Modelling landscape genetic connectivity of the mountain pine beetle in western Canada

The current mountain pine beetle (MPB; Dendroctonus ponderosae Hopkins, 1902) outbreak has reached more than 25 million hectares of forests in North America, affecting pine species throughout the region and substantially changing landscapes. However, landscape features that enhance or limit dispersal during the geographic expansion associated with the outbreak are poorly understood. One of the obstacles in evaluating the effects of landscape features on dispersal is the parameterization of resistance surfaces, which are often constructed based on biased expert opinion or by making assumptions in the calculation of ecological distances. In this study, we assessed the impact of four environmental variables on MPB genetic connectivity across western Canada. We optimized resistance surfaces using genetic algorithms and models of maximum likelihood population effects, based on pairwise genetic distances and ecological distances calculated using random-walk commute-time distances. Unlike other methods for the development of resistance surfaces, this approach does not make a priori assumptions about the direction or shape of the relationships between environmental features and their cost to movement. We found highest support for a composite resistance surface including elevation and climate. These results further the understanding of MPB movement during an outbreak. Additionally, we demonstrated how to use our results for management purposes.

Dispersal is an important determinant of ecological and evolutionary dynamics due to its 48 influence on population connectivity (Taylor et al 1993). In turn, connectivity has significant 49 implications for population (Martin and Fahrig 2016) and species persistence (Thomas 2000). 58 One species of particular concern in the boreal forest ecosystem of western North America is the 59 mountain pine beetle (Dendroctonus ponderosae; MPB; ITIS.org Taxonomic Serial Number 60 114918). The MPB is a highly mobile, native and irruptive forest insect pest whose outbreaks 61 have significant ecological and economic consequences as it feeds on the majority of pine 62 species in its range, including among others lodgepole pine (Pinus contorta), sugar pine (Pinus 63 lambertiana), western white pine (Pinus monticola), and ponderosa pine (Pinus ponderosa) and 64 is able to maintain outbreaks in healthy stands (Safranyik and Carroll 2006  209 Next, we sought to identify global parameter optima for this set of retained resistance surfaces, 210 using genetic algorithms. Optima were identified through "evolution" of the model parameters 211 through the processes of "mutation" (probability = 0.2) and "crossover" (probability = 0.9). All 212 steps were repeated until no improvement in log-likelihood was found for 25 iterations. This 213 process was applied to each landscape variable, and combinations of variables, giving us 17 214 parameterized candidate models.

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216 Model selection and performance 217 We selected the best model from our set of candidate models using the sample-size corrected 218 Akaike Information Criterion (AICc) and associated Akaike weights (ω AICc ). A bootstrapping 219 analysis was then conducted to validate the selection of our models (Peterman 2018). The goal of 220 the bootstrapping procedure was to assess how sensitive our conclusions were to outliers (sites).  (Table 1). We identified a monotonically decreasing cost to movement with increasing pine 268 volume and CSI values. Pine volume showed a decreasing relationship with cost that nears a 269 linear relationship (Fig. 2 B). In contrast, CSI showed a more marked plateau of high cost for 270 low values of CSI. Thus, the rate at which CSI-cost decreases is more pronounced at higher D r a f t 13 271 values of climate suitability (Fig. 2 D). The negative effect of elevation is also captured with a 272 transformation showing that the rate of elevation-cost increases is lower at higher altitudes ( Fig.   273 2 A). Drought was fitted with a unimodal transformation with a maximum value at a drought 274 value of 0 which indicates that the highest costs to beetle genetic connectivity are found in 275 conditions with neither moisture deficit nor excess (Fig. 2 C) (Fig. 3), one can notice large areas with low costs in the north. The 306 influence of the Rocky Mountains (high elevation) can be seen, with intermediate costs to 307 movement covering much of the central part of our study area. The eastern part of our study area 308 shows less heterogeneity in cost to movement which is likely the result of reduced variation in 309 elevation relative to BC and western AB (Fig. 3).

311 Model application I -Origin of the Hinton MPB population
312 Based on our genetically-informed, and machine learning optimized model of landscape 313 connectivity, we found that Jasper is the most likely source of beetles in Hinton, and that Hinton, 314 Jasper and Edson are part of a connectivity corridor (Fig. 4). Indeed, connectivity, as measured 315 by commute time distances was the highest between Hinton and Jasper (Fig. 4). Connectivity , and a corridor crossing the Alberta and Saskatchewan border 326 and following the southern limit part of the pine distribution (Fig. 5 A). Prediction using a model 327 based exclusively on pine volume (Fig. 5 B) indicated that beetle connectivity is overall more 328 homogeneous with fewer evident corridors, although one can recognize corridors identified using 329 the Elevation + CSI model. 356 Although elevation emerged as an important predictor of beetle connectivity in our study area, 357 given the lack of significant topography east of the Rocky Mountains, elevation will not likely be 358 a significant factor influencing pine beetle outbreak spread.
359 Pine volume was positively associated with gene flow: resistance decreased with greater pine 360 volume (Fig. 2 B). High-volume stands are generally thought to be more susceptible to MPB 375 Finally, we found that resistance decreased with higher values of climate suitability (Fig. 2 D).
376 Relative to the other monotonic relationships (e.g., elevation and pine volume), the effect of 377 climate suitability on gene flow is less linear, with a plateau of high resistance followed by a 378 sharper decrease of resistance, than the pine single surface for example (Fig. 2) (Fig. 4). Hinton is also well connected with Edson and there seems to be a 417 large corridor of high connectivity from Jasper to Edson. A recent study also showed that beetles 418 east of Hinton are genetically similar to beetles from Jasper (Trevoy et al. 2018). Also, the latest 419 MPB population forecast survey in Alberta showed that based on larval mortality, beetle 420 numbers were strongly increasing in an area ranging from Jasper to the Edson forest area 421 (Alberta Agriculture and Forestry 2017), which is similar to the highly conductive area we 422 described (Fig. 4). From a management perspective, this model could be used to forecast 423 connectivity between attacked and unattacked stands and to prioritize well connected, but not yet 424 attacked, stands for pre-emptive harvest. 425 Our second model application examined potential routes of eastward expansion at a larger, inter-426 provincial scale (Fig. 5 A). Through our exploratory analysis there appears to be few constraints 427 to beetle movement to the east when considering connectivity models, based on elevation and   Habitat fragmentation and its lasting impact on Earth's ecosystems. Sci. Adv. 1(2