Temperature-Dependent Oviposition Models for Monochamus saltuarius (Coleoptera: Cerambycidae)

Simple Summary Longhorn beetles of the genus Monochamus are vectors of the pine wood nematode, which causes incurable pine wilt disease in coniferous trees. We developed temperature-dependent models to describe the oviposition of Monochamus saltuarius, a significant species within this genus. Our study demonstrated that these models effectively capture the nonlinear effects of temperature on the oviposition and aging of M. saltuarius adults. We compared two simulation approaches: one that separately accounted for the sexual maturation phase of adults and another that did not. Both methods proved capable of accurately describing oviposition patterns across various temperature conditions. The insights gained from this study have potential applications beyond estimating oviposition and predicting population dynamics of M. saltuarius. This modeling framework could be adapted to forecast population changes in a diverse range of pest species, offering a versatile tool for pest management strategies. Abstract Monochamus saltuarius Gebler is a serious insect pest in Europe and East Asia regions, including Portugal, Spain, China, Japan, and Korea. It transfers the pine wood nematode Bursaphelenchus xylophilus to conifer trees, resulting in pine wilt disease (PWD). As temperature is a key factor influencing insect population dynamics, temperature-dependent models describing M. saltuarius oviposition could estimate population growth potential and evaluate outbreak risks. In this study, the longevity and fecundity of M. saltuarius females were measured under constant temperature conditions ranging from 20 to 32 °C, and temperature-dependent models were constructed. The longevity of M. saltuarius females ranged from 83.36 days to 22.92 days, with a total fecundity of 141 eggs and 52.77 eggs at 20 °C and 32 °C, respectively. To describe oviposition, we used a single-phase simulation describing oviposition as a single model and a two-phase simulation describing sexual maturation and oviposition as two separate models. These models effectively described M. saltuarius oviposition (r2 > 0.96) under constant temperature conditions, with the two-phase simulation demonstrating greater accuracy overall. Such models could facilitate assessments of PWD risks. The modeling framework of this study shows potential for predicting threats from various forestry and agricultural pests.


Introduction
Pine wilt disease (PWD) is an important disease worldwide caused by the pine wood nematode Bursaphelenchus xylophilus.Coniferous species of Abies, Cedrus, Larix, Picea, Pinus, and Pseudotsuga genera are known to be hosts of B. xylophilus [1].Native to North America, PWD has spread to Europe (e.g., Portugal and Spain) and East Asia (e.g., China, Japan, and Korea), causing fatal damage to various pine trees [2,3].Over 13 species are known to transmit PWD, with longhorn beetles of the genus Monochamus being the most important vectors for B. xylophilus [4].Seven Monochamus species in North America and three in Asia have been identified as potential PWD vectors, of which M. saltuarius and M. alternatus are the main vectors in China, Japan, and Korea [5,6].Compared to M. alternatus, M. saltuarius is relatively more cold-adapted, inhabiting higher latitude regions [5].Notably, PWD was recently first reported in Liaoning Province, northeast China, likely spread by M. saltuarius [4].With climate change, cold-tolerant M. saltuarius appears to be expanding northward and increasing the risk of spreading PWD to new areas.
As with other ectotherms, temperature is likely the dominant environmental factor impacting insect biology, including key reproductive traits such as survival and fecundity [7].Insect body temperature is mainly dependent on ambient temperature.Thus, climate change causing unprecedented thermal fluctuations and extreme events can significantly influence the population density of insects.Along with range expansion, outbreaks of insects are becoming more unpredictable with climate change [8].Understanding M. saltuarius density changes is especially important for PWD management, as the density of this insect vector affects PWD epidemics [9].
Temperature influences insect survival and fecundity species-specifically.This has been described by various models based on experiments [10].In particular, multiple temperature-dependent models, including adult survival, total fecundity, and oviposition rate models, have been combined to estimate daily oviposition under varying temperatures.Although oviposition stage could be divided into sexual maturation (pre-oviposition) and oviposition phases, both phases are temperature-sensitive and often described by a unified model (single-phase simulation) [11,12].However, the shape of a unified model may erroneously depict oviposition occurring during sexual maturation phase.To address this, using a two-phase simulation by separating sexual maturation and oviposition could enable more realistic fecundity estimates [13].Such a simulation can estimate potential population growth across generations and quantitatively assess outbreak risk.
M. saltuarius overwinters as mature larvae and emerges as adults in the following spring [14].After emergence, they undergo a sexual maturation period of 1-2 weeks before oviposition [15].Female adults excavate slits in the bark of pine tree boughs and trunks to lay their eggs.M. saltuarius adults that emerge from infected trees transmit B. xylophilus to healthy pine trees during their feeding and oviposition processes [16].This study investigated the lifespan and fecundity of newly emerged M. saltuarius female adults reared under constant temperature conditions and developed temperature-dependent oviposition models.Models for single-phase and two-phase simulations were constructed, and their performances were compared.These results will aid in our understanding of the relationship between temperature and oviposition in M. saltuarius.They could be used to predict population density changes to enhance PWD management.

Oviposition Experiments
M. saltuarius-infested Korean white pine trees (Pinus koraiensis) were logged from pine stands in Hongcheon-gun, Gangwon-do, Korea (37.76102 • in latitude, 127.8895 • in longitude), in December 2014.These logged trees were kept in a semi-field emergence cage in the National Institute of Forest Science, Seoul, Korea.Newly emerged adults (<24 h) were collected daily and used for oviposition experiments.Individual pairs of newly emerged adults were transferred into cylindrical plastic containers (15 cm in diameter, height of 20 cm).Korean white pine tree trunks were cut into pine bolts.Cut ends were coated with paraffin to prevent desiccation [15].One coated pine bolt, additional twigs, and a watered cotton ball were provided to each pair of M. saltuarius.These containers were kept in environmental chambers (DS-8CL, Dasol Scientific; Hwaseong, Republic of Korea) set at five constant temperatures (20,24,28,30, and 32 • C) with a photoperiod of 14:10 h (light/dark).Survival of female adults was monitored every day.Male adults that died during early stages of the experiment (<1 week) were replaced with new male adults to Insects 2024, 15, 597 3 of 11 ensure mating.Coated pine bolts were replaced every three days.After removing all the bark from the collected pine bolts, we counted the number of eggs under a binocular stereomicroscope (Stemi 305, Carl Zeiss, Jena, Germany) until females died.Females that died within 7 days were not included in the analysis.
Total fecundity, oviposition rate, female longevity, and pre-oviposition period (i.e., period from emergence to first oviposition) were measured.An analysis of variance was conducted to determine differences.Normality of all datasets was verified using the Shapiro-Wilk test.Mean values were compared through Tukey's honest significance test.All statistical analyses were conducted using R 4.3.1 [17].

Model Development
We developed two forms of simulation processes to describe oviposition of M. saltuarius.The single-phase simulation consisted of one model describing oviposition rate from adult emergence.The two-phase simulation was comprised of two separate models, one depicting sexual maturation after adult emergence (pre-oviposition) and the other describing oviposition thereafter (oviposition).Physiological age of adults was estimated using a temperature-dependent aging model.In addition, lifetime total fecundity of female adults was described through a temperature-dependent total fecundity model.In the single-phase simulation, daily oviposition was estimated based on models of agedependent survival rate and cumulative oviposition rate.In the two-phase simulation, the same temperature-dependent aging, total fecundity, and age-dependent survival rate models were employed.However, daily oviposition was determined by first estimating the period to sexual maturity using a temperature-dependent development model, and then by applying a cumulative oviposition rate model.

Temperature-Dependent Aging Model and Age-Dependent Model
Aging rate (1/mean longevity) of female adults is temperature-dependent.It demonstrates a nonlinear relationship with temperature [18].In contrast to nymphs that show a sharp decrease in development rate beyond optimum temperature, the aging rate of adults increases exponentially as temperature rises.Hence, we used the following exponential function to describe the temperature-dependent aging rate of female adults: where A(T) is the aging rate (1/day) at temperature T ( • C), r 0 is the minimum aging rate, and T H and c are estimated parameters.As longevity varied across temperatures, we normalized daily aging rates using the aging rate model, with cumulative daily values of aging rates giving physiological ages of adults.That is, the physiological age reaches 1 at the mean longevity of adults at each temperature [19].
The proportion of surviving females to total number of female adults was used to describe survival of female adults.In addition, survival rate was normalized based on the physiological age for comparison across temperature conditions.Age-specific survival rate (S(P x )) at a physiological age (P x ) was described using a two-parameter Weibull function: where α and β are estimated parameters, with α denoting the physiological age of 50% of the surviving adults and β determining the shape of the curve.

Temperature-Dependent Fecundity Model and Cumulative Oviposition Model
A temperature-dependent total fecundity model was developed to describe the relationship between lifetime fecundity and temperature.Total fecundity over temperature resembled a bell-shaped nonlinear relationship.It was fit by using the Briere-1 function: where F(T) is the total number of eggs yielded over the entire lifespan by a female at temperature T ( • C) with low (T L ) and high (T H ) temperature limits, and α is a fitted constant.For model development, we assumed 10.1 • C as the low threshold temperature for oviposition [20], added this data point to our dataset, and then estimated α, T L , and T H parameters by model fitting.
The cumulative proportion of eggs laid was modeled to characterize the oviposition rate of M. saltuarius.The cumulative oviposition model was normalized by physiological age to allow for a comparison across different physiological ages for multiple temperature conditions.The cumulative oviposition rate was described using a two-parameter Weibull function: where E(P x ) is the cumulative proportion of eggs laid by a female at physiological age (P x ), and η and β are the estimated parameters.Daily oviposition rate was defined as the incremental change in cumulative oviposition rate over time.For example, oviposition rate at day t was E(P xt ) − E(P xt−1 ).

Sexual Development Rate and Completion Distribution Models
Sexual development rate and completion distribution models were developed for a two-phase simulation.Temperature-dependent sexual development rate was characterized using the Briere-2 model: where D pre (T) is the development rate of sexually immature female adults, and T L and T H are the lower and upper temperature limits, respectively.For model fitting, T H was predetermined to be 38.79 • C [21].Parameters α and T L are to be fitted.Physiological age for sexually immature females was accumulated using the temperature-dependent sexual development rate model.To compare across physiological ages, duration distribution to sexual maturation was described using a two-parameter Weibull function (Equation (4)).In the simulation, no oviposition was presumed before completion of sexual maturation.
The aging rate for oviposition upon sexual maturity was expressed as the reciprocal of the total oviposition period and described by an exponential function (Equation (1)).Aging rate for oviposition was accumulated to measure the physiological age for oviposition.Agespecific cumulative oviposition probability distribution was described by a two-parameter Weibull function (Equation ( 2)).To assess potential temperature-dependent differences in the cumulative oviposition probability, we employed a mixed-effects model using the 'lme4' package.The model was constructed with age and temperature as fixed effects, including their interaction, and a random intercept for each experimental unit.
Both single-phase and two-phase simulations were performed to estimate daily oviposition of M. saltuarius under multiple temperature conditions.Model parameters were estimated using 'nls' and 'nls2' functions.All simulations were performed in R 4.3.1 [17].

Results
Temperature significantly influenced the fecundity and longevity of M. saltuarius females (Table 1).Eggs were laid at all experimental temperatures.Among the temperatures tested in this study, the fecundity of M. saltuarius peaked at 20 • C, with a total of 141 eggs laid per female.Fecundity decreased with increasing temperature over the tested range, and this relationship was well described by the Briere-1 model, which assumed no oviposition below 15 • C [22] (F 2,3 = 5.60, p < 0.001, R 2 = 0.789) (Figure 1a and Table 2).In contrast, female longevity decreased exponentially with increasing temperature (Table 1).M. saltuarius females showed an average longevity of 83.36 days at 20 • C and 22.92 days at 32 • C. The temperature-dependent aging rate of M. saltuarius females was estimated as the inverse of mean longevity.Aging rate increased exponentially with temperature (F 2,2 = 228.51,p = 0.004, R 2 = 0.996) (Figure 1b and Table 2).laid per female.Fecundity decreased with increasing temperature over the tested range, and this relationship was well described by the Briere-1 model, which assumed no oviposition below 15 °C [22] (F2,3 = 5.60, p < 0.001, R 2 = 0.789) (Figure 1a and Table 2).In contrast, female longevity decreased exponentially with increasing temperature (Table 1).M. saltuarius females showed an average longevity of 83.36 days at 20 °C and 22.92 days at 32 °C.
The temperature-dependent aging rate of M. saltuarius females was estimated as the inverse of mean longevity.Aging rate increased exponentially with temperature (F2,2 = 228.51,p = 0.004, R 2 = 0.996) (Figure 1b and Table 2).Physiological age, the accumulation of aging rate, was used to compare female agespecific survival and cumulative oviposition.There were no significant differences in the patterns of cumulative survival change over age among the temperatures (survival: X 2 = 0.78, df = 4; p = 0.94; oviposition: X 2 = 2.45, df = 4; p = 0.12).Physiological age-dependent survival was well described by the Weibull function (F1,53 = 869.24,p < 0.0001, R 2 = 0.943) (Figure 2a and Table 2), with 53% survival at mean longevity (i.e., physiological age = 1).The relationship between cumulative oviposition and physiological age was well described by the two-parameter Weibull function (F1,153 = 4414.7,p < 0.0001, R 2 = 0.967) (Table 2), with 83.2% of lifetime fecundity predicted to occur by mean longevity.Physiological age, the accumulation of aging rate, was used to compare female agespecific survival and cumulative oviposition.There were no significant differences in the patterns of cumulative survival change over age among the temperatures (survival: X 2 = 0.78, df = 4; p = 0.94; oviposition: X 2 = 2.45, df = 4; p = 0.12).Physiological agedependent survival was well described by the Weibull function (F 1,53 = 869.24,p < 0.0001, R 2 = 0.943) (Figure 2a and Table 2), with 53% survival at mean longevity (i.e., physiological age = 1).The relationship between cumulative oviposition and physiological age was well described by the two-parameter Weibull function (F 1,153 = 4414.7,p < 0.0001, R 2 = 0.967) (Table 2 The developmental rate for sexual maturation was estimated as the inverse of the pre-oviposition period.The relationship between temperature and sexual maturation rate was described by the Briere-2 model (F1,3 = 12.936, p = 0.037, R 2 = 0.812) (Figure 3a and Table 2).Using this relationship, physiological age for sexual maturation was separately estimated.The relationship between physiological age and cumulative proportion of sexual maturation was described by the Weibull function (F1,18 = 411.71,p < 0.0001, R 2 = 0.960) (Figure 3b and Table 2).The developmental rate for sexual maturation was estimated as the inverse of the pre-oviposition period.The relationship between temperature and sexual maturation rate was described by the Briere-2 model (F 1,3 = 12.936, p = 0.037, R 2 = 0.812) (Figure 3a and Table 2).Using this relationship, physiological age for sexual maturation was separately estimated.The relationship between physiological age and cumulative proportion of sexual maturation was described by the Weibull function (F 1,18 = 411.71,p < 0.0001, R 2 = 0.960) (Figure 3b and Table 2).Following the sexual maturation phase, aging rate during the oviposition phase was estimated as the inverse of the period from first oviposition until female death.The relationship between temperature and aging rate was described by an exponential function (F2,2 = 98.493, p = 0.010, R 2 = 0.990) (Figure 4a and Table 2).Cumulative oviposition rate was estimated by physiological age following sexual maturation.The relationship between cumulative oviposition rate and physiological age was well described by the Weibull function (F1,111 = 3724.9,p < 0.0001, R 2 = 0.971) (Figure 4b and Table 2).Following the sexual maturation phase, aging rate during the oviposition phase was estimated as the inverse of the period from first oviposition until female death.The relationship between temperature and aging rate was described by an exponential function (F 2,2 = 98.493, p = 0.010, R 2 = 0.990) (Figure 4a and Table 2).Cumulative oviposition rate was estimated by physiological age following sexual maturation.The relationship between cumulative oviposition rate and physiological age was well described by the Weibull function (F 1,111 = 3724.9,p < 0.0001, R 2 = 0.971) (Figure 4b and Table 2).Following the sexual maturation phase, aging rate during the oviposition phase was estimated as the inverse of the period from first oviposition until female death.The rela tionship between temperature and aging rate was described by an exponential function (F2,2 = 98.493, p = 0.010, R 2 = 0.990) (Figure 4a and Table 2).Cumulative oviposition rate was estimated by physiological age following sexual maturation.The relationship between cu mulative oviposition rate and physiological age was well described by the Weibull func tion (F1,111 = 3724.9,p < 0.0001, R 2 = 0.971) (Figure 4b and Table 2).Estimated models were used to predict daily oviposition from 10 to 40 °C by single and two-phase simulations (Figure 5).The two-phase simulation predicted a shorter pe riod of intensive oviposition compared to the single-phase simulation.Peak daily ovipo sition was predicted at 37 and 33 °C in the single-phase and two-phase simulations, re spectively.Outputs of single-phase and two-phase simulations were compared to the observed cumulative proportions of oviposition at each temperature condition (Figure 6) Both simulations described daily oviposition well across all temperature ranges (Table 3) Estimated models were used to predict daily oviposition from 10 to 40 • C by singleand two-phase simulations (Figure 5).The two-phase simulation predicted a shorter period of intensive oviposition compared to the single-phase simulation.Peak daily oviposition was predicted at 37 and 33 • C in the single-phase and two-phase simulations, respectively.Outputs of single-phase and two-phase simulations were compared to the observed cumulative proportions of oviposition at each temperature condition (Figure 6).Both simulations described daily oviposition well across all temperature ranges (Table 3).At all temperatures except 24 • C, the two-phase simulation demonstrated higher predictive power than the single-phase simulation.At all temperatures except 24 °C, the two-phase simulation demonstrated higher predictive power than the single-phase simulation.

Discussion
Female M. saltuarius adults were affected by temperature in terms of longevity, sexual maturation, aging rate, and oviposition.Based on the relationships between these traits and temperature, we were able to develop temperature-dependent models and describe the oviposition of M. saltuarius through simulations that connected these models.In this study, five constant temperature conditions (20, 24, 28, 30, and 32 • C) were used to develop temperature-dependent models.However, for total fecundity, there were limitations in covering the low-temperature range where nonlinear correlations with temperature were observed.Nevertheless, we were able to describe these nonlinear relationships with temperature through existing literature data [20].Insect fecundity is an important factor that can be used to predict potential increases in population density.Temperature is one of the most influential factors affecting insect fecundity.Numerous studies have examined temperature-fecundity relationships under different temperature regimes.Here, we showed that under laboratory conditions, the relationship between fecundity and temperature followed a unimodal shape, increasing up to an optimum and then decreasing.Here, we demonstrated that, when combined with existing data [20], the relationship between fecundity and temperature followed a unimodal shape under laboratory con-ditions, increasing up to an optimum and then decreasing.However, the longevity of M. saltuarius female adults decreased with increasing temperature.We also fit nonlinear models describing these relationships that could enable simulating the daily oviposition of M. saltuarius by two types of simulations (i.e., single-phase and two-phase) across diverse temperature conditions.
Newly emerged M. saltuarius adults require a pre-oviposition development period before mating for oviposition [15].Temperature-dependent oviposition models can incorporate this period in different ways.Some models combine pre-oviposition and oviposition phases into a single oviposition model [11,12], while others treat them as distinct phases [13].In this study, we compared single-phase and two-phase simulations for describing the oviposition of M. saltuarius.Our results suggested that both models fit the oviposition similarly well for M. saltuarius.This may be due to the relatively short pre-oviposition period observed in this species (13.64 days at 20 • C and 10.85 days at 32 • C).However, the relative performance of single-phase versus two-phase simulations may vary depending on the duration of the pre-oviposition period in different species.For instance, in species with longer pre-oviposition periods, the differences between these two approaches might be more pronounced.For example, the pre-oviposition period of the oriental fruit fly was 38.1 and 6.2 days at 16.7 and 34.9 • C, respectively, showing significant differences compared to single-phase simulation outputs [13].The choice between single-phase and two-phase simulations may depend on the pre-oviposition period of the species being studied and the level of detail required in the simulation.Further comparative studies across different insect species could provide more insights into the relative strengths and limitations of these modeling approaches.
As a native species in Korea, M. saltuarius emerges from May to June [14], with oviposition occurring mainly from June to August.Later-emerging individuals may experience higher temperatures, potentially resulting in lower fecundity.However, variations in life history traits among local populations may lead to differences in emergence timing [21].For more accurate predictions of specific populations in narrow areas, model calibration may be required.The nonlinear models developed in this study can account for seasonal temperature changes.However, to incorporate daily temperature fluctuations, the current models' time scale could be converted from daily to hourly.
Various techniques have been used to describe insect oviposition, including life table parameters and degree day models [23,24].In this study, both single-and two-phase simulations predicted daily oviposition close to experimental observations under the constant temperature conditions (R 2 > 0.96).Temperature-dependent models offer the advantage of the experimental determination of responses to temperature under different constant temperature regimes, enabling prediction across fluctuating temperatures through nonlinear regression and simulation [18].Simulating such models under thermal variation relies on the assumption that individuals exhibit identical responses at a given physiological age and temperature irrespective of the previously experienced thermal path.However, temperature responses are likely to differ with given developmental and nutritional status as well as physiological age [25,26].Physiological age was used to standardize relative age (days) and incorporate temperature responses into nonlinear models, although it may also be influenced by other factors (e.g., diet, abiotic/biotic stress) and the environment experienced by individuals [27].Furthermore, the ambient temperature conditions may vary depending on the development rate and the timing of diapause termination, which can consequently affect fecundity.Accordingly, diverse environmental validation is essential to evaluate model robustness.
Various model-based forecasting approaches have facilitated our understanding of target pests and enabled practical pest management applications.Phenology models could be used to optimize control timing for target pests, while fecundity models may be used to assess seasonal outbreak potential.Additionally, combining our fecundity models with phenology and winter survival models might enable predictions of population dynamics of M. saltuarius.Furthermore, integrating these models with existing species distribution

Figure 1 .
Figure 1.Temperature-dependent total fecundity (eggs/female) (a) and aging rate (1/mean days of longevity) (b) models for Monochamus saltuarius female adults.Exponential and Briere-1 functions were fitted to aging rate and total fecundity, respectively.

Figure 1 .
Figure 1.Temperature-dependent total fecundity (eggs/female) (a) and aging rate (1/mean days of longevity) (b) models for Monochamus saltuarius female adults.Exponential and Briere-1 functions were fitted to aging rate and total fecundity, respectively.

Figure 2 .
Figure 2. Physiological age-specific survivorship (a) and cumulative oviposition probability curves (b).A two-parameter Weibull function was used to estimate physiological age-specific survivorship and cumulative oviposition probability.

Insects 2024 , 12 Figure 3 .
Figure 3. Temperature-dependent development rate for sexual maturation (a) and cumulative pro portion of age-specific development completion (b) for sexual maturation of Monochamus saltuarius female adults.Briere-2 and two-parameter Weibull functions were applied to estimate developmen rate and cumulative proportion, respectively.

Figure 3 .
Figure 3. Temperature-dependent development rate for sexual maturation (a) and cumulative proportion of age-specific development completion (b) for sexual maturation of Monochamus saltuarius female adults.Briere-2 and two-parameter Weibull functions were applied to estimate development rate and cumulative proportion, respectively.

Figure 3 .
Figure 3. Temperature-dependent development rate for sexual maturation (a) and cumulative pro portion of age-specific development completion (b) for sexual maturation of Monochamus saltuarius female adults.Briere-2 and two-parameter Weibull functions were applied to estimate developmen rate and cumulative proportion, respectively.

Figure 4 .
Figure 4. Temperature-dependent development rate for oviposition (a) and age-specific cumulative oviposition probability (b) of sexually matured Monochamus saltuarius female adults.An exponentia function and a two-parameter Weibull function were applied to estimate development rate and cu mulative oviposition probability, respectively.

Figure 4 .
Figure 4. Temperature-dependent development rate for oviposition (a) and age-specific cumulative oviposition probability (b) of sexually matured Monochamus saltuarius female adults.An exponential function and a two-parameter Weibull function were applied to estimate development rate and cumulative oviposition probability, respectively.

Figure 5 .Figure 5 .
Figure 5. Predicted daily egg production of Monochamus saltuarius in relation to days after emergence and temperature by single-phase (a) and two-phase (b) simulations.

Figure 5 .
Figure 5. Predicted daily egg production of Monochamus saltuarius in relation to days after emergence and temperature by single-phase (a) and two-phase (b) simulations.

Figure 6 .
Figure 6.Comparison of simulation outputs from single-phase and two-phase simulations with the observed cumulative proportion of oviposition at various constant temperatures.Subfigures (a-e) represent different constant temperature conditions: 20, 24, 28, 30, and 32 °C, respectively.

Figure 6 .
Figure 6.Comparison of simulation outputs from single-phase and two-phase simulations with the observed cumulative proportion of oviposition at various constant temperatures.Subfigures (a-e) represent different constant temperature conditions: 20, 24, 28, 30, and 32 • C, respectively.

Table 1 .
Fecundity and longevity (days) of Monochamus saltuarius female adults at various constant temperatures.

Table 1 .
Fecundity and longevity (days) of Monochamus saltuarius female adults at various constant temperatures.

Table 2 .
Parameter estimates (±S.E.) of models for single-phase and two-phase simulations.
), with 83.2% of lifetime fecundity predicted to occur by mean longevity.
Figure 2. Physiological age-specific survivorship (a) and cumulative oviposition probability curves (b).A two-parameter Weibull function was used to estimate physiological age-specific survivorship and cumulative oviposition probability.

Table 3 .
Comparison of adjusted R 2 values between single-phase and two-phase simulation outputs at various constant temperatures (***, highly significant with p < 0.001).