5 and 6 show the probability of the evolution of a nocturnally flowering species when the mutation rate, total number of pollinators, and pollinator proportion varied. In each population, we considered three mutation rates: u ¼10 4, u ¼10 5


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900 800

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700 600 500 400 300 200 100

0

00

00 10

75

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00

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7

generation the diurnally flowering species hybrids with new attractive trait

hybrids with nighttime flowering the nocturnally flowering species

Fig. 3. The time course of the four genotypes, the diurnally flowering species, and the nocturnally flowering species, hybrids with nighttime flowering having the original attractive trait (“hybrids with nighttime flowering” with genotype —A2A2) and hybrids with daytime flowering having the new attractive trait (“hybrids with new attractive trait” with genotype O1O1C1C1–). We chose 10 cases in which the evolution of the nocturnally flowering species was achieved. We assume that Nd1 ¼ Nn1 ¼Nd2 ¼Nn2 ¼ 5, u¼ 10 5 and h1 ¼h2 ¼0.5. The chosen cases are as follows: 10 v¼ 0.4, X1 ¼ 0.8, X2 ¼0.8, m¼0.5, t1 ¼ t3 ¼ 11, t2 ¼ 2, p1 ¼p2 ¼0.33, and q1 ¼q2 ¼ 0.33; (2) v¼0.5, X1 ¼1.0, X2 ¼0.8, m¼ 0, t1 ¼ t3 ¼ 11, t2 ¼ 2, p1 ¼p2 ¼ 0.33, and q1 ¼ q2 ¼0.33; (3) v¼ 0.3, X1 ¼ 0.6, X2 ¼ 0.6, m¼ 0, t1 ¼ t3 ¼11, t2 ¼2, p1 ¼ p2 ¼0.05 and q1 ¼ q2 ¼ 0.9; (4) v¼ 0.6, X1 ¼ 1.0, X2 ¼0.8, m¼0.5, t1 ¼t3 ¼ 11, t2 ¼2, p1 ¼ p2 ¼ 0.05, and q1 ¼q2 ¼0.9; (5) v ¼0.3, X1 ¼ 0.2, X2 ¼ 0.4, m¼ 0.1, t1 ¼ t3 ¼ 11, t2 ¼ 2, p1 ¼p2 ¼ 0, and q1 ¼ q2 ¼ 1; (6) v¼ 0.5, X1 ¼ 0.6, X2 ¼ 0.8, m ¼0.5, t1 ¼t3 ¼ 11, t2 ¼2, p1 ¼p2 ¼ 0, and q1 ¼ q2 ¼ 1; (7) v¼ 0.5, X1 ¼ 0.4, X2 ¼ 0.4, m¼ 0.001, t1 ¼t3 ¼12, t2 ¼0, p1 ¼ p2 ¼ 0, and q1 ¼q2 ¼ 1; (8) v¼ 0.7, X1 ¼ 0.8, X2 ¼ 0.8, m¼ 0.1, t1 ¼ t3 ¼ 12, t2 ¼0, p1 ¼ p2 ¼0.05, and q1 ¼ q2 ¼ 0.9; (9) v¼ 0.3, X1 ¼0.2, X2 ¼ 0.2, m¼ 0.5, t1 ¼ t3 ¼ 12, t2 ¼0, p1 ¼ p2 ¼0.33, and q1 ¼q2 ¼ 0.33; and (10) v¼ 0.5, X1 ¼ 1, X2 ¼ 1, m¼ 0, t1 ¼ t2 ¼ t3 ¼8, p1 ¼ p2 ¼0, and q1 ¼ q2 ¼1. In these 10 cases, we calculated the mean and standard error of the above four genotypes and plotted them against the generation.

Table 5 Estimates of the average probability of the evolution of the nocturnally flowering species with their standard errors with different mutation rates (u) and total numbers of pollinators when Nd1: Nn1: Nd2: Nn2 ¼5: 5: 5: 5 in the Hemerocallis case.

Table 6 Estimates of the average probability of the evolution of the nocturnally flowering species with their standard errors with different mutation rates (u) and total numbers of pollinators when Nd1:Nn1:Nd2:Nn2 ¼ 7:3:3:7 in the Hemerocallis case.

u

Total number of pollinators


u

Total number of pollinators


10 4

4 10 20

0.0137 70.0002 0.0683 70.0003 0.1018 70.0005

10 4

4 10 20

0.0534 7 0.0008 0.0899 7 0.0004 0.11237 0.0004

10 5

4 10 20

0.0008 70.0001 0.0276 70.0003 0.0485 70.0001

10 5

4 10 20

0.01297 0.0002 0.04337 0.0003 0.06107 0.0004

10 6

4 10 20

0.0000 70.0000 0.0014 70.0002 0.0084 70.0002

10 6

4 10 20

0.00017 0.0001 0.0023 7 0.0001 0.0099 7 0.0002

and u¼ 10 6; and three values for the total number of pollinators (diurnal þnocturnal): 4, 10 and 20. The initial pollinator proportions Nd1: Nn1: Nd2: Nn2 were 5: 5: 5: 5 (Table 5) and 7: 3: 3: 7 (Table 6; if the total number was 4, we set Nd1 ¼ Nn2 ¼3 and Nd2 ¼Nn1 ¼ 1). As the mutation rate or the total number of pollinators increased, the probability of the evolution of a nocturnally flowering species increased. Asymmetry in the numbers of pollinators within a population (7: 3: 3: 7 case) increased the probability of the evolution of a nocturnally flowering species slightly but significantly (Table 6) because the nocturnally flowering species has a greater fitness advantage in the population with more nocturnal pollinators and is likely to increase in number under these conditions. This tendency was more pronounced when the migration rate was low (Supplementary Fig. 3). 3.7. Effects of three isolating factors in Hemerocallis Next, we examined the effects of hybrid viability, migration rate and pollinator preference assuming Nd1 ¼ Nn1 ¼Nd2 ¼Nn2 ¼ 5 and u ¼10 4. Fig. 4 and supplementary Fig. 4 show the probability of the evolution of a nocturnally flowering species when hybrid viability, the migration rate and the level of pollinator preference varied. As in Fig. 2, the probability of the evolution of a nocturnally flowering species was high when the hybrid viability was

intermediate and the migration rate was high. For pollinator preference, in contrast to the case that is shown in Fig. 2, an overlapping flowering time made the evolution of a nocturnally flowering species possible with a high probability even when X2 ¼1. Fig. 4 also shows that the effects of X1 and X2 are almost the same in Hemerocallis. As previously explained, the differences between the results that are shown in Figs. 2 and 4 resulted because the overlap of flowering times in the Hemerocallis case increased the gene flow between the diurnally and nocturnally flowering species and consequently increased the importance of isolation by strong pollinator preference for the maintenance of the two species. We found similar results in the cases of two other mutation rates, u ¼10 5 and u ¼10 6, although a reduction of the mutation rate generally decreased the probability of the evolution of the nocturnally flowering species (data not shown). 3.8. Effects of changes in the pollinator movement rate, flowering period and number of seeds in Hemerocallis Finally, we examined how changes in the other parameters, pollinator movement rate a, flowering period g and the number of seeds b would affect the conclusions, assuming u¼ 10 4 and Nd1 ¼Nn1 ¼Nd2 ¼Nn2 ¼ 5, and we briefly summarize the results below.


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evolution of a nocturnally flowering species increased as the pollinator movement rate increased because there was no gene flow in phase 2 (data not shown). Finally, we examined the effects of the number of seeds (b) by setting b ¼5 and 20 and computed the ratios of the probability of the evolution of the nocturnally flowering species to that assuming b ¼10. The ratios of the probabilities with b¼5 and 20 to those with b¼ 10 were 0.15 and 1.21, respectively. In summary, the importance of intermediate hybrid viability and strong pollinator preference for the evolution of a nocturnally flowering species was also observed in Hemerocallis. We also identified another important factor, a large number of mutants in one generation, that can be realized through high mutation rates, a large number of pollinators, high movement rates of the pollinator, a long flowering period or a large number of seeds. This observation will be discussed more fully later.

4. Discussion

Fig. 4. Effects of hybrid viability (v), migration rate (m) and the preferences of the diurnal pollinator (X1) and nocturnal pollinator (X2) on the evolution of the nocturnally flowering species in Hemerocallis. We assumed that Nd1 ¼Nn1 ¼ Nd2 ¼ Nn2 ¼ 5, h1 ¼ h2 ¼ 0.5 and u¼10 4. (A) and (B) show the results with m¼0 and 0.5, respectively. For each parameter set, the simulation was replicated 10 times, and the probability of the evolution of the nocturnally flowering species in each parameter set is shown in grayscale.

First, we assumed the flowering period to be 7 (g¼ 7) in the simulation. Considering the observed flowering period of H. fulva and H. citrina (Hotta et al., 1984), we also examined the case of g ¼14. The probability of the evolution of a nocturnally flowering species when g ¼14 was 2.25 times that when g ¼7. Second, we used a ¼0.1 in the simulation. This value does not differ much from the estimate obtained by Hirota et al. (2012), but we also examined three other cases, a ¼0.05, 0.2 and 0.5. The ratios of the probability of the evolution of a nocturnally flowering species in these three cases to that under a ¼0.1 were 0.15, 1.63 and 0.62, respectively. When the pollinator movement rate is low, the probability of the evolution of a nocturnally flowering species decreases because the population sizes of the plants and consequently the number of new mutations appearing in one generation decrease. We provide a more detailed discussion about the effects of population size on the probability of the evolution of a nocturnally flowering species later. In contrast, a high pollinator movement rate causes an increase in the population sizes of the plants, increasing the probability of the evolution of a nocturnally flowering species. However, if the pollinator movement rate is too high, the probability of the evolution of a nocturnally flowering species decreases, most likely because gene flow increased during phase 2. This decrease did not occur when there was no overlap in the flowering time (t2 ¼0). In this case, the probability of the

In this study, we conducted individual-based simulations and examined whether the evolution of a nocturnally flowering species could occur from a diurnally flowering ancestor. Our results suggest that the evolution of a nocturnally flowering species could occur with high probabilities with intermediate hybrid viability and the existence of pollinator preference. This result suggests that the difference in flowering time alone was not sufficient to cause the evolution of a nocturnally flowering species. However, as shown in Fig. 3, the evolution of a nighttime flowering could induce the subsequent evolution of a new attractive trait and thereby trigger the evolution of a nocturnally flowering species. We also found that a large number of mutations in one generation as caused, for example, by a large number of pollinators or high rates of pollinator movement were important for the evolution of a nocturnally flowering species. Below, we discuss how each factor affects the evolution of the nocturnally flowering species separately. 4.1. Importance of the number of mutations in one generation The number of mutations in one generation is regulated by the population size of plants and the mutation rate. In our simulation, the population size of plants was not explicitly controlled. However, as shown in Supplementary Fig. 5, the population size increases with the number of pollinators. In fact, the plant population size is expected to be approximately proportional to (flowering time) a (number of pollinators) b g if we ignore viability differences. Therefore, if we change any of these parameters (flowering time, a; number of pollinators, b; flowering period, g), the plant population size changes. Generally, as the population size increased, the probability of the evolution of a nocturnally flowering species increased because it increased the number of mutations in one generation at the loci controlling the flowering time and the attractive trait, thus increasing the chance of the appearance of a mutation that can later increase in the population. This pattern is seen in our results, showing positive correlations of the probability of the evolution of a nocturnally flowering species with the mutation rate, number of pollinators, seeds per plant (b) and flowering period (g) (see Tables 5, 6 and Effects of changes in pollinator movement rate, flowering period and number of seeds in Hemerocallis). On the other hand, if the rate of pollinator movement is too high (a¼0.5), the probability of the evolution of a nocturnally flowering species decreased even though population size increased in this case because an increase in a also increases the gene flow in phase 2. Thus, if the rate of pollinator movement is too high, the positive effect of an


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increase in mutations on the probability of the evolution of a nocturnally flowering species appears to be cancelled by the negative effect of increased gene flow. 4.2. Nighttime flowering as a magic trait Traits with pleiotropic effects on both natural selection and assortative mating are referred to as magic traits and are considered to facilitate speciation (Maynard Smith, 1966; Kondrashov and Kondrashov, 1999; Schluter, 2001; Via, 2001; Kirkpatrick and Ravigne, 2002; Gavrilets, 2004). Flowering time as considered in this study is in fact a magic trait. During the early phase of the evolution of a nocturnally flowering species, nighttime flowering can increase the probability of pollination because of the smaller number of flowers competing for pollinators (negative correlation between population density and pollination), thereby increasing the fitness of nighttime flowering plants. At the same time, flowers receive pollen mostly from those flowers flowering at the same flowering time. The function of flowering time as a magic trait in our case is caused by the insect pollination system and thus would not occur in wind-pollinated plants. Incidentally, if the number of daytime flowering plants competing for pollinators is small, evolution in the inverse direction, i.e., from a nocturnally flowering ancestor to a diurnally flowering species, can also occur in our model. Devaux and Lande (2010) noted that a negative densitydependent pollinator visitation rate also induces disruptive selection with respect to flowering periods, resulting in two flowering peaks occurring in a reproductive season. Thus, our finding that a negative correlation is important for increasing the fitness of nighttime flowering plants and consequently for achieving the evolution of a nocturnally flowering species is not new. However, Devaux and Lande (2010) assumed a quantitative genetic model and initial variation in the flowering period. The novelty in our result lies in employing an empirically based three-locus model and showing that different flowering times could evolve from populations that initially exhibited a homogeneous flowering time. Although the population density and pollinator visitation rate per flower were negatively correlated in our model and in that of Devaux and Lande (2010), this result may not hold in general because of the competition between plant species sharing the same pollinator resources. As noted by Pauw (2013), a nocturnally flowering species may have a high fitness only when there are a small number of other nocturnally flowering species or when these nocturnally flowering species can partition pollinator resources, for example, by using different types of nocturnal pollinators. We need to examine whether such a condition is satisfied or not when the possibility of the evolution of a nocturnally flowering species is evaluated. In addition, if other factors cause negative density-dependent regulation of the plant population size (e.g., limitation of the nutrients in soil), the evolution of a nocturnally flowering species might become more difficult. Unfortunately, such information is currently lacking in Hemerocallis. Even though flowering time is a magic trait, our results indicate that the number of loci controlling it must be small, as also shown by other studies (Gavrilets, 2004, 2005; Waxman and Gavrilets, 2005a, 2005b). This condition is indeed satisfied in H. fulva and H. citrina, where only a few loci control the flowering time (Nitta et al., 2010). 4.3. Importance of pollinator preference and reduced hybrid viability for the evolution of H. citrina Our results show that without pollinator preference or reduced hybrid viability, the evolution of a nocturnally flowering species is almost impossible. In fact, without these factors, the homozygotes of nighttime flowering (O2O2C2C2) never attained a high frequency, although an increase in the number of heterozygotes of nighttime

9

flowering (O1O2– or –C1C2) occurred with a high probability (data not shown). These results suggest that although different flowering times can act as a magic trait and have a significant effect on the evolution of a nocturnally flowering species, pollinator preference to an alternative attractive trait and reduced hybrid viability are also important to provide premating isolation. As mentioned in the Introduction, previous studies on pollination have reported that different pollinators have different preferences for flower color or fragrance (Sazima et al., 1999; Waser and Ollerton, 2006; Okamoto et al., 2008; Hirota et al., 2012). As for reduced hybrid viability, H. fulva and H. citrina show a decreased germination rate in their F1 hybrids (Yasumoto, unpublished data). In addition, recent studies of Drosophila, Arabidopsis and maize species suggest that genetic variation that causes genetic incompatibility exists even within species (Russell et al., 2013). Therefore, the accumulation of the effects of such (partially) incompatible genes may make hybrid viability sufficiently low to cause the evolution of a nocturnally flowering species. Previously, some experimental case studies have reported that different flowering times or flower colors can evolve as a result of reinforcement effect (Hopkins, 2013, 2014). The increased probability of the evolution of nocturnally flowering species under reduced hybrid viability is consistent with the expected pattern of evolution by reinforcement (reviewed in Coyne and Orr, 2004). However, in our model, the adaptation to increase the number of visitations had significant effects on the evolution of nighttime flowering and a new attractive trait, and we cannot distinguish the relative effect of this adaptation from the reinforcement effect. Therefore, it is difficult to precisely state how strongly reinforcement affected the evolution of a nocturnally flowering species in this case. 4.4. The effects of assumptions In this study, we made several unrealistic assumptions in the model for the sake of simplicity. We discuss some of them here. First, we assumed that each individual plant was annual and had discrete generations. Although some diurnally and nocturnally flowering species pairs, including H. fulva and H. citrina, are perennial and have overlapping generations, age structure does not introduce radically new behaviors into populations, as noted by Ewens (2004, p. 283). Thus, we expect that our results would be applicable to perennial plant species having overlapping generations. Second, we assumed that the pollinator replaced all of its attached pollen on each visit to a flower. This assumption might be unrealistic. In fact, studies of the visitation of bumblebees on blueweed (Echium vulbare) and honeysuckle (Diervilla lonicea) have suggested that some of the attached pollen grains are replaced (Thomson and Plowright, 1980; Rademaker et al., 1997). If the replacement rate is low, early flowering would result in higher fitness, and thus, the evolution of a nocturnally flowering species would become less likely. Supplementary Table 1 shows the probability of the evolution of a nocturnally flowering species when the pollen replacement rate is 0.5. A decrease in the pollen replacement rate did in fact make the evolution of a nocturnally flowering species less likely. Third, we assumed that the total number of pollinators and the rate of pollinator movement were constant throughout the 10,000 generations. However, these parameters may vary in each generation depending on environmental changes. Although environmental change is an important issue when we consider the applicability of the model, we cannot predict its consequence from our study, which assumed the constancy of those parameters. Thus, we need to investigate the effects of the fluctuation of these parameters in future studies. As noted by Rundell and Price (2009), environmental changes may collapse ecologically differentiated species, and thus, the probability of the evolution of


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10

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a nocturnally flowering species might decrease in a fluctuating environment. Fourth, we assumed that the rate of pollinator movement within a day was also constant but might vary. In fact, pollinators may have discrete activity times in a day, i.e., being active only during a certain period of the day. However, the variable that determines the dynamics of the gamete frequencies in the flowers is the total number of visitations of pollinators to flowers during each phase. Therefore, only the average rate during each phase matters, and variation around the mean does not change the conclusion. Fifth, we assumed that each flower is fertilized by the pollen that was first deposited into its stigma. In this study, we focused on the evolution of premating isolations as an initial stage of speciation. However, plant species may have isolating mechanisms to prevent hybridization even after pollen deposition by affecting the growth of the pollen tube (differences in style length or pollen tube growth rate), and an establishment of such postmating isolation would increase the probability of the evolution of a nocturnally flowering species. In Hemerocallis species, Yasumoto and Yahara (2006; 2008) suggested the existence of such postmating prezygotic isolations. As mentioned by Block and Erhardt (2008), the optimal style length for reproductive success differs between species of pollinators and thus, this trait can be affected by divergent selection. In such a case, the establishment of postmating-prezygotic isolations may occur more easily, and the probability of the evolution of a nocturnally flowering species would increase. However, as in the case of an attractive trait, the establishment of postmating prezygotic isolations alone cannot initiate the evolution of a nocturnally flowering species because a new style length without a switch in the flowering time is not adaptive. Finally, we considered the cases of only three mutation rates (u ¼10 4, u ¼ 10 5 and u ¼10 6), and these values might be too high. Although the actual mutation rates of Hemerocallis and other diurnally and nocturnally flowering species are unknown, if this rate is less than 10 6, the evolution of a nocturnally flowering species would be very difficult. However, because our results suggest the importance of the total number of mutations, the probability of the evolution of a nocturnally flowering species would not be low even with low mutation rates if the size of the plant population is large.

5. Conclusion In conclusion, we found that the evolution of a nocturnally flowering species from a diurnally flowering ancestor is likely to occur when hybrid viability is intermediate to low, the overlap of the flowering times is short, a large number of hybrids flower at night, and the size of the plant population is large. Pollinator preference also has an important effect whose strength depends on the hybrid viability and overlap of the flowering time. Our results suggest that flowering time can act as a magic trait and has a significant effect on the speciation event of the plants. However, the establishment of reproductive isolation requires pollinator preference; thus, the evolution of a nocturnally flowering species, such as H. citrina, from a diurnally flowering species, such as H. fulva, would not be achieved based only on differences in flowering time and reduced hybrid viability. Our results indicate that the evolution of a nocturnally flowering species strongly depends on respective parameter values. However, even in Hemerocallis, some important parameter values (population size and hybrid viability) are still unknown. Thus, we must estimate those parameters as a next step to accurately evaluate the possibility of the evolution of H. citrina from an ancestor, such as H. fulva. For other plant species, it is also important to determine the genetic systems underlying the phenotypes that are responsible for reproductive

isolation and the parameter values to fully understand the speciation process.

Acknowledgment This study was partially supported by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (Nos. 21370013, and 20248017) and by the Environment Research and Technology Development Fund (S-9-2) of the Ministry of the Environment, Japan. We thank Kosuke Teshima Kyushu University, Japan, for his advice on this study.

Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.jtbi.2015.01.036.

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Message ends: RNA 3' processing and flowering time control.