Best organic farming expansion scenarios for pest control: a modeling approach

Organic Farming (OF) has been expanding recently in response to growing consumer demand and as a response to environmental concerns. The area under OF is expected to further increase in the future. The effect of OF expansion on pest densities in organic and conventional crops remains difficult to predict because OF expansion impacts Conservation Biological Control (CBC), which depends on the surrounding landscape (i.e. both the crop mosaic and semi-natural habitats). In order to understand and forecast how pests and their biological control may vary during OF expansion, we modeled the effect of spatial changes in farming practices on population dynamics of a pest and its natural enemy. We investigated the impact on pest density and on predator to pest ratio of three contrasted scenarios aiming at 50% organic fields through the progressive conversion of conventional fields. Scenarios were 1) conversion of Isolated conventional fields first (IP), 2) conversion of conventional fields within Groups of conventional fields first (GP), and 3) Random conversion of conventional field (RD). We coupled a neutral spatially explicit landscape model to a predator-prey model to simulate pest dynamics in interaction with natural enemy predators. The three OF expansion scenarios were applied to nine landscape contexts differing in their proportion and fragmentation of semi-natural habitat. We further investigated if the ranking of scenarios was robust to pest control methods in OF fields and pest and predator dispersal abilities. We found that organic farming expansion affected more predator densities than pest densities for most combinations of landscape contexts and OF expansion scenarios. The impact of OF expansion on final pest and predator densities was also stronger in organic than conventional fields and in landscapes with large proportions of highly fragmented semi-natural habitats. Based on pest densities and the predator to pest ratio, our results suggest that a progressive organic conversion with a focus on isolated conventional fields (scenario IP) could help promote CBC. Careful landscape planning of OF expansion appeared most necessary when pest management was substantially less efficient in organic than in conventional crops, and in landscapes with low proportion of semi-natural habitats.


Introduction 28
The intensification of agricultural systems in recent decades has relied on both an increase in field area 29 and a larger dependency on chemical pesticides (Duru et   Growth: The terms ( , , ( ) ) and ( , , ( )) stand for the pest and predator intrinsic growth 172 functions. They are controlled by parameters rN and rP respectively ( Table 1). The predator being a 173 generalist, it can grow in absence of pests. 174 Mortality: ( , ) ( ) and ( , ) ( ) account for the pest and predator death rates caused by pest 175 management. Mortality is controlled by parameter (Table 1). 176 Predation: The interaction terms − 1 ( ) ( ) and 2 ( ) ( ) describe the effects of predation on 177 the pest and predator growth rates, respectively. We assume standard Lotka-Volterra interactions 178 between the pest population and its predator, which means that the pest death rate increases linearly 179 with the density of the predator, and conversely the growth rate of the predator increases linearly with 180 the pest population density. We also assume that 1 = 2 = (Table 1) 181 The system is scaled so that the carrying capacities of and are both equal to 1 thus the population 182 densities are expressed in units of their respective carrying capacities. 183 184

-Timing of ecological processes 187
The year is divided into equal intervals each corresponding to a dispersal event of pests and predators. 188 The number of intra-annual time steps is thus calculated as 1+ (1/ ). Each year is divided into two periods 189 taxa that include both spring and autumn reproduction) and suffer from intrinsic mortality in crops. Their density increases further in both semi-natural habitats and crops when the pest is present. Predators thus 197 behave as generalist predators that feed on the pest prey, and on alternative prey in semi-natural habitats. 198 Like pests, they are affected by pest management practices in crops during the second half of the year. 199 200   Table 2. Values of the growth functions ( , , ( ) ) and ( , , ( )). is the pest intrinsic 201 growth rate in the crops in the absence of pest management, the natural enemy life expectancy in the 202 absence of resources and the natural enemy birth rate in semi-natural habitats. 203

-Organic farming systems 205
There exists a diversity of organic farming systems with more or less intensive pest management strategies 206 (Marliac et al., 2015) ). To represent this diversity, we considered four theoretical types of organic farming 207 (Table 3). In the most intensive OF systems (Int-Gen and Int-Spe), pest management is as efficient in 208 organic fields as in conventional ones so that the mortality of pests due to pest management practices is 209 the same. These two OF systems differ by the specificity of these control measures that either do not (Int-210 Spe) or do (Int-Gen) affect predators, but less than in conventional fields. Examples of efficient and specific 211 pesticides are microorganisms targeting pests such as viruses (Graillot et al., 2016) or other 212 microorganisms (Deshayes et al., 2017). Other pest management measures such as pesticides (e.g. 213 spinosad) or nets are efficient on pests but also affect some predators (Dib et al., 2010). In the extensive 214 OF systems (Ext-Gen and Ext-Spe) pest management is less efficient in OF fields and pest mortality rates 215 are half those in conventional fields. As before, these two OF systems differ by the specificity of their pest 216 management practices that either do (Ext-Gen) or do not (Ext-Spe) affect predators (Table 3). Table 3. Effects of pest management practices on the pest and the natural enemies in conventional (CF) 219 and organic farming. Four organic farming systems were considered. Int-Spe and Int-Gen correspond to 220 intensive pest management (high pest mortality) while Ext-Spe and Ext-Gen are less intensive. In Int-Spe 221 and Ext-Spe systems, pest management practices are specific to the pest and do not affect predators 222 while in Int-Gen and Ext-Gen systems, management is less specific. 223 Int-Spe 2 0

-Parameter values 225
Intrinsic growth rates: The pest reproduces only during the second half of the year. During one year, the 226 population would increase by a factor of exp(rN)/2 in the absence of any limiting factor. We thus assumed 227 that, under these conditions, the population would increase by a factor of 50 or 100 over the season. We 228 assumed a lesser yearly increase for the predator of exp(rp)=2, i.e. a population doubling in the absence 229 of pests or any limiting factor. To compensate for this increase, we assumed a life expectancy of the 230 predator on the crops of γ=1/2 year, in the absence of pests. 231 Mortality due to pest management practices: We assumed that the mortality rate induced by pest 232 management practices is comparable to pest growth rates (2 ∈2{ln 50, ln 100 }). The mortality due to 233 pest management practices reaches its maximum value for both pests and predators in the conventional 234 fields and for pests only in the most intensive OF systems (Int-Spe and Int-Gen). In these situations, 235 mortality compensates for the pest population's local increase and drastically reduces predator 236 populations. Mortality caused by pest management practices is reduced by half or set to 0 for predators 237 depending on the OF systems (Table 3). Dispersal: The values for dN and dP were chosen so that approximately between 0.1% (dN or dP=0.1/n 2 ) and 239

243
Simulations were run on 9 landscape contexts differing in their proportion of semi-natural habitats (SNH) 244 (either 10, 25, or 50% of total area) and in the fragmentation of these habitats (fr values: 0.1, 0.5 and 0.9). 245 Initially, 10% of crops were organic (OF) and 90% conventional (CF) based on the current national 246 proportions in France (ORAB PACA, 2020) and on the proportion of worldwide cropped and pasture land 247 that is practicing some forms of organic farming (Pretty et al, 2018). Based on that, we generated initial 248 landscapes with three proportions of each land-use, named respectively Qin1 (10% SNH; 9% OF; 81% CF), 249 Qin2 (25% SNH; 7.5% OF; 67.5% CF), and Qin3 (50% SNH; 5% OF; 45% CF). In the remainder of this paper, 250 we refer to these three initial conditions in terms of their SNH proportions (SNH 10%, 25% and 50%). Initial 251 OF crops were allocated randomly among crop cells. Each simulation of the model was run on a different 252 initial landscape. 253  The IP and GP scenarios are two possibly planned scenarios that we compared to the baseline RD scenario 283 in terms of resulting pest densities and predator to pest ratio.

Landscape structure 289
Landscapes can be described in terms of composition, i.e. proportion of the land uses, and configuration, 290 controlled during the simulation. We monitored landscape configuration using three landscape metrics 292 for each land use: the mean patch area, the number of patches, and the edge length (R package landscape 293 metrics, Hesselbarth et al, 2019). For a given land use, patches were made of fields of that given land use 294 that were 4-neighbors to at least one field of the same land use. Together, these three metrics indicate 295 whether, for a given proportion of landscape area, one land use is represented by a few large patches or 296 many small patches. 297

Pest and predator densities 298
For each simulation, the densities of pests and predators were monitored at the end of each year and 299 averaged over each land use (SNH, OF and CF). From these, a median predator to pest ratio was calculated 300 per land use as a proxy of the intensity of pest control by predators. 301 302 6. Simulation study 303 Simulations for the three spatial organic farming expansion scenarios mentioned above were performed 304 for each of the nine types of landscapes (3 proportions of SNH x 3 levels of fr) aiming at 50% OF fields for 305 each of the four types of OF (Table 3). These simulations were performed for all combinations of the 306 values of the 6 parameters (pest and predator dispersal coefficients, pest and predator intrinsic growth 307 rates, predator life expectancy in crops, interaction term,) and the four farming systems governing pest 308 and predator population dynamics (Table 1, Fig. 1) and the three initial densities of pests and predators. 309 This resulted in a total of 11664 Simulations, each run on a different landscape. We performed 11664 310 more simulations without any action on the landscapes. These simulations are referred to as Reference 311 Comparisons of pest and predator densities and predator to pest ratios among conversion scenarios were 313 performed at the end of the simulations (t=50) for each landscape context. As pest density was the main 314 variable of concern regarding OF expansion, we further checked whether the ranking of scenarios was 315 robust with regards to the intensity of OF and the dispersal rate of the pest. Pest and predator densities did not show a clear response to the increase of proportion of semi-natural 330 habitat and they increased with its fragmentation, probably because cultivated fields were more likely to 331 be close to a semi-natural habitat, increasing spill-over of individuals into cultivated fields. These effects 332 were stronger on predators than pests in organic fields, consistent with the higher dependency of 333 predator reproduction and survival on semi-natural habitats. The predator density, in contrast, remained 334 very low in conventional fields due to pesticides. 335 These differential effects of landscape characteristics on pests and predators had two consequences. First, 336 pest densities were 2.6 times larger in organic fields than in conventional fields in landscapes with little 337 semi-natural habitat and little fragmentation (SNH=10%, fr=0.1) while they were only 1.3 times larger in 338 landscapes with large proportions of fragmented semi-natural habitats (SNH=50%, fr=0.9). Second, the 339 predator to pest ratio increased in organic fields but decreased in conventional fields when semi-natural 340 habitat proportion and fragmentation increased. 341

-Pest and predator dynamics during organic farming expansion 342
The cultivated landscape changed during organic farming expansion. Compared to their initial area, at the 343 end of organic farming expansion, conventional patches were generally smaller and organic patches 344 larger. Constraints were furthermore imposed by the spatial distribution of semi-natural areas so that 345 patch area varied more in little fragmented landscapes or when there was little semi-natural area. Because 346 they set different priorities regarding field conversion, the different scenarios led to different cultivated notably always resulted in conventional patches that were larger than the other scenarios while the GP 349 scenario generally resulted in larger organic patches (Supplementary material S1.3). 350 The organic farming expansion affected more predator densities than pest densities for most 351 combinations of landscape contexts and expansion scenarios (Fig. 3). Its impact was also generally 352 stronger in organic than conventional fields and in landscapes with large proportions of fragmented semi- conventional fields, pest densities showed this same pattern with the RD and GP scenarios but not with 361 the IP scenario. With the IP scenario, pest densities in conventional fields tended to decrease slightly over 362 time whatever the landscape context. As a result, at t=50, pest densities were generally smaller with the 363 IP than with the RD and the GP scenario in conventional fields and similar for the three expansion 364 scenarios in organic fields. 365

Predator dynamics 366
In organic fields, the effect of organic farming expansion on predator densities was very large compared 367 to its effect on pest densities (Fig. 3). Predator densities increased for the three expansion scenarios. The 368 increase was larger for the IP scenario than for other scenarios, particularly in little fragmented landscapes 369 with intermediate or large proportion of semi-natural habitats. For example, when SNH=25% and fr=0.1, 370 with the IP scenario the predator density at t=50 was 5.38 times larger than the initial density and was 371 2.44 times higher than the predator density at t=50 with the GP scenario. In contrast, the three scenarios 372 performed similarly in landscapes with the highest proportion and fragmentation of semi-natural habitat 373 (SNH=50%, fr=0.9). In these landscapes, the predator density increased by a factor of 1.34 between t=0 374 and t=50 with the IP scenario and was only 1.20 times higher than with the GP scenario at t=50. The 375 increase in predator density was moderate for the RD and GP scenarios and reached similar values at t=50. 376 Their dynamics were, however, qualitatively different. While predator densities increased steadily for the RD scenario, for the GP scenario, most predator densities showed a transient decrease in the first years 378 following the beginning of organic farming expansion. 379 Note that in landscapes with 50% SNH predator densities were sometimes larger than pest densities in 380 organic fields (Fig. 3). This was most prominent when fragmentation was high, an indication that it 381 resulted from spillover of predators from semi-natural habitats. In organic fields, differences in final pest density were limited among expansion scenarios. Pest density in 396 organic fields responded overall little to landscape characteristics and, in particular, less to the different 397 scenarios of OF expansion, despite differences in organic or conventional patch areas (Fig. S1.3), than to 398 the fragmentation of semi-natural habitats (Fig. 4, upper panel). The highest levels of pest densities were 399 obtained for the highest fragmentation levels. For a given level of fragmentation, pest densities in organic 400 fields tended to be lower for the IP scenario but the amplitude of effect was smaller than for 401 fragmentation. In contrast, final pest density in conventional fields (Fig. 4, lower panel) responded both 402 to the OF expansion scenario and to fragmentation, indicating a dependence on conventional and organic 403 patch area (Fig S1.3). As in organic fields, pest density increased with the level of semi-natural habitat 404 fragmentation. In conventional fields, low levels of pest densities could thus be attained for different 405 fragmentation levels given that conventional patch areas were large, a situation provided by the IP 406 scenario in landscapes with small proportion of semi-natural habitats (SNH=10%). Furthermore, the range 407 of variation of pest densities was larger in conventional than organic fields.

Conservation biological control 413
The predator to pest ratio is an indicator of the potential for conservation biological control: a higher ratio 414 indicates that pests are more likely to come across a predator. As a result of the pest and predator 415 dynamics described above, the predator to pest ratio at the end of the simulation was three to four times 416 larger in organic fields than in conventional fields (Fig. 5). It increased with the proportion of semi-natural 417 habitat, in similar relative proportions in organic and conventional fields, from an average of approx 0.2 418 to 1.25 in organic fields and 0.05 to 0.35 in conventional fields, when the proportion of SNH increased 419 from 10% to 50%. It also increased, but to a much lesser extent with SNH fragmentation. The only 420 significant increase with fragmentation was for landscapes with large proportion of SNH (Fig. 5). More interestingly, we observed a clear ranking of spatial expansion scenarios with IP>RD>GP for the 429 predator to pest ratio in organic fields (Fig. 6). This ranking might be due to the larger increase of predator 430 densities during OF expansion with the IP scenario and the somewhat larger pest densities with the GP 431 scenario (Fig. 3). Relatively to the RD scenario, the predator to pest ratio was from 1.83 times higher 432 (SNH=10%, fr=0.1) to 1.1 (SNH=50%, fr=0.9) times higher for the IP scenario. In contrast, these ratios for 433 the GP scenario ranged from 0.55 (SNH=10%, fr=0.1) to ~1(SNH=50%, fr=0.9) times those for the RD 434

scenario. 435
In conventional fields, predator to pest ratios showed the opposite GP>RD>IP ranking. The difference here 436 was mainly between the IP and the two other scenarios. Ratios were a little larger for the GP scenario 437 than for the RD scenario whatever the landscape context, with values ranging from 1.2 (SNH=10%, fr=0.1) 438 to ~1 (SNH=50%, fr=0.9) times those for the RD scenario. They were the smallest for the IP scenario, 439 particularly in fragmented landscapes with low proportions of semi-natural habitats (from 0.55 440 (SNH=10%, fr=0.1) to 0.8 (SNH=50%, fr=0.9) times higher than with the RD scenario, Fig. 6). Consistent predator densities increased more strongly than pest densities. The predator to pest ratio was about three 470 to four times larger in organic than in conventional fields. Changes in pest and predator densities and their 471 dynamics strongly depended on expansion scenarios in interaction with landscape contexts, i.e. the 472 amount and fragmentation of SNH. Although most scenarios led to overall improvements in predator to 473 pest ratios (seen here as a proxy of conservation biological control, CBC), some led to increases in pest 474 densities, particularly in conventional fields which indicates that in some specific landscapes, carefully 475 planning the spatial expansion of organic farming would be useful to avoid undesirable side effects. 476 From an ecological point of view, the predator to pest ratio dynamics observed in this study appeared 477 driven by the dynamics of predators which was mostly dependent on the amount of semi-natural habitat 478 (SNH). It was striking that only in landscapes with large proportion of SNH (SNH=50%), did predator 479 densities increase very largely in organic fields and even increase slightly in conventional fields, leading to 480 a decrease of pests in both types of fields. CBC also increased with landscape fragmentation in both OF 481 and CF fields but mostly when the proportion of SNH was high. Since SNH fragmentation increased its 482 edge length with cultivated habitats, this synergy between SNH amount and fragmentation on the level 483

of CBC indicates the importance of predators' spillover from semi-natural habitats on biological control. 484
This interaction is also in line with the frequent observation that complex landscapes with more and more 485 generalist predators, such as modeled here, may increase in density even in the absence of pests, thus 503 limiting pest population peaks (Symondson et al., 2002). 504

-A general pattern 506
The similar pest densities with all spatial expansion scenarios indicates that the choice of one scenario 507 over another bears low risks, while potential benefits were more obvious with noticeable effects on 508 predators. Both the level of conservation biological control (CBC) and pest densities have been used to 509 evaluate the efficiency of pest control in spatial pest-predator models (Bianchi et  CBC was a target mostly in organic fields while the main target for conventional fields was the density of 513

pests. 514
Using these criteria, the IP scenario performed better, by improving CBC in organic fields and doing so at 515 the expense of lower CBC, but not higher pest densities, in conventional fields. Regarding CBC, the IP 516 scenario performed overall better for organic fields because of its clear positive effect on the predator to 517 pest ratio. Patterns were more nuanced for conventional fields. While some scenario x landscape context effect of expansion scenarios was weaker when they caused increases in CBC than when they caused 520 decreases in CBC. Additionally, the ranking of scenarios was opposite in conventional vs organic fields 521 (IP>RD>GP in organic fields vs GP>RD>IP in conventional fields). From the conventional farming point of 522 view, the absence of planning (RD scenario) may thus constitute a reasonable scenario. However, pest 523 densities in conventional fields were lower with IP than with the other scenarios. The best ranking of the 524 IP scenario with higher CBC in organic fields and lower pest densities in conventional fields was observed 525 in all landscape configurations, while some landscapes limited the decrease of CBC in conventional fields 526 without canceling it. 527

528
The best performance of the IP scenario resulted from two distinct mechanisms: a predator spillover 529 improving CBC in organic fields, and a combination of 'chemical umbrella' and lesser pest spillover in 530 conventional fields. The IP scenario prioritized the conversion of fields neighboring organic fields or semi-531 natural areas. This meant that new organic fields benefitted from the spillover of predators from SNH, 532 albeit with weak effects on pest density. Indeed, the predator to pest ratio improved mainly by an increase 533 in predator numbers. Such trophic network top-heaviness can be caused by exogenous pathways that 534 transfer energy into communities from across spatial and temporal boundaries: here, transfers from SNH 535

-Effect of the landscape context on differences between scenarios 550
In our simulations, landscape configuration had a strong effect with differences in pest density up to two 551 times for a given scenario. The proportion and fragmentation of SNH were generally of similar importance 552 to the difference in the level of CBC between scenarios, although there was a clear decrease associated 553 with the interaction between the two parameters, i.e. the difference between the IP and GP scenarios 554 decreased with higher proportions and fragmentation of SNH. In conventional fields, this amounted 555 mainly to the IP scenario that benefited slightly from SNH, while SNH did not affect pest density with the 556 GP scenario. In organic fields, IP and GP converged at highest proportion and fragmentation levels, with 557 pest densities of the GP scenario being favored while those of the IP scenario decreased. Interestingly, 558 the IP scenario could bring higher benefits in organic fields in degraded landscapes, while both scenarios 559 brought similar but lower benefits in preserved landscapes. This is consistent with the IP scenario breaking 560 up large clusters of conventional fields, which were less present in landscapes with high proportions and 561 fragmentation of SNH. Consequently, it may be less important to manage the OF expansion scenario in 562 preserved landscapes, while the IP scenario should be favored in degraded landscapes. 563

Robustness of the ranking of expansion scenarios 564
The ranking of OF expansion scenarios appeared robust to both the intensity and specificity of OF systems 565 and the dispersal ability of pests and predators (Supplementary material S2). Varying these parameters 566 did not affect the ranking of spatial expansion scenarios, only their relative differences. For example, 567 intensive OF systems corresponding to intensive pest management (high pest mortality) were 568 characterized by strong control of pest densities, therefore they showed little differences between 569 scenarios. The only clear interaction between OF pest management and expansion scenario was in 570 conventional fields: under extensive OF farming systems, the tendency of the IP scenario towards lower 571 pest densities in conventional fields was reinforced (Supplementary material S2). This is because pest 572 densities were overall higher for extensive OF systems but this did not strongly affect conventional fields, 573 because, by limiting the decrease in CF patch size, the IP scenario resulted in less pest spill-over from 574 organic to conventional fields. Further, dispersal ability had a marginal effect on pest densities 575 (Supplementary material S3). Increasing dispersal tended to increase pest density's response to landscape 576 configuration (in particular to its fragmentation) in conventional fields, thus increasing differences in pest 577 densities among expansion scenarios. 578 long-distance dispersers that would be less affected by landscape structure. We also made strong 595 assumptions about the role of semi-natural habitats for pests and predators, assuming a generalist 596 predator and a crop specialist pest that may survive in semi-natural habitats. Differences among spatial 597 expansion scenarios would, for example, probably have been less if the pest had been able to reproduce 598 in semi-natural habitats and would thus have been less sensitive to the spatial distribution of organic or 599 conventional fields. Interestingly, despite these limitations, our conclusions about the best spatial 600 scenario are consistent with those of the only pest-natural enemy spatially explicit model that, to our 601 knowledge, addressed OF expansion (Bianchi, Ives and Schellhorn, 2013). Using a spatially explicit pest-602 parasitoid model these authors found that the spatial clustering of organic fields allowed a higher level of 603 biocontrol in organic fields by protecting parasitoids from the detrimental effects of insecticides sprayed 604 in conventional fields. In contrast to our results, however, they reported peaks of pests along OF 605 expansion, possibly because, contrary to our assumptions, the parasitoid was specialized on the pest. 606

-Limits and benefits of the modelling approach
A last limitation of our approach is that results were averaged for organic and conventional fields at the 607 landscape level. This simplification was driven by the large number of simulations to analyze. Aggregating agricultural landscape, Zamberletti et al. (2021Zamberletti et al. ( , 2022 showed for example that semi-natural habitats 611 increased the average landscape scale pest density (by reducing the number of necessary pesticide 612 treatments) but locally reduced peaks of pest populations (Zamberletti et al., 2021(Zamberletti et al., , 2022. Further 613 analyses of pest density dynamics at the field level would, thus, be necessary to confirm the better ranking 614 of the IP scenario regarding local CBC and pest densities. 615 Despite these limitations, our approach set in light processes such as increased spill-over of predators in 616 isolated fields, increased pest management efficiency in large patches of conventional fields and the 617 importance of distance between organic and conventional fields, that help understand consequences of 618 diverse organic farming expansion scenarios. They further highlight that landscape planning appeared 619 most necessary when organic pest management had a low efficiency on pests and in landscapes with low 620 quantities of semi-natural habitats. 621 622

623
The scenario that consisted in setting the priority on isolated conventional fields for conversion to organic 624 (IP) appeared as the most promising scenario to limit pest densities in conventional crops and improve 625 CBC in organic crops, without increasing pest densities there. By examining a large number of landscape 626 contexts and population parameters, we found that this result was robust but that landscape planning 627 The model used in this study is based on a model developed by Martinet and Roques (2022)  Increasing semi-natural habitat (SNH) fragmentation (parameter fr) resulted in an increase in the number of patches of each habitat type (SNH but also organic farming (OF) and conventional farming (CF)) ( Figure S1.1) as well as an increase in edge length among habitat type ( Figure S1.

Dynamics of the number and area of organic and conventional patches
As expected, changes in the areas and numbers of organic and conventional patches along organic farming expansion depended on the landscape characteristics (amount of semi-natural habitat and its fragmentation) and on the organic farming expansion scenario. Organic and conventional patches were overall larger and less numerous in landscapes where the amount of semi-natural habitat was small and little fragmented (upper left Fig. S1.3) indicating in particular that the level of semi-natural habitat fragmentation translated to overall landscape fragmentation.
Overall the dynamics of the patch area were driven by two processes. Indeed, the conversion of individual fields from conventional to organic may lead to progressive changes in conventional patch area, either increasing it when converted fields were isolated and/or decreasing it when converted fields were part of a larger patch. In this second situation, the conversion of a single conventional field may occasionally lead to the splitting of a large conventional patch. Such splitting led to large drops in the mean conventional patch area (eg. Fig.S1.3, at 35 years for the GP scenario with fr=0.1 and SNH=10%). The symmetrical process of merging organic patches following the conversion of individual fields may create a sudden large increase in mean organic patch area. This last process occurred when the organic share was high enough over the landscape. Because they set different priorities regarding field conversion, the different scenarios led to different mean patch area dynamics. Constraints were furthermore imposed by the spatial distribution of seminatural areas. The IP scenario always resulted in conventional patches that were larger than the other scenarios. This is because, when available, conventional fields in the smallest conventional patches were converted to organic which resulted in an initial disappearance of small conventional patches and thus an increase in average conventional patch area. When these small patches were all converted, larger ones started being partially converted to organic, leading to a secondary decrease in conventional patch area ( Fig S1.3, after ca. 25 years). These two trends (increase then decrease) were observed in landscapes with both small and large conventional patches initially, i.e. moderately fragmented landscapes with a small to moderate proportion of semi-natural habitat. In little fragmented landscapes with few semi-natural habitats (upper left panel, Fig. S1.3) all conventional patches were large initially so that patch size decreased slowly from the beginning of organic farming expansion. In contrast, in highly fragmented landscapes with a high proportion of semi-natural habitat (lower right panel, Fig. S1.3), there were mostly isolated conventional fields initially so that patch size remained almost constant. The GP scenario, by eroding small parts of large conventional patches at first, slowly and moderately reduced the average conventional patch area. This decrease accelerated in a second step when the erosion incidentally led to the splitting of the still rather large conventional patches into smaller ones. This process was strongest in landscapes with large conventional patches initially, i.e. little fragmented or with a small proportion of semi-natural habitats (left column and upper row panels, Fig. S1.3). Lastly, the RD scenario led to a progressive reduction of conventional patch area by both converting fields located in small patches and reducing the area of large conventional patches.
The effect of organic expansion on the area and number of organic patches was consistent with the above changes to conventional patches. Whatever the expansion scenario, when the landscape was very fragmented and with a large proportion of semi-natural habitat, conversion of conventional fields increased the number of organic fields but not their average area, conventional patches being mostly composed of single fields (lower right panel, Fig.S1.3). Mean organic patch area increased in all other situations.
Mean organic patch area increased most at first with the IP scenario, particularly when the landscape was a little fragmented (left column, Fig. S1.3) because conventional fields that were converted tended to be neighboring already organic fields. In contrast, with the GP scenario, organic fields first tended to be isolated from other organic fields so that the average patch area increased slowly. However, when the landscape was little fragmented (left column, Fig. S1.3), these small organic patches merged when the proportion of organic farming increased and the average organic patch area increased sharply while the number of patches decreased.

SM2 -Effect of the type of organic farming on pest densities and interaction with expansion scenario
Pests were on average more abundant in both types of fields when organic farming was less intensive, i.e. pest management affected pest population growth less (Table 3 ) and, to a lesser extent, when it was less specific, i.e. there was a small differential in pest management-induced mortality between predators and pests (Table 3). In organic fields, the intensity of organic farming affected pest abundance far more than specificity, regardless of the amount of semi-natural habitat and its level of fragmentation.
As expected, the effect of organic farming intensity and specificity was much less pronounced in conventional fields. The effect of specificity was very weak. The effect of OF intensity was observable mainly in landscapes that were characterized by a low fragmentation (figure S2) Interestingly, the response of pest density to expansion scenario showed the same pattern whatever the OF type. It was very similar whatever the expansion scenario in organic fields and pest densities were generally lower for the IP scenario in conventional fields.
The fact that pest management specificity generally had little effect except for the extensive OF systems, confirmed the low effect of predators on pest densities in conventional fields, and the high impact of pest management compared to CBC in our simulations. For extensive organic systems, organic fields were possibly a source of pests for surrounding fields. Indeed, we observed more pests in conventional fields when organic farming systems were extensive, possibly indicating pest spillover from OF fields with higher pest populations. The latter is supported by the fact that the effect of OF farming system on pest density in CF was reduced in some landscape configurations. Specifically, conventional fields in landscapes with high proportion of SNH were less sensitive to OF farming system intensity, possibly because of lesser proximity to OF sources, and because of higher predator's spillover from SNH. Figure S2. Effects of organic farming expansion scenario, organic farming type and landscape structure on the density of pests in organic and conventional fields. "ext" and "int": low vs high pest management intensity, respectively. "spe" vs "gen": specific vs generalist pest management practices, respectively (see Table. 3). Error bars represent standard deviations over landscapes.

SM3 -Effect of pests dispersal and SNH fragmentation on pest densities and interaction with OF expansion scenario
Pest dispersal had a lower effect than the other parameters with a maximum delta of ±0.05 in pest densities (Fig.S3). Pest densities in organic and conventional fields were overall higher when pest dispersal was high but this effect was weak, and mainly observable in conventional fields. In both types of fields, the positive effect of dispersal increased with the level of fragmentation of semi-natural habitats (for example, in conventional fields, for the GP scenario, pest density increased by 0.01 when fr=0.1, and by 0.04 when fr=0.9 - Fig. S3). There was one exception to this trend with a small decrease in pest density with dispersal. It was observed with the IP scenario in organic fields (from 0.19 to 0.18 for fr=0.1, Fig. S3).
The increase in densities with dispersal, fragmentation and their interaction was probably due to a higher ability of pests to avoid CBC-heavy areas (near SNH, which are sources of predators) and to reach resource-rich areas. Globally speaking, dispersal ability amplified the effect of every landscape parameter (fragmentation, expansion scenario).