Panu Välimäki, Department of Biology, University of Oulu, PO Box 3000, FI-90014 Oulu, Finland. Tel.: +358 8 553 1256; fax: +358 8 553 1061; e-mail: firstname.lastname@example.org
The length of the favourable season determines voltinism in insect populations. In some insects, there is variation in fecundity and timing of reproduction among females. If the length of the favourable season does not allow all offspring to develop into adults without diapause, the benefits of high early fecundity may outweigh the associated cost of low lifetime fecundity. We tested this by exploring mating frequencies of Pieris napi females along a latitudinal gradient in different generations. Pieris napi is a bivoltine butterfly, and genetically polyandrous females enjoy higher lifetime fecundity than monandrous ones. Polyandry is, however, coupled with a relatively low early fecundity. We found that monandrous females are more likely to produce an additional generation than polyandrous ones under conditions that allow production of only a partial summer generation. Monandrous females were also the first to emerge and slightly over-represented in the summer generation under conditions that allow the development of a complete summer generation. Further, a stochastic model shows that variation in the timing of reproduction between strategies is sufficient to explain the observed patterns. Thus, seasonality may counter-select against polyandry, or more generally against low early reproductive rate, and promote maintenance of polymorphism in life history strategies.
Life history traits are efficient in the study of adaptations because of their close relationship with fitness (Roff, 1992). Either stabilizing or directional selection should lead to a solution that maximizes fitness under prevailing conditions, and thus such a selection tends to erase additive genetic variation in life history traits within populations (Fisher, 1930; Mousseau & Roff, 1987; Falconer, 1989). On that basis, heritable life history variation should be found only among species or among populations inhabiting different environments (Stearns, 1980; Brown, 1983). Existence of additive genetic variation and different genetic morphs is, however, a common phenomenon within many taxa (Grosberg, 1988 and references therein). In the ascidian Botryllus schlosseri, demographic differences between semelparous and iteroparous colonies have a genetic basis, and a temporal switch in dominance hierarchy between the morphs is likely to have evolved as a response to a seasonally changing environment (Grosberg, 1988). Similarly, genetic variation in body size and diapause propensity among individuals in the cricket, Allonemobius fasciatus, is the result of diversifying selection, determined by local conditions (Mousseau & Roff, 1989). Thus, in some cases, seasonality maintains genetic variation in traits affecting fitness.
In temperate regions, seasonal variation is characterized by a regular summer/winter cycle with some stochasticity due to inter-year variation in the length of the time suitable for breeding (hereafter referred to as the season length). Development and reproduction of insects have to be synchronized with favourable times of year, and diapause with unfavourable periods. As a consequence, the production of more than one generation a year involves a choice between alternative developmental pathways: direct development and diapause. If the hibernating stage of development cannot be reached in time or if environmental conditions become adverse as the season proceeds, individuals may not survive. Thus, crucial aspects are whether there is enough time for a whole new generation to complete development, and whether conditions for juvenile development are stable enough throughout the season (Danks, 1987; Wiklund et al., 1992). Generally, individuals, or more precisely genotypes, which are able to complete additional generations successfully within a given time, have a higher intrinsic rate of increase than the ones producing a lower number of generations as long as the number of reproducing offspring is sufficiently high in additional generations (Roff, 1980). The optimal number of generations is found at a point where the generation length multiplied by the number of generations equals the season length. In temperate regions, the optimal number of generations must be truncated to the nearest integer, because all generations combined cannot last longer than the favourable season or the fitness will be zero in the long term (Dempster, 1955; Roff, 1980).
In a predominantly bivoltine butterfly, Pieris napi (Linnaeus, 1758; Lepidoptera: Pieridae), polyandrous females have a higher lifetime fecundity and they live longer than females that mate only once (Wiklund et al., 1993; Kaitala & Wiklund, 1994; Bergström & Wiklund, 2002), which is common among species with male nutrient provisioning (Arnqvist & Nilsson, 2000). Wedell et al. (2002) showed that both the degree of polyandry (i.e. lifetime number of matings) and lifetime fecundity are under genetic control in this species, the heritability estimates for the traits being 0.627 and 0.748 respectively. Due to the limitations of the full-sib design applied, the estimates may include nonadditive dominance variation resulting in exaggerated heritabilities. However, the full-sib method does not necessarily overestimate narrow sense heritability significantly (Mousseau & Roff, 1987; Roff, 1997), and therefore the conclusion that the traits are highly heritable is well-grounded (Wedell et al., 2002). Still, there is intriguing variation in female mating frequency both within and among populations (Bergström et al., 2002; Välimäki & Kaitala, 2006). This requires that the direct benefits of polyandry are not as pronounced over the long term as laboratory experiments within a generation suggest.
Polyandrous females suffer from a low early fecundity due to time costs of mating and they have a longer egg-laying period than monandrous ones (Välimäki et al., 2006). This means that a larger proportion of eggs laid by monandrous females in the spring generation will hatch before the critical day length determining whether offspring will undergo direct development or enter diapause (Wiklund et al., 1991). As a consequence, monandrous females may have a larger contribution to the subsequent summer generation than expected based on their reproductive potential, if only a fraction of the offspring form a directly developing generation. This may act as a counter-selection against polyandry, and more generally, against high lifetime fertility if it is traded off against low early fecundity in seasonal environments. This contradicts earlier findings of polyandrous females having a higher fecundity at all stages (Wiklund et al., 1993). The contradiction arises because the genetic background of mating tactics was not known at the time of Wiklund et al.’s (1993) study, and thus most of the randomly selected ‘monandrous’ females were genetically polyandrous, but with reduced reproductive output due to the lack of mates (see Sauter et al., 2001; Wedell et al., 2002; Kokko & Mappes, 2005).
We examined if seasonality promotes polymorphism in female reproductive strategies in P. napi. Based on the increased offspring production because of multiple mating, the proportion of polyandrous females should increase not only from year to year, but also from the over-wintering spring generation to the directly developing summer generation within populations, assuming no time constraints on juvenile development. Yet, temporal variation in reproductive rate between mating tactics may result in polyandrous females emerging later than monandrous ones in the summer generation. Additionally, monandrous females will disproportionately contribute to an additional generation within a year if only the earliest eggs laid by females in spring develop directly without diapause into adults. Consequently, the long-term fecundity advantage of polyandry will be partially offset in such time-limited environments. This being the case, the average degree of polyandry is expected to decrease and the proportion of monandrous females is expected to increase from spring to summer generation. In southern populations with less-severe time constraints, the prevalence of monandry in the summer generation is expected to be only slightly higher than would be predicted by the relatively low lifetime fecundity associated with the strategy and its prevalence in the spring generation. In populations with more severe time constraints, like in a transition region from bi- to univoltinism, the prevalence of monandry in the summer generation is, however, expected to deviate more from the predicted value. Thus, the pattern may exaggerate along the latitudinal cline towards the north along with shortening season length. A rigorous test of these predictions requires that samples from different regions and different generations are comparable. Therefore, we synchronized the sampling in relation to the date of adult emergence in all study populations in both generations. As there are several confounding factors in the wild (see Discussion), we developed a stochastic model to analyse if the differences in temporal patterns of egg-laying alone are sufficient to produce the expected patterns. We conclude that seasonality may act as counter-selection against polyandry, or more generally against low early reproductive rate.
Material and methods
Life cycle of P. napi
Pieris napi is among the most abundant butterflies in Finland, and its geographical distribution extends up to northernmost Scandinavia (Huldén et al., 2000). Over-wintering takes place obligatorily in the pupal stage. There is a latitudinal cline across P. napi’s distribution, the season length becoming gradually shorter towards the north. In southern Finland, the species is bivoltine, but in the north it is strictly univoltine, regardless of light conditions that promote direct development in more southern latitudes (see Wiklund et al., 1991). In central Finland, there is a transition region where the summer generation is irregular and scarcer than the spring generation. The pattern indicates spatially varying time constraints on reproduction among populations, which results in the production of only a partial summer generation in central Finland (i.e. only a fraction of eggs produced in spring will develop into adults without diapause), and univoltinism in more northern latitudes.
Sampling procedure and determination of female mating tactics
To study if seasonality promotes the existence of different female mating tactics, we explored the frequencies of monandrous and polyandrous females in different generations. This was carried out with wild-caught females whose intrinsic mating tactics were determined in the laboratory. We collected samples from eight populations. Four southern populations (59°–60° N: 23°–25° E) originated from the region where environmental conditions allow direct development of butterflies resulting in a complete summer generation. Four populations from central Finland (64°–65° N: 25°–26° E) represented populations with a partially bivoltine life cycle. The northernmost populations were not treated here for two reasons. First, our preliminary focus was to study the maintenance of monandry within a particular phenology (i.e. bivoltinism). Secondly, data on the proportions of different mating tactics in univoltine populations are already available (Välimäki & Kaitala, 2006).
We captured butterflies from the bivoltine and partially bivoltine populations on three and two occasions respectively. Thus, we ended up with 20 samples, each consisting of 25–35 females. Temporal variation in egg-laying rate among females may result in asynchronous emergence of adults with different mating tactics in summer. To avoid any bias due to the sampling procedure (age distributions of females within samples need to be identical in both bivoltine and partially bivoltine populations), we standardized sampling dates across populations based on the beginning of the flight season. The spring generation samples from both bivoltine and partially bivoltine populations were taken in the middle of the flight season, 10–12 days after the first butterflies were seen on their wings (cohort 1). The bivoltine populations were sampled for a second time 4–6 days after the first individuals of the summer generation were observed (cohort 2), and for a third time 9–10 days later (bivoltine cohort 3). The partially bivoltine populations were sampled for a second time 12–17 days after the first butterflies of the summer generation were seen (partially bivoltine cohort 3). Cohorts 3 represent ‘true’ summer generation individuals sampled in the middle of the flight season in both regions. Thus, cohorts 1 and 3 are comparable samples from the spring and summer generations respectively.
Wild-caught females were marked based on their origin with a permanent marker pen and released into flight cages (0.65 × 0.65 × 0.65 m3) in a laboratory with large windows so that butterflies were exposed to natural light during day time. Females from each population within a cohort were divided evenly into two cages randomly selected among 30 available ones. The total number of cages used for the spring and summer generation females were 16 and 24 respectively. Females were constantly accompanied by 1.5 times as many males randomly selected from the same origin, the maximum number of individuals per cage being 50. The offered male-biased sex ratio ensured that females always had access to potential mates (see Bissoondath & Wiklund, 1996; Wiklund et al., 1998). Butterflies were exposed to a light rhythm of 7 : 17 h and a temperature regime of 30 : 20 °C (light : dark). The cages were provided with fresh shoots of natural host plants (Thlaspi arvense, Rorippa palustris, Erysimum cheiranthoides) for egg-laying, natural nectar sources that were replaced daily and sticks with cotton wool tips soaked twice a day with 20% liquid honey solution for adult feeding. We let females mate and lay eggs until they died. Deceased females were dissected, and the number of spermatophore (one is delivered at each mating) residues in each female’s bursa copulatrix was counted (see Drummond, 1984). The procedure allowed us to determine the mating frequency of each female reliably because residues of depleted spermatophores remain in the female throughout her life (Wiklund et al., 1993).
All statistical analyses were performed with r 2.3.1 statistical software (R Development Core Team, 2006). We used residual deviances of the models (see below) as the criterion in the evaluation of the model goodness-of-fit.
To test if there is variation in average female mating frequency among cohorts, we first analysed the mating frequency distributions with respect to cohort among populations within regions (bivoltine/partially bivoltine). We did this by fitting a generalized linear mixed-effect model to the data with the mating frequency of an individual female as the dependent variable, cohort as a fixed factor and population as a random factor. Because mating frequency is always a positive integer, we chose the Poisson error distribution. The link function was logarithmic. Parameters of the model were estimated with maximum likelihood utilizing Gauss–Hermite quadrature as implemented in the r-package glmmML (Broström, 2006). The number of quadrature points was set to 20, which is enough in most cases (McCulloch & Searle, 2001). By utilizing the inverse of the link function, confidence intervals for average mating frequencies in different cohorts were back-transformed to the scale of observations. In a second analysis, we compared mating frequency distributions between the bivoltine and partially bivoltine populations in cohorts 1 and 3 to see if the change in average female mating frequency between generations varies with voltinism. A generalized linear mixed-effect model was fitted to the data as previously, but both cohort and region were set as fixed factors. The interaction between cohort and region was included in the model to test if the change in the average degree of polyandry from the spring to the summer generation is similar between regions with either partial or complete summer generations.
Thirdly, to test if the prevalence of monandry shows temporal variation within a year, we compared the observed proportions of monandrous females between cohorts separately for the bivoltine and partially bivoltine populations. We placed observations in three-dimensional contingency tables, where cohort, population and mating tactic (dichotomous: monandry/polyandry) formed the classes. The data were analysed with log-linear models fitted with function glm. Poisson distribution and logarithmic link function were utilized. A saturated model, i.e. a model with all possible interactions and main effects, was first fitted to the data. Then the model was hierarchically reduced by removing unnecessary factor combinations to get the definitive model.
Female lifetime number of matings varied between one and six in both bivoltine and partially bivoltine populations. The average mating frequency of females from the completely bivoltine populations was dependent on cohort (Table 1a). Mating frequency of spring generation (cohort 1) females averaged over all bivoltine populations was 2.38 (95% CI: 2.16–2.63). The average mating frequency of females from the early summer generation [cohort 2; 1.83 (1.59–2.12)] was significantly lower than that observed in the cohort 1. There was no difference between cohorts 1 and 3, the average female mating frequency being 2.64 (2.30–3.02) in the latter (Fig. 1a). In the partially bivoltine populations, the average female mating frequency was lower in the summer generation [i.e. cohort 3; 2.20 (1.90–2.55)] than in the spring generation [i.e. cohort 1; 2.41 (2.17–2.68)], but the difference was not statistically significant (Table 1b). The qualitative trend observed was, however, consistent among individual populations within regions. This combined with a marginally significant cohort 3 × region interaction (Table 2) suggests that the change in the average mating frequency between generations depends on voltinism such that, in completely bivoltine populations, average mating frequency tends to increase, whereas in partially bivoltine populations it decreases from the spring to the summer generation (Fig. 1b).
Table 1. Generalized linear mixed-effect model table for average female mating frequency in relation to cohorts in (a) bivoltine and (b) partially bivoltine populations.
Variable (mating frequency)
Intercept (cohort 1)
Model goodness-of-fit: χ2 = 283; d.f. = 370; P =1.000
Intercept (cohort 1)
Model goodness-of-fit: χ2 = 177; d.f. = 228; P =0.995
Table 2. Generalized linear mixed-effect model table for change in the average degree of polyandry in relation to the region of origin.
Intercept (cohort 1)
Cohort 3 × region
Model goodness-of-fit: χ2 = 269.3; d.f. = 468; P =1.000
The frequency of monandrous females varied among cohorts in the bivoltine populations (Table 3a). About 17% of all females captured from the bivoltine populations in the spring generation were monandrous, whereas in the cohort 2 captured during the early days of the summer generation, the proportion of monandry was 37% (Fig. 2). However, like the average mating frequency, the proportion of monandrous females in the cohort 3 was approximately the same as observed in the cohort 1 in populations with a completely bivoltine life cycle. In the partially bivoltine populations, the proportion of monandrous females was higher in the summer (cohort 3) than in the spring generation (cohort 1) (Fig. 2; Table 3b).
Table 3. Log-linear models for the frequency of monandrous females in relation to cohort in (a) bivoltine and (b) partially bivoltine populations.
Variable (frequency of monandry)
The definitive model (cohort × mating tactic included) is compared with the reduced ones; the null model includes only intercept. Residual deviances measure model goodness-of-fit.
6.985 × 10−17
1.635 × 10−17
2.65 × 10−25
Cohort × mating tactic
5.41 × 10−5
3.904 × 10−12
2.611 × 10−12
2.38 × 10−18
Cohort × mating tactic
Finally, we performed a visual investigation of observed and expected proportions of monandrous females in the additional summer generation within all studied populations. Given that polyandrous females have at least 1.44 times higher lifetime fecundity on average than monandrous ones (Wiklund et al., 1993), the expected proportion of monandrous females in the additional summer generation P(m) can be estimated as:
where p(m) and p(p) are the observed proportions of monandrous and polyandrous females in the spring generation respectively. In our dataset, the observed proportion of monandrous females in the summer generation was higher than expected in each population, the difference being more pronounced in partially bivoltine than in bivoltine populations (Fig. 3). The probability that this qualitative difference would occur independently eight times equals 0.58 (≈ 0.0039), and is thus improbably generated by chance. Reliability of the expected proportions of monandrous females in summer generations depends on how accurately the difference in lifetime fecundity between the two reproductive strategies was estimated. Female fecundity is positively correlated with the amount of spermatophore material received (Karlsson, 1998; Stjernholm & Karlsson, 2000) suggesting that female reproductive output increases steadily with increasing mating frequency (see also Arnqvist & Nilsson, 2000). As a consequence, our lowest available estimate (1.44) based on comparing average fecundity of monandrous females to that of females with either two or three partners (Wiklund et al., 1993) is likely conservative, as even higher mating frequencies were observed here.
A stochastic model for the maintenance of life history polymorphism in P. napi
The data above are based on wild-caught females and may therefore be confounded by several uncontrolled factors. Hence, we developed a stochastic model in order to analyse if the temporal differences in egg-laying between the reproductive strategies is sufficient to produce the observed patterns alone.
In P. napi, female lifetime fecundity increases with mating frequency, but so do the time costs of reproduction, which results in low early fecundity of polyandrous females (Välimäki et al., 2006). The observed distributions of egg-laying times of the two different strategies, dichotomized here as ‘monandry’ and ‘polyandry’, for simplicity, closely resemble gamma distributions (data from Välimäki et al., 2006). This enabled us to model P. napi reproduction with gamma distributions having appropriate parameters (summarized in Table 4). We estimated the parameters with maximum-likelihood methods by function fitdistr (Venables & Ripley, 2002) in r (R Development Core Team, 2006).
Table 4. Parameters of the model.
Estimated values are shown for the parameters that define the life histories of different strategies. For other parameters, values used in simulations are given when relevant.
**Constant determining the upper limit of the number of surviving larvae that hatch on a particular day.
††Parameter determining the type of competition; values −1 ≤ w <0 refer to scrambles among larvae of similar age, the effect becoming weaker with increasing values of w; values w >0 refer to contest where older larvae have a negative effect on the survival of younger ones, the effect becoming stronger with increasing values of w; if w =0, all older larvae alive have an equal effect on the survival of larvae in a particular cohort.
‡‡Time from the beginning of pupal development in spring to the critical day length (days).
§§Time from the critical day length to the end of the favourable season for larval development (days).
Shape parameter of gamma distribution, α
Rate parameter of gamma distribution, β
Lifetime fecundity (female offspring), F*
Larval development time (days), tl†
Standard deviation of larval development time (days)‡
Pupal development time (days), tp§
Standard deviation of pupal development time (days)¶
−1, 0 or 1
Lifetime fecundities of both strategies were estimated as observed mean fecundities divided by two, because only female offspring matter here. In our individual-based model, lifetime fecundity is derived separately for each female from a Poisson distribution of fecundities corresponding to her intrinsic mating tactic, and the time of oviposition is derived for each egg in the population from the appropriate gamma distribution. Time is discrete, so the derived egg-laying times are rounded up to the nearest integer to avoid any egg-laying before the first day of reproduction in the adult stage (defined to be day 1).
Development times from egg-laying to pupation (hereafter larval development, tl) and from the beginning of pupal development to adult eclosion (hereafter pupal development, tp) are derived randomly for each individual from the known distributions of the development times, and rounded to the nearest integer. Mean larval and pupal development times were estimated from data on larvae reared under natural conditions outdoors and pupae-reared indoors respectively (laboratory data from Välimäki & Kaitala, 2007). There were data for only 24 larvae-reared outdoors. Therefore, the standard deviation for tl was estimated from laboratory-reared individuals (n = 132) for accuracy. All else being equal, the development rate of ectotherms is largely determined by temperature, and hence tp observed under laboratory conditions (n = 105) translates to the corresponding time in nature as:
Possible variation in tl between strategies (Wedell et al., 2002) was ignored here because polyandrous individuals seem capable of taking advantage of their potential for higher growth rate only in optimal conditions (Välimäki & Kaitala, 2007), which may not occur in the wild-like suggested by late emergence of polyandrous females in summer generation (see Results; Fig. 2).
Competition among larvae may affect the relative successes of monandry and polyandry. In P. napi, larval competition is asymmetric at high densities so that older larvae have a competitive advantage over younger ones (Kivelä & Välimäki, 2008). Accordingly, we assumed that the survival of larvae hatching on a given day depends on the number of older larvae alive in the population on that particular day. Hence, the number of larvae alive in each of the i days older cohorts (i.e. larvae hatched i days earlier than the present cohort) was weighted according to
where w is a parameter determining the strength and type of competition, and Φw is the cumulative normal distribution function with mean and standard deviation being 8 and 4 respectively. Values −1 ≤ w <0 refer to scrambles among larvae of similar age, the effect becoming weaker with increasing values of w. Values w >0 refer to contests where older larvae have a increasingly negative effects on the survival of younger ones, whereas w =0 refers to interactions where all older larvae alive have an equal effect on the survival of larvae in a particular cohort. Then, assuming mortality is independent of reproductive strategy, the proportion of monandrous and polyandrous larvae surviving within a cohort j is
where N(j) is the total number of hatching larvae on day j, n(j) is the total number of survived larvae that hatched on day j [n(j − i) = 0, when j − i <1] and K defines the maximum number of surviving individuals within the cohort.
The favourable season for growth and reproduction is divided into two parts. T1 defines the number of days from the beginning of pupal development in spring until the critical day length that determines the developmental pathway induced. An individual that reaches the pupal stage within time T1 develops directly into an adult and reproduces immediately, whereas an individual that reaches the pupal stage later enters diapause and reproduces in the following spring. T2 stands for the number of days from the critical day length until the end of the favourable season. Only individuals that manage to pupate before the end of the season survive and contribute to the over-wintering population. We set T1 to be 0.46 times the season length, which maximizes the number of surviving descendants produced by monandrous individuals when season length allows only the first few cohorts of offspring to develop directly into adults. In these conditions, the used T1/(T1 + T2) ratio is nearly optimal also for polyandry, although the optimal switching point for polyandry tends to be earlier than that for monandry as the season length increases. However, the exact turning point from one developmental pathway to another on the time axis does not affect the qualitative results, if the critical day length is the same for both monandry and polyandry, but only the season length where a particular pattern emerges.
We first investigated population dynamics in relation to season length and type of competition, w (see Table 5 for details). Monandry became extinct in all simulations when the univoltine life cycle was not time-limited. On the other hand, monandry remained in a population in all simulations when the life cycle was partially or completely bivoltine, or if the univoltine life cycle was time-limited. In bivoltine populations, the frequency of monandry in the over-wintering population decreased with increasing season length (Table 5), but this effect was weak. In the summer generation, however, the frequency of monandry decreased considerably with increasing season length (i.e. with increasing population size in the summer generation; Table 5).
Table 5. Average frequency (95% CI) of monandry in relation to the season length and type of competition (w) (see Table 4).
Season length 80 days
Season length 110 days
Season length 140 days
The results for the over-wintering spring generation (first generation) are based on 1000 simulations started from one polyandrous and one monandrous female and run for 30 years (a population stabilizes within 15 years in the studied range of season lengths). The frequency of monandry in the summer generation (second generation) was simulated 1000 times within a season by recording the numbers of directly developing monandrous and polyandrous females in each simulation. The initial numbers of monandrous and polyandrous females were derived from normal distributions with means and standard deviations estimated from the spring generation simulations. The season lengths of 110 and 140 days facilitate partially bivoltine and completely bivoltine life cycle respectively.
Next, we investigated the invasion ability of the strategies in relation to season length because a stable polymorphism prevails only if a polyandrous population is vulnerable to invasion by monandry, and vice versa. The growth of the resident population was simulated for 10 years. A single mutant female was introduced into the spring generation of a population, which had reached its maximum size within the 10 years. Then the population dynamics was further simulated over one season to see if the mutant is able to invade the population, which would be indicated by an increase in its frequency. Density of the rare mutant was also allowed to contribute to density dependence. This was essential to derive realistic survival estimates for the latest cohorts of polyandrous larvae when a polyandrous mutant was introduced into a monandrous population, because the egg-laying period of polyandry is longer than that of monandry. The procedure was repeated 1000 times for each possible season length and for both reproductive strategies with each of the three values of w (−1, 0 and 1). Invasion probability of monandry was the highest in regions where the strategy persists in a population, i.e. in the bivoltine range and in the extremely time-limited part of the univoltine range (Fig. 4). Even outside of those regions, the invasion probability was higher than zero due to random fluctuations in the size of the resident population. When the resident population happens to be relatively small, an inferior mutant may increase its frequency in the short term due to stochastic events, although it would become extinct in the long term. The intensity and type of competition affected only slightly the invasion probability of monandry, whereas that of polyandry significantly decreased towards the contest end on the competition continuum (Fig. 4).
Within the bivoltine polymorphic region, monandry has a lower frequency than polyandry independently of w (see Table 5). Monandry has also lower invasion probability than polyandry within the same region except under intense contest competition among larvae. These results suggest that the stability of polymorphism is sensitive especially to the invasion ability of monandry. Therefore, a sensitivity analysis was performed to investigate how small changes in either the distribution parameters defining the egg-laying times or the relative lifetime fecundity disadvantage of monandry affect the invasion probability of the strategy (see Table 6 for details). We changed only one parameter at a time. The resulting invasion probability was compared to the reference point obtained with the estimated parameter values at two different season lengths, promoting either the univoltine life cycle and monomorphism for polyandry or the bivoltine life cycle and polymorphism. Changing the parameter values affected the invasion probability only slightly, the new probabilities falling mostly within the 95% confidence interval of the reference probability (Table 6). Hence, our model is quite robust against changes of some key parameters.
Table 6. Sensitivity of the average invasion probability of monandry investigated in relation to changes in both the distribution parameters defining the egg-laying times of the strategies and relative fecundity of monandry (estimates derived from 1000 simulations).
Parameters changed for
Season length 80 days
Season length 110 days
Correlated shape and rate parameters (α and β) of either monandry or polyandry were changed together at a time while holding all the other parameters constant. The investigated values of the parameters were chosen from the end of the major axis of the ellipse that excludes 5% of the probability mass of the bivariate normal distribution of the parameters. The mean fecundity of monandry (Fmonandry) was changed to correspond the lower and upper bounds of the 95% CI of the estimated fecundity. Analysis was carried out for season lengths that facilitate either univoltine (80 days) or partially bivoltine (110 days) life cycle. Values of parameters held constant were: T1 = 37, T2 = 43 (for shorter season), T1 = 51, T2 = 59 (for longer season), Fpolyandry = 107, K =30, w =0. Reference is the average invasion probability of monandry when the estimated values of all parameters are used.
*Shape and rate parameters (α and β) equal 3.073 and 0.7528 for monandry, 2.885 and 0.3788 for polyandry respectively.
†Shape and rate parameters (α and β) equal 3.917 and 0.9775 for monandry, 3.236 and 0.4292 for polyandry respectively.
‡Fmonandry = 59; Fpolyandry = 107.
§Fmonandry = 75; Fpolyandry = 107.
¶The means of the reference values are not included in all cases within the intervals between the means obtained with changed parameter values, because of uncertainty of the means (95% CIs of the means are relatively wide in relation to the number of simulations). However, the 95% confidence intervals of the references overlap with the interval between the means obtained with changed parameter values, as expected.
Reference (95% CI)
In the partially bivoltine P. napi populations, the prevalence of monandry increased from the spring to the summer generation. Even if environmental conditions allowed the production of a complete summer generation, monandrous females were the first to emerge in the summer generation. The results suggest that the prevalence of monandry in an additional summer generation is higher than would be expected based on the reproductive potential of that strategy. This is especially the case if the summer generation is only partial. Our modelling effort shows that variation in the timing of reproduction between monandry and polyandry may alone explain the observed patterns. These findings together with inter-year variation in season length may explain the maintenance of low mating frequencies in P. napi.
There is additive genetic variation in female mating frequency in P. napi (Wedell et al., 2002), although polyandry corresponds to ca. 1.61 (range: 1.44–1.78) times higher lifetime fecundity than monandry (Wiklund et al., 1993; see also Bergström & Wiklund, 2002; Välimäki et al., 2006). In central Finland, the proportion of monandrous females increased from the spring to the summer generation, which explains the simultaneous decrease in average mating frequency. The observations are understandable if a high proportion of offspring produced by polyandrous females in the spring generation developed into over-wintering pupae, whereas monandrous females produced offspring that developed without diapause. Hence, our results are in a good agreement with the ideas that only the first offspring produced in spring will develop directly into adults without diapause, and female genotypes with a high early fecundity are more likely to produce an additional summer generation than genotypes with delayed reproduction in seasonal environments (Vepsäläinen, 1974; Seger & Brockmann, 1987; Wiklund et al., 1991).
As a result of the obvious benefits of polyandry, things are more complex in the region with complete summer generation. Although the difference in the average female mating frequency between generations (cohorts 1 and 3) was not significant, the number of matings increased rather than decreased from the spring to the summer generation, as Bergström et al. (2002) suspected. Despite the slight increase in the average mating frequency, the prevalence of monandry was constant across generations. Therefore, it seems that even in southern Finland, offspring of highly polyandrous females entered diapause in larger numbers than offspring of monandrous ones, implicitly suggesting variation in diapause propensity between the strategies (see below). This is highlighted by the observation that the proportion of monandrous females in the summer generation was higher in each population than expected based solely on their relatively low lifetime fecundity. Anyway, even if decreasing butterfly abundance from the spring to the summer generation indicates that only a fraction of individuals emerge within the same season, increasing butterfly abundance may not indicate that all offspring of the spring generation develop directly into adults (see also Wiklund et al., 1992). Interestingly, focusing only on the average mating frequencies would have resulted in misleading conclusions, which emphasizes the need to explore exact frequencies of different mating tactics rather than relying on average mating frequencies.
Because the variance in the number of descendants produced within a generation is important in addition to the average number of descendants in the long term (Dempster, 1955; Gillespie, 1977; Seger & Brockmann, 1987), annual fluctuations in the season length may well promote the co-existence of different female mating tactics. In the partially bivoltine region in central Finland (Oulu), thermal summer on average has begun on 30 May (range: 6 May–16 June), and has lasted until 7 September (21 August–27 September) during 1971–2000 (Finnish Meteorological Institute, 2007). The average dates for the onset and end of thermal summer in southern Finland (Helsinki) during the same period were 18 May (26 April–6 June) and the 23 September (3 September–16 October) respectively. Therefore, there may occasionally be such years even in southern Finland when only a partial summer generation will emerge. It thus follows that high early fecundity (low mating frequency) results in relatively constant reproductive output, whereas the adaptive significance of high lifetime fecundity associated with a long egg-laying period (high mating frequency) is more variable, depending on environmental conditions in a particular year.
All else being equal, the developmental stage sensitive to diapause-inducing cues will be reached earlier by an average offspring of monandry line than that of polyandry line due to the different fecundity schedules of the strategies. Consequently, the proportion of offspring that undergo direct development will be larger in the monandry than in the polyandry line. The variation in the proportion of offspring entering diapause may be reinforced by increased diapause propensity of polyandrous lines, evolved by means of reproductive depression avoidance. Pupation dates of offspring produced by polyandrous females will be distributed over a disproportionately longer time scale compared to offspring of monandrous females in the summer generation. Late-hatching offspring in the summer generation may not reach the over-wintering stage before the onset of winter, and hence the optimal switching point between the developmental pathways tends to be earlier in the season for polyandry than for monandry. This response is predicted by our model. Given that juvenile development to the pupal stage lasts 29.96 (95% CI: 29.48–30.43) days in the wild, the above reasoning likely holds true especially in central Finland, where the summer generation flies until mid-August and autumn frosts are common already in early September. Moreover, a head start of 4–8 days induces strong asymmetry in juvenile competition in favour of older larvae in P. napi (Kivelä & Välimäki, 2008). Thus, offspring of polyandrous females will suffer from a high mortality under resource competition, which is most likely to occur among offspring of the complete summer generation due to relatively high population density. Increased risk of competition in the summer generation should select for increased diapause propensity associated with polyandry.
What we expect is a saw-tooth cline in mating frequencies like the one proposed by Masaki (1972) for body size in crickets with alternative life cycles. First, consider the univoltine northern region. At the northern boundary of the species range, the season length is more or less the same as juvenile development time. Thus, only eggs that are laid early in the season will reach the over-wintering stage in a set time, which favours monandry. In accordance, the proportion of monandrous females increases towards the north, being as high as 35% in some of the northernmost populations (Välimäki & Kaitala, 2006; Fig. 2). As we move southwards along the latitudinal gradient, the prevalence of monandry will decrease as the season length increases. Actually, our model predicts that monandry should vanish when moving south until production of a summer generation becomes possible for monandry, which is coupled with a relatively short generation length. At this point, monandry can again remain within a population, and there should be a sudden shift towards low mating frequencies. Within the bivoltine range, the predicted frequency of monandry again decreases in the summer generation as season length increases. Monandry is, however, maintained with a relatively high frequency in all bivoltine populations because monandrous females are relatively numerous in partial summer generations, and they are the first to emerge and lay eggs in complete summer generations. Consequently, monandry escapes competition with polyandry in the summer generation, and thus is not excluded from the population. Hence, the predictions of the model by Roff (1980) exploring clinal variation in development time and body size may well be applicable to any life history trait interdependent with generation length.
Poor weather conditions not allowing polyandrous females to take advantage of their late life benefits in the wild in spring may alternatively explain the observed patterns. Furthermore, there may be phenotypic plasticity in the mating frequency due to larval conditions, or males of the summer generation transfer relatively larger ejaculates that take longer to be depleted than those of the spring generation. The two former explanations are unlikely because weather conditions were exceptionally favourable in the year of our study (as indicated by an abundant summer generation even in central Finland), and female mating frequency is quite insensible to nutritional stress during larval development (Bergström & Wiklund, 2002). The last possibility requires that males should achieve relatively larger size than co-existing females in the summer than in the spring generation. This is because the male trait with the most obvious effect on female remating behaviour is ejaculate volume (Sugawara, 1979; Rutowski et al., 1981; Kaitala & Wiklund, 1994), which is positively correlated with male size (Svärd & Wiklund, 1989; Bissoondath & Wiklund, 1996). Accordingly, there is selection for constant male size independently of development time in nuptial gift-giving species (Wiklund et al., 1991). Although a large ejaculate delays female remating (Kaitala & Wiklund, 1994), variation in male size does not account for monandry in P. napi (Wedell, 2001). Thus, the last explanation is not satisfactory either. In addition, our modelling effort shows that the differences between monandry and polyandry in the timing of reproduction may produce the observed patterns alone.
Seasonality is a factor to bear in mind when considering the adaptive significance of alternative life history strategies, as Roff (1980) pointed out. Our results suggest that monandrous P. napi females contribute relatively more to the following generations than expected based on the difference in the reproductive potential among strategies, especially when the production of an additional generation within a season is time-limited. This combined with variation in season length among years may explain why life history strategies associated with low mating frequencies and relatively low lifetime fecundities are maintained in wild butterfly populations. A general implication of this would be that a high reproductive rate in the early days of sexual maturity is not only beneficial in growing populations (Roff, 1992; Stearns, 1992), but also in stable ones under time limitation.
We are indebted to W. Blanckenhorn, J. Itämies, Annukka Kaitala, B. Karlsson, J. Kotiaho, S. Rytkönen, T. Tammaru, C. Wiklund and our research group members and several anonymous referees for comments on the manuscript. This study was partly financed by the Ella and Georg Ehrnrooth foundation, EnviroNet (the joint graduate school of the University of Oulu and NorNet), the Jenny and Antti Wihuri foundation, Societas pro Fauna et Flora Fennica (grants to S.M.K.) and Oskar Öflund foundation (grant to P.V.). The original idea of the study was developed by the authors P.V., S.M.K. and A.K., the two former ones being mainly responsible of writing the manuscript. The empirical part was conducted by L.J., P.V. and S.M.K., whereas the modelling effort was put forward by S.M.K., V.K. and J.O. All of Finland’s guidelines and legal requirements for the use of animals in research were followed.