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Phytochemical responses to herbicide exposure and effects on herbivorous insects

8. Modelling changes in the content of two phenolic compounds

It was observed in Chapter 7 that the survival of G. polygoni larvae was correlated to the concentration of two phenolic compounds, namely those denominated as compound 2 and compound 3 in Chapter 2. The simple linear regression analysis showed that the concentration of the two compounds explained between 25 and 41% of the variation in larval survival. The concentration in the plant was measured over time (time intervals of 3 days), whereas the survival data integrate the impact throughout development or over longer periods. However, a larva feeding on a certain leaf at a certain point in time carries the history of earlier uptake unless the metabolism of the compounds are so fast and efficient that the compound is irrelevant and practically non-existing in the insect.

It is evident from the previous chapters that a range of factors affects the concentration of these two phenolic compounds. They were correlated both to chlorsulfuron treatment (Chapters 4 and 5), to herbivory and UV-B radiation (Chapter 6), time (Chapters 4 and 5) and for compound 2 also development (Chapter 2).

The complexity of the system governing the concentration of these phytochemicals in the plant makes it attractive to develop a model which calculate the concentration as a function of the aforementioned parameters. The model can be used to improve the description of herbivore mortality from time related content of these compounds and the consumption and growth of the herbivorous larvae.

8.1 Materials and methods

8.1.1 Plant model

The model, which will be presented below, is built on the assumption that the impact factors governing the concentration of compounds 2 and 3 are independent of each other. However, we involved an interaction coefficient for dosage and time because it has been suggested that many herbicides rejuvenate the treated plants. In the present study, it most likely means that the developmental progression of the phytochemical profile is slowed down or stopped and the effect of dosage is altered. It has, for example, been observed that F. convolvulus stopped producing leaves after treatment with chlorsulfuron, but after a period of ten days it resumed the previous exponential growth (Kjær, 1994).

The overall structure of the model is therefore as follows:

where Concentration is the concentration of either compound 2 or 3 in the leaves of F. convolvulus. The model was parameterised by using the data on effects of herbivory, UV-B radiation, chlorsulfuron dosage and time on the concentration of compounds 2 and 3 presented in previous chapters.

Based on the data in Chapter 5 we assumed the effect of Dosage could be described by means of a sigmoid dose-response curve:

Dosage:

,

where x is the herbicide dosage, ddose is the response at dosage = 0, adose is the asymptotic response. X₀dose is the dosage at the point of inflexion of the curve and bdose is the slope parameter at the inflexion point.

The change in concentrations of compounds 2 and 3 with time was described by a parabolic function, because the concentration in the single leaf first increase and then decrease (Chapters 4 and 5), and a similar pattern has been seen in the studies of . Further, there was an initial increase in the concentration after spraying, which declined after some time either due to metabolism of the compounds or due to growth dilution (Chapter 5). Time in the equation below is the age of the single leaf.

Time:           atime ´ t² + btime ´ t,

where t is the leaf age in days, atime and btime are rate coefficients of the curve.

The effects of Herbivory and UV-B radiation was described as simple linear relationships i.e.:

where aUV and aherb are rate coefficients.

The Interaction between time and dosage was described by:

atime ´ dose ´ x ´ t ,

where atime ´ dose is the rate constant, x is the herbicide dosage, t is leaf age (e.g. time).

The data presented in Chapter 7 on relationship between content of compounds 2 and 3 and herbivore survival was not used for parameterisation, but saved to validate the output of the model.

In order to homogenise the variance the data were transformed by a Box-Cox transformation where the power parameter was found by a maximum likelihood approach (Seber and Wild, 1989 p.71). The transformed model was fitted to the transformed data assuming normal distributed residuals using FindMinimum in Mathematica (Wolfram, 1996). The significance of the different effects included in the model was tested using log-likelihood tests.

Regression analysis was used on the relationship between estimated intake of the phenolic compounds selected and the survival of G. polygoni larvae.

8.1.2 Intake of phenolics by G. polygoni larvae over time

There was a large variation in the regression between observed survival and the concentration of compound 2 and compound 3 in Chapter 7. It was hypothesised that this was a consequence of the fact that survival expresses effects on the larvae population over a longer period, but the chemical data only represent spot check of the content over the development. In order to adjust for this, a model for intake of the compounds was needed. The plant model together with unpublished data on consumption and larval growth were used to calculate the body burden, i.e. the consumed amount of the compound per unit body weight, per day. The equation for the body burden of a larva at a certain point of development is:

where Concentration is the concentration on a specific day as predicted by the Plant model, Consumption is the food intake on a daily basis (mg DW) and weight is the weight of the larvae on that specific day. By this equation it is assumed that the compounds are not metabolised at all or that metabolism is weight dependent.

The Body burden was calculated for the conditions in the experiment described in Chapter 7 and related to the average survival of the larvae.

8.2 Results

8.2.1 Plant model

The following parameters were tested in the log likelihood ratio test: ddose, atime, aherb, aUV, and atimedose. Only the interaction equation (atime´ dose) was non-significant for the description of content of compound 2 (Table 8.1). There was an interaction between time and dosage for compound 3. ddose was significant for compound 2, which mean that the concentrations in the untreated plants were significantly different from zero. For compound 3 ddose was not significant, i.e. control plants do not contain detectable amounts of this compound. atime was significant for both compounds, indicating that the parabolic function described the effect of time better than a linear response. Both atime and aherb were significant, that is both UV-B and herbivory have an effect on the content of compound 2 and compound 3.

Table 8.1
Test values and limits of significance for the parameters in the mathematical model produced

Table 8.2 presents the parameter value to the model estimated in the fitting process.

Table 8.2
Parameter estimates for the model describing plant content of compound 2 and compound 3.

8.2.2 Validation

The parameterised model was validated against the data presented in Chapter 7 by visual inspection of the residual plot of the predicted values (Figure 8.1). The residuals were homogeneously distributed around zero, which means that the predicted values did not depart systematically from the observed values.

Figure 8.1
Residual plots of the predicted concentration of compound 2 and 3 in the experiment presented in Chapter 7.

8.2.3 Body burden estimates as descriptor for larvae mortality

Regression analysis of the calculated body burden and the average survival of G. polygoni larvae gave a clear correlation (Table 8.3 and Figure 8.2). The relationships involving compound 2 have by far the best correlation.

Table 8.3
Regression analysis of body burden of combination of compound 2 and 3, and survival of G. polygoni larvae. The relationship is of the form: Number of survivors = a ´ Compound concentration + b.

Figure 8.2
Mean survival of larvae as a function of calculated body burden of compounds 2 and 3 in three situations: A: Body burden of both compound 2 and 3, B: Body burden of compound 3, C: Body burden of compound 2. Bars represent Standard Error of Mean.

8.3 Discussion

The plant model clearly fitted best for compound 2. The strong correlation between the modelled concentration and the survival of the larvae clearly suggest that the compound is connected to the effect mechanism. Furthermore, it suggests that inclusion of the cumulative uptake of these compounds increased the confidence in the relationship. It is therefore tempting to assume that compound 2 or the sum of compounds 2 and 3 are the prime elicitor of effects because the variation in compound 2 also explains the high mortality in the control treatments. However, a strict demonstration of the effect of these compounds is lacking before a cause – effect relationship is established. Due to the fit of the regression analysis we do not reject our working hypothesis that these two compounds are likely to elicit toxic effects or repellence.

The analysis included both control plants and herbicide treated plants. As there was a high mortality of herbivores on the control plants and compound 3 is only found in treated plants this can not explain all mortality.

The models fitted for both compound 2 and compound 3 showed that herbivory causes a slight increase in the concentration of these compounds (i.e. the rate parameter was positive). This is contradictory to the data presented in Chapter 6, which showed that the concentration decreases with increasing herbivory. The only explanation to this is that the negative relationship between herbivore load and the compounds 2 and 3 was weak and largely governed by the highest herbivore load i.e. defoliation equal to 40 larvae per plant. Most of the experiments included for the fitting only employed 20 larvae, and consequently the weight and variation at this level will determine the sign of the slope. According to the regression lines presented in Chapter 6. Plants exposed to artificial herbivory equal to 0 and 20 larvae differ in the concentration between 11 and 22% and for actual differences between 14 and 30%.

The presented model could potentially be used to calculate risks for defined scenarios, e.g. various herbicide drift scenarios. This issue will be pursued later.

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