Temporal variation in spatial genetic structure during population outbreaks: Distinguishing among different potential drivers of spatial synchrony

Abstract Spatial synchrony is a common characteristic of spatio‐temporal population dynamics across many taxa. While it is known that both dispersal and spatially autocorrelated environmental variation (i.e., the Moran effect) can synchronize populations, the relative contributions of each, and how they interact, are generally unknown. Distinguishing these mechanisms and their effects on synchrony can help us to better understand spatial population dynamics, design conservation and management strategies, and predict climate change impacts. Population genetic data can be used to tease apart these two processes as the spatio‐temporal genetic patterns they create are expected to be different. A challenge, however, is that genetic data are often collected at a single point in time, which may introduce context‐specific bias. Spatio‐temporal sampling strategies can be used to reduce bias and to improve our characterization of the drivers of spatial synchrony. Using spatio‐temporal analyses of genotypic data, our objective was to identify the relative support for these two mechanisms to the spatial synchrony in population dynamics of the irruptive forest insect pest, the spruce budworm (Choristoneura fumiferana), in Quebec (Canada). AMOVA, cluster analysis, isolation by distance, and sPCA were used to characterize spatio‐temporal genomic variation using 1,370 SBW larvae sampled over four years (2012–2015) and genotyped at 3,562 SNP loci. We found evidence of overall weak spatial genetic structure that decreased from 2012 to 2015 and a genetic diversity homogenization among the sites. We also found genetic evidence of a long‐distance dispersal event over >140 km. These results indicate that dispersal is the key mechanism involved in driving population synchrony of the outbreak. Early intervention management strategies that aim to control source populations have the potential to be effective through limiting dispersal. However, the timing of such interventions relative to outbreak progression is likely to influence their probability of success.


Box 1
The processes underlying large-scale spatial synchrony in outbreaks of forest insect pests have fascinated population ecologists for centuries. Two central hypotheses have been proposed to describe these dynamics: (a) synchrony due to dispersal (i.e., the "epicenter hypothesis"); or (b) synchrony due to spatially correlated environmental conditions (i.e., the Moran effect). Distinguishing between these two processes can help us to better understand the spatial dynamics of population irruptions and is needed to develop effective early intervention strategies to mitigate the negative effects of pest outbreaks.
Spatio-temporal analysis of geo-referenced molecular markers offers a powerful tool to assess the relative weight of the two processes and to infer population dynamics over extensive geographic and temporal scales. This objective is nonetheless challenging because both the epicenter process and the Moran effect can lead to similar spatial genetic patterns when an outbreak is at or near its peak. Given the temporal contingency of outbreaks and the genetic patterns within and among populations, spatio-temporal approaches to analyzing spatial genetic structure are required to assess the relative strength of these two processes in driving spatial synchrony. Here, we illustrate the hypothesized development of synchronous spatial genetic structure under these two processes.
The upper panel illustrates the development genetic structure under the epicenter hypothesis, and the lower panel illustrates the development genetic structure under the Moran effect, in a chronological order from the initiation of the outbreak to the peak phase (from left to right). Panel a1 ("epicenter") shows three distinct populations, one of which is increasing in population density and spatial extent.
The other two populations remain at a low density. In this case, we expect genetic structure to manifest as a gradient extending from the source population (i.e., the epicenter, panels b1 & c1) and significant isolation by distance. This rapidly spreading epicenter population can then subsume the other sites, effectively swamping out their genetic variation (d1) and leading to eventual panmixia (panel e1).
In contrast, panel a2 ("Moran effect") shows three distinct populations that are each increasing in density and extent, presumably in response to regionally synchronous environmental conditions. Because each population's growth is independent and does not rely on dispersal from other populations, we expect the development of patchy genetic differentiation (panels b2, c2 & d2). Boundaries between populations become less clear as the outbreak progresses as a result of both the spatial expansion of the populations and dispersal among them (panel d2), leading to high levels of genetic admixture between populations (panel e2) and eventual panmixia. Genetic diversity at panmixia due to the Moran effect is (panel e2) expected to be higher than that due to the epicenter hypothesis (e1), due to the genetic contributions of multiple, versus a single, populations.
Using this framework, collection and analysis of spatial genetic data from multiple years can be used to distinguish between the processes underlying outbreak synchrony. However, successful identification of the dominant process requires that sampling occurs early enough during the outbreak, before panmixia is reached. After panmixia is reached (i.e., panels e1 and e2), the genetic legacy of the previous outbreak collapse may no longer be detectable. The specific rate at which these historical legacies in spatial genetic structure fade is likely a function of multiple demographic parameters such as effective population size, dispersal capacity, and genetic diversity within the population of interest. The precise roles of these factors remain to be further investigated.
Dispersal is the more difficult of the two mechanisms to directly quantify (Ims & Andreassen, 2005). Indirect approaches using population genetic information are increasingly used to measure dispersal (Broquet & Petit, 2009). Spatial analyses of geo-referenced molecular markers can be used to assess genetic connectivity between populations and quantify the strength, spatial scale, and effectiveness of dispersal (Baguette, Blanchet, Legrand, Stevens, & Turlure, 2013). Significant genetic differentiation between populations indicates low levels of gene flow and limited dispersal. In contrast, the absence of genetic differentiation indicates high levels of gene flow and a high degree of effective dispersal between populations.
In demographically complex outbreaking populations (i.e., populations with rapid change in population density), the strength and spatial scale of population genetic structure, as well as the inferences one can make regarding dispersal and spatial synchrony, can depend on the ecological context in which the data were collected (James et al., 2015). Here, ecological context can include standard drivers of spatial population genetic variation such as effective population size, generation time, and dispersal capacity (Charlesworth, 2009).
Context can also include when during the outbreak cycle samples are collected. Samples collected during the endemic phase of an outbreak, where distant populations experience limited genetic connectivity, are likely to express relatively strong genetic spatial structure.
In contrast, samples collected near the peak of an outbreak may see their original structure muted owing to the dominant signature of individuals immigrating from high-density populations (James et al., 2015). Temporally explicit approaches to measuring spatial genetic structure are needed to better understand the spatial dynamics of outbreaking populations.
Although the two synchrony-inducing mechanisms referred to above can be difficult to distinguish on the basis of spatial patterns alone, we expect their spatio-temporal patterns to be unique (Box 1). Spatio-temporal strategies that monitor changes in genetic diversity (Devillard, Santin-Janin, Say, & Pontier, 2011) and evaluate how genetic differentiation between populations changes through time (Hoffman, Schueler, & Blouin, 2004) can be used to help us understand the underlying processes. When dispersal is driving synchrony, one expects to observe the spatial spread resulting in a genetic gradient. When the Moran effect is driving synchrony, one expects patchy genetic differentiation as a result of the independent growth of each population, with the boundaries among populations becoming less clear as the outbreak progresses (Box 1). Thus, an explicitly temporal approach allows one to overcome the limitations of the single snap-shot approach commonly used in population genetics (Draheim, Moore, Fortin, & Scribner, 2018;Tessier & Bernatchez, 1999). However, spatio-temporal population genetics studies of irruptive populations remain scarce in the literature (but see Berthier, Charbonnel, Galan, Chaval, & Cosson, 2006;Rikalainen, Aspi, Galarza, Koskela, & Mappes, 2012).
Large-scale spatial synchrony of SBW outbreaks is a common feature in North American forests, particularly in the eastern part of its range (Blais, 1983;Pureswaran, Johns, Heard, & Quiring, 2016;Williams & Liebhold, 2000). However, despite a century of research, there remains opportunity to improve our understanding of these large-scale population processes, including how dispersal contributes to spatial synchrony (Anderson & Sturtevant, 2011;James et al., 2015;Myers & Cory, 2013;Pureswaran et al., 2016).
In this paper, we use multi-year spatial genetic data, covering the extent of an ongoing SBW outbreak, to investigate the spatial processes involved in synchronous outbreak dynamics. Specifically, we investigate whether outbreaking populations are synchronized as a result of (a) exposure to a common regional disturbance (i.e., the Moran effect, Moran, 1953;Royama et al., 2005) resulting in demographically independent populations and thus, high levels of population genetic differentiation (Box 1); or (b) dispersal of adults moths (i.e., the "epicenter hypothesis," Hardy et al., 1983;Peltonen et al., 2002;Williams & Liebhold, 2000) leading to low genetic differentiation among populations (Box 1). We also assess how the relative support for these two hypotheses evolved over a 4-year period. Distinguishing between the epicenter and Moran hypotheses is critical for large-scale forest management strategies against the SBW in Canada and the United States (Pureswaran et al., 2016).

| Study area
The study was conducted in the boreal and mixed-boreal forest (Rowe, 1972) in Quebec, Canada (398,000 km 2 , Figure 1). In 2006, a new outbreak was detected on the north shore of the Saint Lawrence River in Quebec (Bouchard & Auger, 2014). Since then, the area affected has increased to >8.2 million ha in Quebec (Ministère des Forêts, de la Faune et des Parcs [MFFP], 2018) and is currently moving toward other jurisdictions (e.g., New Brunswick and Maine, where larvae densities are still low) to the south. Spruce budworm larvae were collected over a 2-week period in June, from 25 locations in 2012 (n = 527), 14 locations in 2013 (n = 420), 17 locations in 2014 (n = 260), and 10 locations in 2015 (n = 163). In 2012, sites were selected to cover all the outbreak patches. Not all sites were identical from one year to the next. Some sites were discarded due to low larvae density or trouble accessing the site, but close (i.e., <10 km) replacement sites were selected when possible. When substitute sites were selected, we considered the original and the substitute site to be a single site through time (Table S1).
Each year, we sampled only larvae (no moths) from all defoliated zones to ensure that all individuals were associated with their site and the possibility of migrants from outside the study area would not affect the results. Many sites were sampled successively in all years, whereas some were sampled for only a single year ( Figure 1).
Larvae were collected on live foliage from branch tips (Dobesberger & Lim, 1983) on both spruce and fir when they were both present at

| Sequencing
All DNA samples were prepared for genotyping-by-sequencing

| Filtering SNP loci
SNPs with a minor allele frequency (MAF) <5% were removed to exclude putative sequencing errors and keep only the most informative SNPs (Marees et al., 2018). Similarly, SNPs in high linkage disequilibrium (LD) at a threshold of r 2 ≥ .2 were discarded to remove highly correlated variants that add minimal extra information and could overly influence some methods (Price et al., 2008;Zou, Lee, Knowles, & Wright, 2010), using the snpgdsLDpruning function of the SNPRelate package (Zheng et al., 2012) in R (R Core Team, 2017). SNPs showing deviation from expected Hardy-Weinberg equilibrium (HWE) in more than 15% of the sites were also removed as deviation from HWE can be indicative of genotyping errors (Anderson, Epperson, et al., 2010;Anderson, Pettersson, et al., 2010), null alleles (Brookfield, 1996), or selection (Wittke- Thompson, Pluzhnikov, & Cox, 2005). HWE was calculated using the hw.test function of the pegas package in R (Paradis, 2010) and using a Bonferroni correction for multiple comparisons. Finally, as our aim was to quantify the neutral evolutionary process of gene flow, we removed all SNPs identified as potentially under selection (Beaumont & Nichols, 1996) using the pcadapt function of the pcadapt package in R (Luu, Bazin, & Blum, 2017).

| Genetic diversity
For each site and for each year, we calculated observed (Ho) and expected (He, heterozygosity expected under Hardy-Weinberg equilibrium that accounts for both the number and the evenness of alleles) heterozygosity, rarefied allelic richness (Ar, El Mousadik & Petit, 1996), inbreeding coefficient (Fis), and total number of alleles (n.all) using the hierfstat R package (Goudet & Jombart, 2015). The degree of structuring between subpopulations (Fst) was computed within each year also using hierfstat.

| Inter-individual genetic distances
We calculated inter-individual genetic distances using principal components analysis (PCA). We first created multiple principal components (PC) using a matrix of allele occurrence (0, 1, or 2) using adegenet (Jombart, 2008) and then derived a distance matrix from the Euclidean distances between individuals in the multidimensional space created by the first 64 PC axes (Shirk, Landguth, & Cushman, 2017).

| Spatio-temporal genetic variation
To examine the effects of space (sampling sites) and time (year of sampling) on patterns of genetic variation, we conducted a permutation-based multivariate analysis of variance using the function adonis of the vegan package (Oksanen et al., 2017) in R. This method partitions sum of squares for distance matrices in a manner similar to AMOVA, but allows for both nested and crossed factors.
We tested for the effects of space (sampling sites) and time (

| Clustering
If populations are not connected, their growth will be independent as it does not rely on dispersal from other populations. In this case, we expect individuals to cluster into genetic groups that correspond to geographic provenance. We searched for genetic groups using discriminant analysis of principal components (DAPC) implemented in the adegenet (Jombart, 2008) package in R. DAPC maximizes differences among clusters while minimizing variation within. DAPC does not rely on a particular population genetic model, such as Hardy-Weinberg equilibrium, which is unrealistic for outbreaking populations (Whitlock, 1992). For each year, we applied the function find.clusters to determine the number of potential clusters. Minimization of a Bayesian information criterion (BIC) was used to identify the most probable number of clusters (K) present in the data. DAPC provides membership probabilities to these clusters for each individual, which we examined for geographic structure.

| Isolation by distance
If populations are connected through dispersal, then the genetic similarity between two populations is a function of the geographical distance between them. Consequently, genetic and geographic distances are expected to be correlated (i.e., isolation by distance, IBD; Wright, 1943

| Cryptic spatial structure
When populations exchange individuals, they tend to become genetically similar. The integration of geographic and genetic information can improve our ability to identify weakly differentiated populations and can provide accurate spatial locations of cryptic clusters or genetic barriers (Storfer et al., 2007). Given the weak overall structure (i.e., clusters and IBD; see below), we also tested for cryptic spatial genetic structure within each year using spatial principal component analysis (sPCA ;Jombart, Devillard, Dufour, & Pontier, 2008). This spatially explicit multivariate method employs Moran's index (I) of spatial autocorrelation (Moran, 1948) to detect global structures . We used the spca function implemented in the adegenet ) R package.
We used the inverse distance method for weighting connectivity in the network, given that: (a) Sampling sites were unevenly spread over the study area; (b) we had no a priori hypothesis about their connectivity. Significance was assessed using permutation test (n = 9,999) . The individuals' scores of the first principal component were geographically mapped and interpolated to reveal spatial patterns of interest.

| Genotyping
Sequence processing through the fast-GBS pipeline (Torkamaneh et al., 2017)  Most SNPs (73,489; 99.4%) had at least one missing genotype which was then imputed (mean fraction of missing genotype per SNP ± SD = 0.17 ± 0.15; range = 0-0.49; Figure S1) and 0.7% (480) of imputed SNPs were removed when filtering for R 2 . Many SNPs (69,045; 94%) were discarded when filtering for MAF and LD. Of the remaining SNPs, 4.1% (182) deviated from HWE in more than 15% of the sampling sites. About 16% (691) of the remaining SNPs were detected as potentially under selection and removed. In total 3,562 SNPs met our strict selection criteria and were retained for final analysis.
TA B L E 1 Annual summary of sampling sites. Annual (±SD) sample size (n), observed heterozygosity (Ho), expected heterozygosity (He), allelic richness (Ar), total number of alleles (n.all), and inbreeding coefficient (Fis) averaged over all sites of a given year.  Figure S2). Global Fst remained low for all years examined (0.002-0.0046; Table 1). Detailed information per year and per sampling site can be found in the Supporting Information (Table S1).
We found that He varied spatially and temporally (Figure 2). In 2012, western sites showed low He values while eastern sites showed a mix between high and low He values (Figure 2a). From 2013 to 2015, He was higher and more homogeneously distributed (Figure 2a-d).

| Spatio-temporal genetic variation partitioning
Using a permutation-based multivariate analysis of variance, we found a significant interaction effect among years and sites (F 25, 1,162 = 1.32, p < 10 -4 ; Table 2) on spruce budworm genetic variation. The rarefied bootstrap approach showed that with a standardized number of sites per year and number of individuals per site, the effect of the year and the site were significant in 100% of the 9,999 replications. The effect of the interaction was significant in 70% of the replications. This indicates that the processes generating spatial  TA B L E 2 Permutation-based multivariate analysis of variance to determine the percentage of variance explained by the effects of sampling sites, year of sampling and their interaction on the matrix of PCA-based genetic distance. Significance was assessed using 9,999 permutations genetic structure were dynamic, rather than static, over the four years we analyzed. Consequently, analyses were undertaken for each year separately (Figures 2, 4, and 5).
The two clusters initially identified in 2012 were no longer present from 2013 to 2015; instead, K = 1 had the greatest support ( Figure   S3). We found some evidence for geographic structure within the that had been sexed, we verified that the clustering was not based on sex (not shown).

| Isolation by distance
For all years examined, we found no evidence for significant individual-level IBD (all p = 1, Figure 4). The point density for 2012 showed two clusters of individuals with the same level of genetic differentiation, suggesting the presence of two populations that seemed to be genetically distinct (Figure 4a), which supports our clustering result described above. These clusters were no longer present from 2013 to 2015 (Figure 4b-d) and the variance of the genetic distance decreased, suggesting a genetic homogenization as the outbreak progressed.

| Cryptic spatial structure
We identified significant global cryptic spatial structure for each year (all p ≤ .01). However, the first positive eigenvalue, which represents global spatial genetic structure, decreased in magnitude from 2012 to 2015 compared to the other eigenvalues ( Figure S4), indicating a genetic homogenization over the years. The scores of the first positive eigenvalue have been interpolated and displayed on the area map ( Figure 5).
In 2012, our results regarding global structure indicated that individuals belonged to two genetically homogeneous clusters, one large cluster distributed all over the study area, and a second one only present at the northeast (Figure 5a). Individuals on the south shore of the Saint Lawrence River belonged to the more extensive genetic cluster and were different from the nearest individuals of the north shore. In 2013 (Figure 5b), we found clinal variation from west to east, with the notable exception of a group of individuals at the east that were similar to some western individuals. In 2014, the first positive eigenvalue revealed a complex pattern. Two genetic clusters were found with no clear geographical delimitation (Figure 5c).
One cluster was spread all over the study area while the smaller one showed a patchy distribution, with most of its individuals located in the center and east of the study area. Individuals on the south shore of the Saint Lawrence River were assigned to both clusters. The pattern found in 2015 was similar to that of 2014 ( Figure 5d).

| D ISCUSS I ON
Spatial synchrony is a fundamental but poorly understood, component of spatial population dynamics. Regionally, synchronous population fluctuations can be caused by dispersal or spatially correlated environmental conditions (Moran, 1953;Peltonen et al., 2002;Ranta, Kaitala, Lindstrom, & Helle, 1997;Ranta, Kaitala, Lindstrom, & Linden, 1995;Royama, 1984), although in general, we do not know the relative importance of each of these factors and how they vary through space and time (Liebhold et al., 2004).
Distinguishing these mechanisms and their effects on synchrony can help us to better understand spatial population dynamics, design conservation, and management strategies, and predict climate change impacts.
In 2006, a new SBW outbreak was detected on the north shore of the Saint Lawrence River that has since spread to over 8 million hectares in size. Using 4 years of genetic data covering the majority of the outbreak area (i.e., 398,000 km 2 ), we quantified temporal changes in spruce budworm spatial genetic structure and estimated gene flow through space and time. Our goal was to use spatial genetic information to better understand the relative importance of dispersal to spatial outbreak synchrony (Box 1) and to contribute to improved budworm management. We found evidence for fast genetic admixture, long-distance dispersal, and increases in genetic diversity. Together, these findings suggest a more important role of dispersal relative to autocorrelated environmental variation in the spatial synchrony of this species during an outbreak.

| Spatio-temporal connectivity in SBW
Disentangling the effects of epicenter and Moran processes on spatially synchronous SBW population dynamics is challenging because both processes can lead to similar genetic patterns when the outbreak is at or near its peak (Box 1). We found greater support for the epicenter hypothesis for the period covered by this study. In 2012, a single genetic cluster was found over the entire study area whereas a second one was restricted to a smaller region in the northeast, overlapping with the first cluster (Figures 3-5). We interpret these results to indicate that an isolated population, possibly the legacy of the previous outbreak collapse (James et al., 2015) (i.e., the larger cluster), expanded to encompass a second population (i.e., the second, smaller cluster). This process of an initial isolated population expanding via dispersal fits the pattern expected from an epicentric population dynamic (Box 1).
We cannot entirely reject the possibility that the first cluster may have been present before the outbreak and the small cluster represents immigrants from outside the study area. However, we collected samples from all defoliation zones (Figure 1) (Brown, 1970). That is, defoliation was first observed in the western part of Quebec, further indicating that dispersal from this area to the east may account for the observed topological complexity in spatial genetic structure. If the

| Long-distance dispersal
Rapid change in SBW genetic composition on the south shore between 2012 and 2014 indicates long-distance dispersal and successful establishment; that is, the eggs laid by dispersing females successfully hatched ( Figure 5). Previous studies have shown that SBW moths can disperse up to 20 km with a maximum recorded passive dispersal distance of 450 km (Greenbank et al., 1980). More recently, Boulanger et al. (2017) documented a mass dispersal over more than 200 km in 2013 from the north to the south shore of the Saint Lawrence River using weather surveillance radar data.
Although our ability to infer source populations and dispersal capacity is somewhat constrained by the limited genetic structure we observed (Muirhead et al., 2008), we have demonstrated for the first time that long-distance dispersal events result in successful establishment, and hence can be considered as effective dispersal.
Long-distance dispersal is common in Lepidoptera (Showers, 1997) and has a disproportionately high influence on gene flow and genetic structure (Clobert, Baguette, Benton, Bullock, & Ducatez, 2012;Jordano, 2017). It can connect disparate populations, allowing for genetic connectivity and range expansion (Baguette & Schtickzelle, 2006;Ronce, 2007;Trakhtenbrot, Nathan, Perry, & Richardson, 2005). Comparative studies suggest that species that can disperse farther tend to be synchronized over larger areas (Paradis, Baillie, Sutherland, & Gregory, 1999;Sutcliffe, Thomas, & Moss, 1996). In SBW, several long-distance mass exodus flights of millions of individuals have been observed (Boulanger et al., 2017;Dickison, 1990;Greenbank et al., 1980;Sturtevant et al., 2013). Such events have the potential to initiate new epicenters (Clark, 1979) and to synchronize the dynamics of different SBW populations over large geographic areas (Muenkemueller & Johst, 2008;Peltonen et al., 2002). In their study, Bouchard, Régnière, and Therrien (2017) suggested that dispersal may play a prevalent role in SBW outbreak synchrony once outbreak levels have been reached. Through the growing phase of the outbreak, long-distance dispersal events may have contributed to the observed genetic admixture and may still be contributing to the spread of the outbreak over a large territory in Quebec and adjacent provinces and U.S. states (e.g., New Brunswick and Maine).

| The challenge of cyclic populations
The application of population genetic approaches to the study of cyclic species is challenging because of frequent deviations from theoretical predictions due to highly variable population dynamics and dependence on ecological context (James et al., 2015). The observed decline in spatial genetic structure through time with outbreak spread fits well with the predictions of James et al. (2015) that spatial genetic structure decreases as the outbreak spreads and connectivity increases. These results indicate that temporal approaches are needed to characterize the role of population periodicity on the spatial patterns in neutral genetic variation (Box 1).
Spatial patterns of genetic diversity are the result of multiple factors that interact through space and time. Molecular studies usually present a single snap-shot description of spatial genetic structure, assuming temporal stability (Draheim et al., 2018;Tessier & Bernatchez, 1999). It is increasingly recognized that temporal aspects matter in population genetics but also in landscape genetics studies (Anderson, Epperson, et al., 2010;Anderson, Pettersson, et al., 2010;Martensen, Saura, & Fortin, 2017;Skoglund, Sjodin, Skoglund, Lascoux, & Jakobsson, 2014). However, the utility of temporal approaches in molecular studies of wild populations has mostly been limited to the comparison of historical and contemporary samples (Ruggeri et al., 2012). We have demonstrated here that temporal sampling can be used to identify the relative impor-  (Fahrig, 2003).

| Conclusion
Through novel spatio-temporal analysis of genetic data, we found support for the epicenter hypothesis as the central driver of synchronous SBW dynamics in Quebec. We also found evidence for long-distance dispersal (>140 km), which indicates that SBW moths can not only travel large distances (e.g., Greenbank et al., 1980), but can also successfully reproduce at landing sites. Knowledge of the importance of effective dispersal to outbreak synchrony is essential to the development and implementation of "early intervention" forest management strategies (Régnière et al., 2001) that aim to mitigate forest losses due to defoliation.
In Quebec, SBW populations are currently well connected and exhibit genetic panmixia. Such panmixia poses a challenge to forest managers seeking to contain the spread of SBW outbreaks from Quebec into other areas, such as Atlantic Canada. Early intervention strategies (Pureswaran et al., 2016) entail suppressing global population growth by finding and treating emerging local "hot spots." One of the key factors contributing to hot spots in currently unaffected areas is moths' dispersal from Quebec.
Using genetic data, our study further confirms that SBW moths can disperse very long distances (e.g., Boulanger et al., 2017;Greenbank et al., 1980). In addition, we also demonstrate that this dispersal contributes to local population growth; that is, dispersal is "effective." However, it remains to be seen whether the demographic impact of dispersers can overwhelm control efforts in areas, especially in relatively low density areas where populations have yet to establish. Characterization of dispersal and, in particular, the frequency distribution of the dispersal distances, could help to better delineate the range and distribution of dispersing moths throughout a region, which could help to guide survey efforts for both population studies and control efforts.
Our ability to distinguish between different drivers of outbreak synchrony will vary depending on the characteristics of the species being studied. For example, our approach may be sensitive to species-specific factors such as effective population size, generation time, dispersal capacity, outbreak frequency, and landscape heterogeneity, as all of these factors influence the spatial distribution of genetic variation (Gauffre et al., 2015;Landguth et al., 2010;Row, Wilson, & Murray, 2016). Further exploration of the temporal dynamics of spatial genetic structure during population outbreaks under different contexts remains a promising avenue for future research.
Simulation-based approaches using spatially explicit demo-genetic models (e.g., Nemo, Guillaume & Rougemont, 2006;or CDMetaPOP, Landguth, Bearlin, Day, & Dunham, 2017) hold great promise to isolate and quantify the relative effects of these different factors on the development of spatial genetic structure and spatial synchrony, and to refine our understanding of what drives these large-scale spatial ecological phenomena.

ACK N OWLED G EM ENTS
We thank Olivier Pontbriand-Paré and the many other student vol-

CO N FLI C T O F I NTE R E S T
None declared.