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Dispersal has been least understood in mountain pine beetle ecology. We developed a novel regional dynamic conceptual model of mountain pine beetle infestation using the tree mortality estimated from the British Columbia annual aerial overview survey to quantitatively determine short-distance dispersal (SDD) and long-distance dispersal (LDD) at local (forest district) and regional (provincial) scales. The dispersal patterns were characterized based on distances between a sink patch to its nearest source patch. At the regional scale, SDD accounted for 85.3% of mountain pine beetle dispersal to non-infested areas and 96.8% of beetle dispersal to infested areas. Although SDD was a dominant dispersal mode, LDD played a more important role in the early stage of the current mountain pine beetle outbreak. At the local scale, three patterns of dispersal to non-infested areas were identified. First, LDD dominated in the forest districts where only sparse infestations occurred. Second, LDD was a dominant or important factor in the early stages of the infestations in some districts. Third, SDD dominated throughout the infestations in more severely infested forest districts. However, for dispersal to infested areas, SDD was a dominant mode in most of the forest districts. We conclude from the spatiotemporal patterns of dispersal observed at local and regional scales that LDD is a key factor in the initiation and early stage of the infestations in new remote areas, and SDD dominate in the spread and expansion of the outbreak as the infestations intensify and reach epidemic levels. However, it should be conscious that there is uncertainty that LDD might have been over emphasized in the dispersal before local dynamics is fully taken into account.
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Dispersal, defined as the movement of individuals away from their source populations, or place of birth (Nathan et al. 2003), is an important driver of insect population dynamics at local and regional scales. It can play a significant role in generating spatial synchrony in local population dynamics, facilitating shifts of insect population epidemic levels (Liebhold et al. 2004, Aukema et al. 2008, Raffa et al. 2008). While outbreaks of native forest insects have occurred through history (Ryerson et al. 2003, Taylor et al. 2006, Alfaro et al. 2010), and play a critical role in driving large-scale ecological processes such as ecosystem disturbance, multitrophic interactions, and forest succession, and altering biogeochemical and biophysical processes such as carbon, water, and nutrient cycling (Kurz et al. 2008, Raffa et al. 2008), they can cause substantial economic losses and even more damage with climate warming (Carroll et al. 2004, Negron et al. 2008, Raffa et al. 2008). Spatial dynamics is an integral part of insect outbreaks (Logan et al. 1998). A better understanding of dispersal can provide valuable insights into insect outbreak dynamics, helping to minimize outbreak impacts and achieve sustainable forest management goals.
The mountain pine beetle (Dendroctonus ponderosae Hopkins) is indigenous to pine (Pinus spp.) forests of western North America. Its population has recently been at an epidemic level, causing the largest infestation on record in British Columbia, Canada (Taylor et al. 2006). The geographic expansion of climatically suitable habitats for beetles and a dramatic increase in host availability resulting from forest management practices are the primary explanations put forth for the record-breaking outbreak (Carroll et al. 2004, Jackson et al. 2008). As of 2009, approximately 47% or 630 million m3 of merchantable pine has been killed in British Columbia since 1999 (Walton 2010). The current mountain pine beetle outbreak has generated extensive ecological and economic impacts (Safranyik and Carroll, 2006, Negron et al. 2008).
Mountain pine beetle is typically univoltine, completing a single generation each year. In British Columbia, the lodgepole pine (Pinus contorta Douglas ex Louden var. Latifolia Engelm. ex S. Watson) is the most common host but the beetle may also infest western white pine, white bark pine, and ponderosa pine. Beetles colonize host trees through a pheromone-mediated mass attack that overcomes tree defenses with help of several associated microorganisms, particularly two blue stain fungi (Grosmannia clavigera and Ophiostoma montium) that the beetles carry into the trees. Adult beetles bore into the phloem, copulate, and excavate galleries along which they lay eggs. The larvae feed on phloem tissues and develop through four instars by excavating mines or tunnels that terminate in pupal chambers, from which brood adults emerge between mid-July and mid-August in the following summer. Newly emerged beetles disperse and attack new host trees. The infested tree usually retains green foliage until May and June of the year following attack, after which it gradually fade from green to yellow to red. By the end of the summer and into the fall, over 90% of infested trees are dead, having red needles and a new generation of beetles have dispersed to new healthy hosts. Most dead trees lose all needles three years after being attacked (Safranyik and Carroll 2006, Wulder et al. 2006).
Mountain pine beetles may disperse over short or very long distances (Safranyik and Carroll 2006, Robertson et al. 2007, 2009, Jackson et al. 2008). Short-distance dispersal (SDD) under the forest canopy within a stand is mediated both by host tree volatiles and attractive aggregation pheromones emitted from beetles (Safranyik et al. 2010). There are two modes of SDD. Emerged beetles may either attack the nearest suitable host trees, in which case beetle populations spread from a central location in a stand (i.e., spot growth), or beetles may fly over somewhat greater distances for a longer period of time in search of suitable hosts, causing infestations at new locations within a stand (spot proliferation) (Safranyik et al. 1992, Robertson et al. 2007, 2009). Long-distance dispersal (LDD) occurs when beetles get caught in convective upward drafts and are transported long distances above the forest canopy by wind (Safranyik and Carroll 2006, Robertson et al. 2007, 2009).
Robertson et al. (2007) inferred spatial patterns of mountain pine beetle SDD by analysing the spatial patterns of red and green attacked trees at the forest stand scale in Morice, west central British Columbia for two year periods 2003 and 2004. They found that SDD dramatically increased from 66% (of plots with green trees found) in 2003 to 92% in 2004 as the beetle infestations erupted in 2004. The distances of SDD were most often around 30 meters and 50 meters. Spot proliferation dominated in SDD, which also more often occurred in more suitable habitats but were not closely associated with availability of host trees, implying that the beetles dispersed to new locations even susceptible host trees were available nearby. Robertson et al. (2009) also analysed spatiotemporal patterns of mountain pine beetle infestation movement events in three mountain passes through the Canadian Rockies from 1999 to 2005. They concluded that spot proliferation was dominant mode of dispersal during periods of low range expansion and marginal increases in infestation areas, whereas spot growth became dominant mode of dispersal for periods of rapid expansion. LDD may play a key role in establishment of new beetle populations in remote areas, which, however, was likely dependent upon regional weather patterns and influenced by local topography. De la Giroday (2009) examined how landscape features and their orientation affect patterns of mountain pine beetle establishment which were assumed to be results of LDD in northeast British Columbia between 2004 and 2006. She found that large glacially-eroded valleys, canyons, deeply incised streams, local and mid-slope ridges or small hills in valleys and plains, and open slopes were positively associated with infestations, implying important influences of the interaction of meteorological events and local topography on spatial patterns of the beetle establishment from LDD.
Aukema et al. (2006) studied spatiotemporal patterns and spatial synchrony of mountain pine beetle spread at the regional scale in British Columbia for two periods, incipient years 1990–1996 and epidemic years 1999–2003. They revealed that the present outbreak first started from an epicenter, an area in west central British Columbia and then spread eastward. More importantly, they found that many localized infestations erupted in different isolated areas, particularly in southern parts of British Columbia. They also found that the distance at which beetle infestations were spatially synchronous was much smaller for incipient years (<200 km) than one for epidemic years (<900 km). Aukema et al. (2008) also tried to determine factors important to outbreaks of mountain pine beetle populations and examined how spatial synchrony of infestations change at local and regional scales throughout the outbreak in Chilcotin Plateau of British Columbia during 1972–1986. In the autologistic regression model, they found that spatial and temporal dependencies (presence of the outbreak within 18 km and presence of the outbreak in previous year) contributed most to detect the outbreak. Temperature was another key factor to predict probability of the outbreak. They also found that landscape level synchrony declined as the outbreak collapsed, while local synchrony remained high.
Although these studies have provided extensive insights into dispersal of mountain pine beetle and spatiotemporal patterns of infestation spread, information on mountain pine beetle dispersal spatiotemporal patterns at the regional scale, especially the explicit role of LDD in the present outbreak, is still lacking. In this study, we develop a regional source-transformer-sink conceptual model of mountain pine beetle infestation using the tree mortality estimated from the British Columbia annual aerial overview survey. Under the framework of the model, we determine and quantify dispersal at local (forest district) and regional (provincial) scales, addressing two fundamental questions: (1) What are the spatiotemporal patterns of SDD and LDD? (2) What are the roles of SDD and particularly LDD in the spread and expansion of the current mountain pine beetle outbreak? We also tested the following hypotheses: (1) SDD is a dominant factor in the spread and expansion of the mountain pine beetle outbreak; (2) LDD is a key factor to initiate new infestations in remote areas; (3) The occurrence of LDD is random, and if not, its occurrence is positively correlated to severity and patchiness of the mountain pine beetle infestations.
The study area was defined as the cumulative annual mountain pine beetle infestation areas from 1999 to 2008 (approximately 238,653 km2, West: 133°52′50″ W, East: 110°42′56″ W, South: 48°26′43″ N, and North: 59°57′46″ N) in British Columbia (Fig. 1).
We used the annual infestation raster datasets (400 × 400 meter cell size) in this study, which were produced using the British Columbia aerial overview survey data (1999–2008) (British Columbia Ministry of Forests 2000) by the British Columbia Provincial-Level Mountain Pine Beetle Model (〈ftp://ftp.for.gov.bc.ca/HRE/external/!publish/BCMPB〉). The aerial overview survey is generally conducted from early July through August every year using a fixed-wing aircraft flying at 150 to 170 km/hour and at 500 to 1,000 meters above the terrain. The datasets mapped the tree mortality estimated from the British Columbia aerial overview survey, in which locations and areas of dead trees were detected and estimated based on crown discoloration (i.e., red crown). The datasets were corrected for the errors resulting from human visual omission and poor positional accuracy in the survey (Eng et al. 2006, Wulder et al. 2006). These corrections ensured that the beetle infestations did not occur in unsuitable habitats like lakes and rivers or in forested areas without pines, and no more than 100% of the pine in a forest stand had been killed over the course of infestations (Eng et al. 2006). Five severity classes were assigned to each cell in the annual infestation raster datasets: (1) T (Trace, <1% of the infested forest stands); (2) L (Light, 1–10%); (3) M (Moderate, 11–30%); (4) S (Severe, 31–50%); (5) V (Very Severe, 51–100%). The raster datasets were up scaled to 1200 meters because a grid of the same size was used in the correction procedures (Eng et al. 2006), and finally combined to create a master grid with a spacing of 1200 m (144 ha per cell). The severity for each cell of the grid was calculated from severities of 9 cells of 400 × 400 meters of the annual raster datasets, using an area weighted average in which the middle values of each severity class were used: 0 for the non-infestation class, 0.5 for the T, 5 for the L, 20 for the M, 40 for the S, and 75 for the V. The severities of each cell were re-grouped into two general classes: light infestation (L), combining the severity classes, T, L, and M, and severe infestation (S), combining the severity classes, S and V. The total number of master grid cells was 165,731.
Conceptual model of mountain pine beetle infestation and quantification of dispersal patterns
To determine and quantify the dispersal, we proposed a source-transformer-sink conceptual model of mountain pine beetle infestation (Table 1). At the regional scale, the mountain pine beetle infestation is considered a dynamic system, spatially composed of cells of an infestation grid (1200 × 1200 meters). We defined a sink as a cell where beetles fly in, a source as one where beetles fly out, and a transformer as one where beetles fly in and fly out. As indicated in the section above, the infestation was detected based on red crowns of dead trees and its severity was estimated using tree mortality in the aerial overview survey. Assuming that trees fade from green to red one year after being attacked, the infestation actually occurred one year before the infestation could be detected in the survey. Therefore, we considered Tn as the targeted year when the infestation actually occurred (Table 1). To determine if a cell is a source, a sink, or a transformer, for each targeted year (1999 to 2007), we compared severities of a cell over a pair of consecutive survey years (1999/2000, 2000/2001, 2001/2002, 2002/2003, 2003/2004, 2004/2005, 2005/2006, 2006/2007, and 2007/2008). Each cell, for each targeted year, can be a sink, a source, or a transformer depending upon its state in terms of change in infestation severity from Tn to Tn+1 (i.e., the target year to the next year) (Table 1). Some key assumptions are implied in the conceptual model: (1) The beetles fly from a source to a sink; (2) The infestation severity is a good proxy of beetle population abundance; (3) It takes a year for infested trees to fade from green to red after they have been attacked; (4) The infested trees always produce a brood of beetles in the next year.
Table 1. The dynamic states and types of mountain pine beetle infestation in an infested grid cell.
To characterize the dispersal patterns, the infestation grid cells were grouped into five types: (1) sink, NL and NS; (2) source, LN and SN; (3) transformer, LL and SS; (4) transformer, LS; and (5) transformer, SL (Table 1). For each targeted year, the boundaries of the grid cells of the same type were dissolved, creating the infestation patch polygons for each type; therefore, there were four types of potential sinks: NL and NS; LS; LL and SS; and SL, and four types of potential sources: LN and SN; SL; LL and SS; and LS. For each type of sink and each targeted year, the distances (in meters) were measured from the edge of each individual sink patch to the edge of the nearest individual source patch. The preference for choosing the nearest source patch was given in the order of LN and SN, SL, LL and SS, and LS among source patches with an equal distance, basing on the declining possibility from LN and SN to LS that beetles fly out of the patch. For each type of sink, dispersal to sink patches, based on the distances measured above, was categorized into three modes as defined by Safranyik et al. (1992), spot growth (distance = 0), spot proliferation (distance > 0 and ≤ 2.4 km), and LDD (distance > 2.4 km). The threshold value of 2.4 km, which is used to distinguish SDD and LDD of mountain pine beetle, was modified from the 2 km as used by Robertson et al. (2009) to align with the grid cell size of 1200 meters used in this study. The proportions (number of sink patches) of three modes of dispersal to sink patches were accounted for each type of sink and each targeted year, and were used to describe the spatiotemporal patterns of three dispersal modes. In this paper, we only report the results for two types of sinks, NL and NS, representing dispersal to non-infested areas, and LL and SS, representing dispersal to infested areas, because the proportions of the other two types of sinks, LS and SL, were generally very low (2.5 ± 1.5% for LS and 2.3 ± 1.5% for SL).
To test the hypothesis that the occurrence of LDD is random, the Chi-square goodness of fit (Zar 2010) was first used to test if the occurrences of three modes of dispersal to both non-infested and infested areas are random for each targeted year. In the Chi-square goodness of fit test, a Monte Carlo simulation of 1000 repetitions was used to compute p-values by random sampling from the discrete distributions of three dispersal modes (Hope 1968). The proportions of three dispersal modes for each of two types of sinks (NL and NS, and LL and SS) were used as the observed values. To estimate corresponding expected values, we measured all distances between two individual patches of all five types of patches (NL and NS; LN and SN; LL and SS; LS; and SL) as indicated in the previous section and calculated the proportions of the patches of three dispersal modes for each targeted year, which were used as the expected values. The adjusted Wald confidence intervals (Zar 2010) for the observed occurrences of three dispersal modes were also calculated to further verify if the observed occurrences were significantly different from the expected occurrences for each dispersal mode. If the null hypothesis of the Chi-square goodness of fit test was rejected for LDD, we further tested if the occurrence of LDD was positively correlated to severity and patchiness of the mountain pine beetle infestations by calculating the Spearman rank correlation coefficients (Zar 2010) between the occurrences of LDD to both non-infested and infested areas and the total number of infested grid cells, as well as landscape aggregation indices (McGarigal et al. 2002), at local and regional scales. The values of landscape aggregation indices are between 0 (no aggregation, the patches are maximally disaggregated) and 100% (maximum aggregation, the landscape consists of a single patch) (McGarigal et al. 2002). The higher values indicate higher aggregation and lower patchiness of infestation patches. Significance tests for the rank correlations were also conducted.
Chi-square goodness of fit and the Spearman rank correlation were conducted in the R base module (R Development Core Team 2009, version 2.10.0). The landscape aggregation indices were calculated in the FragStats landscape analysis software (McGarigal et al. 2002).
Dynamics of the mountain pine beetle outbreak
The proportion of cells of infestation initiation and growth increased substantially in 2002 and reached a plateau in 2003 and 2004. Consequently, the outbreak increased rapidly from 2002 to 2004, leading to a peak period of the outbreak in the following three years, 2004 to 2006. The outbreak dropped dramatically in 2007 with a significant increase in the proportion of cells of infestation cessation and subsidence. Actually, significant infestation subsidence already began as early as two previous years, 2005 and 2006. Generally, however, cells of stable infestation development dominated throughout the current mountain pine beetle outbreak, supporting and maintaining infestations at epidemic levels (Fig. 2).
Dispersal at the regional scale
Spot growth was a dominant mode of mountain pine beetle dispersal to both non-infested and infested areas. LDD was the second dominant mode for dispersal to non-infested areas but dropped to the least important mode for dispersal to infested areas (Table 2). The occurrences of LDD to non-infested areas were generally higher in the early stage (1999–2003) of the outbreak, in which the outbreak increased rapidly (Fig. 2), than in late stage (2004–2007) of the outbreak, in which the outbreak reached the peak, stabilizing and then beginning to decline. The overall SDD accounted for 85.3 ± 0.7% of mountain pine beetle dispersal to non-infested areas and 96.8 ± 0.7% of beetle dispersal to infested areas.
Table 2. The occurrences of three modes of mountain pine beetle dispersal in British Columbia, Canada (1999–2007).
For each individual and all years, there was a significant difference between the observed and expected occurrences for each mode of dispersal to both non-infested and infested areas (P < 0.05), except for spot growth in the year 2005, for spot proliferation in the year 2005, and for LDD in all the years and individual years 2001, 2005, and 2006, for dispersal to infested areas (P > 0.05). For dispersal to non-infested areas, the consistent patterns were shown in observed and expected occurrences of three modes. LDD had significantly higher observed occurrences than the expected occurrences, whereas spot growth and spot proliferation had significantly lower observed occurrences than the expected occurrences (P < 0.05). However, for dispersal to infested areas, no consistent patterns of three modes were observed (Table 2).
The distribution of mountain pine beetle dispersal distances was typically leptokurtic with dominance in spot growth mode (74.7% and 82.1% for dispersal to non-infested and infested areas, respectively), as shown in Table 2. LDD to non-infested areas had a much larger variation in the dispersal distances than LDD to infested areas; the LDD medians ranged from 5.1 to 16.3 km to non-infested areas and 3.6 to 4.8 km to infested areas; the maximum LDD distance was 391.9 km to non-infested areas compared to 60.0 km to infested areas. One substantial increase in dispersal distances occurred for LDD to non-infested areas in 2006 (Fig. 3).
Dispersal at the local scale
Generally, for dispersal to non-infested areas, three patterns were identified. First, LDD dominated in the forest districts where there were only sparse infestations occurred (DKM, DSC, and DSS_N). Second, LDD was a dominant or important factor in the early stage of the infestations (1999 to 2002) (DAB, DCH, DCK, DCO, DHW, DKL, DMK, DOS, DPC, DPG, DRM, and DSS_S). Third, spot growth dominated throughout the infestations (1999 to 2007) in more severely infested forest districts (DCC, DCS, DIC, DJA, DKA, DMH, DND, DQU, and DVA) (Fig. 4). In particular, LDD largely contributed to two substantial expansions of infestations, one for DCH in 2002 (56.2%) and the other for DPC in 2006 (79.7%) (Fig. 4). However, for dispersal to infested areas, spot growth dominated in the whole course of the infestations in most of forest districts (Fig. 5).
LDD to non-infested areas has stronger negative rank correlations between its occurrences and total number of infested grid cells, and aggregation indices of the infestations than LDD to infested areas for all districts and for most individual districts (Table 3). Interestingly, for most districts in southeastern parts of the province, which had more patchy infestations (Fig. 6), LDD to non-infested areas had significant negative rank correlations between its occurrences and aggregation indices of the infestations (Table 3).
Table 3. Spearman rank coefficients of occurrences of long-distance dispersal (LDD) with total number of infested grid cells and landscape aggregation indices (AI) of the infestations in British Columbia, Canada (1999–2007).
Some corrections and compensations were made in the datasets used in this study to reduce the errors and inter-year inconsistencies in the aerial overview survey mapping (Eng et al. 2006, Walton 2010). However, they may not be good enough to correct all errors and compensate for all inconsistencies. Some significant defects were detected in the 2008 datasets for some parts of the Northern Interior forest districts (DJA, DMK, DND, DPC, DPG, and DVA; Fig. 1), which were caused by either poor or no surveys for these areas in the 2008 aerial overview survey due to weather conditions and contractor availability (Walton 2010). However, these defects in the datasets used in this study did not seem to affect the patterns of dispersal to both non-infested and infested areas for the year 2007 in these forest districts (Figs. 4 and 5). Therefore, we may assume that the patterns of dispersal determined based on the conceptual model in this study are robust and consistent.
We determined the modes of dispersal based on only one nearest source patch instead of using many neighbor source patches. This may cause loss of certain amount of detailed information but may also avoid some complexities such as the determination of optimum number of the near neighbors as well as more intensive and time consuming processing of large datasets. The focus of our study was not on accurate determination of dispersal distances but on detection of potential dispersal patterns at local and regional scales. One nearest neighbor approach in determining the modes of dispersal should serve our main purposes.
One limitation with our conceptual model is that local dynamics of mountain pine beetle populations was not taken into account. Overlook of the possibility of eruption of local endemic populations due to improved climate conditions or rapid decline in host resistance may cause over emphasis of LDD in the dispersal, especially when infestations occur in those historical areas of mountain pine beetle outbreaks like the mountain areas in southeast parts of British Columbia, and are isolated. However, general patterns of LDD revealed from our model may not be fundamentally changed, particularly for regional infestations at epidemic levels. For example, even in the southeast mountain areas of British Columbia, most LDD sink patches of new infestations scattered in clusters along the valleys (Fig. 7). These patterns were also observed in three mountain passes through the Canadian Rockies by Robertson et al. (2009) and in northeast British Columbia by de la Giroday (2009), implying that new infestations in remote areas could be mostly resulted from LDD rather than eruption of local endemic populations. The patterns of LDD sink patches of new infestations observed in Peace River, northeast British Columbia and Chilcotin, central British Columbia in this study further clearly support this inference (Fig. 7).
Dispersal is a key population processes in mountain pine beetle (Safranyik and Carroll 2006). In theory, dispersal is energetically costly, and energy expended during movement reduces reproductive investment at the host tree and ability to tolerate host defensive compounds (Reid 2008). This may explain why SDD was a dominant mode of mountain pine beetle dispersal (Safranyik and Carroll 2006) as demonstrated in most species (Skalski and Gilliam 2000, Nathan et al. 2003, Lowe 2009). Our results support the hypothesis that SDD is a dominant factor in the spread and expansion of the current mountain pine beetle outbreak at the regional scale (Table 2).
The impacts of LDD at broader (regional and global) scales have been acknowledged as it directly affects spatial spread and colonization rates (Nathan et al. 2003, Jacobson and Peres-Neto 2010). LDD is also a contributing factor for the transition of mountain pine beetle populations from incipient-epidemic level to epidemic level at the landscape scale (Safranyik and Carroll 2006). However, empirical research on LDD is limited and far behind theoretical developments due to the difficulty in detecting and quantifying landscape-level dispersal (Nathan et al. 2003, Lowe 2009, Jacobson and Peres-Neto 2010). This is the case in mountain pine beetle. Jackson et al. (2008) demonstrated occurrences of LDD events of mountain pine beetle in central British Columbia through the radar images and aerial captures. Safranyik and Carroll (2006) suggested that the infestations discovered in the Peace River region of northeastern British Columbia in the early 2000s, where was historically considered climatically unsuitable to mountain pine beetles, were most probably the result of LDD from the source populations in the southwest several hundred kilometres away by crossing the Rocky Mountains. The patterns of dispersal to non-infested areas we observed in the Peace forest district (Figs. 4 and 7) explicitly support this inference. Furthermore, the sparse infestations occurred in the district DKM, DSC, and DSS_N were probably all consequence of LDD to non-infested areas (Fig. 4).
The temporal patterns of dispersal to non-infested areas at the regional scale suggest that LDD may play a more important role in the early stage (1999–2003) of the outbreak (Table 2). An exception of significant increase in the occurrences (Table 2) and a dramatic increase in the distances (Fig. 3) for LDD to non-infested areas in the year 2006 were mainly caused by large expansions of infestations in two forest districts, Peace (DPC) and Mackenzie (DMK), as indicated in Fig. 4.
The patterns of dispersal to non-infested areas at the local scale (DSS_S, DPC, DMK, DCH, DRM, DKL, and DHW; Fig. 4), also reveals that LDD was an important factor in the early infestations, and might play a key role in the spread and expansion of the outbreak by switching the beetle populations from incipient-epidemic level to epidemic level as evidenced by two dramatic expansions of infestations, one in DCH for 2002 and the other in DPC for 2006 (Figs. 4 and 7). Our results reject the hypothesis that the occurrence of LDD to non-infested areas is random (Table 2). The significant negative rank correlations between the occurrences of LDD to non-infested areas and total number of infested cells (Table 3) may further imply the importance of LDD for the colonization of beetles in new remote areas.
These findings seem not to support the hypothesis that a positive correlation exists between the occurrence of LDD and the abundance of beetle populations. They are also contrary to the assumption that LDD is more likely to occur when the beetles face larger population pressure and shortage of suitable hosts (de la Giroday 2009). We assume that rapid depletion of the host resources may also possibly occur in some of the areas where the beetles from LDD are going to land, not just in the areas where the beetles fly up to initiate LDD, as infestations intensify and reach an epidemic level at the regional scale. The decline in availability of quality host resources in the habitats where beetles from LDD land may decrease the possibility of successful colonization for the pioneer beetles because LDD may be more costly in energy and the pioneer beetles from LDD may have a higher expectation and requirement in terms of quantity and quality of the hosts (Reid 2008). This may explain why more LDD to non-infested areas occurred in the early infestations in this study. Our assumption is further supported by the fact that much lower occurrences of LDD to infested areas were observed compared to occurrences of LDD to non-infested areas at both local (Figs. 4 and 5) and regional (Table 2) scales, and by the fact that SDD was dominant mode of dispersal to non-infested areas in the epicentres (the forest districts DND, DQU, and DVA; Fig. 4) of the present outbreak where the infestations originally started and spread (Aukema et al. 2006, Walton 2010). Therefore, we may assume from the patterns of dispersal observed in this study, particularly as demonstrated in the forest districts DPC, DCH, DSS_S, and DMK (Fig. 4), that LDD may be a key factor for the initiation and early stage of the infestations in new remote areas and SDD may subsequently become predominant in the spread and expansion of the outbreak as local populations grow and the infestations intensify, reaching epidemic levels. However, it should be conscious that there is uncertainty that LDD might have been over emphasized in the dispersal, particularly when infestations are still at the early stage of development in the historical areas of mountain pine beetle outbreaks, before local dynamics is fully taken into account in our model.
For dispersal to non-infested areas, the significance test support the hypothesis at the regional scale that the occurrences of LDD are positively correlated to patchiness of the infestations, which was expressed in a significant negative correlation between the occurrences of LDD and landscape aggregation indices (Table 3). It is interesting to note that these correlations were mainly significant in all southeast forest districts of the province except the DCO district (Table 3 and Fig. 1). These districts are historical areas infested by mountain pine beetles and covered mostly by mountain areas (Pojar and Meidinger 1991, Taylor et al. 2006, Alfaro et al. 2010). Recent infestations in these areas were isolated and localized (Aukema et al. 2006), which was further evidenced by the higher patchiness of the infestations observed in these areas than those areas in the epicentre of the current outbreak (DND, DVA, and DQU) and their neighbor districts (DCC, DCH, DIC, DJA, DMH, and DPG) in this study (Figs. 1 and 6). There is no alternative explanation for this observation. However, this hypothesis may not be supported for dispersal to infested areas because the correlations between the occurrences of LDD and patchiness of the infestations were only significant in two districts (DAB and DCS) even though the statistical test was significant at the regional scale (Table 3).
It is a challenge to quantitatively determine dispersal, particularly long-distance dispersal at the regional scale. The conceptual framework of mountain pine beetle infestations proposed in this study provides a practical and analytical approach to quantify dispersal and detect its spatiotemporal patterns at the regional scale. This approach can be applied to other bark beetle species with long-term and sufficient monitoring data. The spatiotemporal patterns of mountain pine beetle dispersal observed at local and regional scales reveal that LDD is a key factor in the initiation and early stage of the infestations in new remote areas and may play a critical role in expansion of the outbreak through facilitating the shifts of the beetle populations from incipient-epidemic levels to epidemic levels. However, it should be conscious that there is uncertainty that LDD might have been over emphasized in the dispersal before local dynamics is fully taken into account.
The spatiotemporal patterns of LDD can be used to detect and map potential conduits of LDD at the regional scale, assisting to identify and prioritize the mitigation areas in strategic and tactical planning. This is important for mountain pine beetle mitigation planning, especially in the context of climate change that beetles may disperse to higher elevation mountain areas and the regions that are climatically unsuitable before via LDD. Furthermore, determinations of sinks and sources for LDD in this study make it possible to further examine the mechanisms driving LDD at the regional scale through linking topographic modeling and meso-scale meteorological modeling, advancing our understanding how topographic features affect spatial patterns of LDD at the regional scale.
We thank Honey-Marie. C. de la Giroday for providing her unpublished MSc. thesis, Felix Andrews for providing the R codes, and Peter Ott for his advice on the statistical analyses. This manuscript was greatly improved with valuable comments from Dr. Gordon Nigh, Dr. Elizabeth Campbell, Dr. Trisalyn Nelson, Dr. Peter Jackson, and Jennifer Burleigh. We also appreciate insightful comments from three reviewers and subject editor Fangliang He.