Abstract Spatial synchrony and cycles are common features of forest insect pests, but are often studied as separate phenomenon. Using time series of timber damage caused by Dendroctonus frontalis Zimmermann (Coleoptera: Curculionidae) (southern pine beetle) in 10 states within the southern United States, this study examines synchrony in D. frontalis abundance, the synchronizing effects of temperature extremes, and the evidence for shared cycles among state populations. Cross-correlation and cluster analyses are used to quantify synchrony across a range of geographic distances and to identify groups of states with synchronous dynamics. Similar techniques are used to quantify spatial synchrony in temperature extremes and to examine their relationship to D. frontalis fluctuations. Cross-wavelet analysis is then used to examine pairs of time series for shared cycles. These analyses suggest there is substantial synchrony among states in D. frontalis fluctuations, and there are regional groups of states with similar dynamics. Synchrony in D. frontalis fluctuations also appears related to spatial synchrony in summer and winter temperature extremes. The cross-wavelet results suggest that D. frontalis dynamics may differ among regions and are not stationary. Significant oscillations were present in some states over certain time intervals, suggesting an endogenous feedback mechanism. Management of D. frontalis outbreaks could potentially benefit from a multistate regional approach because populations are synchronous on this level. Extreme summer temperatures are likely to become the most important synchronizing agent due to climate change. Spatial synchrony is a common feature of the dynamics of many forest insect pests, with population levels or growth rates often correlated across distances of several hundred kilometer. Examples of this phenomenon include the autumnal moth (Epirrita autumnata (Borkhausen) [Lepidoptera: Geometridae]), spruce budworm (Choristoneura fumiferana (Clemens) [Lepidoptera: Tortricidae]), western spruce budworm (Choristoneura occidentalis (Walsingham) [Lepidoptera: Tortricidae]), larch bud moth (Zeiraphera diniana (Hübner) [Lepidoptera: Tortricidae]), forest tent caterpillar (Malacosoma disstria Hübner [Lepidoptera: Lasiocampidae]), mountain pine beetle (Dendroctonus ponderosae) Hopkins [Coleoptera: Curculionidae]), and gypsy moth (Lymantria dispar (L.) [Lepidoptera: Erebidae]) (Myers 1998, Williams and Liebhold 2000, Peltonen et al. 2002, Aukema et al. 2006, Klemola et al. 2006, Price et al. 2006). One commonly observed pattern are regional clusters in which the dynamics are more tightly synchronous. Synchrony on larger scales is often attributed to the Moran effect, in which an exogenous influence like weather affects the dynamics across large spatial scales (Moran 1953). Weather variables such as precipitation and temperature are typically correlated across large distances, which should be synchronizing, but this tendency may be opposed by local differences in population dynamics, or periods of asynchronous weather (Williams and Liebhold 2000, Peltonen et al. 2002, Allstadt et al. 2015). Dispersal is another potential synchronizing factor. Some theoretical studies have found that dispersal can generate a pattern of decreasing synchrony with distance that resembles empirical patterns (Ranta et al. 1995, 1998; Williams and Liebhold 2000), although this result is not universal (Abbott and Dwyer 2008). Peltonen et al. (2002) examined six species with widely varying dispersal abilities, and found similar levels of spatial synchrony, suggesting that the Moran effect is more important in these systems than dispersal. Haynes et al. (2013) statistically compared the effects of distance and weather on synchrony in gypsy moth, and found that synchrony in precipitation was sufficient to explain population synchrony in this system. This appears to be the only study where the explanatory power of distance versus weather were statistically compared. Population cycles occur in many forest insect pests, especially Lepidoptera. Systems where these cycles have been extensively studied include the western tent caterpillar (Malacosoma californicum pluviale (Dyar) ), the autumnal moth, and the larch budmoth (Myers and Cory 2013). Natural enemies (parasitoids) generate delayed density-dependence in all three systems, and are likely the main cause of the cycles, but there can also be declines in adult fecundity. Although the gypsy moth also shows population cycles generated by interaction with a viral pathogen, there are intervals where no cycles are apparent (Allstadt et al. 2013). Similar dynamics were observed in a model combining the viral pathogen with a generalist predator, suggesting their combined effects were sufficient to explain this pattern, rather than environmental changes. However, a recent warming trend is thought to have extinguished outbreak cycles in the larch budmoth, cycles that had persisted for 1,200 yr (Esper et al. 2007). The southern pine beetle, Dendroctonus frontalis Zimmermann (Coleoptera: Curculionidae), is another economically important pest species whose populations undergo dramatic fluctuations. A number of studies have examined D. frontalis dynamics at different spatial and temporal scales. Turchin et al. (1991) examined a long-term record of D. frontalis infestations (spots) in East Texas and found cyclic dynamics and delayed density dependence, as did a study that directly measured the impact of natural enemies (Turchin et al. 1999). A subsequent analysis using additional years of data (Friedenberg et al. 2008) suggested both density dependence and weather variables were important, but the fitted models were not cyclic. Martinson et al. (2013) examined a spatially extensive but shorter-term data set from a south wide trapping program (Billings and Upton 2010), in which traps are deployed over 4 wk in the spring to catch D. frontalis and a common predator, Thanasimus dubius (Fabricius) (Coleoptera: Cleridae). These authors found evidence for alternate equilibrium points (high vs very low densities) at the scale of trapping locations. Weed et al. (2016) fitted discrete-time predator-prey models to these same data, and found evidence for density dependence and a predator effect, but with no time delays. They also reported significant spatial autocorrelation in D. frontalis and T. dubius abundance to a distance of several hundred kilometer, which they attribute to exogenous factors like weather. Similar levels of spatial synchrony in abundance were found by Okland et al. (2005), using a 39-yr record of county-level outbreak data. Despite this range of studies, however, the mechanism generating synchrony remains uncertain, and the general prevalence of cycles across the range of D. frontalis is unknown. Although there are spatially extensive trapping data across the range, these are relatively short in duration, making long-term cycles difficult to observe. Using time series of timber damage caused by the southern pine beetle (D. frontalis) in 10 states within the southern United States (Price et al. 1998, Pye et al. 2011), this study examines spatial synchrony in D. frontalis abundance, the synchronizing effects of temperature extremes, and the evidence for shared oscillations among state populations. These time series extend farther back in time than most previous studies, and include several large fluctuations in D. frontalis abundance. One issue with analyzing these long-term data sets is that D. frontalis dynamics may have changed over time (Clarke et al. 2016), possibly driven by changes in stand composition and management practices. For this reason, I relied on nonparametric tests and time series methods that allow for changes in the dynamics over time. Cross-correlation and cluster analyses are used to quantify synchrony across a range of geographic distances and to identify groups of states with more synchronous dynamics. Similar techniques are used to quantify spatial synchrony in weather variables thought important in D. frontalis dynamics and to examine their relationship to synchrony in D. frontalis populations. Cross-wavelet analysis is then used to examine pairs of time series for shared periodic components. This technique does not assume that the time series are stationary, and can identify changes in the dynamics through time. Materials and methods Data Sources Data on D. frontalis damage were obtained from a state-level compilation of timber damage through 2004 in the Southeastern United States (Price et al. 1998, Pye et al. 2011). Pulpwood (cords) and sawlog (MBF = thousand board foot) volumes were estimated for each state and year using spot (infestation) counts, ground checks of spots, and other available information (Price et al. 1998, Pye et al. 2011). To obtain an overall measure of timber damage, pulpwood cords were converted to MBF (1 MBF = 1.536 cords) and added to the sawlog volume. Out of 12 states, 10 had sufficiently long records for time series analysis. These will be denoted in the remainder of the paper by their postal codes (AL = Alabama, AR = Arkansas, FL = Florida, GA = Georgia, MS = Mississippi, LA = Louisiana, NC = North Carolina, SC = South Carolina, TN = Tennessee, TX = Texas). The two states with insufficient data were Kentucky and Virginia. The longest records available were for TX (1960–2004) and NC (1962–2004), while the other states began in the early 1970s. As Price et al. (1998) discuss, data collection methods differed among states and through time, likely affecting the estimates of timber damage to some extent. Populations of D. frontalis can undergo enormous fluctuations in abundance, however, and changes of this magnitude should be reflected in timber damage despite differences in methodology. Another question is whether timber damage is a useful proxy for D. frontalis abundance, which is often quantified using the number of D. frontalis infestations (spots) in an area. To examine this issue, a long-term record of spots was compared with timber damage in East Texas. Spot records were obtained from the Texas Forest Service, College Station, TX. A measure of the geographic distance between states was also needed for several of the statistical analyses, which should reflect locations where D. frontalis activity was historically high. Unfortunately, the timber damage data were calculated at a state level and not geographically referenced. As a proxy for locations of previous activity, I identified counties where the current hazard was moderate or high, using the rating system developed by the Forest Health Technology Enterprise Team (FHTET), USDA Forest Service (http://www.fs.fed.us/foresthealth/technology/nidrm_spb.shtml). Counties were ranked by the percentage of area with moderate or high hazard, and the top three counties for each state identified. These counties typically had large areas of host pines. The centroid of these three counties was then calculated, with the distance between centroids used as a measure of the geographic distance between states. Similar results were obtained using the geographic centers of each state as the centroid, so the analyses did not appear sensitive to this assumption. Previous studies have identified temperature extremes as a factor in D. frontalis growth rates, such as hot summer and winter minimum temperatures (McClelland and Hain 1979, Ungerer et al. 1999, Tran et al. 2007, Friedenberg et al. 2008). Given these findings, it seems plausible that temperature extremes could be a synchronizing agent across states for D. frontalis dynamics. To evaluate this possibility, mean monthly maximum and minimum temperatures for the high-risk counties were obtained from the PRISM Climate Group (http://www.prism.oregonstate.edu/). See the study by Daly et al. (2008) for details of how these values are derived from weather station data and factors including elevation and topography. Four temperature variables were chosen for further analysis: mean minimum temperature in December and January, and mean maximum temperature in July and August. The values for the three counties in each state were averaged. The temperature data spanned the interval 1970–2005, approximately matching the timber damage records. Cross-Correlation Analysis As a simple measure of synchrony among states in damage, I calculated the cross-correlation function across a range of time lags for all possible pairs of states (Ranta et al. 1995, Koenig 1999). The damage data were log-transformed (base 10) before analysis. To deal with zero damage levels on some dates, 10 was added to each observation before transformation. The time series did not appear to be stationary, and so the observations were differenced before calculating the cross-correlation function (Chatfield 1989, Cryer and Chan 2008). Note that differencing of the log-transformed data converts them to growth rates, which means the cross-correlation examines synchrony in growth rates rather than damage levels. The lag 0 correlation was the largest one for most pairs of states, and was selected for all subsequent analyses. These computations were carried out using the ccf function in R (R Core Team 2016). A P value was calculated for each cross-correlation between states, under the assumption that the cross-correlation is N(0,1/n)under the null hypothesis. This assumption is questionable for some types of time series, and so these P values should be viewed with caution (Chatfield 1989, Buonaccorsi et al. 2001, Cryer and Chan 2008). Similar methods were used in calculating the cross-correlation (lag 0) for TX spot numbers versus damage levels, to determine whether these two measures of D. frontalis abundance were related, and cross-correlation (lag 0) among states in mean minimum January temperature, as well as the other three weather variables. The weather cross-correlations are a measure of the synchrony in these variables across states. Preliminary analyses found that the cross-correlations for minimum December and January temperatures were very similar, and so subsequent analyses only used the January data. Cluster Analysis Hierarchical cluster analysis was used to identify potential groups of synchronous states (Ranta et al. 1995). The matrix of cross-correlation values was first converted to a dissimilarity matrix by calculating 1−r for each value, where r is the cross-correlation. The clusters were then found using Ward’s method (Johnson and Wichern 1998) as implemented in the R function hclust. Mantel Tests A Mantel test was used to examine the relationship between the cross-correlation in timber damage among states versus geographic distance (Koenig 1999). One matrix for the test contained the cross-correlation in damage among states, while the second was geographic distance (km). This procedure was carried out using the mantel function in the R package ecodist (Goslee and Urban 2007). Mantel tests were also used to examine the relationship between the cross-correlations in timber damage versus cross-correlations in minimum January temperature, as well as the maximum July and August temperatures. These analyses examine if weather synchrony contributes to synchrony in D. frontalis damage. Partial Mantel tests were then conducted for the cross-correlation in damage versus geographic distance, controlling for weather. If this reduces the effect of geographic distance, it suggests that weather contributes to synchrony in damage levels. Maximum August temperature was not used in this analysis because it appears unrelated to synchrony in timber damage. Cross-Wavelet Analysis Wavelet analysis is a statistical technique for identifying periodic components in time series, especially non-stationary series where these components may vary over time (Torrence and Compo 1998, Cazelles et al. 2008). Wavelets are oscillatory functions that are localized in time and whose width and period can be varied. A wavelet analysis compares these functions with a time series, and partitions its fluctuations into components with different periods at many locations within the time series. For example, it can determine whether oscillations of a certain period occur in a time series, the time interval over which they occur, and whether the period changes over time. Cross-wavelet analysis is an extension of this procedure for pairs of time series, and is used to identify periodic components shared between them (Grinsted et al. 2004). The R package biwavelet (Gouhier 2014) was used to carry out a cross-wavelet analysis of the timber damage data for each pair of states, using the Morlet wavelet. Both time series were scaled to have zero mean and unit variance before analysis. The output is a graph where warmer colors indicate more powerful shared periods between the two time series (see Figs. 2–4). Areas where the shared periodic components are significant at the 0.05 level are enclosed with a black line, with an AR(1) process for the two time series as the null hypothesis (Torrence and Compo 1998, Grinsted et al. 2004). Large areas of significance are taken as evidence a particular periodic component is present in the time series. The arrows within the figure indicate the phase of the two time series. An arrow pointing to the right indicates that the fluctuations are in phase, which was the main outcome in these analyses. The white line indicates the cone of influence. Areas below the line indicate regions where the power may be reduced because of edge effects in the wavelet analysis, which are greater for longer-period components (Torrence and Campo 1998). Although these time series are relatively short for wavelet analysis, they are within the recommended limits of length and period (Cazelles et al. 2008). Fig. 1. View largeDownload slide Cross-correlations (lag 0) in timber damage versus geographic distance (km) between states (see text for details). The line was generated using the R function lowess. Fig. 1. View largeDownload slide Cross-correlations (lag 0) in timber damage versus geographic distance (km) between states (see text for details). The line was generated using the R function lowess. Fig. 2. View largeDownload slide (A) Scaled timber damage levels versus year for AR and TX. (B) Cross-wavelet analysis showing the period of oscillation (years) on the left y-axis, while the right one indicates the shared power of the two time series. Areas where the shared power was significant are enclosed with a black line. Arrows pointing to the right indicate the fluctuations are in phase across the two time series. The white line indicates the cone of influence, below which power may be reduced from edge effects in the wavelet analysis. Fig. 2. View largeDownload slide (A) Scaled timber damage levels versus year for AR and TX. (B) Cross-wavelet analysis showing the period of oscillation (years) on the left y-axis, while the right one indicates the shared power of the two time series. Areas where the shared power was significant are enclosed with a black line. Arrows pointing to the right indicate the fluctuations are in phase across the two time series. The white line indicates the cone of influence, below which power may be reduced from edge effects in the wavelet analysis. Fig. 3. View largeDownload slide (A) Scaled timber damage levels versus year for AL and SC. (B) Cross-wavelet analysis showing the period of oscillation on the left y-axis, while the right one indicates the shared power of the two time series. See Fig. 2 for further details. Fig. 3. View largeDownload slide (A) Scaled timber damage levels versus year for AL and SC. (B) Cross-wavelet analysis showing the period of oscillation on the left y-axis, while the right one indicates the shared power of the two time series. See Fig. 2 for further details. Fig. 4. View largeDownload slide (A) Scaled timber damage levels versus year for NC and TN. (B) Cross-wavelet analysis showing the period of oscillation on the left y-axis, while the right one indicates the shared power of the two time series. See Fig. 2 for further details. Fig. 4. View largeDownload slide (A) Scaled timber damage levels versus year for NC and TN. (B) Cross-wavelet analysis showing the period of oscillation on the left y-axis, while the right one indicates the shared power of the two time series. See Fig. 2 for further details. Results Relationship Between Timber Damage and Spot Numbers The cross-correlation (lag 0) between timber damage and spot numbers was large and highly significant ( r=0.785,P<0.0001), suggesting that damage levels are a useful proxy of D. frontalis abundance as measured by spots. Synchrony in Timber Damage Between States The cross-correlation (lag 0) in timber damage was significant or highly significant in 16 of 45 possible pairs of states (Table 1). The largest correlations were often between pairs of adjacent states. A cluster analysis based on these correlations divided the states into three groups whose fluctuations were more synchronous. These were TX-LA-AR-MS, AL-GA-SC-FL, and NC-TN. Table 1. Cross-correlation (lag 0) between timber damage levels in 10 states, with P values TX LA AR MS AL GA SC NC TN FL 0.355 0.512 0.141 0.119 0.297 0.115 −0.013 −0.001 0.329 TX – 0.0416 0.0043 ns ns ns ns ns ns ns 186 302 449 648 1078 1234 1649 940 1007 0.379 0.416 0.180 0.131 0.190 −0.240 −0.333 0.036 LA – 0.0346 0.0187 ns ns ns ns ns ns 151 291 489 904 1056 1467 754 869 0.243 0.174 0.267 0.092 −0.096 −0.037 0.303 AR – ns ns ns ns ns ns ns 335 511 877 1016 1411 682 905 0.493 0.496 0.388 0.215 0.042 0.2824 MS – 0.0060 0.0058 0.0282 ns ns ns 199 633 794 1216 549 580 0.592 0.696 0.381 0.323 0.433 AL – 0.0008 <0.0001 0.0311 ns 0.0143 447 614 1040 437 394 0.671 0.316 0.271 0.487 GA – 0.0002 ns ns 0.0058 169 595 306 366 0.498 0.328 0.304 SC – 0.0042 ns ns 426 375 501 0.589 0.377 NC – 0.0010 0.0330 732 880 0.334 TN – ns 597 TX LA AR MS AL GA SC NC TN FL 0.355 0.512 0.141 0.119 0.297 0.115 −0.013 −0.001 0.329 TX – 0.0416 0.0043 ns ns ns ns ns ns ns 186 302 449 648 1078 1234 1649 940 1007 0.379 0.416 0.180 0.131 0.190 −0.240 −0.333 0.036 LA – 0.0346 0.0187 ns ns ns ns ns ns 151 291 489 904 1056 1467 754 869 0.243 0.174 0.267 0.092 −0.096 −0.037 0.303 AR – ns ns ns ns ns ns ns 335 511 877 1016 1411 682 905 0.493 0.496 0.388 0.215 0.042 0.2824 MS – 0.0060 0.0058 0.0282 ns ns ns 199 633 794 1216 549 580 0.592 0.696 0.381 0.323 0.433 AL – 0.0008 <0.0001 0.0311 ns 0.0143 447 614 1040 437 394 0.671 0.316 0.271 0.487 GA – 0.0002 ns ns 0.0058 169 595 306 366 0.498 0.328 0.304 SC – 0.0042 ns ns 426 375 501 0.589 0.377 NC – 0.0010 0.0330 732 880 0.334 TN – ns 597 The third entry in each cell is the geographic distance (km) between states (see text for details). ns (not significant). View Large Synchrony in Timber Damage Versus Distance and Weather A Mantel test relating the cross-correlation values with geographic distance between states was highly significant (Fig. 1, Table 2). The Mantel tests for timber damage versus weather were highly significant for two of three weather variables, the exception being maximum August temperature (Table 2). The values of the Mantel r were nearly as large for weather as for geographic distance. The partial Mantel tests for timber damage versus geographic distance, controlling for weather, showed smaller values of r when weather variables were included, and the effect of distance was no longer significant. Table 2. Mantel tests examining the relationships between the cross-correlation (lag 0) of timber damage, geographic distance, and the cross-correlation across states in three weather variables Variables Mantel r P value Timber damage vs geog. distance −0.557 0.0026 Timber damage vs min. Jan. temp. 0.536 0.0024 Timber damage vs max. July temp. 0.544 0.0040 Timber damage vs max. Aug. temp. 0.248 0.0644 Timber damage vs geog. distance | min. Jan. temp. −0.248 0.0858 Timber damage vs geog. distance | max. July temp. −0.212 0.1180 Timber damage vs geog. distance | min. Jan. + max. July temp. −0.184 0.1574 Variables Mantel r P value Timber damage vs geog. distance −0.557 0.0026 Timber damage vs min. Jan. temp. 0.536 0.0024 Timber damage vs max. July temp. 0.544 0.0040 Timber damage vs max. Aug. temp. 0.248 0.0644 Timber damage vs geog. distance | min. Jan. temp. −0.248 0.0858 Timber damage vs geog. distance | max. July temp. −0.212 0.1180 Timber damage vs geog. distance | min. Jan. + max. July temp. −0.184 0.1574 The last three entries are partial Mantel tests, examining the relationship between timber damage and geographic distance, given two weather variables (see text for details). View Large Shared Oscillations Among States The cross-wavelet analysis appeared to divide the states into three groups. The three most western states (TX, AR, and LA) showed significant shared oscillations with a period of 8–11 yr for much of the time series, then disappeared as timber damage fell to zero toward the end. The outcome for TX and AR is shown in Fig. 2, with the other two pairs of states showing similar patterns. A second group, consisting of AL, GA, SC, and possibly FL, showed a different pattern (Fig. 3). The significant area on the left of the graph was generated by a sharp collapse and rebound of damage levels, while the remainder had no significant areas. Another pattern occurred for TN and NC, with the two states showing a significant area of 3- to 4-yr oscillations early in the time series (Fig. 4). Pairs of states outside these groups showed relatively few significant areas. MS did not match with any group. Discussion The analyses presented here suggest there is substantial synchrony among states in D. frontalis populations, as measured by the cross-correlation values. This synchrony decays with the geographic distance between states, on a scale that is comparable with other forest insect pests (Peltonen et al. 2002, Klemola et al. 2006, Aukema et al. 2006), and with previous studies of D. frontalis (Okland et al. 2005, Weed et al. 2016) using other data sets. In addition, there appear to be groups of states where the population fluctuations are more synchronous, and have similar cross-wavelet spectra. These include a western group (TX-LA-AR), a coastal and southern group (AL-GA-SC-FL), and a northern one (NC-TN). The dynamics of MS were anomalous, falling within the coastal and southern group according to cluster analysis, but no group using cross-wavelet analysis. What are the possible mechanisms underlying the pattern of spatial synchrony in D. frontalis populations? Weather variables like temperature are often hypothesized to drive synchrony at this level, through the Moran effect (Moran 1953). Evidence for this effect was found in D. frontalis for two of three temperature variables, involving summer and winter extremes. The effect of geographic distance on population synchrony was also reduced after accounting for these same weather variables. This argues for some level of population synchronization through weather across states, a pattern also seen (but to a greater degree) in the gypsy moth (Haynes et al. 2013). A specific example of a synchronizing event was likely a period of extremely low temperatures in the winter of 1976–1977 for the more eastern states, which resulted in severe brood mortality (McClelland and Hain 1979). Populations were already in decline at this point, but this event likely exacerbated it (see Figs. 3 and 4). Although the analyses presented here suggest weather extremes contribute to synchrony in D. frontalis at the state level, they do not preclude some role for dispersal. Dispersal rates have been directly measured for D. frontalis and its predator T. dubius (Turchin and Thoeny 1993; Cronin et al. 1999, 2000). These studies indicate dispersal distances on the order of 1–2 km per generation, which seems insufficient to synchronize the dynamics across states, even with multiple generations per year. Another possible synchronizing mechanism, however, is a combination of dispersal and high reproductive rates. Models of single-species or predator-prey systems with dispersal can show traveling waves whose velocity depends on both dispersal ability and reproduction (Murray 2002, Hsu et al. 2012). Given the high rates of population growth observed during D. frontalis outbreaks, this mechanism would amplify the speed at which an outbreak propagates through space. It could potentially be observed through detailed spatial mapping of D. frontalis abundance. If it were operating, one would expect to see a wavelike spread of local infestations moving faster than predicted by dispersal. It is also possible that there are some long-range dispersal events that were not detected through mark-recapture studies. Evidence for long-range dispersal comes from studies of genetic heterogeneity in D. frontalis (Schrey et al. 2008, 2011) using microsatellite markers. Populations are relatively homogeneous across multistate regions, with structure only emerging at larger scales, such as eastern versus western states (Schrey et al. 2011). The results from the cross-wavelet analysis may provide some insights into D. frontalis dynamics. One is that the dynamics do not appear stationary, and that different regions can apparently display different dynamics. For example, there is evidence for shared 8- to 10-yr oscillations in the TX-LA-AR group, but these disappeared toward the end of these time series, when no timber damage was recorded in all three states. The AL-SC-GA group shows a single enormous fluctuation in timber damage, but no other shared oscillations. The NC-TN group shows yet another pattern, an interval of 3- to 4-yr oscillations. Given the varied dynamics across regions and through time, it is not surprising that studies with different spatial and temporal windows have come to different conclusions with respect to the underlying dynamics (Turchin et al. 1991, 1999; Friedenberg et al. 2008; Martinson et al. 2013; Weed et al. 2016). Significant oscillations do appear present in some states over certain intervals, suggesting an endogenous feedback mechanism operating with a delay. This could include long-lived natural enemies such as T. dubius (Reeve 1997, 2000; Costa and Reeve 2012) or competitors such as cerambycids (Stephen 2011). There are several potential explanations for non-stationary behavior observed in this system. One would be changes through time in stand composition and management practices for D. frontalis, which have the goal of reducing the potential for outbreaks (Clarke et al. 2016). As these changes more fully took effect, the frequency of outbreaks has apparently decreased over time. Another is the existence of a low equilibrium point possibly maintained by interspecific competition, from which the system stochastically escapes (Martinson et al. 2013). This mechanism might be expected to generate outbreaks at irregular intervals, with potentially long periods at low density. Another explanation could involve natural enemies with a ratio-dependent functional response, which can in theory drive the prey species extinct (Arditi and Ginzburg 2012). The predator T. dubius has this kind of functional response (Reeve 1997), and models of the system can generate long periods of low D. frontalis density (Reeve and Turchin 2002). Another kind of non-stationary behavior could arise from complex interactions between various natural enemies and other sources of mortality, such as hypothesized in the gypsy moth (Allstadt et al. 2013). One management implication of the results presented here is the spatial scale of D. frontalis dynamics, including outbreaks. Both the cross-correlation and cross-wavelet analyses suggest that the dynamics of D. frontalis populations fall into three groups. If populations are problematic in one state within a group, then similar issues could be expected in other members of the group, which argues for a regional approach to D. frontalis management. Another is the effect of summer and winter temperature extremes, which have the potential to synchronize populations on large spatial scales. The extreme winter cold of 1976–1977 was one such event observable in these data. Analyses of recent temperature records suggest that extreme summer temperatures are becoming more common and affecting larger areas of the continental United States, as a result of climate change (Duffy and Tebaldi 2012, Abatzoglou and Barbero 2014). This suggests that summer temperatures could become the more important synchronizing agent in the future. Acknowledgments This study was supported by a cooperative agreement with the Southern Research Station, USDA Forest Service, and NSF DEB 1021203. I thank John Pye, Stephen Clarke, and James T. 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