Management assessment of mountain pine beetle infestation in Cypress Hills, SK

19 Insect epidemics such as the mountain pine beetle (MPB) outbreak 20 have a major impact on forest dynamics. In Cypress Hills, Canada, the 21 Forest Service Branch of the Saskatchewan Ministry of Environment 22 aims to control as many new infested trees as possible by conducting 23 ground-based surveys around trees infested in previous years. Given 24 the risk posed by MPB, there is a need to evaluate how well such a 25 control strategy performs. Therefore, the goal of this study is to as- 26 sess the current detection strategy compared to competing strategies 27 (random search and search based on model predictions via machine 28 learning), while taking management costs into account. Our model 29 predictions via machine learning used a generalized boosted classiﬁca- 30 tion tree to predict locations of new infestations from ecological and 31 environmental variables. We then ran virtual experiments to determine 32 control eﬃciency under the three detection strategies. 33 The classiﬁcation tree predicts new infested locations with great ac- 34 curacy (AUC = 0.93). Using model predictions for survey locations 35 gives the highest control eﬃciency for larger survey areas. Overall, the 36 current detection strategy performs well but control could be more eﬃ- 37 cient and cost-eﬀective by increasing the survey area as well as adding 38 locations given by model predictions. 39

and finally emerge as adults later in the summer (Safranyik & Carroll, 2006). 67 Trees are seriously injured by the gallery excavation process and the devel-

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At a landscape level, two types of dispersal strategies have been observed 75 for MPB (Safranyik & Carroll, 2006;Robertson et al., 2007) : long-distance 76 dispersal, passive downwind flight over the canopy, and short-distance dis-77 persal, active flight a few meters above ground. Researchers estimate the 78 short-distance dispersal range to be within a stand (Safranyik & Carroll,79 2006) at the order of 20 to 50 meters, although some beetles can go as far 80 as 100 meters (Robertson et al., 2007). By way of contrast, long-distance 81 dispersal range is tens to hundreds of kilometres (Safranyik & Carroll, 2006; 82 D r a f t Center Block, in Saskatchewan (58 km 2 ). For the purpose of this paper, our 91 study focuses on the Saskatchewan portion of the park. Therefore the use of 92 "the park" and "Cypress Hills" in the text refers to the Saskatchewan portion. to determine how well this strategy is working. 128 Given this management strategy and the MPB context in Canada, our 129 study aims to answer the question : Are there ways to improve detection 130 strategies without increasing management costs ? If managers completely re-131 moved infested trees coming from MPB short-distance dispersal inside the 132 park, the remaining source of infestation would be long-distance dispersal 133 events from outside the park which are often considered spatially random 134 when observed at a small scale (Long et al., 2012;Powell et al., 2018 at the end of the winter-are exposed to extreme temperatures (Cole, 1981;169 Safranyik & Carroll, 2006;Régnière & Bentz, 2007). Drought in the spring 170 reduces pines' ability to defend themselves and increase MPB attacks' success 171 rate (Safranyik, 1978;Creeden et al., 2014;Sidder et al., 2016). Additionally,

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MPB individuals need at least 833 degree-days above 5.5°C over a year to 173 complete their growth (Safranyik et al., 1975;Carroll et al., 2006;Safranyik 174 et al., 2010). In the park, over the time period studied, the minimum num-175 ber of degree-days above 5.5°C was 923, which is above the threshold and 176 so degree-days was not included in our model. Furthermore, high numbers of 177 degree-days are not an issue as MPB rarely present multivoltinism (Bentz & 178 Powell, 2014). We included the MPB presence at the same location and in 179 the neighbourhood the year before in order to take into account the spatio-180 temporal autocorrelation of the data (Fig. 1). The beetle pressure from out-   The remaining 25%, 49 502 observations, were used to validate the model. for a range of probability thresholds, the true positive rate (or 1 -false neg-213 ative rate, also referred to as sensitivity) against the false positive rate (also 214 referred to as 1 -specificity). We used Youden's method (Youden, 1950) to    To be able to compare similar survey areas among detection strategies, 249 we needed to be able to fix the number of search locations, and therefore 250 the search area, from the classification tree output. We could simply select 251 a certain number of locations with the highest probabilities. However, if the 252 number of selected locations is small like it is the case here, some locations 253 with relatively high probabilities might not be chosen whereas locations with 254 slightly higher probabilities due to random noise will. To bypass this issue, we  (equation (2)). To get to the next step, we assumed that the management The net survey area value corresponding to the minimum management cost 305 per controlled tree would be the optimal area to survey.

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However, one could also assign a cost θ to a missed green infestation as year. We then compared the optimal survey area for the management cost 317 and for the total cost depending on the strategy used. We also investigated 318 the dependence of the optimal survey area on θ in Appendix B.

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The generalized boosted classification model has a good predictive abil- Youden's index is 0.003, which means that it is optimal in terms of mis-324 classified instances to consider any probability value above this threshold 325 as an infestation. Using this threshold, we calculated the confusion matrix 326 ( We calculated the variables' impact on the classification tree output (i.e. control efficiency is higher than the local control efficiency (Fig. 4) The management cost increases linearly with the net survey area (Fig. 5). 354 We numerically obtain the net survey area values corresponding to the mini-  (Fig. 6a). We obtain the matching radius 50 me-358 ters using equation (2) for the local search. However, it is highly probable 359 that the cost of missing a green infestation θ is non-negligible. As the man-360 agement cost increases with the survey area and the avoided cost decreases, 361 the total cost shows a minimum value larger than zero (Fig. 7 for θ = 1000).

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Therefore, the minimum total cost per controlled tree with θ = 1000 gives 363 survey area values ranging from 3 010 378 to 5 062 968 m 2 and corresponding 364 to the radius 60 to 65 meters using equation (2) for the local search (Fig. 6b).      Table 1 Description     D r a f t

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When the fixed survey area is equivalent to the one used in the current strat-760 egy (2 200 000 m 2 ), we can see that the local control efficiency is always 761 higher than the predictions control efficiency no matter the exponent value.

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However, for a net survey area of 5 000 000 m 2 , the prediction control effi-763 ciency is larger than the local control efficiency for an exponent value from 764 about 1-1.5 to 5. We varied the cost of a missed green infestation θ from 0 to 2000 and 768 investigated its impact on the optimal survey area and the minimum cost 769 per controlled tree depending on the detection strategy.

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The optimal net survey area increases with θ for both the local and pre-771 dictions strategies, although the optimal area is consistently larger using 772 the predictions strategy (Fig. B1a). However, the minimum total cost per 773 controlled tree associated with the optimal survey area is lower for the pre-774 dictions strategy than the local strategy for θ ⩾ 500 (Fig. B1b).

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This means that the more expensive a green infestation, i.e. the more new 776 infestations produced by one infested tree, the better in term of costs it is to 777 increase the management effort now rather than controlling the additional 778 new infestations in the future.