Adaptation to the new land or effect of global warming? An age-structured model for rapid voltinism change in an alien lepidopteran pest


  • Takehiko Yamanaka,

    Corresponding author
    1. Laboratory of Applied Entomology, Graduate School of Agricultural and Life Sciences, The University of Tokyo, Bunkyo-ku, Tokyo 113-8657, Japan; and
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  • Sadahiro Tatsuki,

    1. Laboratory of Applied Entomology, Graduate School of Agricultural and Life Sciences, The University of Tokyo, Bunkyo-ku, Tokyo 113-8657, Japan; and
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  • Masakazu Shimada

    1. Department of Systems Sciences (Biology), The University of Tokyo 3-8-1, Komaba, Meguro-ku, Tokyo 153-8902, Japan
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*Correspondence and present address: T. Yamanaka, Biodiversity Division, National Institute for Agro-Environmental Sciences, 3-1-3 Kannondai, Tsukuba, Ibaraki 305-8604, Japan E-mail:


  • 1Hyphantria cunea Drury invaded Japan at Tokyo in 1945 and expanded its distribution gradually into northern and south-western Japan. All populations in Japan were bivoltine until the early 1970s, at which time trivoltine populations appeared in several southern regions. Presently, H. cunea exists as separate bivoltine and trivoltine populations divided around latitude 36°. In the course of this voltinism change, the mean surface temperature in Japan rose by 1·0 °C.
  • 2To determine whether and how this temperature increase might be responsible for the voltinism change, we constructed an age-structured model incorporating growth speed driven by actual daily temperature and detailed mechanisms of diapause induction triggered by both daily photoperiod and temperature.
  • 3The simulation result suggests that both the acceleration of the growth speed and the prolongation of diapause induction are necessary to cause changes in voltinism, regardless of temperature increase. We concluded that the H. cunea population changed its life-history traits as an adaptation parallel with its invasion into the south-western parts of Japan.
  • 4Though the temperature increase had little effect on the fitness and heat stress in bivoltine and trivoltine populations, the trivoltine life cycle has become advantageous at least in marginal regions such as Tokyo.


Insects living in temperate climates usually enter winter diapause to avoid the impact of harsh environments on sensitive life stages (Taylor & Karban 1986; Danks 1987). They often face alternatives of whether to develop an extra generation within the limited growing season between severe winters, or to diapause for safety. In many insect species, diapause is programmed well in advance using environmental cues such as day length, temperature and occasionally food quality (Danks 1987; Denlinger 2002). Theoretical biologists have been fascinated with such the insect strategies, how they adapt themselves to the climatic conditions in their habitat range. Especially, many studies are focusing on geographical variations in the two main life-history traits related to diapause: photoperiodic response and developmental speed. To summarize the studies’ findings, generations of multivoltine species discontinuously increase toward southern regions when we consider cases in the northern hemisphere (e.g. Masaki 1972; Kikukawa & Chippendale 1984). Northern populations are more sensitive to day length after summer and more readily diapause than do southern ones for the sake of risk hedging against the sudden onset of winter (Taylor 1986; Danks 1987).

Besides the theoretical context, adaptation of alien insects to the new land climate is also an emerging issue in applied ecology. If evolutionary changes of their life-history traits are fairy rapid, we cannot make facile prediction for their expansion based on the properties in their original lands. The fall webworm Hyphantria cunea Drury is an introduced lepidopteran pest in Japan. All H. cunea populations in Japan were bivoltine until the early 1970s, at which time trivoltine populations appeared in several southern regions. Presently, H. cunea exists as separate bivoltine and trivoltine populations divided around latitude 36°. H. cunea provides an opportunity to investigate directly how insects can change their life-history traits to adapt to an alien habitat, as its invasion was relatively recent and many life-history studies on it have been conducted by Japanese ecologists, from the 1960s (e.g. Itô, Miyashita & Yamada 1968; Masaki, Sekiguchi & Kawasaki 1968) up to more recent years (e.g. Gomi & Takeda 1996; Gomi 1997). Thus, we can directly query the reason for rapid change in life-history traits of this insect instead of inferring it based on current geographical conditions.

In this paper, an age-structured model was developed to untangle the questions of how and why the trivoltine population arose in the southern part of Japan. Age-structured model analysis is a powerful tool for understanding the role of insect life-history traits, because key parameters can be easily and exhaustively evaluated in virtual systems before conducting massive experiments in the real world (Gurney & Nisbet 1998; Caswell 2001). In our study, two major life-history traits were analysed: (1) the mechanism of diapause induction triggered by daily photoperiod and temperature, and (2) developmental speed driven by daily temperature. The effect of leaf senescence was also incorporated because it may interact with the two major traits. First, a change in voltinism was associated with changes in both major life-history parameters in the Tokyo population. Second, the effect of the date of leaf senescence on voltinism was examined in the Tokyo population. Finally, fitness measured as the annual growth rate of the population was compared using temperature data sets of the 1960s and 1990s among eight regions south to north to see how fitness varies at various times and places in association with temperature increase. Additionally, the cost is also calculated as the heat stress that burdens diapausing pupae before winter. Based on these simulation results, we discuss how H. cunea have developed a trivoltine life cycle in the southern part of Japan.

Study insect

H. cunea is native to North America, and was accidentally introduced into Tokyo (35°42′ E, 139°45′ N) in 1945 (Ishii 1966). H. cunea has rapidly extended its distribution in Japan in both the northern and southern directions (Fig. 1).

Figure 1.

H. cunea distribution and its voltinism in the 1960s (a; right) and in the 1990s (b; right). Dark and light grey represent bivoltine and trivoltine life cycles, respectively. Temperature in 1960 (a; left) and the mean temperature increase from the 1960s to the 1990s (b; left) are also shown. Isotherms were generated by kriging after an exponential model was fitted to the mean temperature recorded at 157 meteorological stations (Japan Meteorological Agency; using the R library, ‘sgeostat’. The voltinism records of the 1960s were based on Itô (1972) and those of the 1990s on Gomi (1997), and they were updated by information provided by local governments (bivoltine: dark grey, trivoltine: light grey areas in the right side panels).

Gomi (1996a, 1997) found that acceleration of the larval growth speed and the prolongation of diapause induction occurred in the south-western populations between 1970 and 1990. He found that trivoltine population growth acceleration occurred mainly in larval stages and that the reduction was caused by the increased incidence of sixth instar, instead of seventh instar, maturation.

H. cunea is known to possess a typical long-day photoperiodic diapause response (Morris 1967; Masaki et al. 1968). Namely, the long-day condition from spring to early summer prevents diapause, but shorter days from late summer to autumn induce and maintain diapause. For Japanese populations, Masaki et al. (1968) reported that the critical day length (CDL) above which diapause was excluded was 14 h 35 min. This finding was fairly constant across a wide range of temperatures (17–27 °C), and little variation was observed among bivoltine populations until 1970 (Fig. 1a; right). From 1993 to 1995, Gomi (1997) resurveyed 12 geographical populations in regard to CDL and found that there was a great reduction of CDL in the trivoltine populations. These populations showed not only shortened CDL but also developed temperature dependence. CDLs at 20 °C in the trivoltine populations were about 14 h 25 min, which is not very different from those of the old bivoltine population (about 14 h 35 min). However, CDLs at 25 °C had drastically declined to about 13 h 50 min in the trivoltine populations.

On the other hand, the temperature has increased broadly all over Japan. Kiritani (2006) reported that the temperature in Japan has increased by 1·0 °C on average during these 40 years. In fact, the difference in mean temperature between the 1960s and 1990s was over 1·0 °C and was conspicuous in the northern and inland parts of Japan (Fig. 1b, left panel). To discuss the geographical adaptation and the effect of the temperature increase, two types of life-history parameter combination were set up for this study, hereafter designated the ‘new type’ and ‘old type’. The new type corresponds to the current trivoltine life-history traits in the south-western part of Japan while the old type is the old bivoltine one from the 1960s and those remaining in the northern part of Japan even into the 1990s. As shall be seen in the next sections, data concerning the Tokyo and adjacent populations were used to estimate parameters for both the new and old types, though certain variations have been reported in the current southern populations (Gomi, Inudo & Yamada 2003). It is assumed in this paper that the difference between the new and the old type is much more conspicuous than the difference within each type.

Model formulation

The model is a discrete and deterministic numerical simulation. Simulations are run annually with 365 daily time steps (t) and are driven by actual meteorological data. One thousand post-diapause pupae (Nini) are inputted on day –0 (1 January) of every 1-year simulation. Their emergence and the subsequent age structure of their descendants were observed daily until day –365 (31 December). Post-diapause pupae are reset to Nini every year. Daily minimum (TLt) and maximum (THt) temperatures in each location were retrieved from the Japan Meteorological Agency ( Day length (DLt) used in simulations was also based on actual records in each location published by the National Astronomical Observatory of Japan (, but one extra hour was added in order to include the effects of twilight at dawn and sunset (Takeda & Masaki 1979).

Schematic procedures in the model are shown in Fig. 2 as a flow chart. The model consists of six parts: diapausing pupa, adult, egg, young larva, old larva and pupa processes. All six except the adult process exhibit temperature-dependent growth (the grey-shade valves in Fig. 2) while all the adults oviposit the next generation on the day they emerge and soon disappear from the simulation. All the simulations and the analysis were executed in a statistical environment; R (Ver2·21: CRAN,, in which a library of age-structured growth was programmed with C language specifically for this study.

Figure 2.

Basic structure of the model. Solid arrows indicate the daily steps and dashed arrows provide information for the calculation. Grey-shaded valves represent temperature-dependent growth and hollow valves are numerical regulations.

development of cohorts

In the model, a group of individuals laid as eggs by all female moths ovipositing on the same day i is called a ‘cohort’ (Li,t: where i is the day of oviposition and t is the current day of the calculation). These cohorts are assumed to grow linearly in relation to daily temperature as long as it is within an effective range, as is the case with most poikilotherms. It is well known that the total summation of this effective temperature is rather constant for passing each stage and is called the ‘thermal constant.’ In our study, the effective temperature is calculated by the single triangle method with a horizontal cut-off (Roltsch et al. 1999) considering the effect of the diurnal fluctuation of the temperature and the growth retardation of H. cunea in high temperatures (Itôet al. 1968). In this method, the trend of diurnal temperature is schematized as an isosceles triangle whose apex is the maximum temperature (THt) and whose base is the minimum temperature (TLt). The effective temperature of the day is calculated as the overlapping area between the temperature triangle and the optimal minimum (Tmin) to maximum (Tmax) growth range. In the model, the cohort (Li,t) accumulates its heat unit (Hi,t) from day i up to day t, calculated by this method (denoted as trianglefunc in eqn 1).

Hi,t = Hi,t–1 + trianglefunc(TLt,THt) (eqn 1)

When Hi,t exceeds the thermal constant of the egg, Cegg, the cohort Li,t is assumed to eclose into larvae at day t. When Hi,t exceeds the summed thermal constant of the egg and the larva, Cegg + Clarvae, the cohort Li,t is assumed to pupate at day t. Though all individuals in the cohorts are assumed to grow up simultaneously until the pupal stage, growth variation among individuals in a cohort was generated in the process of adult emergence (see next section).

All the parameters used in the model are listed in Table 1. According to Itôet al. (1968) and Gomi (1996a), the minimum and maximum thresholds were fixed as Tmin = 10·5 and Tmax = 28·0 for all stages. The thermal constant of the new type for egg, larva and pupa were fixed as Cegg = 146, Clarvae = 388 and Cpupa = 183, respectively. These values were re-calculated with the new minimum threshold defined in our study (Tmin = 10·5) based on laboratory experiments for the trivoltine population near Tokyo (Gomi 1996a). For the old type, only the larval thermal constant was higher Clarvae = 461, based on the old Tokyo population data (Itôet al. 1968).

Table 1.  A list of the model parameters and the default values used in simulations
ParameterDescriptionCanonical valueUnit
Simulation settings
TimestepSimulation period in 1 year365day
NiniInitial input number of pupae in diapause1000
rGrowth rate between generations1·0
DendEnd day of leaf senescenceEstimated by the phenomenological regression model (eqns 6 and 7)Julian day
DstartStart day of leaf senescence (Moore 1965; Millard & Proe 1991)Dend–30Julian day
New type (Tokyo population in 1990s)
TminThermal threshold of development (Itôet al. 1968)10·5°C
TmaxOptimal temperature for development (Itôet al. 1968)28·0°C
CeggCumulative heat unit required for passing egg stage (Gomi 1996a)146·0day-degree
ClarvaeCumulative heat unit required for passing larval stage from hatching (Gomi 1996a)388·0day-degree
CpupaCumulative heat unit required for passing pupal stage from pupation (Gomi 1996a)183·0day-degree
CDpupaCumulative heat unit required for passing pupal stage from pupation (Gomi 2000)275·0day-degree
σpupaStandard deviation of the Cpupa (Itô & Endo 1970)60·0day-degree
CDL25Critical day length for diapause at 25 °C (Gomi 1997)13·9h
CDL20Critical day length for diapause in 20 °C (Gomi 1997)14·4h
Old type (Tokyo population in 1960s)
CDL25Critical day length for diapause at 25 °C (Masaki et al. 1968)14·6h
CDL20Critical day length for diapause in 20 °C (Masaki et al. 1968)14·6h
ClarvaeCumulative heat units required for passing young larval stage from hatching (Itôet al. 1968)461·0day-degree

Emergence of the overwintering (post-diapause) pupae is also linearly related to the effective cumulative heat units (Itô & Endo 1970), regardless of the timing of diapause induction in the previous year (Gomi 1996b). We estimated the thermal constant (CDpupae) for post-diapause development based on field data from 1965 to 1969 (Itô & Endo 1970) and from 1993 (Gomi 1996b) at locations near Tokyo using our single triangle method. The thermal constant for post-diapause emergence was determined as CDpupa = 275 for both new and old types because it was calculated at approximately 275 based on data from both the 1960s and the 1990s.

adult emergence and reproduction

In order for the cohort emergence to exhibit dispersion similar to populations in nature, it was assumed that the emergence on day t takes place according to a Gaussian distribution (normal(x), a function of the effective heat units x with mean = Cegg + Clarvae + Cpupae and SD = σpupa). The number of newly emerging adults (At) is the sum of the product of the total number of pupae pupating on day k and their emergence probability on day t.

image(eqn 2)

It should be noted that the initial pupae (Nini) input into the simulation are assumed to have terminated their diapause, never to diapause again; their effective cumulative heat units are considered the starting point of pupal development (Hi,0 = Cegg + Clarvae). They also emerged according to a Gaussian distribution, though with a different mean (Cegg +Clarvae + CDpupae) from normal pupae, though they had the same SD (i.e. σpupa = 60) to the nondiapausing pupae, based on the calculation from our triangle method for the field records of overwintering generations near Tokyo, 1965–69 (Itô & Endo 1970).

All adults emerged on day t were assumed to produce progeny (Lt,t) on the same day, and the adults were removed. Asexual reproduction was implicitly assumed in the model as it was the simplest and most tractable, as well as because it reflects the biology of H. cunea. The adults emerge at dusk during the summer and start mating in the morning of the next day (Masaki 1975). They are quite ephemeral because they do not have mouthparts and suffer strong predation by birds (Hasegawa & Itô 1967). The total number of eggs oviposited at day t is multiplied by the generational growth rate r, and their effective cumulative heat units start at zero.

image(eqn 3)

The parameter r was the composite value including fecundity and mortalities for each stage and was assumed to be a fixed value for all seasons. Though r is an important parameter determining the abundance of each generation, there is no appropriate method to estimate it based on field census. This is because we did not incorporate any form of population regulation. Therefore, we arbitrarily set r equal to 1·0. Population size will not change unless individuals are killed by the shortage of the food (see Host phenology). Though it is an unrealistic assumption, the pure effect of the timing of diapause on fitness and heat stress can be explored by simulation analysis.

diapause induction

In the model, the diapausing pupae were assumed to stop their growth and only they can survive to the end of the year (Nend in Fig. 2). Masaki (1975) reported that the first half of the larval period is the most sensitive to day length, even though the organisms diapause at the pupal stage. Therefore, cohorts are destined to diapause or not, when they are just at the mid-larval stages (Hi,t = Cegg + Clarvae/2; the black diamond in Fig. 2). At this timing, the day length (DLt) was compared with CDL. To incorporate the temperature dependence in the model, CDL was linearly extrapolated from CDL at 25 °C (CDL25) and 20 °C (CDL20).

image(eqn 4)

The temperature used in eqn 4 (the first element in parenthesis in the first term) is the 5-day average of maximum and minimum temperatures around day t. The second term in eqn 4 regulates CDL25 to be the singular value of CDL when CDL25 exceeded CDL20 in the simulations analysis.

For the old type, the CDLs at 20 °C and 25 °C are identical (CDL25 = CDL20 = 14·6) according to Masaki et al. (1968). The new type has a slightly shorter CDL at 20 °C (CDL20 = 14·4) and has a much shorter one at 25 °C (CDL25 = 13·9), as reported by Gomi (1997).

host phenology

Though it has been reported that some of the diapause induction of some herbivore insects was affected by the quality of their foods (e.g. Feeny 1970; Danks 1987; Denlinger 2002), that of H. cunea is not (Gomi et al. 2005). None the less, the timing of leaf senescence (Dstart) is still crucial for determining the voltinism of H. cunea because it causes larval starvation after late autumn. On the other hand, it was hard to designate an exact date for Dstart in various years and locations.

Therefore, an absolutely phenomenological regression model was constructed and was used to estimate Dstart for each simulation in various places and years. The Japan Meteorological Agency keeps records of the dates when all the leaves of a particular maple species Acer palmatum (Thunberg), which is one of the suitable hosts trees for H. cunea, changed their colour. However, many of such values are missing for various times and locations. Thus, a generalized additive model was constructed to complement them based on the locations and temperatures:

image(eqn 5)

end is the estimated date when almost all of the leaves change their colours. The predictors, tempSep, tempOct and tempNov, are the monthly mean temperature of September, October and November, respectively, at eight cities picked up in this study (Fig. 1a) from 1953 to 1994. lat, lon and alt are the latitude, longitude and altitude of the cities. s-function expresses the nonlinear relationship using the cubic smoothing spline (all s-function has 4 d.f.; Hastie & Tibshrani 1990). All these regression analyses were conducted by the library ‘gam’ in R. After the AIC-based selection procedure (Chambers & Hastie 1993), the final model was determined as

image(eqn 6)

All the predictor had nonlinear effects except for tempOct s(alt), tempOct and s(tempNov) had statistically significant effects at the 0·1% level on end (F167,4 = 1136·5, F167,1 = 834·1, F167,4 = 1043·0, respectively). In short, leaves change their colours earlier in places of high altitude and low temperatures in October and November. end, however, cannot be used directly as the timing of leaf senescence as it gradually proceeds 60–80 days before the leaves’ total colour change (Moore 1965; Millard & Proe 1991). Therefore, we determine Dstart arbitrary subtracting 30 days from the estimated end.

image(eqn 7)

The effect of Dstart on H. cunea dynamics is also examined through a sensitivity analysis in regard to the old and new Tokyo populations.

Simulation analysis

comparison between model prediction and field census

Figure 3(a) shows the results of the simulation of the new type with the temperature data set from 1994 and 1995 and the Tokyo day length. The timing and duration of the adult prevalence were perfectly predicted in comparison with the field census (dashed lines in Fig. 3a) in both 1994 and 1995.

Figure 3.

Comparison between simulations and field census data. (a) Pheromone trap catches of the males at Tokyo in the 1990s (Yamanaka et al. 2001), (b) percentage of the light trap catches within a generation at Hiratsuka, near Tokyo, in the 1960s (Itô & Endo 1970), and (c) pheromone trap catches of males of the Shiojiri population in 2000s (referring to the report of the Nagano Plant Protection Office with their permission; Simulations were executed using the temperature and day-length data sets of each region. The new type was used in (a) and the old types were used in (b) and (c). In the upper panels of all figures, solid lines represent the simulation results and dashed lines the field data. Lower panels represent the age composition of each simulation. DP, pupae after diapause; OA, adults in overwintered generations; 1P–2P, pupae in the first and the second generation, 1A–2A, adults in the first and second generation; 3DP, diapausing pupae in the third generation; black, diapausing pupae; white, adults; light grey, egg; medium grey, larvae; dark grey, nondiapausing pupae.

Simulations of the old type were also executed using the old Tokyo temperature from 1965 and 1966 and with the temperature in 2003 and 2004 at Shiojiri (the current bivoltine region; 36°6′ E, 137°56′ N; high land city in Fig. 1) to check if our model assumptions are valid even in bivoltine cases. Actual day-length data in each region was used in each simulation. The simulation using the old-type parameters successfully revived the bivoltine phenology in the 1960s (Fig. 3b). All the diapausing pupae were from the second generation in this simulation (the black areas in Fig. 3b, lower panel). The timing and duration of the adult prevalence were also remarkably accurate even in the 1960s. The simulation results for old-type parameters using the current temperature and day-length data at Shiojiri are also shown in Fig. 3(c) (the field capture data was collected by Nagano Plant Protection Office). The simulations in 2003 and 2004 also produced the bivoltine phenology and their timing and duration were also successful.

voltinism changes with various cdl25 and clarvae for tokyo populations

To examine the sensitivity of the two major parameters, Clarvae and CDL25 in association with temperature increase in Tokyo, simulations were executed with progressive changes (every 7 day-degree for Clarvae and every 4·5 min for CDL25). The other parameters were canonical values as listed in Table 1. For every combination, simulations were executed annually with the temperature data from 1990 to 1999 (1990s hereafter) and from 1961 to 1970 (1960s hereafter) and with the day length of Tokyo. The conditions in Tokyo were specifically picked up in this section because the Tokyo population had been bivoltine until 1970, after which it has gradually changed to trivoltine and has been well studied from the 1960s.

Our model always produces mixed-voltinism life cycles as the number of individuals is expressed in double precision. Therefore, if trivoltine pupae were the majority (> 66·7%) over a 10-year period (1960s or 1990s), we categorized them as trivoltine, or vice versa, as bivoltine.

The result regarding the 1990s is shown in Fig. 4(a). It is clear that the new type (the white circle in the white area) is located on the trivoltine area, while the old type (the black circle in the black area) is located on the transient area. The result regarding the 1960s is also shown in Fig. 4(b). It is surprising that bivoltine region did not largely prevail in the 1960s; no drastic change was observed from Fig. 4(b) to Fig. 4(a) though the average temperature of the 1990s in Tokyo had increased 1·6 °C from that of the 1960s. These results suggest that the old type would not be able to show a typical trivoltine life cycle even if they were transplanted to Tokyo in the 1990s and vice versa.

Figure 4.

Voltinism regimes in Tokyo with various combinations of the two parameters, the thermal constant for larvae (Clarvae) and the critical day length at 25 °C (CDL25). (a) The temperature data set in the 1990s, and (b) in the 1960s. The white area represents the trivoltine, the black area bivoltine, and the grey area the transitional voltinism. The white circle represents the parametric values of the 1990s (Gomi 1996a) and the black circle those of the 1960s (Itôet al. 1968; Masaki et al. 1968).

It was expected that the 1·6 °C increase at Tokyo seemed sufficient to favour the trivoltine population in a much wider parameter region in Fig. 4(b). However, careful consideration is needed because the 1·6 °C increase was converted into a 239 day-degree increase by the calculations of eqn 1. This is much smaller than the simple multiplication of 1·6 °C by 365 days. To visualize the effect of the temperature increase in Tokyo, in Fig. 5 the minimum and maximum temperatures were depicted together with the day length and the critical day length of the new and the old types. The reason for this discrepancy thus becomes apparent: the temperature increase was most prominent for the minimum temperature in winter and autumn. An increase in winter minimum temperature will not contribute to the increase of cumulative heat units as the temperatures are lower than the minimum threshold for growth. In addition, an increase in autumn's minimum temperature also will not accelerate H. cunea growth as it has already entered diapause, though it was accounted for in the 239 day-degree increase.

Figure 5.

Day length and temperature increases in Tokyo. The horizontal line in the upper panel indicates the critical day length in the 1960s (CDL25(60s)) and the grey-shaded range indicates the critical day length in the 1990s (from CDL25 to CDL20). The horizontal line in the lower panel is the minimum threshold of growth. Mean daily maximum and minimum temperatures were averaged daily and smoothed (d.f. = 9) using the ‘gam’ library in R from 1961 to 1970 (dashed lines) and from 1990 to1999 (solid lines).

sensitivity analysis of dstart for voltinism in the tokyo population

Though the date of leaf senescence (Dstart) was calculated based on actual field data, 30 days was arbitrarily subtracted from the estimation by the regression model (eqn 7). Moreover, H. cunea feeds on various types of deciduous trees (Warren & Tadic 1970) and the actual date of leaf senescence might have some variation among trees. Therefore, Dstart was examined in conjunction with the larval thermal constant (Clarvae) and the critical day length at 25 °C (CDL25); i.e. voltinism was calculated changing Dstart every 4·5 days from 23 September to 17 December.

Simulations were executed in four series. In the first series, the temperature data set from the 1990s was used for all the simulations (Fig. 6a). Accompanying the Dstart change, CDL25 was also changed every 4·5 min while Clarvae was fixed as 388 (the growth speed of new type). Estimated Dstart from 1990 to 1999 are also simultaneously plotted on the perpendicular line CDL25 = 13·9 (the value of the new type). In short, we examined the mixed effects of both Dstart and CDL25 in the situations of 1990s. In the second series, all the procedures were as same as the first one, but the temperature data set and other conditions were from the 1960s (Fig. 6b). Clarvae was fixed as 461 (the growth speed of old type). Estimated Dstart from 1961 to 1970 are plotted on the perpendicular line CDL25 = 14·6 (the old type). In the third series, the temperature data sets were those from the 1990s and Clarvae was changed for every 7 day-degrees while CDL25 was fixed as 13·9 (the new type; Fig. 6c). Estimated Dstart from 1990 to 1999 are also simultaneously plotted on the perpendicular line Clarvae = 388 (the new type). The mixed effects of both Dstart and Clarvae were examined in this series with the situations of the 1990s. In the fourth series, all the procedures were the same as the third one, but the temperature data set was from the 1960s. CDL25 was fixed as 14·6 (the old type; Fig. 6d). Estimated Dstart from 1961 to 1970 are plotted on the perpendicular line Clarvae = 461 (the old type) in Fig. 6(d).

Figure 6.

Sensitivity analysis for the date of leaf senescence (Dstart). (a) Dstart and the critical day length at 25 °C (CDL25) are examined with temperature in the 1990s. For comparison, Dstart estimated for 10 years from 1990 to 1999 are also plotted (black circles). (b) as same as (a) but temperature data and estimated Dstart (white circles) are those from the 1960s (c) Dstart and the thermal constant for larvae (Clarvae) with temperature in the 1990s. Dstart estimated for 1990s are also plotted (black circles). (d) Same as (c) but temperature data and estimated Dstart (white circles) are those from the 1960s. The shaded area in the left bottom of (b) represents extinction of the population.

In Fig. 6, the date of leaf senescence (estimated Dstart) was retarded almost a month (23·8 days on average) for a period of 30 years. In the series from the 1990s (Fig. 6a,c), trivoltine regions prevailed over a wide range of parameters and Dstart had a little effect on voltinism. This was because temperature had increased in favour of the trivoltine life cycle and the counterpart parameters that were fixed are those of the new type. Therefore, the simulations for the new type in the 1990s are consistently trivoltine in a wide range of Dstart.

In the series from the 1960s, individuals are strongly affected by the timing of Dstart up to the old-type value of CDL25 (Fig. 6b) and Clarvae (Fig. 6d). This was because individuals who have small CDL25 or Clarvae will produce the transient dynamics from bivoltine to trivoltine. The partial trivoltine larvae will starve after early leaf senescence. A small extinction area is seen in Fig. 6(b) (left bottom) in which all the individuals cannot move into diapause in early summer because of small CDL25 yet cannot survive in autumn because of their slow growth speed. Large values of CDL25 and Clarvae (Fig. 6b,d, right side) produce a steady bivoltine population for a wide range of Dstart because such large values will not produce partial trivoltine larvae in autumn.

From these results, the typical bivoltine life cycle of the old type in the 1960s and the typical trivoltine one of the new type in the 1990s would not be altered even if Dstart had been shortened or lengthened within a month. Though retardation of the date of leaf senescence by itself cannot promote a trivoltine life cycle, it contributed slightly to it subsidiary to the change of main two life-history parameters, CDL25 and Clarvae.

fitness of eight regional populations in association with a temperature increase

H. cunea must have changed its life-history traits in Tokyo regardless of the temperature increase. But why did this occur? They could have maintained their previous life-history traits, continuing as the old type. In this section, fitness is defined and calculated for the new and old types using temperature and day-length data of various regions in the 1960s and 1990s. Some of the old theoretical works hypothesized that an increased number of generations increases fitness far more than does producing a larger number of offspring (Cole 1954; Levins 1969; Charnov & Schaffer 1973). However, this may not be true for insects that have discrete generations because inappropriate timing of diapause induction will cause high mortality. In an age-structured model, Taylor (1986) calculated fitness as the number of successfully overwintering individuals. His model assumed a narrow window for the diapause stage before the onset of the winter.

Though fitness might be a compound value of viability and fertility for an individual (Falconer & Mackay 1996), it was fixed as a constant in our study (r = 1·0) and cannot be used to compare the effect of temperature increase. Therefore, fitness for the new and the old types was calculated as annual population growth, after Taylor (1986), as follows:

image(eqn 8)

The total number of diapausing pupae in each year (Nend(i)) was divided by Nini = 1000 to determine the annual growth rate. The mean annual growth rate during 10 years (1960s and 1990s) was calculated as fitness in eqn 8. Both new and old types were tested in terms of the temperature and day-length conditions in the 1960s and 1990s for eight regional populations: Tokyo, Aomori (40°49′ E, 140°45′ N), Sendai (38°16′ E, 140°52′ N), Niigata (37°55′ E, 139°2′ N), Shiojiri, Osaka (34°41′ E, 135°30′ N), Kochi (33°33′ E, 133°32′ N) and Kumamoto (32°48′ E, 139°2′ N) (Fig. 1a, left). The average temperature increased in all eight regions from 0·2 to 1·2 °C within 30 years.

Simulation results are listed in Table 2. In the southern regions (Tokyo, Osaka, Kochi and Kumamoto), the new types have a high level of fitness (> 0·5) in the 1990s as well as in the 1960s in comparison with the northern regions. Though it slightly contradicted our expectation, the old type showed slightly greater fitness than did the new type in the southern regions even in the 1990s. It was, however, a natural consequence of our model; that is, the individuals that can easily diapause can elude the risk of starvation in late autumn if they can complete their second generation.

Table 2.  Fitness of the new and the old types in each site with temperatures of 1960s or 1990s
 Temperature data set of 1990sTemperature data set of 1960s
Old typeNew typeOld typeNew type
  1. Fitness was calculated as the mean of the yearly growth rate of the population for 10 years. Notes in the parentheses are the predicted voltinisms: bi, bivoltine; tri, trivoltine; –, transient phase. Fitness over 0·5 was marked in bold.

Aomori0·093 (bi)0·284 (bi)0·009 (bi)0·064 (bi)
Sendai0·578 (bi)0·361 (bi)0·371 (bi)0·489 (bi)
Niigata0·633 (bi)0·123 (–)0·852 (bi)0·062 (bi)
Shiojiri0·623 (bi)0·095 (bi)0·412 (bi)0·173 (bi)
Tokyo0·844 (–)0·756 (tri)0·687 (bi)0·518 (tri)
Osaka0·940 (tri)0·858 (tri)0·795 (–)0·848 (tri)
Kochi0·939 (tri)0·867 (tri)0·829 (–)0·877 (tri)
Kumamoto0·949 (tri)0·867 (tri)0·858 (–)0·852 (tri)

In the northern regions (Shiojiri, Niigata and Sendai), the fitness of the new type was consistently low both in the 1990s and the 1960s. It was predicted that the new type would have a higher level of fitness at Aomori than the old type both in the 1990s and the 1960s though both showed lower fitness levels. The old type, which has slow growth speed, has difficulty in completing the second generation at Aomori. Hence, it is anticipated that the far northern populations such as that at Aomori may currently be accelerating their growth speed in comparison with the other old types. Further laboratory experiments are needed to confirm this.

In summary, the new type has a level of fitness as high as the old type in the southern regions, while the old type still has a large advantage over the new type in the northern regions. The effect of temperature increase over 30 years was ambiguous as there is no clear difference between the results using temperature data sets of the 1960s and 1990s. However, the new type in Tokyo showed an increase in fitness from 0·518 to 0·756. This result encourages us to think that at least a marginal population such as that in Tokyo favours trivoltine life-history traits in accordance with temperature increase.

heat stress in association with temperature increase

Though, so far, little attention has been paid to the drawbacks of the early induction of diapause, some researchers have pointed out the importance of heat fatigue during diapause (Pullin & Bale 1989; Bradshaw, Zani & Holzapfel 2004). The heat stress considered here is not that caused by instances of extremely high temperature but that of metabolic consumption required by long-term mild temperatures. Actually, Gomi (2000) reported that weight loss and mortality in H. cunea in the early timing of diapause was greater than that in the latter one. In our study, such heat stress was defined as follows:

image( eqn 9)

where DPi,j is the number of diapausing pupae at day j in year i. Simulations were executed for the old and the new types for the decades of the 1990s and 1960s in each region, as in the previous section. The numerators in eqn 9 represent total cumulative heat units after diapause for all individuals and the denominators are the total number of diapausing pupae (Nend(i)) for 10 years. Therefore, heat stress is the mean cumulative heat unit acquired by the diapausing pupae.

Though the definition of heat stress is rather easy, it is difficult to interpret it in physiological sensu. If H. cunea is a type of insect that nearly completes its physical development of pupa before winter and restarts its remnant development the next spring, heat stress above the normal cumulative heat units for the pupal development (Cpupa) will be in a state of surplus. In contrast, if they stop their physical development just after the pupation as do many lepidopteran species (Danks 1987), almost all of the heat units received after pupation will be surplus and a great extent will be heat stress. As we do not have any data regarding physical development during diapause, a threshold Cpupa + CDpupa (= 458) was arbitrarily set up above which diapausing pupae suffer heavy heat stress.

Simulation results are listed in Table 3. Generally speaking, the old type suffers heavy heat stress in the southern regions while not in the northern ones. Because there is no systematic difference between the results of the 1960s and the 1990s, the effect of temperature increase seemed indiscernible. Though the new type has lower heat stress than the old type in southern regions, they suffer greater changes from 1960 to 1990 than do the old type. In contrast, the old type experienced greater heat stress but the changes were not prominent. In Tokyo, Osaka and Kumamoto, the heat stress of the old type has even decreased. Though this was a counterintuitive result, it may be interpreted by the voltinism shift in the old type. The old type in Tokyo is predicted as a transient phase in the 1990s, while the old type in Osaka, Kochi and Kumamoto has changed from transient phase to trivoltine (Table 2). Therefore, the old type in the 1990s and in the southern regions contains partial or majority trivoltine individuals. They experience less heat stress than does the new type as they grow late into autumn. To clarify this point, we also calculated the heat stress suffered only by bivoltine individuals (the numbers in the parentheses in Table 3). Such individuals of the old type suffer heavy heat stress, and it has been accentuated in the past 30 years in the southern regions.

Table 3.  Heat stress of the new and old types in each site with temperatures from the 1960s or 1990s
 Temperature data set of 1990sTemperature data set of 1960s
Old typeNew typeOld typeNew type
  1. Heat stress was calculated as the total heat units per year and per diapausing pupae (10 years average). The heat stress above Cpupa + CDpupa (= 458) are marked in bold assuming that those marked individuals suffer from heavy mortality. Numbers in parenthesis indicate the heat stress experienced by the bivoltine population only.

(228·5)(237·2)(176·1) (204·1)

From these analyses, the old type has been suffering high heat stress in the southern regions since the 1960s. Though the total heat stress for the old type has not largely changed, their bivoltine individuals in the southern regions suffered the increased heat stress in the 1990s while those in northern regions did not. The difference of heat stress between the old and the new type was most conspicuous in Tokyo. This is because the old type in Tokyo was typical bivoltine in the 1960s and in the transient phase in the 1990s (Fig. 4).


Our simulation analyses revealed that temperature increase itself was not sufficient to promote voltinism change, because the increase was not conspicuous in the growing season (Fig. 5). H. cunea has changed its life-history traits to be trivoltine in the southern regions as reported by previous studies (Gomi & Takeda 1996; Gomi 1997). We tried to explain the reason for this life-history change, specifically focusing on fitness as expressed by the annual growth rate and heat stress as cumulative heat units acquired after diapause. We found that, in the southern regions, the fitness of the new type was as high as that of the old type and the heat stress experienced by the new type was less than the old type. These findings are completely concordant with the current voltinism regime in the 1990s (Fig. 1b). Fitness of the new type has increased in Tokyo and the bivoltine individuals were burdened with increased heat stress in all the southern regions, though the effect of temperature increase was equivocal in other southern regions than Tokyo. The retardation of the date of leaf senescence may contribute to facilitation of the trivoltine life cycle during the course of change. We also calculated fitness and heat stress in relation to the date of leaf senescence, finding that the general conclusion was not different from the default definition of Dstart (results not shown).

Summarizing these results, we postulate the invasion process of H. cunea as follows. It was quite difficult for the old H. cunea population to propagate in southern areas of Japan due to the high heat stress in autumn up until 1970, as we can see it in Fig. 1(a). Thereafter, the trivoltine life cycle, which has a fast growth speed and prolonged diapause induction, was selected for and gradually prevailed in various parts of southern Japan. In parallel to this change, the old bivoltine populations in marginal regions such as Tokyo also became trivoltine. We conclude that these processes can be interpreted as an adaptation to the new habitat rather than to consider that the temperature increase promotes the trivoltine life cycle in the southern regions. However, the trivoltine life cycle is gradually forging its way into northern areas in order to escape heat stress while increasing fitness in marginal regions.

It is reasonable to assume that all H. cunea populations in Japan originated from a relatively small area in North America, based on mitochondrial DNA analysis (Ozaki & Ohbayashi 2001; Gomi, Muraji & Takeda 2004). We can rule out the possibility of phenotypic plasticity because laboratory rearing experiments confirmed that each geographical population has its own established CDL and Clarvae (Gomi 1997; Gomi et al. 2003). Thus, we conclude that they have rapidly evolved new life-history traits within only 30 years as an adaptation to their new habitat. Response to the selection for diapause induction is regarded as being fairly rapid (Tauber & Tauber 1981; Danks 1987). The critical day length of H. cunea is under polygenic control (Gomi 1997), and we are postulating that their evolutionary change can be achieved within at least 30 years and maybe much faster. By contrast, the acceleration of developmental speed is much more complicated due to the number of biological constraints (Tauber & Tauber 1982; Tauber, Tauber & Nechols 1987). However, H. cunea can contract its larval period by shrinking the number of instars without the loss of pupal weight (Gomi 1996a), though the genetic background of this change is still unknown. In addition, they can feed on an extremely broad range of deciduous trees (Warren & Tadic 1970). That is why they can accelerate their growth at the current thermal constant.

The global surface temperature has drastically increased in the twentieth century (Kerr 2000). Entomologists are starting to draw attention to an increase in the number of generations of insects based only on the cumulative heat units by referring to the current life-history traits (Porter 1995; Yamamura & Kiritani 1998). However, temperature increase itself was not sufficient to extensively change the voltinism of H. cunea, though it expressed local effects in promoting them to trivoltine in marginal regions such as Tokyo. On the other hand, H. cunea rapidly adapted to the new environment in Japan during the past 30 years by existing as separate bivoltine and trivoltine populations divided around latitude 36°. We hope that our approach employing an age-structured model may help others clarify the conglomeratic effects of global warning and the evolution of life-history traits.


We thank two anonymous reviewers for their helpful discussions and comments. We appreciate the guidance of Sandy Liebhold and Koji Yamamura in improving the logic of this manuscript. We also thank Dietmar Schwarz, who used to be TY's great neighbour in Long Meadow Lane, for his important comments. Hiroyuki Fujisawa, Dr Taneda and Dr Sugiura gave us useful information regarding tree phenology. We appreciate the Nagano Plant Protection Office ( for permitting us to use their valuable data on the current bivoltine population in Japan.