**5. Sensitivity analysis of physiological resistance development to pesticides**

Studying resistance development in controlled populations is, in addition to being highly laborious, associated with some basic concerns. The frequency of resistance alleles in a giv‐ en pest population is typically extremely low (one in a 1,000 or less) and therefore requires individual analysis of very large numbers (millions or billions) of individuals. And when small laboratory populations are subjected to intensive insecticide based selection pressure, there is a considerable risk of unforeseen recessive genetic defects being expressed and af‐ fecting the observed population dynamics. [27] provided an in depth discussion and re‐ view of the concerns related to rearing of laboratory cultures for studies of how fast pest populations are able to develop resistance. In brief, they mentioned how the rearing may lead to "genetic bottlenecks" or selection pressures, which are different from those im‐ posed on field populations. Consequently, it is highly likely that a laboratory strain carries major resistance alleles at frequencies that are very different from field pest populations and that studies of resistance development in laboratory strains therefore are unable to mimic actual field conditions. Finally, numerous factors are considered important when as‐ sessing the likelihood of a pest population developing physiological resistance, and based on [41], they can be divided into four categories: 1) genetic factors (i.e. frequency, domi‐ nance, and expressivity of resistant alleles and their interactions with other alleles, past se‐ lection pressures in pest population, and whether the resistance is monogenic or polygenic), 2) biological factors (fecundity, generation and development times, mating be‐ haviour, level of polyphagy, migration/dispersal and mobility, fitness costs of resistance de‐ velopment, and feeding biology), 3) operational (mode of action of insecticide, residual effect of the insecticide, adjuvants added to sprayed formulations, timing of applications in relation to pest population development (which life stages are targeted), dosage applied, crop density at the time of application, type of spray nozzles used, height of spray boom, and 4) weather conditions (which are known to greatly affect spray depositions, see above). With such complexity of factors involved, it is not surprising that much of the current un‐ derstanding of pesticide resistance development in pest populations is based on genetic population modelling and theoretical sensitivity analyses [10, 42-45]. Such modelling ef‐ forts are in many ways constructive and can be used to develop strong justifications for specific research projects and management practices. However at the same time, their val‐ idity depends on the assumptions used in their construction [46, 47].

surfaces or baits containing the active ingredient. With regards to contact insecticides, it is possible that a combination of frequent and low performing pesticide applications creates a selection pressure which favours pest individuals avoiding treated portions of crop leaves, as individuals: 1) have ample opportunity to recover after sub-lethal exposures and there‐ fore "learn" to avoid insecticide treated surfaces, and 2) will be under a directional selection pressure for non-feeding on treated surfaces. However, we are unaware of experimental studies actually addressing the possible relationship between insecticide spray coverage in agricultural field pest populations and behavioural resistance in target pest populations. It is likely that the most important pests will continue to develop resistance to insecticides, as certain traits in their biology and/or ecology appear to enable them to adapt to these severe selection pressures. Thus, continued emphasis on almost exclusive insecticide-based pest control may be a strategy that deserves serious revision, as it seems to play to one of the key "strengths" (their adaptability) of the most important pests. The fundamental challenge is therefore to develop management practices, which minimize the risk of resistance develop‐ ment, and theoretical modelling is critically important in this context, because it can be used as a working tool to examine changes in population genetics over time and under different selection pressures. That is, instead of waiting until growers actually face the severe conse‐ quences of insecticide resistance, we can use theoretical modelling to predict its progress

**5. Sensitivity analysis of physiological resistance development to**

Studying resistance development in controlled populations is, in addition to being highly laborious, associated with some basic concerns. The frequency of resistance alleles in a giv‐ en pest population is typically extremely low (one in a 1,000 or less) and therefore requires individual analysis of very large numbers (millions or billions) of individuals. And when small laboratory populations are subjected to intensive insecticide based selection pressure, there is a considerable risk of unforeseen recessive genetic defects being expressed and af‐ fecting the observed population dynamics. [27] provided an in depth discussion and re‐ view of the concerns related to rearing of laboratory cultures for studies of how fast pest populations are able to develop resistance. In brief, they mentioned how the rearing may lead to "genetic bottlenecks" or selection pressures, which are different from those im‐ posed on field populations. Consequently, it is highly likely that a laboratory strain carries major resistance alleles at frequencies that are very different from field pest populations and that studies of resistance development in laboratory strains therefore are unable to mimic actual field conditions. Finally, numerous factors are considered important when as‐ sessing the likelihood of a pest population developing physiological resistance, and based on [41], they can be divided into four categories: 1) genetic factors (i.e. frequency, domi‐ nance, and expressivity of resistant alleles and their interactions with other alleles, past se‐ lection pressures in pest population, and whether the resistance is monogenic or polygenic), 2) biological factors (fecundity, generation and development times, mating be‐

and hopefully find ways to slow it down.

208 Insecticides - Development of Safer and More Effective Technologies

**pesticides**

The following section is a sensitivity analysis based on genetic population modelling, which expands on work presented in two theoretical modelling papers [26, 41]. Although publish‐ ed almost 40 years ago, these studies present the basic modelling framework needed to ex‐ amine fairly simple/basic questions about resistance development. Results presented here are based on a theoretical arthropod pest population "X" with an initial population of 11,000 individuals followed over 20 subsequent generations, and it is assumed that: 1) adults only give offspring in one generation, 2) each generation was exposed to a single insecticide ap‐ plication, 3) resistance development occurs in a single locus with two alleles, r (resistant) and s (susceptible), 4) p = 0.0001 is the gene frequency of r and q= 0.9999 is the gene frequen‐ cy of s, 5) genotypes occur in Hardy-Weinberg proportions, 6) dominance is assumed to be intermediate, so that, under insecticide based selection pressure, the survival of genotypes is rr > rs > ss, and 7) resistance was associated with a "fitness cost", which is defined as resist‐ ant genotypes having lower fitness than susceptible genotypes in the absence of the particu‐ lar insecticide [45]. Based on a review by [45] of 77 studies of Bt resistance, it was assumed that physiological insecticide resistance was associated with a "fitness cost" of 15.5% for each allele. Although the possible importance of "incomplete resistance" [42] and "hybrid vigor" [45] have been highlighted, these factors were not included in this analysis. The fol‐ lowing sensitivity analysis of r allele frequency and pest population density is based on 1,000 simulations of different scenarios with random variables. Similar to [26], the popula‐ tion density after each discrete generation, N', was assumed to be density-dependent and described by the following equation 1:

$$\begin{aligned} N' &= \left[ W\_{rr} \times N\_{rr} \times \exp\left(r\_{rr} \times \left(K - N\_a / K\right)\right) \right] + \\ & \left[ W\_{rs} \times N\_{rs} \times \exp\left(r\_{rs} \times \left(K - N\_a / K\right)\right) \right] + \\ & \left[ W\_{ss} \times N\_{ss} \times \exp\left(r\_{ss} \times \left(K - N\_a / K\right)\right) \right]. \end{aligned} \tag{1}$$

In which W denotes the survival of each genotype, N denotes the number of adults in the previous generation, K denotes the carrying capacity, and Na denotes the initial population.

In the following, we present modelling results from two scenarios, and the main point is to demonstrate some of the advantages of using modelling as part of demonstrating how phys‐ iological insecticide resistance appears to develop across a very wide range of scenarios.

studies of genetic populations are based on large populations (i.e. 10,000 individuals), and it is assumed that individuals mate randomly within these large populations. This is highly unlikely and is the main reason why recent genetic population modelling uses a meta-pop‐ ulation modelling approach, in which a large population is considered to be composed of many smaller and somewhat segregated populations. Such meta-population based ap‐ proaches include assumptions about movement between populations and sizes of sub-pop‐ ulations, and these assumptions were not included in this analysis. Another approach is to use individual-based modelling [10]. Based on the analysis of scenario 1, we have high‐ lighted that the influences of incorporating varying crop carrying capacity and reproduc‐ tive fitness into modelling predictions of population densities over 20 generations were modest, when the fitness cost was kept constant (15.5%), and they had negligible effect in‐

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211

fluence on r allele frequency.

**Pest population**

**0**

**2000**

**4000**

**6000**

**8000**

**10000**

**12000**

**14000**

**a**

Figure 6. Effects of varying reproductive fitness and carrying capacity

**Figure 6.** Effects of varying reproductive fitness and carrying capacity

**0.5**

**0.6**

**0.7**

**0.8**

**0.9**

**1.0**

**b**

**R allele frequency in pest population**

effect influence on r allele frequency.

In all 1,000 scenarios, the initial pest population was reduced by >99.9% after the initial infestation (N = 11,000) was exposed to the first insecticide application. After the initial knock-down, the pest population remained low for about 8 generations, after which the pest population density started to increase steadily (Fig. 6a). Almost complete insecticide failure (back to initial pest population density due to complete physiological resistance) was achieved within 20 generations. Comparison of the average curve of the pest population density under varying reproductive rate and carrying capacity and that of fixed variables [with constant reproductive fitness (Wrr = 5, Wrs = 5.775 and carrying capacity (K = 11,000)] suggested that incorporation of variability into reproductive fitness and carrying capacity had limited effect. That is, the average of the 1,000 simulations was very similar to that of fixed variables and but only a few and rare simulations (indicated by the curve of maximum pest population) reduced the time to complete physiological resistance be a few years (shifted the curve to the left). Fig. 6b showed that varying crop carrying capacity and reproductive fitness had almost negligible impact on the r allele frequency in the pest population (as expressed by the range of minimum and maximum curves). Most sensitivity studies of genetic populations are based on large populations (i.e. 10,000 individuals), and it is assumed that individuals mate randomly within these large populations. This is highly unlikely and is the main reason why recent genetic population modelling uses a meta-population modelling approach, in which a large population is considered to be composed of many smaller and somewhat segregated populations. Such meta-population based approaches include assumptions about movement between populations and sizes of sub-populations, and these assumptions were not included in this analysis. Another approach is to use individual-based modelling [10]. Based on the analysis of scenario 1, we have highlighted the importance of incorporating varying crop carrying capacity and reproductive fitness into modelling predictions of population densities over 20 generations were modest, when the fitness cost was kept constant (15.5%), and they had negligible

**Average**

**Fixed variables**

**Minimum and maximum**

**Generations 0 5 10 15 20**

**5 10 15 20**

Scenario 1: Effects of reproductive fitness and crop suitability on resistance development. Using Equation 1 to estimate total population and r allele frequency over 20 generations, the following settings for allele frequencies were kept constant: p = 0.0001 and q = 0.9999, and survival rates of the 3 genotypes (W) were: Wrr = 1, Wrs = 0.5, Wss = 0. Thus, in this scenario, none of the susceptible individuals (Wss) were expected to survive and did therefore not contribute to the sensitivity analysis. [26, 41] assumed the reproductive fitness of pest popu‐ lation X, "r", to be constant and equal to ln(5) between generations, and many subsequent and more recent studies have also been based this assumption. Here, the reproductive fit‐ ness of the resistant genotype was assumed to vary randomly from ln(3)-ln(7) (random numbers with two-decimal points) between generations. With the reproductive fitness of the resistant genotype varying randomly between ln(3)-ln(7) and the fitness cost of resistance being 15.5%, that of the heterozygous genotype, rrs = rrr × 1.155. A constant carrying capacity implies that a certain habitat can sustain the same pest population in all growing seasons and irrespectively of regional differences in environmental conditions. Seasonal variations in growing conditions (i.e. drought stress levels and fertilizer regimes) clearly cause marked variations in number of pest individuals a crop plant can harbour. For instance, nutritional composition of crops can vary considerably in response to drought stress [48-51] and is known to vary considerably between growing seasons [52, 53]. [54] estimated varying carry‐ ing capacity of the milkweed-oleander aphid [*Aphis nerii* Boyer de Fonscolombe (Hemiptera: Aphididae) on one of its host plants, milkweed (*Asclepias tuberosa*) in response to nitrogen applications. Based on data collected under controlled conditions, the authors obtained ranges from 29.5-35.1 (19%) aphids. Thus, here we assumed a 20% random variation in car‐ rying capacity between growing seasons (K ranging randomly from 10,000-12,000 between subsequent generations).

In all 1,000 scenarios, the initial pest population was reduced by >99.9% after the initial in‐ festation (N = 11,000) was exposed to the first insecticide application. After the initial knock-down, the pest population remained low for about eight generations, after which the pest population density started to increase steadily (Fig. 6a). Almost complete insecticide failure (back to initial pest population density due to complete physiological resistance) was achieved within 20 generations. Comparison of the average curve of the pest popula‐ tion density under varying reproductive rate and carrying capacity and that of fixed varia‐ bles [with constant reproductive fitness (Wrr = 5, Wrs = 5.775 and carrying capacity (K = 11,000)] suggested that incorporation of variability into reproductive fitness and carrying capacity had limited effect. That is, the average of the 1,000 simulations was very similar to that of fixed variables except for a few and rare simulations (indicated by the curve of max‐ imum pest population) reduced the time to complete physiological resistance by a few years (shifted the curve to the left). Fig. 6b showed that varying crop carrying capacity and reproductive fitness had almost negligible impact on the r allele frequency in the pest pop‐ ulation (as expressed by the range of minimum and maximum curves). Most sensitivity studies of genetic populations are based on large populations (i.e. 10,000 individuals), and it is assumed that individuals mate randomly within these large populations. This is highly unlikely and is the main reason why recent genetic population modelling uses a meta-pop‐ ulation modelling approach, in which a large population is considered to be composed of many smaller and somewhat segregated populations. Such meta-population based ap‐ proaches include assumptions about movement between populations and sizes of sub-pop‐ ulations, and these assumptions were not included in this analysis. Another approach is to use individual-based modelling [10]. Based on the analysis of scenario 1, we have high‐ lighted that the influences of incorporating varying crop carrying capacity and reproduc‐ tive fitness into modelling predictions of population densities over 20 generations were modest, when the fitness cost was kept constant (15.5%), and they had negligible effect in‐ fluence on r allele frequency.

In the following, we present modelling results from two scenarios, and the main point is to demonstrate some of the advantages of using modelling as part of demonstrating how phys‐ iological insecticide resistance appears to develop across a very wide range of scenarios.

210 Insecticides - Development of Safer and More Effective Technologies

Scenario 1: Effects of reproductive fitness and crop suitability on resistance development. Using Equation 1 to estimate total population and r allele frequency over 20 generations, the following settings for allele frequencies were kept constant: p = 0.0001 and q = 0.9999, and survival rates of the 3 genotypes (W) were: Wrr = 1, Wrs = 0.5, Wss = 0. Thus, in this scenario, none of the susceptible individuals (Wss) were expected to survive and did therefore not contribute to the sensitivity analysis. [26, 41] assumed the reproductive fitness of pest popu‐ lation X, "r", to be constant and equal to ln(5) between generations, and many subsequent and more recent studies have also been based this assumption. Here, the reproductive fit‐ ness of the resistant genotype was assumed to vary randomly from ln(3)-ln(7) (random numbers with two-decimal points) between generations. With the reproductive fitness of the resistant genotype varying randomly between ln(3)-ln(7) and the fitness cost of resistance being 15.5%, that of the heterozygous genotype, rrs = rrr × 1.155. A constant carrying capacity implies that a certain habitat can sustain the same pest population in all growing seasons and irrespectively of regional differences in environmental conditions. Seasonal variations in growing conditions (i.e. drought stress levels and fertilizer regimes) clearly cause marked variations in number of pest individuals a crop plant can harbour. For instance, nutritional composition of crops can vary considerably in response to drought stress [48-51] and is known to vary considerably between growing seasons [52, 53]. [54] estimated varying carry‐ ing capacity of the milkweed-oleander aphid [*Aphis nerii* Boyer de Fonscolombe (Hemiptera: Aphididae) on one of its host plants, milkweed (*Asclepias tuberosa*) in response to nitrogen applications. Based on data collected under controlled conditions, the authors obtained ranges from 29.5-35.1 (19%) aphids. Thus, here we assumed a 20% random variation in car‐ rying capacity between growing seasons (K ranging randomly from 10,000-12,000 between

In all 1,000 scenarios, the initial pest population was reduced by >99.9% after the initial in‐ festation (N = 11,000) was exposed to the first insecticide application. After the initial knock-down, the pest population remained low for about eight generations, after which the pest population density started to increase steadily (Fig. 6a). Almost complete insecticide failure (back to initial pest population density due to complete physiological resistance) was achieved within 20 generations. Comparison of the average curve of the pest popula‐ tion density under varying reproductive rate and carrying capacity and that of fixed varia‐ bles [with constant reproductive fitness (Wrr = 5, Wrs = 5.775 and carrying capacity (K = 11,000)] suggested that incorporation of variability into reproductive fitness and carrying capacity had limited effect. That is, the average of the 1,000 simulations was very similar to that of fixed variables except for a few and rare simulations (indicated by the curve of max‐ imum pest population) reduced the time to complete physiological resistance by a few years (shifted the curve to the left). Fig. 6b showed that varying crop carrying capacity and reproductive fitness had almost negligible impact on the r allele frequency in the pest pop‐ ulation (as expressed by the range of minimum and maximum curves). Most sensitivity

subsequent generations).

In all 1,000 scenarios, the initial pest population was reduced by >99.9% after the initial infestation (N = 11,000) was exposed to the first insecticide application. After the initial knock-down, the pest population remained low for about 8 generations, after which the pest population density started to increase steadily (Fig. 6a). Almost complete insecticide failure (back to initial pest population density due to complete physiological resistance) was achieved within 20 generations. Comparison of the average curve of the pest population density under varying reproductive rate and carrying capacity and that of fixed variables [with constant reproductive fitness (Wrr = 5, Wrs = 5.775 and carrying capacity (K = 11,000)] suggested that incorporation of variability into reproductive fitness and carrying capacity had limited effect. That is, the average of the 1,000 simulations was very similar to that of fixed variables and but only a few and rare simulations (indicated by the curve of maximum pest population) reduced the time to complete physiological resistance be a few years (shifted the curve to the left). Fig. 6b showed that varying crop carrying capacity and reproductive fitness had almost negligible impact on the r allele frequency in the pest population (as expressed by the range of minimum and maximum curves). Most sensitivity studies of genetic populations are based on large populations (i.e. 10,000 individuals), and it is assumed that individuals mate randomly within these large populations. This is highly unlikely and is the main reason why recent genetic population modelling uses a meta-population modelling approach, in which a large population is considered to be composed of many smaller and somewhat segregated populations. Such meta-population based approaches include assumptions about movement between populations and sizes of sub-populations, and these assumptions were not included in this analysis. Another approach is to use individual-based modelling [10]. Based on the analysis of scenario 1, we have highlighted the importance of incorporating varying crop carrying capacity and reproductive fitness into modelling predictions of population densities over 20 generations were modest, when the fitness cost was kept constant (15.5%), and they had negligible

Figure 6. Effects of varying reproductive fitness and carrying capacity **Figure 6.** Effects of varying reproductive fitness and carrying capacity

effect influence on r allele frequency.

Scenario 2: Effect of varying pesticide spray performance. In this scenario, varying repro‐ ductive fitness rates and carrying capacity were maintained as described in scenario 1. The survival rate due to pesticide applications was kept constant for the homozygous resistant (Wrr = 1), but this scenario was conducted with varying survival rates of Wrs and Wss. That is, it was assumed that low and inconsistent spray coverage would in some generations in‐ crease the survival of Wrs and Wss. The basis for investigating this scenario with varying sur‐ vival rates of Wrs and Wss was supported by the field spray data presented in Fig. 3: Out of the 91 insecticide spray data sets, several data sets showed spray coverage ranges above 50 times (difference between minimum and maximum). It therefore seems reasonable to as‐ sume that there is considerable variation in insecticide dosages and therefore survival rates of subsequent pest population generations. Consequently, a random number function was used to generate survival rates from 0.3 to 0.7 for Wrs, and survival rates below 0.5 were con‐ sidered to be equal to 0.5. In other words, the random function generated one of five out‐ comes (0.3, 0.4, 0.5, 0.6, or 0.7) with equal probability, and three of these (0.3, 0.4, and 0.5 or 60% of the outcomes) were equal to 0.5, and there was a 50% chance [(0.7-0.5)×100/(0.7-0.3)] of increased survival due to low and inconsistent spray coverage for Wrs genotypes. Regard‐ ing genotype Wss, the same random function approach was applied to generate random sur‐ vival rates from -0.2 to 0.2, and all rates equal to or below 0 denoted no survival. In other words, there was about 50% chance of Wss genotypes contributing at least some offspring to the next generation. As in scenario 1, a 15.5% fitness cost was maintained for each resistant allele, which meant that the reproductive fitness of rrs = rrr × 1.155 and that of rss = rrs × 1.155. In other words, the survival of Wss genotypes had the potential of contributing substantially to subsequent generations in simulations with Wss > 0.

losses. Thus, here it is highlighted that with a consistent selection pressure (all generations of pest individuals subjected to a pesticide applications) the performance of pesticides and negligi‐ ble development of resistance are antagonistic. In other words, growers should not expect to ac‐ complish both: a high-performing pesticide application will create a strong selection pressure and therefore lead to resistance development. On the other hand, low and inconsistent pesticide applications appear to reduce the likelihood of pest populations developing resistance, but it will also reduce the performance of pesticide applications. However, it is likely that low and in‐ consistent insecticide applications increase the risk of target pest populations developing be‐ havioural resistance, but that is not incorporated into the modelling presented here. A recent modelling based study of herbicide resistance in weeds addressed this specific question about the effect of dosage [10]. The authors concluded that in cases of monogenic resistance, pesticide dosage had negligible effect on the number of generations before complete failure. However, they also pointed out that in cases of resistance being "non-target specific" (i.e. metabolic and/or polygenic resistance), there is growing evidence of herbicide resistance developing faster under low-dosage selection pressure. There are important differences in factors leading to resistance in weed and insect pest populations (i.e. reproduction/mating biology, generation time, and dis‐ persal strategies), so it may not be accurate to assume the exact same responses by insects and weeds. However, it is clear that reliable and accurate sensitivity analysis of how certain varia‐ bles affect the likelihood of a pest population developing resistance requires that the underlying genetics are sufficiently understood (especially whether resistance in mono- or polygenic).

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**6. Some realities associated with rotation of insecticides**

It may be argued that the scenarios outlined above are far too simplistic and do not take into account that growers are rotating insecticides as part of resistance management prac‐ tices. The core of resistance management programs is to rotate between active ingredi‐ ents, as cross-resistance to multiple insecticides is much less likely to develop. Regarding transgenic crops expressing Bt toxins, incorporation of non-treated refuges in cropping systems is also being advocated [see [45] for review). We are unaware of recommenda‐ tions about non-treated refuges for any other insecticide treatments. Consequently rota‐ tion of classes of active ingredients is the only widespread resistance management strategy, but there are crop-pest systems in which only a few active ingredients are regis‐ tered for use. For instance in Western Australia, there are three species of aphids [The cabbage aphid, *Brevicoryne brassicae* (L.), the turnip aphid, *Lipaphis erysimi* Kalt, and the green peach aphid, *Myzus persicae* (Sulzer) (Hemiptera: Aphidae)] attacking canola dur‐ ing the flowering/podding period – yet only ONE insecticide (Pirimicarb 500) is regis‐ tered for use against these pests! In addition, active ingredients are increasingly being faced out (banned) - so growers are left with only a few options. And if one particular pest is under a single insecticide selection pressure in one cropping system, then this may be the source for a resistant pest population to emerge. In addition, rotation of in‐ secticides is only an effective option as long as cross-resistance is close to negligible, al‐ though there are ample examples of arthropod pests developing resistance to a many

In this scenario with varying survival rates of Wrs and Wss, the population density after the initial knock-down was, on average, 95%, but there were simulations in which it was below 80%. It should be expected, that increased survival due to low and inconsistent pesticide applications increased the pest population growth during 20 generations, but, in comparison with scenario 1, the effect on pest population was actually quite modest (Fig. 7a). As an example, in scenario 1 (with no survival of homozygous susceptible individuals) the average population density was about 6,000 individuals after 15 generations, while it was about 7,000 individuals in scenario 2. Thus, with half of the simulations allowing 1-20% survival of homozygous susceptible individu‐ als there was only a modest increase in average pest population density. However as indicated by the maximum curve, there were indeed scenarios in which high pest populations were ach‐ ieved within about 11 generations. With fixed variables and assumption about Hardy-Wein‐ berg allele frequencies, the r allele frequency obviously stayed above 50% and increased as the homozygous resistant genotype increased in relative proportion. Fig. 7b showed, as expected, that the varying survival of homozygous susceptible individuals (when Wss > 0) led to a decrease in r allele frequency. In fact after 20 generations, none of the 1,000 simulations led to a higher r al‐ lele frequency than 93%, while with fixed variables it was >96%. In other words, this simple exer‐ cise suggested that by allowing susceptible genotypes some level of survival, low and inconsistent pesticide applications appear to postpone development of complete resistance. However, low and inconsistent pesticide applications also lead to higher risk of high pest popu‐ lation densities (comparing Fig. 6 a and 7 a) and therefore crop damage and corresponding yield losses. Thus, here it is highlighted that with a consistent selection pressure (all generations of pest individuals subjected to a pesticide applications) the performance of pesticides and negligi‐ ble development of resistance are antagonistic. In other words, growers should not expect to ac‐ complish both: a high-performing pesticide application will create a strong selection pressure and therefore lead to resistance development. On the other hand, low and inconsistent pesticide applications appear to reduce the likelihood of pest populations developing resistance, but it will also reduce the performance of pesticide applications. However, it is likely that low and in‐ consistent insecticide applications increase the risk of target pest populations developing be‐ havioural resistance, but that is not incorporated into the modelling presented here. A recent modelling based study of herbicide resistance in weeds addressed this specific question about the effect of dosage [10]. The authors concluded that in cases of monogenic resistance, pesticide dosage had negligible effect on the number of generations before complete failure. However, they also pointed out that in cases of resistance being "non-target specific" (i.e. metabolic and/or polygenic resistance), there is growing evidence of herbicide resistance developing faster under low-dosage selection pressure. There are important differences in factors leading to resistance in weed and insect pest populations (i.e. reproduction/mating biology, generation time, and dis‐ persal strategies), so it may not be accurate to assume the exact same responses by insects and weeds. However, it is clear that reliable and accurate sensitivity analysis of how certain varia‐ bles affect the likelihood of a pest population developing resistance requires that the underlying genetics are sufficiently understood (especially whether resistance in mono- or polygenic).
