Negative frequency-dependent selection (NFDS) is one of the most powerful selective forces maintaining genetic polymorphisms in nature. Recently many prospective cases of polymorphisms by NFDS have been reported. Some of them are very complicated, although strongly supportive of the NFDS. Here we investigate NFDS in wild populations of the dimorphic damselfly Ischnura senegalensis, in which females occur as andromorphs and gynomorphs. Specifically, we (1) test fitness responses to morph frequencies, (2) built a simple population genetic model, and (3) compare the observed and predicted morph-frequency dynamics. Fitnesses of the two morphs are an inverse function of its own frequency in a population, and are about equal when their frequencies are similar. Thus the conditions necessary for NFDS are satisfied. The long-term field surveys show that the morph frequencies oscillate with a period of two generations. Morph frequencies in a small population undergo large oscillations whereas those in a large population do small oscillations. The demographic properties of the observed dynamics agree well with those of our model. This example is one of the simplest confirmed cases of NFDS maintaining genetic polymorphisms in nature.

Because both selection and drift tend to reduce genetic variation in local populations, maintenance of genetic variation constitutes a classic problem in evolutionary biology (Gray and Mckinnon 2007). Several possible mechanisms have been proposed for the maintenance of genetic polymorphisms in nature: negative frequency-dependent selection (NFDS), overdominance, and the spatial and temporal mosaics of selective values or microhabitats (Futuyma 2009). Among them, NFDS, where rare morphs have a selective advantage over common morphs, has been recognized as a most powerful selective force maintaining genetic polymorphism.

Many prospective cases of NFDS have been reported both in animals and plants (e.g., Punzalan et al. 2005). One of the best examples of NFDS is the evolution of a balanced sex ratio (West 2009). According to Fisher's theory (Fisher 1958), the investments by parents to male and female offspring should be equal because the evolutionary game of sex allocation results in NFDS (e.g., Conover and Van Voorhees 1990; Basolo 1994; West and Sheldon 2002; West 2009). Recently, from the aspect of population persistence in relation to mating opportunities, a slightly male-biased (from 1:1) sex ratio has been shown to become optimal when there is male-biased mortality (Tainaka et al. 2006).

In some cases, the properties of NFDS (e.g., rare morph advantage) are demonstrated experimentally in the laboratory (Fitzpatrick et al. 2007) or in the field (Gigord et al. 2001; Olendorf et al. 2006). In other cases, clear cyclical morph-frequency oscillations over many generations are reported as an evident fluctuation induced by NFDS (Hori 1993). In a few splendid but rather complicated cases, the causal linkage between rare morph advantage and morph frequency dynamics has been clarified in the natural population (Sinervo and Lively 1996; Svensson et al. 2005).

Female polymorphism has been reported in many animal taxa (Robertson 1985; Roulin et al. 2003), and may be an evolutionary outcome of sexual conflict via NFDS (Gavrilets and Waxman 2002). In some damselflies, one female morph resembles the conspecific male in color and pattern (the andromorph) whereas one or two other morphs are distinctively different from the male (the gynomorph) (Fincke et al. 2005; Van Gossum et al. 2008; see also Corbet 1999). The color morphs are controlled by a single autosomal diallelic locus, with expression limited to females (Johnson 1964, 1966).

Some empirical studies suggest that male mating harassment concentrates on common female morphs in a frequency-dependent manner (Svensson et al. 2005; Takahashi and Watanabe 2009); such harassment is extremely costly to females (Takahashi and Watanabe 2010a). Therefore, the reproductive success of the common morph is predicted to be lower than that of the rare morphs, resulting in stable coexistence of multiple female morphs in local populations (Svensson et al. 2005).

Here we demonstrate NFDS in female color dimorphism of a common bluetail (Ischnura senegalensis) (Fig. 1) with both empirical tests of reproductive success and the observations of wild morph-frequency dynamics. Further, we build a simple model of genetic polymorphism and compare its dynamics with those of natural populations under two different sets of parameters. The current case is the simplest confirmed case of NFDS in nature.

Figure 1.

Female color polymorphism in common bluetail, Ischnura senegalensis. Andromorphs (middle panel) resemble the conspecific male (top panel) in color and pattern, whereas gynomorphs (bottom panel) are distinctively different from the male.

Materials and Methods


Ischnura senegalensis is a nonterritorial damselfly inhabiting the edge of ponds, and is bivoltine with spring (late-May to late-June) and summer generations (August to September). Although males are monomorphic, females exhibit color dimorphism, consisting of andromorphs and gynomorphs (Fig. 1). The female color morphs are controlled by two alleles at a single autosomal locus with sex-limited expression, where andromorphic allele is recessive to gynomorphic allele (Y. Takahashi and M. Watanabe, unpubl. data), as in the case of other female-dimorphic damselflies (Johnson 1964, 1966).

Although in some coenagrionid damselflies, andromorphs mate less often than gynomorph irrespective of the morph frequency in a population (Cordero et al. 1998; Cordero Rivera and Sánchez-Guillén 2007; Hammers and Van Gossum 2008), Takahashi and Watanabe (2009) showed no difference in mating frequency in I. senegalensis between morphs during mating activity period, the morning. Nevertheless, during daily oviposition and foraging period, the afternoon, males of I. senegalensis exhibit frequency-dependent mating attacks toward females (Takahashi and Watanabe 2009). These mating attacks concentrate on common morphs, resulting in severe harassment against common morphs. This harassment hinders females from oviposition and foraging activities and consequently reduces the number of eggs laid (Takahashi and Watanabe 2010a). Hence it is expected that the reproductive success of one morph decreases drastically when its frequency becomes higher than the other in a population.


To explore the equilibrium and dynamics of morph frequency, we constructed simple population genetic models of NFDS acting only on female phenotypes. Given a diploid population undergoing nonoverlapping, discrete generations, two color morphs, andromorph (A) and gynomorph (G), are determined by one autosomal locus with two alleles, D (dominant) and d (recessive), with sex-limited expression. That is, the genotypes with “DD” and “Dd” express the gynomorph, and those with “dd,” the andromorph. Let pt, qt, and rt (pt+qt+rt= 1) be the frequencies of DD, Dd, and dd, respectively, in a population at the beginning of generation t.

Let RG and RA be the frequencies of gynomorphs and andromorphs in a population, respectively, that is, RG+RA= 1. We assume that the relative fitness reduction of each morph (WG and WA) decreases with its frequency (RG and RA), such that


where the function w(x) is the decreasing function of frequency x of a morph with w(0) ≈ 1 and w(1) ≈ b (0 ≤bw≤ 1). Here the constant b is the maximum fitness reduction when there is only one female morph (R= 1). We specifically use a sigmoid function for w(x) because the effects of harassment are expected to be significant and nonlinear, such that w(x) = (1 − b)/(1 + exp[a(2x− 1)]) +b. Here the nonlinearity parameter a (0 ≤a) represents the sensitivity of fitness w(x) to morph frequency x. A large a indicates a drastic decrease in fitness near x= 0.5 (see Fig. 2A).

Figure 2.

Simulation-based morph frequency dynamics. (A) Fitness responses to andromorph frequency in andromorphs (solid line) and gynomorphs (broken line) (thin: a= 2, b= 0; thick: a= 9, b= 0; extra-thick: a= 20, b= 0). (B) The genotype frequency converges to equilibrium (r= 0.5) regardless of the allele frequencies at the beginning generation (a= 2, b= 0). (C) The bifurcation boundary between the stable equilibrium (white area) and the limit cycle (shaded area) depending on the combination of two parameters, a and b (N=∞). (D–F) The changes in frequency dynamics with parameter a. The demographic oscillations occur when N is finite and becomes severe when population size N is small (D: N= 10000; E: N= 800; F: N= 100). (G) Temporal dynamics of morph frequency when N is large (N= 800, a= 9, b= 0, upper) and N is small (N= 100, a= 9, b= 0, lower). The amplitude of oscillation is larger when N is smaller.

We here assume that male fitness is constant regardless of genotype because of the female-limited expression genes. We also assume random mating (Takahashi and Watanabe 2009) and Mendelian segregation. The probability of DD, Dd, and dd (pt+1, qt+1, rt+1) in the progeny at (t+ 1), can be calculated using relative fitness w(x) of each genotype in the current generation (see Supporting Information Text and Table S1). The frequencies of genotypes in the next generation are given by the multinomial distribution of the progeny genotypes (pt+1, qt+1, and rt+1), with a given population size N. Here demographic noise effects appear when N is small (see Supporting Information).


Four local populations were selected in Ibaraki (local population A, B, and C) and Fukui Prefecture (local population D), all of which were located on the same latitude in the warm-temperature zone of Japan (see Table 1 in Results).

Table 1.  Morph frequency and the number of eggs laid in each morph (/day) for four local populations.
Local populationLocationHabitat size (m)Census dateLength of census line (m)Proportion of andromorphsAndromorphGynomorph
InhibitedAllowedNo. eggs laidInhibitedAllowedNo. eggs laid
  1. ( ): Sample size.

  2. Inhibited: the number of eggs loaded in females when oviposition was inhibited.

  3. Allowed: the number of eggs remained when females laid eggs freely.

A36° 9′28″N, 140° 3′47″E 7505 Jun 200740021.8% (55)275.3±27.2 (7) 23.6±5.5 (8)251.7219.9±31.2 (9)80.5±23.2 (11)139.4
B36° 2′29″N, 140° 8′50″E138012 Jun 200750036.8% (38)234.1±10.0 (6)  9.0±3.3 (7)225.1236.0±17.0 (8)24.2±5.7 (5)211.8
C36°14′40″N, 140°19′10″E 2302 Sep 200820071.9% (32)225.2±46.4 (6) 12.0±3.0 (6)213.2392.0±66.0 (6)14.2±12.8 (6)377.8
D36°13′42″N, 136°10′52″E 2106 Jun 200920080.0% (75)234.9±29.9 (10)104.1±9.9 (10)130.8302.9±27.2 (10)73.9±14.1 (10)229

Emergent plants were found along the margin of each pond, for example, Phragmites australis, Schoenoplectus spp., and Typha spp. These plants provide perching sites and oviposition substrates for I. senegalensis. Morph frequency at the water's edge was measured using the line transect method in each population. Census lines (A: 400 m; B: 500 m; C: 200 m; D: 200 m) were set up along the ponds. Each line census was carried out at 1000–1100 on each day of the experiment. We walked slowly along the line so as not to disturb any individuals. For each individual within 1 m on both sides of the line, sex, morph, and age (sexually immature or sexually mature) were recorded. Age was determined according to the body color, because the two female morphs change body color as maturing. In the immature stages, the ventral side of the abdomen is yellow and it becomes brown when maturing. The details of the four study populations and the frequencies of the two morphs in each local population are summarized in Table 1.

In previous studies, to estimate female reproductive success, females captured in the field were allowed to lay eggs in oviposition jars during a few days, and then the number of eggs laid (i.e., clutch size) was counted (e.g., Gosden and Svensson 2007). However, Takahashi and Watanabe (2010a) pointed out that actual daily reproductive success of females was affected by male sexual harassment during their oviposition activity in I. senegalensis. Therefore, to estimate correctly the daily number of egg laid, we should take into account the effect of male harassment during oviposition activity. In the current study, to estimate the number of eggs laid in the afternoon, we measured and compared the average number of eggs loaded in females when oviposition was inhibited and the average number of eggs remained in the ovary when females had laid eggs freely under the male harassment. To estimate egg load, sexually mature females of both morphs were captured at the water's edge around noon (1130–1230), that is, just before the onset of daily oviposition activity. These females were individually put into small plastic cups to prevent oviposition. They were placed in the shaded understory of shrubs to avoid direct sunlight until the evening, then fixed with absolute ethanol at 1600–1700. To evaluate the number of eggs remaining, females were captured in the evening (1600–1700: after the daily oviposition activity), and were fixed with absolute ethanol immediately after capture. The number of mature eggs in the ovary of the females was counted directly under a stereomicroscope.

The daily number of eggs (D) laid in each morph in each population was calculated as D=IF, where I is the mean egg load when oviposition was inhibited, and F that which remained when oviposition was allowed to occur. Relative reproductive success of the andromorph and the gynomorph (/day) was calculated as RSA= ln (DA/DG) and as RSG= ln (DG/DA), respectively, where the subscript of RS and D represented each morph (A or G). The mean egg load and the estimated number of eggs laid were summarized in Table 1. The daily number of eggs laid is a key component of the female lifetime reproductive success in damselflies (Corbet 1999). Especially in I. senegalensis, because there is no difference in interclutch interval: every female oviposit every afternoon (Takahashi and Watanabe 2010a), the daily number of egg laid must be an important determinant of female lifetime reproductive success.


A long-term survey was conducted for the morph-frequency dynamics in the two local populations B and C (in Table 1 in the results) from 2005 to 2009. Morph frequency was measured using the line transect method in the spring and summer generations of each year (see Table S1). The number of females of each morph was recorded to estimate the morph frequency, population density, and population size at the study site. Population density was calculated as the number of females per 50 m. Population size was estimated using population density and the length of water's edge (habitat size) where the adults of this species occurred (see Table 1).


All statistical analyses were performed using R version 2.9.0 (R Development Core Team 2009, Vienna, Austria). All values were presented as means with the standard error of the mean. Morph frequency was analyzed by the chi-square test. The relationship between morph frequency and female reproductive success was analyzed by Pearson's correlation test. All statistical tests were two tailed.


Figure 2 shows the qualitative results of the model. The effects of fitness reduction in females depend on the nonlinearity parameter a of w(x) (Fig. 2A). The equilibrium morph frequency (ESS mixed frequency) was predicted at r= 0.5 (i.e., r=RA=RG= 0.5), irrespective of the shape of fitness function w(x). The morph dynamics generally approach (or converge to) this equilibrium, where the allele frequencies f of D and d are fD= 1 − 1/√2 (≈0.29) and fd= 1/√2 (≈0.71), where P*= 3/2 −√2, q*=√2 − 1 and r*= 1/2 (Fig. 2B).

When population size N is ∞, morph frequency either converges at the equilibrium or oscillates with the limit cycle with a period of two generations, depending on the combination of two parameters, a and b. The bifurcation boundary between the stable equilibrium and the limit cycle is shown in Fig. 2C. The bifurcation point for a when b= 0 is a≈ 9.66. The demographic oscillations occur when N is finite and becomes severe when N is small (Fig. 2D–F), even when a is lower than the bifurcation point. This is also shown as the temporal dynamics of morph frequency (Fig. 2G).

The negative frequency dependence (NFD) in female reproductive success is assessed in four local populations located in Ibaraki (populations A–C) and Fukui Prefecture (population D). Morph frequencies are varied significantly among four populations (Table 1). To estimate the daily reproductive success (D) of each morph, we calculate the differences in mean egg load between females with (F) and without (I) daily oviposition activity, that is, D=IF (Table 1). Figure 3A shows the relative reproductive success of each morph plotted against the frequency of andromorphs, showing that the fitness of a common morph is reduced drastically with its frequency. The two regression lines (the straight lines in Fig. 3A) are overall symmetrical at their intersection (WA=WB). Equilibrium frequency (RA= 0.47), in which both morph have same fitness, is nearly 0.5. This provides the conditions necessary for NFDS. Based on the behavioral data of male harassment in I. senegalensis, we assume that the fitness reduction in females is a switching function (e.g., the sigmoid curves in Fig. 3A) (Takahashi and Watanabe 2010a).

Figure 3.

The fitness and temporal dynamics of female morphs. (A) The relationship between andromorph frequency and the relative reproductive success of andromorphs (open symbols) and gynomorphs (filled symbols). The solid straight lines indicate the linear regression (Pearson's correlation test for andromorph: Y= 0.91–1.96X, r=−0.98, n= 4, P= 0.023; note that it is the same for gynomorph, because of the mirror image). The dashed curves show an example of symmetric sigmoid responses (a= 30, b= 0.55 see text for the equation). (B, C) Frequency dynamics in natural and simulated populations. Frequencies oscillated with about a two-generation period in both natural (B) and simulated (C) populations. For simulated population, dynamics from 100th to 110th generation was shown as examples. The amplitude of oscillation was larger in smaller population (filled symbols) and smaller in larger populations (open symbols). The mean size of population C was smaller than that of population B. The observed and simulated oscillations are very similar to each other.

Figure 3B shows the temporal dynamics of andromorph frequency in the two natural populations B and C (Table S1). The density in population C is 7.3 ± 1.3 (individuals/50 m, n= 13), which is slightly lower than the density of population B (9.1 ± 0.9 individuals/50 m, n= 9) (U= 36.5, P= 0.15). However, the size of population C (33.6 ± 6.2 individuals, n= 13) is significantly smaller than that of population B (251.5 ± 25.4 individuals, n= 9) (U= 0.0, P < 0.001).

In these natural populations, oscillations with nearly a period of two generations are observed (Fig. 3B). The small population (population C) shows a larger oscillation; the large population (population B), a smaller oscillation (Fig. 3B). The corresponding simulated dynamics behave in a similar fashion (Fig. 3C), suggesting that oscillation observed in the wild population has been resulted from the NFDS.


The maintenance on genetic variations in nature is one of the most important issues of the conservation of biodiversity (Frankham et al. 2002). Genetic polymorphisms with a supposed NFDS have been widely reported (e.g., Punzalan et al. 2005). Most previous studies showed experimentally that the fitness feature of each morph is negatively frequency dependent (Gigord et al. 2001; Olendorf et al. 2006; Fitzpatrick et al. 2007). A few studies have reported apparently cyclical oscillations in natural populations (Hori 1993); some of these have been analyzed with mathematical models (e.g., Takahashi and Hori 1994; Sinervo and Calsbeek 2006; Van Gossum and Sherratt 2008). Some elegant studies have provided all of the following: (1) NFD fitness condition, (2) natural oscillations, and (3) a comparison with a mathematical model (e.g., Sinervo and Lively 1996; Svensson et al. 2005; Sinervo and Calsbeek 2006). The two widely recognized studies on a lizard (Sinervo and Lively 1996) and a damselfly (Svensson et al. 2005) came with the combination of these three components whereas these cases are rather complicated NFDS. The current example of I. senegalensis is another confirmed, but a rather simple case of NFDS with all these combinations.

The previous studies dealt with trimorphic systems that are based on rather complicated ecological interactions, such as the Rock-Paper-Scissors (RPS) game (Sinervo and Calsbeek 2006). The RPS game is a straightforward example of NFDS, but no clear oscillations of the morph frequency were observed in these systems. Such complicated oscillations may be due to the complexity of the systems that are affected by various factors. However, the current example is originated only the male interference, and shows simple oscillations around unity. Although such regular cyclic oscillation is also observed in dimorphic females in a lizard species, it is shown to be derived from the differing density responses between the two morphs (Sinervo et al. 2000).

In our case, regular oscillations are derived from the NFD condition. In addition, the NFD condition in this system is almost symmetric between the two morphs. Thus the current system is extremely simple symmetric case of NFDS, so that it has been easily confirmed and evaluated.

Most models of genetic polymorphisms for NFDS are specifically tailored to the target model systems and involve many parameters (Takahashi and Hori 1994; Nakajima et al. 2004; Van Gossum and Sherratt 2008). Therefore, it is difficult to confirm that the observed dynamics is actually derived from the model principles. The current model is one of the simplest models consisting of only essential parameters. It can correctly predict the natural dynamics of the morph frequency in the different condition (large and small populations). Thus we could confirm the validity of the model without any complications.

We observe a deviation in the average frequency of one morph in natural population C, which cannot be explained by the current simple model (Fig. 3). The average frequency E(r) of andromorphs is 0.35 for population C, in contrast with E(r) = 0.46 (close to 0.5) in population B. The asymmetry in morph frequency may be originated from the differences of adaptive responses in the two morphs. In I. senegalensis, the andromorphs have adopted an r-strategic morph whereas gynomorphs adopt a K-strategic morph (Takahashi and Watanabe 2010c). K-strategic morphs are typically advantageous than the r-strategic morphs at high population density (Sinervo et al. 2000). Therefore, the dominance of the gynomorph over the andromorph in the high-density population (population C) may result from the difference in life-history strategy.

Interpopulation variations in the equilibrium morph frequency and the pattern of dynamics were reported in damselflies (e.g., Svensson and Abbott 2005; Van Gossum et al. 2007). In some coenagrionid damselflies, a positive relationship between density and andromorph frequency has been reported (Cordero 1992; Forbes et al. 1995; Cordero Rivera and Egido Perez 1998), and this may be caused by intraspecific sexual mimicry of andromorph (Van Gossum et al. 2010). Phenotypic differences between morphs in various traits were observed in many damselfly species, for example, some behavioral traits (Robertson 1985; Sirot and Brockmann 2001; Van Gossum et al. 2001) and physiological traits (Abbott and Svensson 2005; Gosden and Svensson 2007; Takahashi and Watanabe 2010c). Bots et al. (2009) pointed out environmental variation like temperature might be affecting the morph frequency in a population. To explain the intraspecific variation in the morph frequency and its dynamics, additional parameters, such as morph specific behavior and life-history strategy or the effect of intraspecific mimicry, should be introduced to our simple and general model.

In the present study, fitness reduction by male harassment was evaluated from the number of eggs laid per day. However, male harassment can often reduce longevity of females as well (Clutton-Brock and Langley 1997; Chilvers et al. 2005). Therefore, the fitness reduction in the common morph is expected to be far more severe than our estimate. These effects may also contribute to the nonlinearity (sigmoid response) of NFDS (see the dashed lines in Fig. 3A).

In this system, NFDS in female polymorphisms is caused by the selective mating harassment. The frequency dependence in male mating preference results from the experience-based behavioral changes of individual males (Takahashi and Watanabe 2009, 2010b). Thus, our study also provides empirical evidence that behavioral plasticity of individuals has an important effect on maintenance and evolutionary dynamics of genetic variation in a population.

Associate Editor: S. West


We thank Dr. D. G. Miller III of California State University at Chico, for critical review and grammatical correction of an earlier version of the manuscript. We also thank S. A. West, T. Asami, and anonymous referee for their comments on the manuscript. This study was supported in part by the Research Fellowship of the Japan Society for the Promotion of Science (JSPS) for Young Scientists (20–104) to YT and the grant-in-aids from the JSPS KAKENHI 19740234 to SM, 22255004 and 22370010 to JY.