Temperature‐Dependent Population Model of Apple Leafminer, Phyllonorycter ringoniella (Lepidoptera: Gracillariidae)

ABSTRACT

The Asiatic apple leafminer, Phyllonorycter ringoniella (Matsumura), is a significant secondary pest of apple trees in Northeast Asia. To better understand its population dynamics, a population model based on temperature‐developmental relationships was constructed. This model includes three sub‐models: spring emergence, immature stage transition, and adult oviposition. Field data were collected from sex‐pheromone baited traps in apple orchards in Andong, Korea, during 2015 and 2016 to validate the model. Simulations under six pesticide‐natural enemy scenarios showed that the population size of each generation was best simulated when weighted mortality factors for pesticides and natural enemies were applied. Using daily temperature inputs, the model demonstrated that P. ringoniella typically undergoes five generations per year, with peak times predicted within a 7‐day margin of field data. Sensitivity analyses revealed that population size was influenced by total fecundity and the larval stage model, but peak times remained consistent despite parameter changes. Higher temperatures led to earlier adult peak dates, especially in summer generations. This model serves as a fundamental tool for estimating population dynamics and abundance changes of P. ringoniella and can guide the timings of pesticide application. Further validation is necessary to test the model's efficacy in controlling pests in apple orchards.

The temperature‐dependent population model of P. ringoniella was constructed.

Summary

• Temperature significantly influence development and oviposition of P. ringoniella.

• The temperature‐dependent population model of P. ringoniella was constructed.

• The structure and method for insect population model was introduced.

1. Introduction

The Asiatic apple leafminer, Phyllonorycter ringoniella (Matsumura), is a significant insect pest of apple trees in Korea, Japan, and China (Lee et al. ^1985a; Sugie et al. ¹⁹⁸⁶; Kumar et al. ²⁰¹⁴; Geng et al. ²⁰¹⁹). This pest can produce four to six generations per year, which with their leaf mines affect photosynthesis, hasten defoliation, inhibit new bud growth, and ultimately cause premature ripening and premature fruit drop (Lee et al. ^1985b; Sugie et al. ¹⁹⁸⁶; Geng et al. ²⁰¹⁹).

Temperature is a crucial abiotic factor affecting various biological processes of insects, including development, survival, longevity, fecundity, and demographic parameters (Ahn et al. 2020; Choi et al. ²⁰²⁰; Li et al. ²⁰²⁰; Power et al. ²⁰²⁰; Hiroyoshi et al. ²⁰²¹; Ji et al. ²⁰²¹; Nielsen et al. ²⁰²¹; Papadogiorgou and Papadopoulos ²⁰²⁵; Wen and Gao ²⁰²⁵). Understanding the relationship between temperature and these developmental stages is essential for comprehending population growth and dynamics, predicting seasonal occurrences and outbreaks (Michel et al. 2021; Mo and Stevens ²⁰²¹; Neta et al. ²⁰²¹. Riemer et al. ²⁰²¹; Smyers et al. ²⁰²¹; Baser et al. ²⁰²⁵), and developing effective pest management strategies (Gamarra et al. 2020; Nika et al. ²⁰²¹; Régnier et al. ²⁰²²; Wang et al. ²⁰²²).

Mathematical models are critical tools for describing insect responses to variable environmental conditions and predicting population dynamics across different geographic zones and climates (Shaffer and Gold 1985; Kim and Lee ²⁰¹⁰). Various studies have introduced mathematical functions to depict these relationships based on an insect's thermal characteristics at different temperatures. A population model can enhance our understanding of insect pest dynamics under a variety of environmental factors and aid in developing integrated pest management tactics through simulations (Kim and Lee 2010; Choi et al. ²⁰²⁰).

In temperate regions, a population model for arthropod species typically requires three basic components: a spring emergence model, a temperature‐dependent development model for immature stages, and an oviposition model (Kim et al. 2000; Kim and Lee ²⁰⁰³; Kim and Lee ²⁰¹⁰; Choi and Kim ²⁰¹⁶; Ahn et al. ²⁰²⁰; Choi et al. ²⁰²⁰). These models have been mathematically described and applied to various temperature‐dependent and stage‐structured models of insects and mites. They can also be used to calculate developmental thresholds, optimal temperatures, thermal constants, survival rates, longevity, and fecundity, aiding in predicting geographic distribution, phenology, and providing precise forecasting systems (Power et al. 2020; Ji et al. ²⁰²¹).

Understanding the population dynamics of P. ringoniella in apple orchards is vital for developing effective management strategies. The objective of this study is to develop and validate a population model for P. ringoniella using field data. This information will help us comprehend the population dynamics of this pest and formulate effective management strategies for apple orchards.

2. Materials and Methods

2.1. Model Construction

The P. ringoniella population model was constructed to include five developmental stages: overwintering pupa, egg, larva, pupa, and adult (Figure 1). Each stage was divided into separate cohorts of individuals, which entered the stage on a given day and were treated as different age groups within the stage (Kim and Lee 2010). However, the overwintering pupae with which the model started, consisted of a single cohort, with the assumption that individuals of this cohort were physiologically identical (Kim et al. 2000).

FIGURE 1.

Schematic diagram of the population model for Phyllonorycter ringoniella. DIS: distribution model for each stage (Equation 1: Table 1), DEL: developmental model (Equations 2, 3: Table 1), S: survival rate (Equation 5: Table 1), O: Oviposition model, T: temperature, and PA: physiological age. OP, E, L, and P indicate overwinter pupae, eggs, larvae, and pupae, respectively.

The population model was consisted of three component models (Figure 1): the spring emergence model (Geng and Jung ^2018a), the oviposition model (Geng and Jung ^2017a), and the stage transition model (Geng and Jung ^2018b). The spring emergence model predicted adult emergence from overwintering pupae using the two‐parameter Weibull function based on accumulated degree days. The adult oviposition model consisted of four temperature‐dependent components: the developmental (aging) rate model, total fecundity model, age‐specific oviposition rate model, and age‐specific survival rate model. The stage transition model for each immature stage included the temperature‐dependent developmental rate model and the developmental distribution model.

At any given time, each cohort was defined by two variables (Shaffer and Gold 1985): aij(t), the physiological age of cohort j within stage i at time t; and Nij(t, a), the number of individuals in cohort j of physiological age a at time t. The output of the model is Ni(t), the total number in stage i at time t, calculated by summing over the cohorts.

Temperature was the only meteorological factor included in the model; other variables, such as relative humidity, were not considered. The model starts with the overwintering pupal stage with an arbitrarily defined number of individuals. Model computations used a daily time‐step, assuming all mortality occurred at the transition to the next stage. It was also assumed that there was no emigration or immigration of P. ringoniella adults. The population model was simulated using PopModel 1.5 (Choi and Kim 2017).

2.2. Sub‐Models and Their Process Functions

The process functions and their parameters (Tables 1 and 2) were obtained from previous studies, the spring emergence model from Geng and Jung (2018a), the adult oviposition model from Geng and Jung (2017a), and the stage transition model from Geng and Jung (2018b).

TABLE 1.

Equations used in the population model of Phyllonorycter ringoniella.

No.	Model	Equation
1	Two‐parameter Weibull function	$y=1-\text{exp}\left[{-\left(\frac{x}{a}\right)}^b\right]$
2	Lactin‐1	$r\left(T\right)=\text{exp}\mathrm{}\left(\rho T\right)-\text{exp}\mathrm{}[\rho T_{\max }-\left(\frac{T_{\max }-T}{∆T}\right)]$
3	Briere‐1	$r\left(T\right)=\mathit{aT}\left(T-T_{\min }\right)\sqrt{\left(T_{\max }-T\right)}$
4	Inverse second‐order polynomial	$r\left(T\right)=\frac{a}{1+b\bullet T+c{T}^2}$
5	Extreme value function	$f\left(T\right)=\omega \bullet \text{exp}[1+\left(\epsilon -T\right)/\delta -\text{exp}(\left(\epsilon -T\right)/\delta )]$
6	Three‐parameter Weibull function	$p\left(P_x\right)=1-\text{exp}\left[-{\left(\frac{P_x-\alpha }{\beta }\right)}^{\gamma }\right]$
7	Sigmoid function	$s\left(P_x\right)=\frac{1}{1+\text{exp}[\left(\eta -P_x\right)/\theta ]}$

TABLE 2.

Parameter values of each equation used in the population model of Phyllonorycter ringoniella.

Models	Eqs.	Parameters (± SEM)			r2
Spring emergence model	1	a	b
		353.349 ± 3.1223	4.104 ± 0.1909		0.83
Development model		ρ	T max	ΔT
Eggs	2	0.1575 ± 0.00489	34.3922 ± 0.18388	6.3332 ± 0.19438	0.99
		a	T min	T max
Larvae	3	0.00004 ± 0.000005	4.8463 ± 2.02694	33.5695 ± 0.32969	0.97
Pupae	3	0.00011 ± 0.000009	7.5904 ± 0.89274	35.5845 ± 0.44517	0.99
Distribution of development time		a	b
Eggs	1	0.9786 ± 0.00707	7.2970 ± 0.54226		0.96
Larvae	1	1.0343 ± 0.00660	5.5455 ± 0.27600		0.92
Pupae	1	0.9866 ± 0.00401	14.8415 ± 1.03858		0.98
Survival rate model		ω	ε	δ
Eggs	5	0.914 ± 0.0272	20.340 ± 1.3763	20.457 ± 5.3569	0.57
Larvae	5	0.759 ± 0.0536	17.988 ± 0.4533	6.947 ± 1.1520	0.87
Pupae	5	0.923 ± 0.0351	21.845 ± 0.4333	8.353 ± 0.6850	0.94
Oviposition model
Adult aging rate	4	a	b	c
		0.0213 ± 0.00323	‐0.0542 ± 0.00342	0.0009 ± 0.00009	0.98
Total fecundity	5	ω	ε	δ
		71.3686 ± 4.90491	17.8132 ± 0.46966	6.1431 ± 0.68516	0.95
Oviposition rate	6	α	β	γ
		0.0545 ± 0.02963	0.5286 ± 0.03284	1.7591 ± 0.13074	0.98
Survival rate	7	η	θ
		1.0416 ± 0.00529	‐0.1926 ± 0.00472		0.99

2.2.1. Spring Emergence Model

Daily spring adult emergence was estimated using Weibull distribution model (Equation 1: Table 1). This model uses cumulative degree‐days with a base temperature of 7.06°C from January 1 as an independent variable (Geng and Jung ^2018a).

2.2.2. Adult Oviposition Model

This model included four component functions, the adult aging rate function (Equation 4: Table 1), temperature‐dependent total fecundity function (Equation 5: Table 1), age‐specific oviposition rate function (Equation 6: Table 1), and age‐specific survival rate function (Equation 7: Table 1). Since total egg production by female adults could be influenced by temperatures experienced by them earlier, the average temperature during the 5 days before oviposition was taken as input variable in the total fecundity model. Daily egg production was estimated by the PopModel 1.5 (Choi and Kim 2017) according to the computational process of Kim and Lee (2003). The sex ratio (female proportion) was assumed to be 0.5 (Geng and Jung ^2017b).

2.2.3. Stage Transition Models

These models simulate the proportion of individuals transitioning from one stage to the next, comprising a temperature‐dependent development rate function and a cumulative distribution function.

2.2.4. Immature Survival Model

The survival rates of eggs, larvae, and pupae at different constant temperatures (13.3–32.2°C) were examined in the laboratory. The survival rates were simulated using an extreme value equation (Equation 5: Table 1), with parameter values presented in Table 2.

2.2.5. External Mortality Model

Parasitism is a major biological external mortality factor for the apple leafminer (Lee et al. ^1985b), while insecticides are the major nonbiological external mortality factor. Given the mining behavior of the larvae, an insecticide‐driven mortality averaging 86.1%, was considered only for the egg stage, which is directly exposed to the pesticide spray (Sun et al. 2000). The insecticide was assumed to be effective against eggs oviposited 5 days before and 5 days after the spraying date (Sun et al. 2000; Kim and Lee ²⁰¹⁰). Parasitism rates of larvae and pupae were assumed to be 29.5% in a conventional orchard (Lee et al. ^1985b) and 54.9% in a pesticide‐free orchard (unpublished data).

2.3. Simulations Under Six Scenarios

The population model was simulated under six scenarios:

• Scenario A: original run, was without insecticide effects or natural enemies. The population increased naturally.

• Scenario B: based on scenario A, with the pesticide effect added to the egg stage. Pesticide was sprayed ten times, starting on Julian date 115, at 15‐day intervals.

• Scenario C: based on scenario B, with the natural enemy effect added to the larval stage. A parasitoid rate of 29.5% was applied.

• Scenario D: based on scenario C, with the natural enemy effect added to the pupal stage. A parasitoid rate of 29.5% was applied.

• Scenario E: based on scenario A, with the natural enemy effect added to the larval and pupal stages. A parasitoid rate of 29.5% was applied.

• Scenario F: same as scenario E, but with a parasitoid rate 54.9%.

These scenarios were simulated using PopModel 1.5, with meteorological data from 2015 to 2016 in Andong, South Korea.

2.4. Field Population Data Collection

To validate the model against field data, the flight occurrences of P. ringoniella adults were monitored in 28 conventional and one pesticide‐free apple orchard in Andong, from April 10 to October 24, 2015, and from March 1 to October 26, 2016. Most apple orchards were cultivated by mix varieties but dominated by ‘Fuji' and ‘Hongro'. Commercial pheromone traps (GreenAgro Tech, Kyeongsan, Korea) baited with synthetic sex pheromone lures containing a 6:4 ratio of E4,Z10‐14:Ac and Z10‐14:Ac (Boo and Jung 1998), were used for monitoring. One trap was hung 1.5 meters above ground in each orchard and checked weekly or twice a week. The lures were changed every 2 months, and the sticky inserts were changed weekly.

2.5. Meteorological Data

The meteorological data of daily average, maximum, and minimum temperatures, were obtained from Andong meteorological station (http://www.kma.go.kr). The biofix for degree day accumulation was set to January 1 for simplicity (Ahn et al. 2012).

2.6. Sensitivity Analysis

Temperature data of 2015 were used for all simulations during the sensitivity analyses. Simulations were carried out under Scenario F, starting from the spring emergence model with 100 overwintered pupae as the initial input.

The sensitivity of parameter changes was examined by altering certain parameter values by 10% (Shaffer and Gold 1985; Kim and Lee ²⁰¹⁰). Several model outputs were evaluated: the total number of eggs, larvae, pupae, and adults, and the peak date (Julian date) of each generation. The parameters of the developmental models were excluded from the sensitivity analyses due to invalid equation solutions with parameter changes. The average effect and nonlinearity index were used for sensitivity analysis (Shaffer and Gold 1985; Kim and Lee ²⁰¹⁰):

$$\text{Average effect}=0.5[F\left({1.1p}_0\right)-F\left({0.9p}_0\right)]$$ (1)

$$\text{Non}-\text{linearity index}=0.5[F\left({1.1p}_0\right)+F\left({0.9p}_0\right)]-F\left(p_0\right)$$ (2)

Where F(p) is the output at parameter value p, and p ₀ is the parameter value in original run.

The sensitivity of temperature change was conducted by running the model with temperatures in 2015 decreased or increased 1°C.

3. Results

3.1. Simulation and Validation

The seasonal population dynamics of P. ringoniella in the conventional and pesticide‐free orchards in 2015 and 2016 are shown in Figure 2. P. ringoniella exhibited five annual occurrences with overlapping 4th and 5th generations. The population model successfully simulated the typical pattern of P. ringoniella, accurately predicting the number of generations and the peak time of each generation (Figures 3 and 4, Table 3). However, the model did not accurately predict the population size for each generation. To test the effects of pesticides and natural enemies on population dynamics, the population model was simulated under six scenarios (Figures 3 and 4). The pesticide influenced both population size and peak time (Table 3), whereas natural enemies only decreased the population size without affecting the peak time of each generation.

FIGURE 2.

Seasonal occurrence patterns of Phyllonorycter ringoniella males caught in pheromone traps in 28 conventional apple orchards and one pesticide‐free apple orchard in Andong in 2015 and 2016.

FIGURE 3.

Comparison of model outputs with actual pheromone trap data in 28 conventional apple orchards and one pesticide‐free apple orchard in Andong in 2015. The population model was simulated under six scenarios, (A) original run. (B) based on scenario A, with the pesticide effect added to the egg stage. (C) based on scenario B, with the natural enemy effect added to the larval stage. (D) based on scenario C, with the natural enemy effect added to the pupal stage. (E) based on scenario A, with the natural enemy effect added to the larval and pupal stages. A parasitoid rate of 29.5% was applied. (F) same as scenario E, but with a parasitoid rate 54.9%.

FIGURE 4.

Comparison of model outputs with actual pheromone trap data in 28 conventional apple orchards and one pesticide‐free apple orchard in Andong in 2016. The population model was simulated under six scenarios, (A) original run. (B) based on scenario A, with the pesticide effect added to the egg stage. (C) based on scenario B, with the natural enemy effect added to the larval stage. (D) based on scenario C, with the natural enemy effect added to the pupal stage. (E) based on scenario A, with the natural enemy effect added to the larval and pupal stages. A parasitoid rate of 29.5% was applied. (F) same as scenario E, but with a parasitoid rate 54.9%.

TABLE 3.

The predicted and actual peak time (Julian date) of each generation of Phyllonorycter ringoniella in 2015 and 2016.

Year	Generation	Model output under scenariosa						Actual data
		A	B	C	D	E	F	Conventional	Pesticide‐free
2015	1st	122	122	122	122	122	122	122	—
	2nd	164	166	166	166	164	164	172	151
	3rd	204	195	195	195	204	204	205	191
	4th	231	236	236	236	231	231	245	245
	5th	271	276	276	276	271	271	263	256
2016	1st	117	117	117	117	117	117	101	101
	2nd	165	165	165	165	165	165	162	162
	3rd	200	192	192	192	200	194	202	202
	4th	230	235	235	235	230	230	243	237
	5th	271	253	254	254	271	271	258	258

^aSix scenarios, A: original run. B: based on scenario A, with the pesticide effect added to the egg stage. C: based on scenario B, with the natural enemy effect added to the larval stage. D: based on scenario C, with the natural enemy effect added to the pupal stage. E: based on scenario A, with the natural enemy effect added to the larval and pupal stages. A parasitoid rate of 29.5% was applied. F: same as scenario E, but with a parasitoid rate 54.9%.

3.2. Sensitivity Analysis

The average effect is proportional to a numerical approximation of the partial first derivative of the output with respect to the parameter, and the nonlinearity index is proportional to an approximation of the partial second derivative (Shaffer and Gold 1985; Kim and Lee ²⁰¹⁰). In most cases, the absolute value of the average effect is larger than the nonlinearity index, indicating a stronger linear relationship between model outputs and the parameters (Table 4). Negative average effect values imply that model outputs decrease as parameter values increase. Negative nonlinearity values indicate a convex curve relationship between the outputs and parameters. If both values are negative, the model outputs decrease along a convex curve with increasing parameter values (Kim and Lee 2010). The most influential parameter was found in the total fecundity model. The total number of eggs, larvae, pupae, and adults increased as the parameters ω and/or ε increased. Both average effects and nonlinearity were observed in our sensitivity results, suggesting that parameter changes can influence the population model in a complex manner.

TABLE 4.

Sensitivity analyses for parameter changes of the population model for Phyllonorycter ringoniella.

Model	Parameter	Index	Total Number				Adult peak Julian date
			Eggs	Larvae	Pupae	Adult	1st	2nd	3rd	4th	5th
Spring emergence model	a	Average	‐13916	‐2261.7	‐1179.9	‐462.4	2.5	2.5	0	0.5	0.5
		Nonlinear	‐11.3	‐205.2	‐23.4	‐6.2	‐3	2.5	4	‐1	‐1
	b	Average	1097	502	123.2	44.3	0	0	0	0.5	0
		Nonlinear	‐228.5	‐79.9	‐21.9	‐8.3	0	0	0	‐1	‐1
Distribution of development time
Eggs	a	Average	‐14465.4	‐2482.1	‐1193.4	‐472	0	0	0	0.5	0
		Nonlinear	‐6517.9	‐438.7	‐596.8	‐226.6	0	0	0	‐1	0
	b	Average	510.8	69.3	42.1	16.6	0	0	0	‐1	‐1
		Nonlinear	‐59.8	‐6.7	‐5	‐2	0	0	0	‐1	‐1
Larvae	a	Average	‐43033.8	‐7155.5	‐3560.5	‐1404.3	0	2	0	4.5	5
		Nonlinear	‐5521.5	1905.1	‐643	‐210.3	0	0	0	‐1	3
	b	Average	2440.8	231.5	208.2	80.6	0	2.5	0	‐1	0
		Nonlinear	‐219.2	‐21.8	‐19.9	‐7.5	0	‐3	0	‐1	0
Pupae	a	Average	‐15618.2	‐1712.7	‐1167.6	‐485.6	0	0	‐1	‐2	1
		Nonlinear	‐2574.4	185.6	‐243	‐85.1	0	0	2	1.5	0
	b	Average	326.3	28.2	24.5	10.1	0	0	‐2	‐1	0
		Nonlinear	‐20.4	‐1.6	‐1.5	‐0.6	0	0	2	‐1	0
Oviposition model
Total fecundity	ω	Average	52662.8	18295.5	3673	1394.2	0	0	0	0	0
		Nonlinear	8952.6	2333.9	444.1	167.5	0	0	0	0	0
	ε	Average	44982.3	18654	3654.5	1380.2	0	0	‐2	0.5	0.5
		Nonlinear	‐2912.2	‐93.6	‐68	‐29.6	0	0	2	‐1	‐1
	δ	Average	22712.7	8391.7	1653.7	628.6	0	0	0	0.5	0
		Nonlinear	‐609.7	‐288.3	‐63.5	‐24.3	0	0	0	‐1	0
Oviposition rate	α	Average	‐2023.5	‐405.1	‐154.5	‐60.6	0	0	0	0.5	0.5
		Nonlinear	‐1.1	1	‐0.3	‐0.1	0	0	0	‐1	‐1
	β	Average	‐21046.3	‐5167.1	‐1581.5	‐611	0	0	0	0.5	0.5
		Nonlinear	746.3	‐190.5	35.9	16.8	0	0	0	‐1	‐1
	γ	Average	4856.4	2214.6	334.5	120.9	0	0	2	0.5	0.5
		Nonlinear	‐623.9	‐230.8	‐43.2	‐16.2	0	0	2	‐1	‐1
Survival rate	η	Average	9162.9	4184	603.2	226.1	0	0	0	0.5	0.5
		Nonlinear	‐2367.1	‐984.4	‐177.3	‐66.6	0	0	0	‐1	‐1
	θ	Average	272.3	139.3	16.8	6.3	0	0	2	0.5	0
		Nonlinear	‐18.1	‐9	‐1.1	‐0.4	0	0	2	‐1	0

Increased temperature led to earlier adult peak dates, especially for the summer generations, while decreased temperature delayed the adult peak time (Figure 5).

FIGURE 5.

Sensitivity of population model outputs to temperature changes. “Original” means the model was run by actual daily average temperature, “Original+1°C” means the model was run by Temperature=actual daily average temperature +1°C, “Original‐1°C” means the model was run by Temperature=actual daily average temperature ‐ 1°C.

4. Discussion

The population model provided a fundamental structure for understanding the population dynamics of P. ringoniella in apple orchards. While the model successfully simulated the typical occurrence patterns of P. ringoniella, it showed some discrepancies when compared with actual field observations. Specifically, the peak times of each generation, especially the 4th and 5th generations, differed between the actual data and the simulated results. Additionally, the model tended to overestimate the population sizes of the summer generations, particularly when pesticide and natural enemy effects were not included.

The most influential factors affecting peak times were the parameters of the developmental models. When these models are based on lower and upper threshold temperatures, insect development can be underestimated or overestimated at extreme temperatures (Kim and Lee 2010). Previous insect population dynamic models have demonstrated that considering micro‐environmental weather conditions can significantly improve model accuracy regarding population peak times and sizes (Toole et al. 1984; Gold et al. ¹⁹⁸⁷). Internal temperatures of leaves and fruits can differ from ambient air temperatures by as much as 13°–14°C (Landsberg et al. 1973; Thorpe ¹⁹⁷⁴). Overestimating these internal leaf temperatures results in a leftward shift in the larval distribution model, leading to earlier peak times for the third generation in this study.

The population occurrence patterns of P. ringoniella were estimated under six scenarios. However, the simulated outputs were not sufficient to fully explain actual field observations, because the model incorporated pesticide and natural enemy effects in a simplified manner. To improve the model, factors such as pesticide residue effects, pupae diapause, and adult survival should be included (Kim and Lee 2010).

The present population model demonstrated the typical patterns of P. ringoniella population dynamics in apple orchards. Similar temperature‐dependent models for other insect species have been reported in previous studies to predict developmental rates (Nika et al. 2021; Régnier et al. ²⁰²²), spring emergences (Smyers et al. 2021; Mo and Stevens ²⁰²¹; Riemer et al. ²⁰²¹), and population dynamics (Neta et al. 2021; Cañedo et al. ²⁰²²). This model enhances our understanding of the role of a warming climate in the population dynamics and ecology of this insect pest, providing useful guidance for managing this pest species (Shaffer and Gold 1985).

For a population model to be used as a practical management tool, it must accurately reflect actual observations and predict the timing and number of control procedures (Shaffer and Gold 1985; Kim and Lee ²⁰¹⁰; Michel et al. ²⁰²¹). While the current model can predict adult peak times effectively, further validation is needed to test the model's efficacy in controlling P. ringoniella in apple orchards. Consequently, we expect the model to be useful in evaluating new management practices and in estimating population dynamics and abundance changes of P. ringoniella in response to climate changes, such as global warming.

Author Contributions

Shubao Geng: conceptualization, methodology, validation, writing – original draft, project administration, investigation, funding acquisition, software, formal analysis. Lei Chen: writing – review and editing, data curation, formal analysis. Heli Hou: investigation, validation, formal analysis, software. Li Qiao: validation, supervision, data curation, writing – review and editing. Shibao Guo: formal analysis, data curation. Zhou Zhou: visualization, writing – review and editing. Hongtao Tu: resources, supervision. Chuleui Jung: conceptualization, methodology, supervision, resources, project administration, writing – review and editing, writing – original draft, funding acquisition, software, validation.

Conflicts of Interest

The authors declare no conflicts of interest.

Geng, S. , Chen L., Hou H., et al. 2025. “Temperature‐dependent Population Model of Apple Leafminer, Phyllonorycter ringoniella (Lepidoptera: Gracillariidae).” Archives of Insect Biochemistry and Physiology 120: e70094. 10.1002/arch.70094.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.