Uptake and translocation of pesticides in pepper and tomato plants

Abstract

BACKGROUND

In this study, field and greenhouse experiments were done with spray application of the insecticides acetamiprid, indoxacarb, deltamethrin, λ‐cyhalothrin, spinosad, chlorantraniliprole on pepper and tomato plants. Results were interpreted with numerical modeling.

RESULTS

Observed fruit concentration dynamics could be described overall well by modeling. After application, concentrations decreased in pepper and (slower) in tomato fruits (lower degradation and dissipation for tomato). Chemical input to individual above‐ground compartments (fruit, leaf, stem, soil), arising from spray, was among the unknowns and hence estimated. Input to fruits was estimated 1–13% and 1–17% of the total applied amount; input to stem, leaf and/or soil 0–13% and 0–26% (pepper and tomato). Input showed high variation across compounds, with considerable uncertainty due to a partly low sensitivity of stem/leaf/soil input to fruit concentrations. The pathway stem‐fruit was relevant for all compounds except λ‐cyhalothrin (pepper, tomato) and deltamethrin (tomato). The pathways soil‐root‐stem‐fruit and leaf‐stem‐fruit (phloem) were only sensitive for acetamiprid and chlorantraniliprole.

CONCLUSION

The dynamic model approach, implementing the appearance and growth of individual fruits, was after calibration successful in describing insecticide fate in pepper and tomato plants. Special consideration was given to dynamic modelling of plant growth and connected xylem and phloem flow. The dynamic approach was superior to assuming constant plant mass and transpiration, where growth dilution is described by rate constants. Information on the time‐window of experiments within the vegetation period and on the number and appearance of individual fruits is important for adequately describing growth and thus chemical fate within plants. © 2024 The Author(s). Pest Management Science published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Field and greenhouse experiments were done with spray application of different insecticides, and results were interpreted using numerical modeling. The dynamic model approach, implementing the appearance and growth of individual fruits, was, after calibration successful in describing insecticide fate in pepper and tomato plants and quantified important processes including degradation.

1. INTRODUCTION

Pesticides (i.e., chemical active ingredients in plant protection products) are used extensively in agricultural production to protect plants from diseases, pests, and weeds. The global application of 3–4 million tons of active ingredients was estimated for recent years. ¹ , ² , ³ Released into the environment, the compounds are the subject of various transport and fate processes and can pose threats to groundwater, non‐target ecological receptors and human health. Pesticides have been reported in soil, groundwater, and surface water, where they are partly accumulating or transformed into possibly harmful metabolites. ⁴ , ⁵

Portions of the applied pesticide may remain on the treated plant surfaces or be translocated to other plant parts. As a result of intensive use, pesticides can accumulate in plants and eventually form residues in related agricultural products, reaching the end consumer. Pesticide residues can reduce the economic value of the products and pose risks to human and animal health. ⁶ , ⁷ Pesticide residues in food are strictly monitored and regulated by authorities. ⁸ , ⁹ , ¹⁰

Transport and fate of applied pesticides are complex, including plant uptake from soil via the xylem, uptake from treated surfaces and the atmosphere through the cuticle and stomata, translocation within the plant via xylem and phloem, as well as dissipation from treated plant surfaces and biodegradation. ¹¹ , ¹² , ¹³ For the estimation of emissions, risks and human and ecological impacts related to pesticide application, knowledge on relevant transport routes and expected residues in crops and environmental matrices (like soil and groundwater) is required. ¹⁴ , ¹⁵ , ¹⁶ Although the accumulation and transport of pesticides in plants depend on the applied pesticide amounts, also morphological plant characteristics, physicochemical properties of the pesticides, and the produced biomass affect pesticide concentrations at harvest time. Authorities use mathematical models for managing pesticide residues and minimizing food hazard risk, aimed at avoiding the exceedance of maximum residue limit (MRL) values. Most of these models depend on the bioconcentration factor (BCF). Later, dynamic mathematical models were used to estimate pesticide uptake and transport. ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ , ²² , ²³ These models deal with the plant's physiological processes and the main organs of the plant. Furthermore, empirical methods are used to estimate how long the pesticide remains in the plant and provides protection, however such regression models are not sufficient for determining the input and interpreting the results from a mechanistic point of view, concerning the involved processes. ¹² Therefore, a more reliable method for growing plants and fruits has been developed for the methomyl insecticide for tomatoes. ¹⁸

The main purpose of this study was to develop a mathematical model that considers plant growth dynamics to be used for simulating pesticide crop residues from applications on tomatoes and peppers. These are important crops, where 182 million tons of tomatoes and 0.7 million tons of pepper are produced annually in the world. ²⁴ The advantage of using dynamic mathematical models for estimating pesticide uptake and transport in plants is that it can provide a more accurate estimation of the amount of pesticide residues that may remain in the plant at harvest time. This can help authorities in regulating the use of pesticides to ensure that MRL values are not exceeded, thereby minimizing the potential health risks associated with pesticide residues in food products. Additionally, the model developed in this study may also provide valuable information on the optimal application rates and patterns of specific pesticides for tomato and pepper crops, as well as concerning the effects of different pesticides on plant growth and yield. This information can be useful for farmers and agronomists in developing strategies for pesticide application that minimize risks to human and animal health, while maximizing the economic value of their crops. A reliable and calibrated prediction tool for pesticide residues can also assist in designing more sustainable pesticides, and to promote more sustainable use of existing pesticides.

2. MATERIALS AND METHODS

2.1. Experimental settings

Tomatoes (Solanum lycopersicum L., variety Olgun; purchased from Yuksel seeds) were planted in a greenhouse in Aydın province, Turkey (37°47′43″ N 27°59′32″ E) with a row spacing of 50 cm and inter‐row spacing of 70 cm for experimentation purposes. The experiments were arranged in three rows for each treatment, with 30 plants used per row for each replication. Peppers (Capsicum annuum L., variety Varol; purchased from Yuksel seeds) were planted on a field within the borders of Sarayköy district of Denizli province, Turkey (37°53′56″ N 28°57′14″ E). The pepper plants were planted with a row spacing of 25 cm and inter‐row spacing of 70 cm. Three rows were selected for each treatment, and 50 plants were chosen per row for each replication. The plants were irrigated using drip irrigation from planting to harvest, with water levels adjusted as needed to maintain optimal growth conditions without water stress.

The following pesticides were applied: acetamiprid, deltamethrin, indoxacarb, λ‐cyhalothrin, spinosad (pepper, only) and chlorantraniliprol (tomato, only). Pesticides were applied via spray as individual compounds to different experimental plots. Applied pesticide amounts and application patterns are summarized in Table S1 of the Supporting Information (SI). In addition, control experiments were done without pesticide application.

2.2. Sampling and sample preparation

Fruits were sampled 11 times in the first set of experiments (0.08, 1, 3, 5, 10, 10.08, 14, 17, 21, 28, 35 days after the first application) and eight times in the second and third sets of experiments (0.08, 1, 3, 7, 14, 21, 28, 35 days after the first application). The control was sampled at the beginning, on day 14 and day 35. Approximately 1.5–2.0 kg of fruit mass was collected per sample and stored at −20 °C until extraction and analysis.

2.3. Analysis of plant residues

The QuEChERS (Quick, Easy, Cheap, Effective, Rugged, and Safe) method was used for extraction and clean‐up of tomatoes and peppers. In the first step, the fruits were thoroughly homogenized, and 10 g of the homogenized sample was placed into a 50 mL centrifuge tube. Then, the sample was mixed with 10 mL of acetonitrile: citric acid (99:1 v:v ratio) by vortexing for 1 min. Next, 4 g of MgSO₄, 1 g of NaCl, 1 g of trisodium citrate dihydrate (C₆H₉Na₃O₉), and 0.5 g of disodium hydrogen citrate sesquihydrate (C₁₂H₁₈Na₄O₁₇) mixture were added and shaken for 1 min. After that, the mixture was centrifuged for 5 min at 4000 rpm. The upper phase was then transferred to a 15 mL tube containing 25 mg of primary secondary amine (PSA), and vortexed again for 1 min. Finally, the upper layer (1 mL) was filtered using a 0.25 μm PTFE filter and stored in 2 mL vials until analysis. ²⁵ , ²⁶

Chemical analysis was done using liquid chromatography with tandem mass spectrometry (Schimadzu LC–MS/MS) for all compounds except for λ‐cyhalothrin. The latter compound was analyzed with gas chromatography/mass spectrometry (Schimadzu GC/MS). LC–MS/MS analysis was performed using a C18 column, with an injection volume of 20 μL at a flow rate of 0.4 mL min⁻¹. The auto sampler temperature was set to 5 °C and the column temperature to 40 °C. The MS parameter of the interface voltage was set to 4.5 kV, with a nebulizing gas flow of 3.0 L min⁻¹. The desolvation line temperature was maintained at 250 °C, while the heat block temperature was set to 400 °C. Data on pesticide recoveries, considered retention times and mass‐to‐charge ratios during selected ion monitoring (SIM) are given in Supporting Information, Table S2. SIM was selected in mass spectrometry to improve the detection limit of the instrument and increase the signal‐to‐noise ratio of the ions of interest.

For GC analysis, a capillary column TRB‐5MS, (95%) methyl‐(5%) phenyl polysiloxane, was used with helium as a carrier gas (constant flow rate of 1 mL min⁻¹). A split/split‐less inlet was used and a sample volume of 20 μL was injected at 270 °C. The temperature program was chosen as follows: an initial temperature of 90 °C was held for 2 min, followed by an increase of 11 °C min⁻¹ up to a temperature of 200 °C. Temperature was then further increased by 20 °C min⁻¹ up to 300 °C, which was held for 3 min.

2.4. Modeling of chemical plant uptake

For simulating fruit concentration and translocation of the neutral pesticides (deltamethrin, indoxacarb, λ‐cyhalothrin), the Multi‐Cascade approach was used. ²⁷ , ²⁸ The underlying differential equations were also solved numerically, and the model approach was extended for ionizable pesticides (for acetamiprid, spinosad, chlorantraniliprol). These ionizable compounds, in particular spinosad (a base with a pK_a near intracellular pH) may be present as weak electrolytes that undergo additional processes including electrochemical interaction and the ion trap process. ²⁹ , ³⁰ This was considered in the Cell Model, coupled to the dynamic plant uptake model as described in detail in section S2 of the SI. In addition, phloem flux from leaves to stem and further to (i) fruits and (ii) roots and soil is relevant for ionizable compounds, so that the differential equations underlying the Multi‐Cascade approach were extended by this ‘downward’ phloem flux, accordingly, as illustrated in Supporting Information, Fig. S1. In summary, a system of coupled ordinary differential equations was solved numerically, for describing the change of chemical mass with time, dm/dt, in the compartments soil, root, stem, leaf and fruit. These chemical mass balance equations are given in section S2.

The model was extended to consider the growth of individual fruits. This is necessary for plants like pepper and tomatoes, where fruits are harvested continuously over a certain period (in contrast to crops like wheat and maize, where all plants are harvested at once). Thus, Eq. (S8) (in the SI) was adjusted for the fruit compartment in order to sum up the contribution of individual fruits (index i):

$$\frac{d{M}_F}{\mathit{dt}}=\sum _{i=1}^{n_F}\frac{d{M}_{F,i}}{\mathit{dt}}$$ (1)

with

$$\frac{d{M}_{F,i}}{\mathit{dt}}=\left\{\begin{array}{c}{k}_{\mathit{gr},F,i}\bullet M_{F,i}\left(1-\frac{M_{F,i}}{M_{\mathit{max},F,i}}\right) \mathrm{if}t\ge t_{\mathit{lag},F_i}\\ 0 \text{if}t<t_{\mathit{lag},F_i}\end{array}\right.$$ (2)

There is a continuous growth of total fruit mass M _F as long as new fruits are appearing and continue to grow. Phases between the appearance of individual fruits are specified by t _lag,F,i (d), indicating a lag phase between growth start. n _F is the total number of fruits.

Whereas the Multi‐Cascade approach considers a diagonal matrix (with an analytical solution), the differential equation system extended for phloem flux used here adds further components to the diagonal matrix (Supporting Information, Fig. S1), for which no analytical solution has been found to date. Therefore, the differential equation system was solved numerically using the ODE45 solver (Runge–Kutta scheme with variable step size) within Matlab R2023b. This code was mathematically validated against a model set up within an Excel spreadsheet, using a Euler one‐step solutions scheme. In order to make the numerical solution procedure and post‐processing within Matlab more efficient (enabling coherent solution matrices), we have differentiated Eq. (S8) with respect to time, yielding:

$$\frac{d^2{M}_j}{d{t}^2}=2\frac{{k_{\mathit{gr},j}}^2}{{M_{\mathit{max},j}}^2}{M_j}^3-3\frac{{k_{\mathit{gr},j}}^2}{M_{\mathit{max},j}}{M_j}^2+{k_{\mathit{gr},j}}^2{M}_j$$ (3)

Using solver ode15s within Matlab, numerical integration of the whole equation system was done (integration of dm _i/dt for obtaining chemical mass m _i as a function of time in compartment i, Eq. S1–S5; of dM _j/dt for obtaining plant mass M _j and (surface areas) in plant compartment j, Eq. S8 and 1–2; of d² M _j/dt ² for obtaining transpiration, Eq. S9–S11 and 3). This yields one solution matrix containing all dependent variables.

Pesticide application was described as single or dual pulse, depending on experiment, by specifying initial concentrations C ₀ for the above‐ground plant parts (stem, leaf, fruit) and soil. These initial concentrations were among the fitting parameters and needed to be estimated from total chemical input during pesticide application (cf. Supporting Information, Table S1).

Least‐squares fitting of predictions to the measured data was performed with manual expert adjustment of model parameters in an iterative procedure. Model input parameters are summarized in Supporting Information, Table S3‐S6. The leaching rate Q _l was generically assumed as 0.27 L/d (showing a very low sensitivity) and the surface water runoff rate Q _r was set to zero (assumed negligible during the experiments).

2.5. Overall dissipation of observed fruit concentrations

In addition to the numerical simulations, first‐order dissipation rate constants k _diss,F (1/d) were fitted to measured fruit concentrations, for each pesticide application. This was done to describe overall reduction in observed fruit concentration, which may result from growth dilution, degradation, wash‐off, and volatilization. ³¹ , ³² Dissipation half‐life t _1/2,F was calculated as t _1/2,F = ln (2) / k _diss,F .

3. RESULTS AND DISCUSSION

Observed pesticide concentration dynamics were simulated with the goal of identifying the contribution of processes and quantifying their rates. Pesticides were applied via spray, expected to reach above‐ground plant parts (fruits, leaves, stems) and, at least to some extent, soil. The input to each of these compartments was among the unknowns, as well as the degradation rate constants. Furthermore, plant growth dynamics and the appearance of individual fruits needed to be estimated, which showed significant influence on fruit concentrations.

3.1. Chemical dynamics

The interception of sprayed insecticides by plants and the degradation rate within plants are required to conduct model simulations but could not be determined experimentally. Hence, input into plants and soil as well as degradation rate constants within plant compartments were fitted by model calibration to measured concentrations. We have compared two different simulation scenarios: input only to fruits as a base case (‘mod 0’) and possible input to all above‐ground compartments (fruit, leaf, stem, soil). We fitted best estimate curves (‘mod b.e.’) together with an uncertainty range (upper and lower estimate; gray‐shaded areas in Figs 1 and 2). If the base case (mod 0) corresponds to the best fit (mod b.e.), the model approach could substantially be simplified by considering the fruit compartment only.

Figure 1.

Uptake of acetamiprid (AC, a), deltamethrin (DM, b), indoxacarb (IN, c), λ‐cyhalothrin (LC, d) and spinosad (SP, e) into pepper plants. Concentrations in pepper fruit as a function of time, measured (meas) versus modeled (mod). Mod b.e.: best estimate (best model fit); mod 0: base case (assuming input to fruit, only); gray areas indicate minimum‐maximum range of plausible model fits. Red x on the x‐axis indicates the time of pesticide input.

Figure 2.

Uptake of acetamiprid (a), chlorantraniliprole (b), deltamethrin (c), λ‐cyhalothrin (d, e, f) and indoxacarb (g, h) into tomato plants. Concentrations in tomato fruit as a function of time, measured (meas) versus modeled (mod). Mod b.e.: best estimate (best model fit); mod 0: base case (assuming input to fruit, only); gray areas indicate minimum‐maximum range of plausible model fits. Three experiments for λ‐cyhalothrin and two experiments for indoxacarb (cf. Supporting Information, Table S7). Red x on the x‐axis indicates the time of pesticide input.

Figure 1 shows measured versus modeled pesticide concentrations in pepper fruits as a function of time. Simulated concentrations in the other compartments (soil, root, stem, leaf) can be seen in Supporting Information, Fig. S2. Fitted parameters and statistical evaluation of curve fits are summarized in Table 1. Chemicals were applied at day 0 and 10 of the experiment and readily decreased after the respective applications, in most cases.

Table 1.

Fitted parameters for modeling of pesticide uptake into pepper plants (one fruit per plant appearing every 7 days, with 10 fruits per plant in total): total input of chemicals at application and fitted individual input to fruit, leaf, stem, and soil, as well as fitted degradation rate constants in plant and soil

Compound	Acetamiprid	Deltamethrin	Indoxacarb	λ‐cyhalothrin*	Spinosad
Input (mg):
Total (applied)	16.2	3.2	13.8	6.5	28.3
	16.2	3.2	13.8	6.5	28.3
To fruit (I em,F )	0.72 (0.72–0.75)	0.065 (0.065–0.068)	0.8 (0.8–0.9)	1.4	2.4
	1.35 (0.62–1.35)	0.13 (0.13–0.14)	0.7 (0.7–0.72)	1.0 (0.9–1.1)	3.0 (2.8–3.0)
To leaf (I em,L )	0	0 †	0 †	0 †	0 †
	1.5 (0–1.5)	0 †	0 †	0 †	0 †
To stem (I em,St )	0	1.0 (0–1.0)	2.0 (0–2.0)	0 †	0 (0–2)
	0 (0–2.4)	0	2.2 (0–2.2)	0 †	0 (0–2)
To soil (I em,S )	0.7 (0–0.7)	0 †	0 †	0 †	0 †
	0.7 (0–0.7)	0 †	0 †	0 †	0 †
Degradation rate constants (d −1 ):
k F	0.23 (0.22–0.25)	0.08 (0.07–0.10)	0.14 (0.12–0.14)	0.38 (0.33–0.39)	0.11 (0.11–0.12)
k L	0	0	0	0	0
k St	0	0.08 (0–0.08)	0.3 (0–0.3)	0	0
k S	0	0	0	0	0
Dissipation rate constant k diss,F (d −1 ) and half‐life t 1/2,F (d) fitted to measured fruit concentrations (with t 1/2,F   = ln(2) / k diss,F ):
k diss,F	0.28	0.046	0.138	0.15	0.13
	0.13	0.090	0.116	0.063	0.16
t 1/2,F	2.48	15.07	5.02	4.62	5.33
	5.33	7.70	5.98	11.00	4.33
Statistical curve fit evaluation (measured vs. modeled fruit concentration):
R 2 (‐)	0.935 (0.906–0.935)	0.942 (0.912–0.942)	0.953 (0.941–0.953)	0.984 (0.978–0.984)	0.987 (0.985–0.987)
RMSE (mg kg −1 )	0.094 (0.094–0.110)	0.008 (0.008–0.011)	0.066 (0.066–0.084)	0.063 (0.063–0.073)	0.125 (0.124–0.126)
ME (mg kg −1 )	0.028 (−0.004–0.059)	−0.001 (−0.004–0.001)	0.01 (−0.033–0.042)	−0.020 (−0.039–0.006)	0.064 (−0.031–0.064)

Input, dissipation rate constant and half‐life: first line refers to 1st application (day 0 of experiment), second line to 2nd application (day 10). Numbers indicate best estimates, brackets include ranges (mod 1–3, cf. Figure 1). R², coefficient of determination; RSME, root mean square error; ME, mean error.

^*Best fit assuming constant background concentration in air (best estimate 1.6 μg m⁻³, range 1.4 to 1.6 μg m⁻³).

^† Sensitivity on simulated fruit concentration is very low.

For acetamiprid (AC), mod 0 (chemical input only to fruits) yielded an underestimation of fruit concentrations after the 2nd application (orange curve in Fig. 1(a)). The best estimate (mod b.e.) was obtained by assuming additional input to leaf and soil (black curve), and upper and lower estimates involve additional input to stem (bounding the gray area). Only a portion of the sprayed chemical seems to have entered the plants, and there are remarkable differences between the two applications: for the best fit (mod b.e.), 0.72 mg have entered fruits and 0.7 mg soil at the 1st application, whereas 1.35 mg went to fruits plus 1.5 mg to leaves and 0.7 mg to soil at the 2nd application (cf. Table 1). This corresponds to 9% and 22% of the total chemical mass applied at the 1st and 2nd application (16.2 mg), respectively. The remaining fractions might have drained or washed off the plants, not reaching the plant roots during experiment time, or were deposited outside of the planted row. Although uptake from soil is sensitive to AC concentration in fruit, input to soil higher than 0.7 mg seems unlikely since this would result in curve characteristics differing from the observation (too low reduction of fruit concentrations, or too steep curves following application if higher degradation rate constants are chosen).

For deltamethrin (DM) and indoxacarb (IN) (Fig. 1(b), (c)), best fits were obtained when assuming input to stem, in addition to fruit (mod 0 gives a lower‐bound estimate). The sensitivity of input to stem for fruit concentration can be explained by an effective translocation to fruits.

Input to soil and leaf was insensitive to fruit concentration. For λ‐cyhalothrin (LC) and spinosad (SP) (Fig. 1(d), (e)), the best fit (mod b.e.) corresponds to mod 0 and thus assuming input to fruit, only (input to soil and leaf insensitive, input to stem low‐sensitive for fruit concentrations of LC). Concerning LC, the assumption of a constant background in air (best estimate 1.6 μg m⁻³) yielded the best fit for explaining elevated concentrations that remained during the last 16 days of the experiment. In the experiments with control plants (without pesticide input), none of the applied chemicals were detected in soil and plant samples.

Uptake from soil as well as input to leaves was sensitive to fruit concentrations for AC, only. This can be explained by the low apparent octanol to water partition coefficient, log D, of this compound (0.95, Supporting Information, Table S4), making the phloem pathway leaf‐stem‐fruit relevant and effectively allowing compounds to follow the soil‐root‐stem‐fruit pathway. The log D describes lipophilicity, considering both the neutral and ionic species; log D can thus be more accurate than log K _OW for ionizable compounds, depending on the prevailing pH. ³³ For AC, phloem flux downwards through the plant has a significant contribution for the time after the second application (day 10 of experiment and later), when chemical input is on leaf and stem (as described above) so that the leaf‐stem‐fruit pathway is important. This can be seen from Supporting Information, Fig. S3, where presence and absence of phloem flux ‘downwards’ is compared for three scenarios of pepper fruit growth.

In summary, direct input to pepper fruits was estimated 0.6–16.7% of total input (pesticide application), and input to other above‐ground compartments 0–13.0% which is associated with considerable uncertainty, due to a low sensitivity to fruit concentrations, depending on the case. Input to stem (pathway stem‐fruit) was sensitive for all compounds except for LC (comparatively low for DM and SP), input to soil (pathway soil‐root‐stem‐fruit) and to leaf (phloem pathway leaf‐stem‐fruit) only for AC (cf. Table 1).

Concerning degradation rate constants (k _i in Eqs. S1‐S5), highest values for fruits (k _F) were fitted for LC (0.38 d⁻¹), followed by AC (0.23 d⁻¹), IN (0.14 d⁻¹), SP (0.11 d⁻¹) and DM (0.08 d⁻¹; best estimate values, cf. Table 1). Degradation in root, stem and leaf was insensitive to fruit concentrations in most cases (except DM up to 0.08 d⁻¹, and IN up to 0.3 d⁻¹ in stem, Table 1).

As expected, in most cases, values of k _F are lower than overall dissipation rate constants k _diss,F (cf. Table 1). The latter were obtained by fitting exponential curves to measured fruit concentrations and describe total dissipation, including processes such as growth dilution (considered in the model by growing plant mass), degradation (fitted k _F) and wash‐off. It has to be noted that k _diss,F was fitted individually for the two applications, whereas k _F refers to the total time of observation. Corresponding half‐lives t _1/2,F range between 2.48 and 15.1 days (cf. Table 1). Values vary between chemicals and also between the first and second application, so that we recommend reporting experimental conditions, including application patterns, together with dissipation rate constants and half‐lives. We therefore find it necessary to carry out dynamic plant modeling for quantifying the contributions to overall dissipation, being characteristic for the whole cultivation period, instead for individual pesticide application events.

Using lower application rates (2–4 mg m⁻²), Sanyal et al. ³⁴ found t _1/2,F of AC in pepper fruits of 2.24–4.84 days, which are similar to our estimates of 2.48 and 5.33 days (Table 1). Concerning DM, t _1/2,F of 2.05–2.45 days (polyhouse) and 1.51–1.86 days (open field) were obtained by Guru et al. ³⁵ Half‐lives were clearly shorter than in our case (pepper field experiment, 7.7 to 15 days). Kaur et al. ³⁶ found t _1/2,F between 3.46 and 4.77 days for IN (application rate 11 mg m⁻² versus 13.8 mg m⁻² in this study), and thus slightly shorter than our half‐lives (5.02–5.98 days). For LC, Shalaby ³⁷ estimated t _1/2,F of 2.68 days, which is shorter than in our case (4.62–11.0 days) at a lower application rate (4.46 versus 6.5 mg m⁻²). Sulaiman et al. ³⁸ found a half‐life of 5.41 days for SP, being slightly above our range (4.33–5.33 days). Differences might be explained by different cultivation and climate conditions. In our study, fruit concentration in pepper at harvest time was below maximum residue level (cf. Supporting Information, Table S4) for all compounds except LC (ratio 1.5 for LC, 0.09–0.18 for all other compounds).

Pesticide concentrations in tomato fruits as a function of time (measured and modeled) are shown in Fig. 2. For simulated concentrations in soil, root, stem and leaf, cf. Supporting Information, Fig. S4. Fitted parameters and statistical evaluation of model parameters are given in Table 2. Two experiments were conducted for IN and three experiments for LC, where findings are summarized in Table 2 and details for the individual experiments are given in Supporting Information, Table S7. Compared to the experiments with pepper (Fig. 1), a higher scattering of measured concentrations can be seen, and concentration decrease after application(s) was often slower. Nonetheless, fruit concentration in tomato at harvest time was below maximum residue level (Supporting Information, Table S4) for all compounds (ratio 0.05–0.35). For AC and chlorantraniliprole (CA), best estimates were obtained with input to fruit and stem (Fig. 2(a), (b), mod b.e.). Additional input to soil also yielded plausible curve fits, as well (upper/ lower bounds, cf. gray areas). Mod 0 (input only to fruits) was inadequate for AC but close to mod b.e. for CA, except for the initial phase. For IN (one pesticide application), input to fruit and stem (experiment IN 1) or only to fruit (experiment IN 2) gave best fits. For DM and LC (experiment LC 1 with two pesticide applications, LC 2 and 3 with one application), input only to fruits (mod 0) was successful to describe observations (cf. Figure 2, Table 2 and Supporting Information, S7).

Table 2.

Fitted parameters for modeling of pesticide uptake into tomato plants (one fruit per plant appearing every 3.4 days, with 30 fruits per plant in total): total input of chemicals at application and fitted individual input to fruit, leaf, stem, and soil, as well as fitted degradation rate constants in plant and soil

Compound	Acetamiprid	Chlorantraniliprole	Deltamethrin	Indoxacarb*	λ‐cyhalothrin*
Input (mg):
Total	8.57	4.2	1.7	10.5 *	3.5 *
	8.57	4.2	1.7		0–3.5 *
To fruit (I em,F )	0.2 (0.2–0.2)	0.1 (0.1–0.12)	0.1 (0.09–0.11)	0.4–0.5	0.165–0.40
	1.0 (1.0–1.05)	2.2 (1.9–2.25)	0.07 (0.07–0.085)		0–0.06
To leaf (I em,L )	0	0 †	0 †	0 †	0 †
	0	0 †	0 †		0 †
To stem (I em,St )	2.2	0.7 (0.7–1.0)	0 †	0–3	0 †
	2.2 (2.0–2.2)	0 (0–1.0)	0 †		0 †
To soil (I em,S )	0 (0–2)	0	0 †	0 †	0 †
	0 (0–2)	0 (0–1)	0 †		0 †
Degradation rate constants (1/d):
k F	0.02 (0.02–0.029)	0.011 (0.011–0.013)	0.019 (0.019–0.023)	0.006–0.01	0.008–0.012
k L	0	0	0	0	0
k St	0	0	0	0–0.01	0
k S	0	0	0	0	0
Dissipation rate constant k diss,F (d −1 ) and half‐life t 1/2,F (d) fitted to measured fruit concentrations (with t 1/2,F   = ln(2) / k diss,F ):
k diss,F	0.070	0.060	0.014	0.013–0.026	0.013–0.040
					0.020
	0.017	0.030	0.047
t 1/2,F	13.86	11.55	49.51	26.66–46.21	17.33–53.32
	40.77	23.10	14.75		34.66
Statistical curve fit evaluation (measured vs. modeled fruit concentration):
R 2 (−)	0.588 (0.564–0.588)	0.696 (0.688–0.696)	0.367 (0.360–0.367)	0.380–0.519	0.116–0.336
RMSE (mg kg −1 )	0.032 (0.032–0.034)	0.051 (0.050–0.052)	0.003 (0.003–0.004)	0.007–0.014	0.004–0.016
ME (mg kg −1 )	0.003 (−0.002–0.007)	0.009 (0.003–0.01)	−0.001 (−0.002–0.001)	−0.001 − 0.001	‐0.001‐0.005

^*Summary of two experiments for indoxacarb (with one application on day 10) and three experiments for λ‐cyhalothrin (1× with application on day 0 and day 10, 2× with one application on day 10; details on individual experiments given in Supporting Information, Table S7).

^† Sensitivity on simulated fruit concentration is very low, or, in case of chlorantraniliprole and leaves, low.

Input, dissipation rate constant and half‐life, unless noted differently: first line refers to 1st application (day 0 of experiment), second line to 2nd application (day 10). Numbers indicate best estimates, brackets include ranges (mod 1–3, cf. Figure 2). R², coefficient of determination; RSME, root mean square error; ME, mean error.

In summary, for tomato, estimated direct input to fruit was in the range 0.9–13.4% of total input (similar to pepper) and input to stem, leaf, and/or soil 0–25.7%. The latter ranges higher than for pepper plants (up to 13.0%) and is again associated with uncertainty, with partly low sensitivities to fruit concentrations. Input to stem (pathway stem‐fruit) was sensitive for the most polar insecticides AC, CA and IN (cf. Table 2). In contrast to pepper plants, sensitivity of input to stem for DM was very low. This can be explained by a higher fruit to stem mass ratio for tomato than for pepper (9.3 versus 4.3, based on final masses, cf. Supporting Information, Table S6), leading to lower influence of chemical input to stem for tomato. Input to soil (pathway soil‐stem‐root‐fruit) and was sensitive for AC and CA, only. The phloem pathway leaf‐stem‐fruit was sensitive for AC, and it showed some (low) sensitivity for CA (moderate log D of 3.76, Supporting Information, Table S4), however it was insensitive for the other chemicals (Table 2).

Degradation rate constants in fruit k _F were 0.02 d⁻¹ as best fit for AC, 0.011 d⁻¹ for CA, and 0.019 d⁻¹ for DM. For IN and LC, model curves were difficult to fit, due to a large scattering of observed concentrations or apparent trends in the data that could not be reproduced by modeling (such as for two experiments with LC, Fig. 2(e), (f), and one experiment with IN, Fig. 2(g)). We found k _F for IN and LC in the range of 0.006 to 0.01 and 0.008 to 0.012 d⁻¹ (best estimates), respectively. Overall dissipation rate constants (k _diss,F) were mostly higher than k _F, however there was considerable uncertainty due to the large scattering of measured concentrations. The corresponding dissipation half‐lives were between 11.6 and 53.3 days (Table 2) and thus higher than for pepper (2.48–15.1 days, Table 1). This can be explained by the greenhouse conditions for tomato, where controlled conditions are expected to result in slower dissipation compared to field conditions (pepper experiments). Values are exceeding other observations for AC (1.04–1.79 days ³⁹ , ⁴⁰ ), CA (3.30 days ⁴¹ ), DM (1.84–1.95 days ⁴² ) and IN (2.16–12.2 days ⁴³ , ⁴⁴ , ⁴⁵ , ⁴⁶ ) or are in the upper range (LC: 3.12–23.0 days ⁴⁷ , ⁴⁸ ). Possible explanations include different experimental conditions, where a lower relative air humidity and higher air circulation tend to increase pesticide dissipation. The numbers on dissipation (k _diss,F and corresponding half‐lives) were obtained from fitting an exponential curve to the observed decline of concentrations in fruits, individually after each application. This enables only a rough and integral view on dissipation in fruit. Our numerical simulations, instead, allow analyzing contributions to such dissipation, including degradation (k _F ), growth dilution, chemical uptake and flow from/to plant compartments, as well as volatilization as separate processes.

3.2. Growth dynamics and transpiration

A crucial part of simulating chemical plant uptake and translocation is the estimation of plant growth and transpiration. Growing plant mass leads to growth dilution (reduction of chemical concentration) and induces transpiration (advective transport). Understanding their dynamics in each plant compartment is important for an adequate description of chemical concentration distributions as a function of time. This includes an adequate determination of the ‘growth window’ (time frame of experimental observations within the vegetation period) and logistic growth curves for each plant compartment (cf. Eq. S8, 1 and 2). Details are described in Section S5 for pepper and tomato. In summary, best estimates were obtained by assuming that one fruit per plant was appearing consecutively every 7 days (pepper, Supporting Information, Fig. S5) and 3.4 days (tomato, Supporting Information, Fig. S7), with a total number of 10 (pepper) and 30 (tomato) fruits. During the time of observation (concentration measurement), transpiration was mainly driven by fruit growth.

3.3. Dynamic versus constant plant mass and transpiration

Furthermore, we have analyzed the assumption of constant plant compartment mass and transpiration, which could strongly simplify modeling. In this case, the dilution of chemical concentration due to plant growth is considered by first‐order growth rate constants for each plant compartment. Details are given in Section S6. In summary, under the growth conditions of our experiments, fully dynamic plant mass and transpiration consideration was required for both pepper and tomato, instead of assuming constant conditions for plant mass and transpiration combined with first‐order rate constants to describe growth dilution (which led to significant under‐ or overestimation, depending on the assumptions for fruit appearance).

4. CONCLUSION

Our dynamic plant uptake model, suited for neutral and ionic compounds, was successfully applied for simulating observed pesticide concentration dynamics in pepper and tomato fruits. The model allows the choice (i) neutral or ionic compound, (ii) with or without phloem flux ‘downwards’, and (iii) dynamic or constant plant mass and transpiration. As a new aspect, the continuous appearance of individual fruits was implemented in the model, required to adequately calculate the growth of total fruit mass. It was found that the time‐window of cultivation, within the vegetation period, needs to be known, as well as the number of fruits and the frequency of their appearance in the considered period. This determines the dynamics of growth and induced transpiration, having decisive influence on the dynamics of concentrations in harvested fruits.

Chemical input to the individual compartments (above‐ground plant parts and soil), resulting from pesticide spray, and degradation rates were among the unknowns for the pesticides investigated. In addition to direct input to fruits, input to stem was sensitive to fruit concentrations for all studied compounds, except for LC (pepper and tomato) and DM (tomato). Input to soil (with uptake into root and translocation to stem and fruit) was sensitive only for AC and CA, and also input to leaves (phloem pathway leaf‐stem‐fruit) was relevant for these two compounds, only, which are characterized by a low and moderate log D, respectively.

Pesticide concentrations were readily decreasing in pepper fruits during experiment time (except for λ‐cyhalothrin with somewhat elevated concentrations), with fitted degradation rate constants k _F between 0.08 and 0.38 d⁻¹. Experiments were more difficult to describe for tomato, due to a larger scattering of measured fruit concentrations. Pesticide concentrations were decreasing, however slower than in pepper so that elevated concentrations were still found at the end of the experiment, with lower k _F between 0.006 and 0.02 d⁻¹.

The model can readily be applied for other compounds and plants, provided related chemical and plant characteristics data are available. In order to reduce uncertainties, it is recommended to record the number of individual fruits and their appearance during experiments and to determine the time‐window of the experiment within the vegetation period. Modeled pesticide concentrations can be used as input for risk and impact assessment investigations. Moreover, a reliable and calibrated prediction tool for movement and fate of insecticide residues in crops may also be employed for the design of improved active ingredients, which better target the unwanted pest and spare desired insects, such as valuable pollinators, promoting an overall more sustainable plant protection.

CONFLICT OF INTEREST

The authors declare no competing financial interest.

Supporting information

Supporting information may be found in the online version of this article.

DATA AVAILABILITY STATEMENT

Data are provided within the publication; further data can be obtained from the authors upon request.