Pesticides do not significantly reduce arthropod pest densities in the presence of natural enemies

Abstract Chemical pesticides remain the main agents for control of arthropod crop pests despite increased concern for their side effects. Although chemical pesticide applications generally result in short‐term decreases of pest densities, densities can subsequently resurge to higher levels than before. Thus, pesticide effects on pest densities beyond a single pest generation may vary, but they have not been reviewed in a systematic manner. Using mathematical predator–prey models, we show that pest resurgence is expected when effective natural enemies are present, even when they are less sensitive to pesticides than the pest. Model simulations over multiple pest generations predict that pest resurgence due to pesticide applications will increase average pest densities throughout a growing season when effective natural enemies are present. We tested this prediction with a meta‐analysis of published data of field experiments that compared effects of chemical control of arthropod plant pests in the presence and absence of natural enemies. This largely confirmed our prediction: overall, pesticide applications did not reduce pest densities significantly when natural enemies were present, which concerned the vast majority of cases. We also show that long‐term pesticide effectiveness is underreported and suggest that pest control by natural enemies deserves more attention.


Supplementary information S1. Further analysis of the basic predator-prey model
It is well-known that the original Rosenzweig-McArthur model can give rise to cycles of increasing amplitude with increasing carrying capacity K (the so-called paradox of enrichment Rosenzweig 1971). Adding constant pesticide-induced mortality can therefore stabilize the dynamics, but at higher pest levels. This can easily be seen from a phase-plane analysis of the model (Fig. S1).
In this figure, the prey isoclines are given in blue and the predator isoclines in orange. The vertical orange lines are the predator isoclines. It is well-known that the positive equilibrium is stable when this vertical orange predator isocline crosses to the right of the maximum of the blue parabola of the prey isocline (here marked by the green dot) and unstable if it crosses to the left (the orange dot). Because the isoclines change with pesticide application, the equilibrium can become stable with increasing pesticide-induced mortality.
However, this also results in higher pest densities. The black dashed spiral to the right in the figure shows that the populations of the pest and natural enemy spiral from the initial densities (black dot) towards the stable equilibrium (green dot) after several fluctuations when pesticides are applied (p = 0.12). In contrast, without pesticides (p = 0), the dynamics spiral away from the unstable equilibrium (orange dot).   Fig S2a). When natural enemies do suffer from pesticide-induced mortality (q > 0), equilibrium pest densities go up with increasing pesticide-induced pest mortality (Fig. S2a, all lines except the black). Equilibrium densities of natural enemies go down with increasing pesticide-induced pest mortality (Fig S2b), even when the enemies are insensitive to the pesticide ( Fig S2b, thin black curve).
We simulated the dynamics of the pest and natural enemies during five pest generations in the part of parameter space with a transition from an unstable (p = 0) to a stable equilibrium (p = 0.12). It shows that, although pesticide applications can stabilise the dynamics, this results in an increase of average pest densities  Effects of pesticide-induced mortality (p, horizontal axis) on average pest densities (vertical axis) during five pest generations. Colours and thickness of curves indicate different initial pestnatural enemy ratios (ratios: black = 1 pest per enemy; dark blue = 5 (standard value); light blue =10; orange = 15; brown = 20). Increasing line thickness corresponds to increasing pest-enemy ratio. Lefthand column: basic predator-prey model; right-hand column: food web model without alternative prey. Pesticide-induced natural enemy mortality (q) was zero (a, b), equal to (c, d) or twice as high as that of the pest (e, f). Pesticide-induced pest mortality (p) Average pest density

Supplementary information S2. Stage-structured model
Besides the basic predator-prey model and the tritrophic/food web model, we formulated a stage-structured model designed to capture the dynamics of an important plant pest (the Western flower thrips Frankliniella occidentalis) and one of its predators used to control it (the predatory mite Iphiseius degenerans), and was validated by greenhouse experiments (van Rijn et al. 2002). The version used here includes alternative food (pollen, A) for the predator only (not for the prey as in the original model, to make the model more general).
The pest population was modelled as consisting of three stages: first-instar larvae that were vulnerable to predation (N1), other juvenile instars (N2) that were invulnerable to predation, and invulnerable reproducing adults (N3). The predator population was also modelled in three stages: a non-predatory juvenile stage (P1), a predatory juvenile stage (P2) and a predatory adult stage (P3), with the adult stage having the highest predation rate. We further modified the model by making reproduction of the pest a decreasing function of its density to avoid unlimited increases of the pest population in the absence of predators. The dynamics were modelled as follows: Pollen (A) is produced at a constant rate (a), decays with rate b, and is consumed by predatory juveniles (P2) and adults (P3), with juveniles consuming at a fraction j of consumption rate of adult predators. Pollen consumption follows a type II saturating functional response with fA being the maximum consumption rate by the predators, Nf the half-saturation density of vulnerable prey, Φ the food value of pollen relative to prey, and k the reduction in predation of the pest because of the presence of pollen (van Rijn et al. 2002). First-instar pest larvae (N1) are produced by adults (N3), with net per capita reproduction r being reduced at increasing densities of the pest, C is a constant determining the carrying capacity of the pest. The vulnerable stage is consumed by predators (P2 and P3) with a saturating functional response, in which fN is the maximum predation rate and the other parameters (Nf, Φ , k) as above. All prey stages incur a pesticide-induced per capita mortality of p (varied).
Surviving individuals develop into invulnerable juveniles with per capita rate d1, which develop into adults with rate d2. Adult pests have a natural mortality of v in addition to the pesticide-induced mortality p.
Predator juveniles, corrected for sex ratio and juvenile survival, are produced by adult predators (P3) as a result of the consumption of pest individuals and of pollen, following a Michaelis-Menten function for substitutable food types (van Rijn et al. 2002): with g the maximum rate of reproduction, Ng the half-saturation pest density and m maintenance costs. Nonpredatory juveniles develop into predatory juveniles with rate e1. All predator stages experience pesticideinduced mortality pq as above. Predatory juveniles (P2) develop into adults with rate e2. The rate of development of these juveniles into adults is independent of the food density, whereas the food-dependent juvenile survival is included in the net reproduction rate of the adults. Per capita adult predator (P3) mortality increases with decreasing food availability, modelled as the inverse of a Michaelis-Menten function (van Rijn et al. 2002): Simulations with the stage-structured model showed the effects of differential vulnerability of pest stages to pest resurgence: only the pest stage vulnerable to predation showed some resurgence, whereas densities of the two invulnerable pest stages were reduced by the pesticide (Fig. S4a), resulting in a reduction of the overall pest density.
It should be noted that the vulnerable larval stage in this model is short (3 days) relative to the invulnerable larval (15 days) and adult stages (9 days). To further investigate the effect of the duration of the invulnerable stage, we exchanged the duration of the vulnerable larval stage (to 15 days) with that of the invulnerable larval stage (to 3 days), whereas the adult pests were still assumed invulnerable. This assumption of vulnerability of the stages of this pest holds for larger predators such as predatory bugs, which attack both larval stages (van den Meiracker & Sabelis 1999).
Increasing the duration of the vulnerable immature stage at the expense of that of the invulnerable immature stage resulted in increased pest resurgence, even with the adult stage being invulnerable to predation ( Fig. S4b). Hence, pests with longer periods of vulnerability to natural enemies will more likely show pest resurgence with pesticide applications than pests with shorter vulnerable periods.
We again estimated the effects of pesticides on average pest densities over 5 generations by repeated simulations with varying pesticide-induced pest and natural enemy mortality and various pest application methods, as was done for the two models presented in the main text. The stage-structured model showed increases in average total pest densities (all stages combined) for intermediate values of pesticide-induced mortality for the pest and high mortality of the natural enemy ( Fig. S5a, b). All other combinations of mortality of the pest and natural enemy resulted in lower average pest densities. Varying the pesticide application frequency with a pesticide-induced pest mortality (p) of 1 day -1 , resulted in no increase or decrease of average pest densities with low pesticide application frequencies (Fig. S5c), and an increase for higher frequencies and high natural enemy mortality (q > 1, Fig. S5c, d). Pesticides reduced average pest densities only with high application frequencies and low natural enemy mortality (q < 1), coinciding with the near extinction of natural enemies (Fig. S5d). Similar patterns in average pest and natural enemy densities as with pesticide applications every 2 weeks (Fig. S5a, b) were observed for threshold and continuous pesticide applications (Fig. S5e-h). In conclusion, compared to pests without stages that are invulnerable to natural enemies, pests with long invulnerable stages are better controlled with pesticides (compare Fig. 2 and 3 with S5).
With an increased period of pest vulnerability, pesticide application often did not result in decreased average pest densities (Fig. S6, most coloured curves at or above the dashed black line), and again resulted in increased pest densities when natural enemies suffered high mortality from the pesticide (  Pesticide-induced pest mortality was p = 1 day -1 and natural enemy mortality half of that (q = 0.5).
Pesticide was applied with a frequency of every 14 days.

Supplementary information S3. Extended analysis of the literature
Insufficient data were available to compare the effects among individual pesticides or substance groups. We used the Pesticides Properties Database of the University of Hertfordshire (Lewis et al. 2016) to assess the activity of the pesticides against the pests investigated. In case of doubt, we sought additional publications using "chemical control" and the scientific name of the pest species as search terms. We identified 9 out of 68 time series in which the activity of the pesticide against the pest was not confirmed. Removing these time series from the data set did not change the results of the meta-analysis in a major way: (natural enemies present locally: effect size = -0.73, conf. int. -1.50 to 0.044; regionally: -0.49, -0.75 to -0.24; no enemies: -1.31, -1.97 to -0.65, cf. Fig. 3b overall effects). Of the studies presenting average pest densities, activity of the pesticide against the pest in question was not confirmed in slightly less than half the cases (47). Upon removing these cases from the data set, meta-analysis results changed somewhat: the overall effect of pesticide use on pest densities still did not differ from zero in the presence of natural enemies locally (effect size: 0.58, conf. int. -0.20 to 1.35) and still did differ from zero when natural enemies were absent (-10.1, -17.5 --2.76), but was no longer different from zero when enemies were present regionally (-1.18, -2.89 to 0.522) (cf. Fig. 3d overall effects). In conclusion, excluding cases where the effect of the pesticide on the pest could not be confirmed did not change our main conclusions in any way.
We assessed the presence of influential cases in both data sets, using Cook's distances and hat values to identify outliers (Viechtbauer 2010). In both data sets, one study contained several influential cases. For the time series data, removal of this study from the analysis resulted in the same patterns of significant and nonsignificant effect sizes as did the analysis of the full data set. After removing the outlier study from the data set of averages, the same results were found as with the full data set, except that the overall effect with natural enemies present regionally did no longer differ significantly from zero (cf. Fig. 4d).
One concern with meta-analysis is the publication bias. The idea is that studies showing non-significant results are less likely to be published (Rosenthal 1979). To estimate the potential effect of this, a simple technique is to calculate the number of studies with a zero effect size that need to be added to render the overall effect just not significantly different from zero (Rosenthal 1979). We calculated these so-called fail-safe numbers for the significant effects shown in Fig. 3 in the main text, showing that most significant effects seem relatively robust for such a publication bias (Table S3). To the best of our knowledge, a test for the opposite, i.e. how many cases should be added to render an effect size significantly different from zero, does not exist because no publication bias is expected for studies showing significant effects. This is perhaps not entirely true for the studies reviewed here: many researchers would probably expect an overall negative effect of pesticide applications on pest densities and would not be keen to publish positive effects. Hence, the lack of a significant overall negative effect of pesticides on pest densities strongly suggests that this is indeed a true phenomenon.
However, if anything, our literature search shows that there is a general lack of studies on the effects of pesticide applications through time.
We also analysed the effect of the experimental plot sizes of those studies for which plot size was given

Supplementary information S4. Alternative food in the stage-structured model
We assume here that alternative food does not change in quality because of pesticide applications. It partly compensates for the reduction of pest densities for the natural enemies due to pesticide applications, and this results in lower pest densities than without alternative food (cf. Fig. S8 and S4). The pest, however, still reaches higher densities than without pesticides for high mortality rates of the natural enemies (q > 1) (Fig. S8).

Fig. S8.
Average densities of the pest (left column) and natural enemies (right column) of simulations of the stage-structured population model (5 generations) with pollen as alternative food for the natural enemies. Per panel, curves with different colours and thickness refer to different pesticideinduced natural enemy mortality relative to pest mortality: thin, black: q = 0; blue: q = 0.5; light blue: q = 1; orange: q = 1.5; thick, brown: q = 2. Increasing line thickness corresponds to increasing enemy mortality. The pest and enemy densities obtained without pesticide application are given as reference by black dashed horizontal lines. See legend to Fig. 2 for further explanation.