Preexisting resistance in cotton bollworm increases the risk of resistance to the 1 concurrently planted Bt cotton and Bt maize 2

23 Background: Transgenic maize expressing toxins derived from the bacterium Bacillus 24 thuringiensis (Bt) may be commercially planted in northern China where Bt cotton has been 25 planted for more than two decades. While Bt maize brings additional benefits for insect control, it 26 complicates the resistance management of cotton bollworm (CBW), Helicoverpa armigera 27 (Lepidoptera, Noctuidae), a common target of Bt cotton and Bt maize. 28 Results: We used a two-locus population genetic model to assess the risk of resistance in CBW 29 when Bt cotton and Bt maize are planted concurrently. Results of model simulations showed that 30 planting Bt maize together with Bt cotton significantly increases the risk of resistance if Bt cotton 31 and Bt maize share a similar Bt toxin. The risk of resistance is higher in the case of one-toxin Bt 32 maize than in the case of two-toxin Bt maize. Parameters associated with the preexisting 33 resistance in CBW all could impact on the risk of resistance but with different extents. Among 34 them, the most notable ones are the dominance of resistance and fitness cost, which can 35 dramatically affect the risk of resistance, especially when the proportion of natural refuges is 36 reduced. 37 Conclusions: We concluded that the preexisting resistance in CBW to Bt cotton can significantly 38 increase the risk of resistance when Bt maize and Bt cotton are planted concurrently and that using 39 two-toxin Bt cotton and maize instead of one-toxin ones are needed in order to reduce the risk of 40 resistance.

4 generations [22]. For the first generation, wheat is the primary host crop when other major host 67 crops like cotton and maize are absent. For the second through fourth generations, most of major 68 host crops are available. An earlier study has shown that abundant non-cotton host crops in 69 northern China served as natural refuges for CBW and contributed to delaying resistance of CBW 70 to Bt cotton [20]. However, a more recent study has found that resistance to Bt cotton in CBW is 71 accelerated by a dominant resistance allele [23]. Simulation models perhaps are the best approach to addessing the questions above. Compared 82 to experimental studies, simulation models have the advantages of reducing complexity and thus 83 are widely used to assess the risk of insect resistance to Bt plants [24][25][26][27][28][29][30]. Simulation models have 84 been used to assess the risk of Helicoverpa zea resistance to Bt cotton and Bt maize in the United 85 States, where H. zea is a closely related species to CBW [31,32]. Similar models can be used to 86 assess the risk of resistance to Bt cotton and Bt maize for CBW in northern China, but must take 87 into account the fact that the Bt cotton and Bt maize varieties and their planting history in China 88 5 are very different from those in the United States. 89 In this paper, a two-locus population genetic model is developed to analyze the resistance 90 evolution of CBW to Bt cotton and Bt maize when the two species of Bt crops are planted 91 concurrently. The model takes into account the actual Bt cotton variety and the existing resistance 92 to Bt cotton. The questions to be addressed include: (1) What are the differences in the risk of 93 resistance between an one-toxin Bt maize (Bt maize-1) and two-toxin Bt maize (Bt maize-2)? (2) 94 How does the preexisting resistance to Bt cotton affect the risk of resistance when Bt cotton and 95 Bt maize are planted together? (3) What are the key parameters that will impact on the risk of 96 resistance? 97

98
The difference between Bt maize-1 and Bt maize-2 99 In the absence of cotton plants, there are both qualitative and quantitative differences in the 100 evolution of resistance between the case of Bt maize-1 and that of Bt maize-2 ( Fig. 1). In the case 101 of Bt maize-1, where resistance is governed by a single locus, the frequency of resistance allele R1 102 increases from its initial value before tending to a stable level (Fig. 1a). However, in the case of Bt 103 maize-2, where resistance is governed by two loci, the frequency of resistance allele R1 decreases 104 from its initial value (Fig. 1b). In the case of Bt maize-2, the frequency of R2 does not increase 105 from its initial value within 90 generations. 106

The impact of Bt cotton 115
When Bt cotton is planted together with Bt maize, the same qualitative differences in the evolution 116 of resistance between the case of Bt maize-1 and that of Bt maize-2 are observed (Fig. 2). In the 117 case of Bt maize-1, the frequency of resistance allele R1 increases from its initial value before 118 tending to a stable level (Fig. 2a), while in the case of Bt maize-2, the frequency of resistance 119 allele R1 decreases from its initial value (Fig. 2b). 120 Compared to without Bt cotton, the frequency of resistance allele R1 evolves faster and higher 7 in both cases of Bt maize-1 and Bt maize-2, while the evolution in the frequency of resistance 122 allele R2 does not increase over time. This is because resistance to Bt cotton is governed by Locus 123 1 only, so adding Bt cotton only affects the evolution of R1, not that of R2. To investigate the impact of fitness cost at Locus 1 on resistance evolution, the time to resistance 134 (TTR) is derived when the fitness cost at Locus 1 varies from 0 to 0.5 (Fig. 3). In the case of Bt 135 8 cotton & Bt maize-1, when the fitness cost at Locus 1 varies from 0 to 0.22, the TTR increases 136 from 20 to >90 generations. In the case of Bt cotton & Bt maize-2, when the fitness cost at Locus 137 1 varies from 0 to 0.17, the TTR increases from 24 to >90 generations. 138 With the same fitness cost at Locus 1, the TTR is always shorter in the case of Bt cotton & Bt 139 maize-1 than that in the case of Bt cotton & Bt maize-2. The higher the fitness cost is, the larger 140 the difference. For example, when the fitness cost is zero the difference in TTR between the two 141 cases is just 4 generations. When the fitness cost is 0.2, the difference is greater than 45 142 To investigate the impact of incomplete resistance at Locus 1 on resistance evolution, the TTR is 151 derived by simulation when the incomplete resistance at Locus 1 varies from 0 to 0.5 (Fig. 4). The impact of initial frequency of resistance allele 187 To investigate the impact of the initial frequency of resistance allele at locus 1 on resistance 188 evolution, the TTR is derived when the initial frequency of R1 varies from 0.001 to 0.1 (Fig. 6). To investigate the impact of the proportion of natural refuge on resistance evolution, the TTR is 205 derived when the proportion of natural refuge varies from 0 to 0.5 (Fig.7). When the proportion of 206 natural refuge varies from 0 to 0.5, the proportion of cotton and maize as a whole varies from 0. Another reason that planting Bt maize together with the first generation Bt cotton could 239 increase the risk of cotton bollworm resistance was that the Bt maize and Bt cotton contain a 240 similar Bt toxin. When the two Bt crops contain a similar Bt toxin, resistance is most likely 241 governed by the same locus or loci [32]. In this case, the resistance to Bt maize is superimposed 242 on that to Bt cotton and therefore evolves much faster than without the preexisting resistance to Bt 243 cotton. Our simulation results confirmed the above scenario. In particular, our results showed that 244 the high initial frequency of resistance could result in a rapid increase in the frequency of 245 resistance when Bt maize is planted and the proportion of natural refuge is reduced. 246 While the preexisting dominant resistance could increase the risk of resistance when Bt 247 15 cotton and Bt maize planted together, our simulation results showed that fitness cost to the 248 resistance might dramatically decrease the risk. In particular, our results showed that when fitness 249 cost was sufficiently large, the frequency of resistance allele might not continue to increase from 250 its initial value and thus never reach the critical level of resistance risk. This is because when the 251 selection for resistance from planting Bt plants just matches the selection against resistance due to 252 fitness cost, an equilibrium may be reached at which the frequency of resistance remains constant 253 Our results showed that planting a pyramid product of two-toxin Bt maize could substantially 257 reduce the risk of resistance than a single-toxin Bt maize, either planted alone or planted together 258 with Bt cotton. This is consistent with our previous work in a more general setting [35]. It is also 259 generally consistent with the results in other literatures [36,37]. In particular, our results showed 260 that when a two-toxin Bt maize variety is planted with an one-toxin Bt cotton that expresses a 261 similar toxin to those in Bt maize, the risk of resistance to the two Bt crops is solely determined 262 by the risk of resistance to Bt cotton.

The effective proportions of Bt cotton, Bt maize and refuges 309
We divided the host crops for CBW into three groups: cotton, maize and other non-Bt host crops 310 and assumed that the effective proportions of the three groups are given. Here the effective 311 proportion is the proportion of planting area weighted by the relative effectiveness in producing 312 susceptible insects [31]. We denoted the effective proportions of cotton, maize and other non-Bt 313 host crops by 1 , 2 , and , respectively, where P1+P2+Pnat=1. Throughout this article, we 314 referred to the "effective proportion" simply as "proportion" unless mentioned otherwise. 315 We assumed that cotton plants consist of Bt and non-Bt plants in seed mixture, with the 316 proportions of Bt and non-Bt plants being PBt1 and 1-PBt1, respectively. Similarly, we assumed 317 that maize plants consist of Bt and non-Bt plants in seed mixture, with the proportions being PBt2 318 and 1-PBt2, respectively. We also assumed that the host crops other than cotton and maize are all 319 non-Bt, which serve as the "natural refuge" for CBW. Based on the above notations, the total 320 proportion of all types of non-Bt host plants or the total proportion of refuges is 321 We adopted a result from Jin et al.
[23] and set P1=0.27 and P2=0.15 as the default (Table 1). 323 Namely, the effective proportions of cotton, maize and natural refuge are 0.27, 0.15, and 0.58, 324 respectively. These two values were derived from real data in northern China in 2016 [23]. In 325 addition, we considered a theoretical case where the proportion of cotton and maize varies from 326 0.42 to 1, or that of natural refuges varies from 0 to 0.58. We assumed that the ratio of the 327 proportion of cotton to that of maize is fixed, which is approximately 0.64 to 0.36. 328 The proportion of Bt in cotton was fixed at 0.75, i.e. PBt1=0.75 (Table 1) In the studying area, the Bt cotton variety that has been planted is an one-toxin product expressing 336 cry1Ac [20,23]. Therefore, we developed our model based on this specific one-toxin Bt cotton. Bt 337 maize has not been planted commercially when this article is written. The Bt maize varieties that 338 may potentially be used include an one-toxin product expressing cry1Ab [41] and a two-toxin 339 product expressing cry1Ab/cry2Aj [42]. In this article, we considered two cases for the Bt maize 340 varieties that might be potentially used. In Case 1, the Bt maize expresses cry1Ab or a similar Bt 341 protein, which is denoted by "Bt maize-1". In Case 2, the Bt maize expresses cry1Ab/cry2Aj or 342 similar Bt proteins, which is denoted by "Bt maize-2". 343 In the case of Bt maize-1, we assumed that resistance to Bt cotton and Bt maize is governed 344 by the same single locus and used a single-locus model to simulate the evolution of resistance. In 345 the case of Bt maize-2, we assumed that resistance to Bt cotton and Bt maize is governed by two 346 loci that are independently segregated and used a two-locus model to simulate the evolution of 347 resistance. Because the single-locus model can be described as a special case of the two-locus 348 model, here we only described the two-locus model. 349 The two-locus population genetic model used here is a discrete-time, frequency-dependent Where WB1(g), WB2(g) and WN(g) represent the fitnesses of the single locus genotype g on Bt 373 cotton, Bt maize and non-Bt plants, respectively. The parameter 0 < q < 1 designates the 374 distribution of fitness over the two larval stages. Throughout the paper, we set q = 0.5. 375 1, , 1, , 1, , and 1, are the probabilities that a larva moves from Bt to Bt, Non-Bt 376 to Non-Bt, Bt to Non-Bt and Non-Bt to Bt cotton plants, respectively. These probabilities could be 377 explicitly calculated as follows.

405
Note that in Equations (9) and (11), the fitnesses of genotypes associated with Locus 2 on Bt 406 plants equal to those on non-Bt plants because the resistance is governed by only Locus 1. 407 We assumed that moths emerged from different host crops mate randomly. This assumption is 408 reasonable because in the study area, host crops are planted by small-holder farmers and it is very 409 common that different host crops are planted side by side in small fields. With the assumption of 410 random mating, the overall fitness of any two-locus genotype G across cotton plants, maize plants 411 and natural refuge is expressed by the following formula: 412 W(G) = 1 × 1 ( ) + 2 × 2 ( ) + (1 − 1 − 2 ) × 3 ( ) (13) 413 With the fitness function given above, the frequency of any genotype G in the next