Geometrid outbreak waves travel across Europe



  1. We show that the population ecology of the 9- to 10-year cyclic, broadleaf-defoliating winter moth (Operophtera brumata) and other early-season geometrids cannot be fully understood on a local scale unless population behaviour is known on a European scale.
  2. Qualitative and quantitative data on O. brumata outbreaks were obtained from published sources and previously unpublished material provided by authors of this article. Data cover six decades from the 1950s to the first decade of twenty-first century and most European countries, giving new information fundamental for the understanding of the population ecology of O. brumata.
  3. Analyses on epicentral, regional and continental scales show that in each decade, a wave of O. brumata outbreaks travelled across Europe.
  4. On average, the waves moved unidirectionally ESE–WNW, that is, toward the Scandes and the Atlantic. When one wave reached the Atlantic coast after 9–10 years, the next one started in East Europe to travel the same c. 3000 km distance.
  5. The average wave speed and wavelength was 330 km year−1 and 3135 km, respectively, the high speed being incongruous with sedentary geometrid populations.
  6. A mapping of the wave of the 1990s revealed that this wave travelled in a straight E–W direction. It therefore passed the Scandes diagonally first in the north on its way westward. Within the frame of the Scandes, this caused the illusion that the wave moved N–S. In analogy, outbreaks described previously as moving S–N or occurring contemporaneously along the Scandes were probably the result of continental-scale waves meeting the Scandes obliquely from the south or in parallel.
  7. In the steppe zone of eastern-most and south-east Europe, outbreaks of the winter moth did not participate in the waves. Here, broadleaved stands are small and widely separated. This makes the zone hostile to short-distance dispersal between O. brumata subpopulations and prevents synchronization within meta-populations.
  8. We hypothesize that hostile boundary models, involving reciprocal host–herbivore–enemy reactions at the transition between the steppe and the broadleaved forest zones, offer the best explanation to the origin of outbreak waves. These results have theoretical and practical implications and indicate that multidisciplinary, continentally coordinated studies are essential for an understanding of the spatio-temporal behaviour of cyclic animal populations.


During recent decades, spatio-temporal behaviour of cyclic populations has attracted increasing attention (Liebhold & Kamata 2000). The reason for this may be the shortcomings of local population models in revealing and explaining ecological processes (Ranta, Kaitala & Lindström 1997; Liebhold & Kamata 2000). Instead, spatio-temporal and gradient studies are advocated (Hansson 2003). Here, we highlight this position by analysing the spatio-temporal behaviour of cyclic geometrid populations on epicentral, regional and continental scales.

Cyclic population behaviour may be manifested as synchronized or non-synchronized fluctuations between disjunct populations. A third behaviour that has recently received much attention is travelling waves in populations of periodic species (e.g. Bjørnstad, Ims & Lambin 1999; Johnson, Bjørnstad & Liebhold 2004). Mostly, ‘travelling waves’ means that the population peak densities move in one main direction across space (Bjørnstad, Ims & Lambin 1999). Travelling waves have two characteristics, that is, the synchrony between outbreaks first declines with the distance then increases again as the distance travelled approaches one wavelength and, the synchrony remains as the distance between outbreaks increases perpendicular to the wave direction (Bjørnstad, Ims & Lambin 1999; Sherratt & Smith 2008).

The expression ‘travelling waves’ was used for the outbreak waves of the tortricid moth Zeiraphera diniana Gn. along the arc of the European Alps (Bjørnstad et al. 2002). Previously, wave behaviour has been named ‘moving outbreaks’ for outbreak waves of the geometrids the autumnal moth, Epirrita autumnata Bkh., and the winter moth, Operophtera brumata (L.), sweeping along the NNE–SSW stretching Scandinavian mountain chain (the Scandes) (Tenow 1972). That study is probably the first where a spatio-temporal behaviour of insect outbreaks is explicitly described as periodic moving outbreaks. ‘Moving outbreaks’, as a synonym for ‘travelling waves’, has also been used recently (Liebhold & Kamata 2000; Johnson, Bjørnstad & Liebhold 2004).

Travelling population waves have hitherto been found for a few, greatly different organism taxa (Liebhold, Koenig & Bjørnstad 2004). The first and one of the most renowned to be described is the peak occurrence of the Canadian lynx (Lynx canadensis Kerr) and its prey, the snowshoe hare (Lepus americanus Erxleh.) that travels every 9th and 10th year across North America (e.g. Elton & Nicholson 1942; Keith 1990; Ranta, Kaitala & Lindström 1997; Ranta, Lundberg & Kaitala 2006). Another example is the waves of ruffed grouse (Bonasa umbellus L.) occurrence, which travel across Canada with about the same periodicity as the hare-lynx waves (Williams 1954). In Europe, the 8- to 9-year cyclic population waves of Z. diniana are one of the most famous and analysed phenomena of its kind (e.g. Baltensweiler & Fischlin 1988; Johnson, Bjørnstad & Liebhold 2004; Büntgen et al. 2009). Among European mammals and birds, travelling waves have been demonstrated in the 3- to 4-year cyclic field vole (Microtus agrestis L.) (Lambin et al. 1998) and the 9- to 10-year cyclic red grouse (Lagopus l. scoticus L.) (Moss, Elston & Watson 2000).

Outbreaks and peaks (hereafter referred to as ‘outbreaks’) in early-season geometrid moths, mainly O. brumata, are associated with pedunculate oak (Quercus robur L.) (Fig. 1), but also with many other hosts, mostly within Rosaceae, for example, fruit trees, and birch (Betula spp.) in northern Europe (Wint 1983). In Scotland, in areas lacking broadleaved hosts, O. brumata has adapted to Sitka spruce (Picea sitchensis Bong) and Common heather (Calluna vulgaris L.) (Vanbergen et al. 2003). Operophtera brumata′s ubiquitous occurrence as a serious, polyphagous defoliator in Europe makes it convenient for a continental-scale study of its spatio-temporal population behaviour. Where its fluctuations have been investigated, O. brumata has appeared as a 9- to 10-year cyclic species in Fennoscandia (Hogstad 2005; Tenow et al. 2007) like E. autumnata (Neuvonen 1988).

Figure 1.

Distributions of Operophtera brumata, its prime host Quercus robur and reported outbreak localities (●) (updated from CAB International Distribution Maps of Plant Pests 1956; Mrkva 1969; Schaminée & Hennekens 2005). The great circle (18°N) parallel to the Atlantic coast = the Western baseline, the great circle perpendicular to it = the Southern baseline, both through Greenwich. Outbreak localities in the Netherlands and Hungary denoted (cf. Fig. 5). South-east of the indicated forest-steppe zone is the steppe zone and north-west of it are broadleaved and mixed needle and broadleaved forest zones (see Fig. S4).

The 9- to 10-year cyclic E. autumnata and O. brumata outbreaks in the Scandes have appeared in three main types: (i) outbreaks occurring contemporaneously all over the Scandes, (ii) moving from northern to southern Scandes or (iii) the reverse (Tenow 1972; Nilssen, Tenow & Bylund 2007). The O. brumata female moth has stunted wings and cannot fly, and the E. autumnata female, although winged, has a limited capacity to fly (Bylund 1995; Snäll et al. 2004). Neonate caterpillars of both species may balloon a few hundred metres (Edland 1971), under favourable conditions up to kilometres (Leggett et al. 2011). An advance of an outbreak front by successive invasions of migrants over the length of the Scandes (c. 1700 km) within a few years is unlikely (Tenow et al. 2007). Cyclicity and fluctuation synchrony should therefore have been imposed on a local or sub-regional scale and have been studied on these scales, (e.g. Bylund 1995; Riihimäki et al. 2006; Hagen et al. 2010). However, to understand the three outbreak types, we find that the population behaviour must be examined on a much larger scale. We investigate two hypotheses: (i) every 9th and 10th year, a continental-scale travelling wave of outbreaks, with its front stretching from high to low latitudes, ‘rolls’ in toward the Scandes from the east and (ii) this wave meets the Scandes either in parallel, resulting in contemporaneous outbreaks all over, or obliquely, causing the illusion of outbreaks moving from the northern to the southern end of the Scandes, or the reverse. Within the frame of the Scandes, a wave moved from the northern to the southern end during the outbreak period of the 1990s (E. autumnata and O. brumata collectively). In the E–W wide extent of northernmost Fennoscandia, the direction was approximately E–W (Nilssen, Tenow & Bylund 2007). On the basis that the wave was on continental scale, a test implication for hypothesis (ii) should then be that the wave of the 1990s passed the Scandes obliquely from the north, that is, moving E–W. On average, the four outbreak waves in 1970–2004 have passed Fennoscandia from NE/E to SW/W (E. autumnata: Klemola, Huitu & Ruohomäki 2006).

Materials and methods

Operophtera brumata has a wide total and outbreak distribution in Europe (Fig. 1). In Western Europe, the distribution of O. brumata and its multitude of hosts are delimited by the Atlantic Sea. In easternmost Europe, climate and edaphic factors prevent the occurrence of O. brumata and its main broadleaved host, Q. robur. Eurasian broad-leaf defoliating moths may be roughly divided in two ecological guilds: one in Europe over-wintering as eggs, weather-exposed in tree canopies and feeding in early season; and one in Siberia and Kazakhstan over-wintering as pupae on the ground protected by snow and feeding in late season (Gninenko 1974). Because of the low air winter temperatures in this region, lethal to eggs (Nilssen & Tenow 1990), the former guild occurs in outbreaks only in Europe. Here, O. brumata and several other geometrids fluctuate synchronized in a 9- to 10-year periodicity (e.g. Tenow 1972; Glavendekić 2002; Raimondo et al. 2004; see also Appendix S1). Most of the species are polyphagous. Also the eastern, late-season feeding guild occurs in 9- to 10-year cyclic outbreaks, mostly on birch (Gninenko 1974). One member of the eastern late-season guild, the geometrid Biston betularia L. also peaks at the Atlantic coast, synchronized with early-season geometrids (Norway: Tvermyr 1968; Belgium: Supporting Information). Here, we use B. betularia as a link between Europe and Siberia.

Qualitative and quantitative data about localities and year(s) of O. brumata and early-season geometrid outbreaks were extracted from literature and printed reports, and from unpublished material provided by authors of this paper following a request issued by O. Tenow. These data (Appendix S1) were used in a meta-analysis of the occurrence of outbreak waves. For France (F. Caroulle), the Netherlands (L. Moraal) and Hungary (G. Csóka), previously unpublished long-term quantitative data series were available. Peak years in these series were included in the meta-analysis as mean values for the countries. Otherwise, all three series were used as separate sets. Together, the information spans from 1949 to 2009 and most European countries. It embraces many host species. The geographical position (Lat. N/Long. E) was determined for each outbreak locality (Appendix S2). When data are averaged from country- or region-wide monitoring, the centre of the surveyed (forested) area, or of the survey plots, was selected as the location for outbreaks. Two perpendicular great circles that intersect at Greenwich (Lat. N 51°28′38″/Long. E 0°0′0″) on the GR80-ellipsoid were rotated (18° from true north) so the N–S oriented circle became approximately parallel to the Scandes (according to the hypotheses, see 'Introduction') and by that with the North Atlantic coast (Fig. 1). In Fig. 1, the two great circles are denoted the Western and the Southern baseline. To reveal any spatio-temporal change in outbreaks, the perpendicular distance of each outbreak locality to each of the two baselines was measured (km) and plotted diagrammatically versus the outbreak year. In addition to data from Europe as a whole (continental scale), French, Dutch and Hungarian data offered detailed information on wave movements on regional and epicentral scales.

For France, information from three nation-wide (95 départements/22 régions) surveys are available for the period 1990–2006: (i) the ‘Geometrid network’ with yearly counts in January of female O. brumata moths caught on sticky traps on oak trees, in the northern half of France 1990–1998, in 1999–2005 extended to SW France; (ii) ‘Expert estimations about defoliations on a large scale’, a qualitative evaluation of the impact of main broadleaf defoliators, 2001–2006; and (iii) ‘Systematic assessment damage network’, spring assessment of light, moderate and heavy foliage loss because of identified defoliator (if possible) per 16 km of forest stand, 1997 onwards, Here, data from the ‘Geometrid network’ were analysed, complemented by data from the two other sources.

France has a wide east–west and north–south extension. If there was a wave front in the 1990s, extending from high to low latitudes and moving toward the Atlantic, it should have passed France on its way westward. Furthermore, if it moved in parallel with the Scandes, it should have approached France from the SE. However, available qualitative data indicate that heavy defoliations in 1990–2005 started in the north-eastern part of the country and then spread westward (Caroulle 2005; Flot 2005). To quantify any E–W progress of a wave, a map of France was divided into nine parallel N–S strips, each 110-km wide. For each available year, the mean number of trapped female moths for all sites within each strip was calculated, for the northern half of the country 1990–1998 and for the whole country 1999–2005. Within each of the three westernmost strips, trapping sites were low in number (N = 1 or 2) and their time series often incomplete. Hence, the catches there were pooled, giving N = 3–6. Within the other strips, the number of sites (N = 4–22) and length of series varied (see Appendix S3).

In area, the Netherlands is comparable to one of the 22 régions of France. The data source ‘Alterra’ at the Research Institute Alterra of the Wageningen University and Research Centre has given the information about the number of parcels (a national 5 × 5 km grid) in 1946–2009 that suffered light, moderate and heavy defoliation by O. brumata. Cf. Moraal & Jagers op Akkerhuis (2011).

For Hungary, the yearly numbers of light-trapped O. brumata (males) were averaged for 25 plots distributed over the 10 districts of Hungary over the period 1962–2009. See also Csóka (1994).

Data are heterogeneous: (i) assessments of attack severity vary from estimates of defoliation degree over counts of O. brumata female moths on sticky traps and male moths in light traps, counts of moths resting on tree trunks, to counts of eggs or caterpillars on twig or leaf samples, (ii) localities are either a latitude/longitude determined locality or an extensive area, sometimes even an entire country, (iii) hosts are various deciduous trees and bushes, mainly oak and fruit trees, but also conifers and heather, (iv) often other guild members participated in outbreaks and contributed to an unknown degree to defoliations, (v) data coverage is generally sparse for individual countries; however, more detailed for France, the Netherlands and Hungary (above), and (vi) outbreaks may have lasted one to several years within an area, when two or more the mean year was used as the peak year.

As to point (a) above, peak years for sticky-trap catches of female moths, light-trapping of male moths, degree of defoliation and counts of caterpillars have been used as compatible units. We know from three studies about the relationship between measures. Büntgen et al. (2009) revealed the tight temporal coherency between observed discoloration of the foliage of the European larch (Larix decidua Mill.) forests and counts of caterpillars of Z. diniana in the European Alps. Edland (1981) demonstrated that light-trap catches of O. brumata and two other geometrids in autumn (males) during an outbreak period in Norway closely predicted the number of caterpillars per unit of fruit-tree leaf the following spring. Thus, counts of male moths on tree trunks (Belgian data) may have predated the defoliation by 1 year. On the other hand, Hungarian data show, in essence, a concordance between light-trap catches of males and defoliations (Leskó, Szentkirályi & Kádár 1999). Therefore, no correction for predating has been carried out when comparing Hungarian male trapping with Dutch defoliation data. Furthermore, it should be noted that in France, O. brumata female moths, caught on sticky traps, were counted early in the same year as caterpillars fed on oak foliage. Hence, there should be no undue time discrepancy between peak catches and the number of caterpillars.

Above all, O. brumata intervenes with economical interests and has therefore been subject to control measures. However, because most such measures have been applied to a limited area of land over time, any bias caused by them should be minor at the continental scale investigated here (cf. Peltonen et al. 2002).

Statistical methods

Year of outbreak was regressed on distance (km) of localities from the Western and the Southern baseline (Fig. 2a, cf. Fig. 1) as independent variable and year of outbreak as dependent variable. We then used the analysis of covariance (ancova) to test the homogeneity among the decades of regression slopes. The same data were also pooled by regressing the last digit of outbreak year in each decade on distance (km) from the same two baselines. A piecewise regression was used here to test for breakpoints in data (Fig. 2b). These statistical analyses were performed using spss, version 18, SPSS Inc., Chicago, Illinois, USA. The extent of global synchrony of outbreaks was explored in a nonparametric spline correlogram (R function spline.correlog ′uni- and multivariate spline correlograms′ in R-package: ncf. Bjørnstad & Falck 2001). Furthermore, the average directional trend in synchrony (anisotropy) of the outbreaks in Europe west of an established breakpoint was estimated. This was performed by using the correlation of mean year in decennium of observed outbreaks and locality as related to distance between localities in different directions. The best fit of a covariance function (R function spline.correlog.2D in package ncf; ′anisotropic nonparametric (cross-) correlation function for univariate spatial data′, R© version 2.13.0; R Development Core Team 2011) was then sought in all compass directions at 22·5° intervals. Bootstrapping with 1000 samples was used to calculate confidence envelopes for the estimated correlograms. We used the kriging interpolation method (Isaaks & Srivastava 1989) implemented by the GSLIB (Deutsch & Journel 1997) to interpolate the spatially irregular raw data into a regular grid. By contouring the grid, a map was obtained with isolines of temporal occurrence of outbreaks. The kriging weights were estimated from a spherical model with nugget effect fitted to an anisotropic semivariogram representing the spatial variability of the data set (Isaaks & Srivastava 1989).

Figure 2.

Year of outbreaks by Operophtera brumata (and associated geometrids) as a linear function of distance from the Western baseline (see Fig. 1). (a) Data per year. Data from eastern and south-eastern European Russia are marked with small circles. (b) The same data pooled per year in decade. A piecewise regression with a breakpoint at 2300 km resulted in the highest combined R2 = 0·56, whereas an ordinary linear regression resulted in R2 = 0·43. Cf. Appendix S1. Definition of outbreak year, see 'Materials and methods'. Table over years and distances, see Appendix S2.


Figure 1 gives the geographical frame within which the spatio-temporal behaviour of the outbreaks takes place. In this area, outbreaks have been reported to occur at a total of 81 localities during six decades (Fig. 1). Some of the localities have experienced outbreaks during several outbreak periods (Appendix S1). When the outbreak records at the 81 localities are plotted according to their distance from baselines and to outbreak years (Fig. 1), they add up to 165 records (Fig. 2a). At about 2400 km from the Western baseline and westward, records (large circles) fall into six groups, one for each of the six surveyed decades (Fig. 2a).

In each group, the first outbreaks occurred furthest to the east at the beginning of the decade and the latest outbreaks furthest to the west at the end of the same decade. Between these, outbreak localities are in approximately linear arrangements. For each decade and for pooled data (Fig. 2b), the slope of the line is highly significant. ancova-tests of the homogeneity of the slopes showed that the regression slopes for the six decades are not significantly different (F = 1·57, d.f. = 5, P = 0·174). Pairwise comparisons of slopes (after Bonferroni′s adjustment) showed that the only significant difference (P = 0·015) was between the 1960s and 1990s and that the time difference between the lines is not significantly different from 10 years (Fig. 2a). Hence, the six lines represent six distinct outbreak waves, one for about every tenth year. When one wave ended in the west, the next one appeared in the east to travel the c. 3000-km long stretch across Europe. Notably, known B. betularia outbreaks just east of the Urals fit with the waves (Figs 1 and 2a). The average speed of waves, calculated from pooled data (Fig. 2b) was 330 km year−1. Multiplied by the average cycle length 9·5 years (for E. autumnata/O. brumata: Tenow 1972; Nilssen, Tenow & Bylund 2007), it gives the average wavelength of 3135 km. Most of the recorded outbreaks in east and south-east European Russia have occurred east of c. 2300 km from the baseline (Fig. 2a). The piecewise regression presented in Fig. 2b yielded a breakpoint with a large discontinuous jump at 2300 km, showing that the easternmost outbreaks did not connect to the trend at distances <2300 km. We therefore find that these outbreaks did not participate in western waves. Outbreak times and locations in central and western European Russia are in line with the predictions made by the regression models (Fig. 2a; Appendix S1).

If the waves really were unidirectional, they should have displayed two traits, that is, synchrony between outbreaks should initially decline with the distance and then increase as the distance approaches one wavelength, and synchrony should remain as the distance between outbreaks increases perpendicular to the wave direction ('Introduction'). Figure 2a shows that in each wave, synchrony between outbreaks about 2400 km from the Western baseline and outbreaks further westward declined proportionately with the distance. At the same time, when a wave had passed about half a wavelength and continued its movement, outbreaks still more westward in that wave became more and more synchronized with the earliest outbreaks in the next wave. Eventually, approximate synchrony occurred between the westernmost outbreaks terminating the first wave and the easternmost outbreaks launching the next wave, that is, outbreaks about one wavelength apart. Perpendicular to the wave direction, local outbreaks in most waves (Fig. 3a) and on average (Fig. 3b) were synchronized irrespectively of the distance between them. Thus, the data display either trait that is characteristic for unidirectional waves.

Figure 3.

Year of outbreaks of Operophtera brumata (and associated geometrids) as a linear function of distance to the Southern baseline (see Fig. 1). Data from eastern and south-eastern European Russia not included. (a) Data per year. (b) The same data pooled per year in decade. Cf. Appendix S1. Definition of outbreak year, see 'Materials and methods'. Table over years and distances, see Appendix S2.

The movement direction of waves was specified in four steps (Fig. 4). (i) A nonparametric spline correlogram (isotropic) shows that synchrony between outbreak year at different locations ceases (correlation (y) = 0, Fig. 4a) at 1470 km distance (c.e.low = 1240 km, c.e.upper = 1760 km) when average outbreak year at all locations west of the breakpoint (cf. Fig. 2b) is included (N = 74). The estimated correlation of outbreak year between neighbouring locations (distance = 0) is (y) = 0·54 (c.e.lower = 0·1, c.e.upper = 1·12). (ii) Directed (anisotropic) nonparametric spline correlograms (Fig. 4b) give a global direction of the waves of 135° from north (or according to the compass, −45°N, i.e. toward NW) when exploring the best fit of the covariance function in directional steps of 22·5° for all directions (correlation (y) = 0·34, c.e.lower = 0·16, c.e.upper = 0·65). In this direction (135°), the correlation disappears at the distance (x) = ±1160 km between locations. (iii) In Fig. 4c, decadal years for western wave outbreaks have been interpolated by kriging. Evidently, isochrones are approximately parallel to the Atlantic coast, showing that the front of the average outbreak wave stretched across Europe from about NNE to SSW, that is, with a travel direction toward WNW. In northern Fennoscandia, waves may have made a forward bend around the Gulf of Bothnia. (iv) The Western baseline was angled as to be approximately parallel to the Scandes and the Atlantic coast (18°N), whereas the Southern baseline was placed perpendicular to the Western baseline, with origo at Greenwich (Fig. 1). To test whether the chosen Western baseline at 18°N is the best angle to explain the movement of the waves of observed attacks, a variety of other Western baselines (from −2°N to 38° N) (with corresponding recalculations of distances from each baseline) was tested in a series of regression analyses (like the left segment in Fig. 2b). The baseline giving the highest coefficient of determination (R2) can be regarded as the best explanatory variable and in this study, the optimal Western baseline. The resulting R2-values from these regressions were plotted as a function of the value of °N of the baseline (Fig. 4d). R2 peaked between 12° and 20°N, but differences within this range were insignificant. The chosen angle, 18°N, was therefore found to be within the optimal baselines and could therefore be applied in the linear regression analyses. This implies that the average movement, for all decades combined, was perpendicular to the Western baseline, that is, directed −72°N or fully WNW. Per definition, the average wave moved westward parallel to the Southern baseline (Fig. 1).

Figure 4.

Wave direction (a–c, see 'Statistical methods' for further details). (a) Nonparametric global (isotropic) spline correlogram of outbreak years and distance between locations with 95% bootstrap confidence envelopes (c.e.), dashed lines. At the distance 1470 km, all similarity in outbreak year between locations (N = 74) cease to occur. (b) A directed nonparametric spline correlogram at the direction 135° revealed the best fit of the spline function when evaluated in eight bearings in 22·5° directional steps. A comparison of locations within this direction range shows that the positive correlation between outbreak years ceased at a distance of (x) = ±1160 km. (c) Isochronal intervals for outbreaks of Operophtera brumata (and associated geometrids) as averaged over year in the decades when they occurred, interpolated with kriging (linear variogram with a nugget effect). An outbreak locality may have experienced maximally six outbreaks over the six outbreak periods (within brackets; number of outbreaks). (d) Test of the effect of different angles of the Western baseline on the regression in Fig. 2b, left segment, by comparing R2-values. The R2-value of the chosen angle of 18°N did not deviate significantly from the range of values between 12° and 20°N and could therefore be considered an optimal angle. Further explanation in the 'Results' section.

Each of steps 1–3 and step 4 represents different, independent analytical methods. As shown, they give similar results, that is, outbreak waves have moved toward the Scandes. Thus, hypothesis (i) is corroborated (see 'Introduction').

Long-term quantitative data for Hungary and the Netherlands (Fig. 5), about 1100 km apart on a line approximately perpendicular to the Western baseline (Fig. 1), show that the peaks in the Netherlands repeatedly occurred with a delay (mean = 3·0 years; N = 5) close to that expected (c. 3·5 years) for waves travelling that distance.

Figure 5.

Occurrence of Operophtera brumata (and associated geometrids) in Hungary and the Netherlands in 1962–2009 according to light trapping and heavy defoliation, respectively (see 'Materials and methods'). 3-year running averages.

In Fig. S1, the position of plots for sticky-trapping of female moths and the east to west division of France in nine strips is shown. The time series (Appendix S3) show a peak in 1998 (Fig. S2a). The first and last high mean number caught may reflect the fading outbreak period of the 1980s and the beginning outbreak period of the first decade of the twenty-first century, respectively. Analysed across strips (Fig. S2b), the outbreak period of the 1990s started in the east, spread rapidly to interior France and finally reached the Atlantic to the west. This lag is significant (Fig. S2c).

In the Netherlands, the outbreak of the 1990s (Fig. S3), with a maximal spread in 1996–1997, started and lasted longest in the north-eastern part of the country. Therefore, and from previous experience, this north-eastern part can be understood as (part of) an outbreak focus, favourable for the build up of O. brumata populations during the wave passages (cf. Fig. 3).

On the scale of the Scandes, the wave of the 1990s travelled from northern to southern Scandes although in the E–W extent of northernmost Fennoscandia, the direction was approximately E–W ('Introduction'). This region experienced a peak in E. autumnata/O. brumata caterpillar numbers in about 1992–1993. About 20° westward and 20° southward, the wave entered NE France in 1994–1997 as revealed by high catches of female moths (Fig. S2b,c). The peak defoliation in the Netherlands in 1996–1997 (Fig. S3) north of NE France corresponds with an E–W movement of the wave. In addition, defoliations occurred in NW Italy in 1996 (Appendix S1) directly south of NE France. Because of this concordance, we conclude that the continental-scale outbreak wave of the 1990s travelled in an E–W direction, not only across northernmost Fennoscandia but also in its extent southward to France and Italy. This direction deviated about 18° from the average direction of the waves.


In confirming hypothesis (i) that a continental-scale wave of outbreaks has reached the Scandes from the east every 9th and 10th year, we unveiled the first example on a European scale, and first ever for insects, of population waves that approach the length of those of the snowshoe hare, Canadian lynx and ruffed grouse, approximated to 4000 km, that is close to the total width of Canada (Introduction). The length of Z. diniana population waves seems not to have been estimated; however, this can be calculated from wave speed (220–250 km year−1) and cycle length (8–9 years) (Bjørnstad et al. 2002; Johnson, Bjørnstad & Liebhold 2004), as c. 2000 km, which is more than twice the length of the European Alps (c. 900 km). At the lower end of spatial scales is the wavelength of 56 km for field voles in northern England (Sherratt & Smith 2008). Indications that lynx population waves may travel unidirectionally across the whole of Canada (cf. Ranta, Kaitala & Lindström 1997) seem incompatible with findings that populations first peak in continental areas of Canada, thereafter in the maritime areas to the east and west (Elton & Nicholson 1942; Stenseth et al. 1999, 2004). However, in the light of our findings, a wave of the assumed length seems quite reasonable by itself.

As we have shown that continental outbreak waves have recurrently reached the Scandes from the east, the prerequisite for discussing the second hypothesis (ii) that the travelling waves meet the Scandes at different angles is set. The continental-scale wave of the 1990s travelled in an E–W direction across Europe and when passing Fennoscandia should have swept the NNE–SSW stretching Scandes obliquely from the north on its way westward to the Atlantic. In conclusion, the outbreak wave that seemed to move along the Scandes from the north in the 1990s was the result of the continental-wide E–W wave passing over the Scandes obliquely. Analogous to this, outbreaks moving from the south or occurring contemporaneously along the Scandes (Tenow 1972; Nilssen, Tenow & Bylund 2007) should have originated from continental-scale waves meeting the Scandes obliquely from the south or in parallel. Thus, hypothesis (ii) is supported.

Periodic travelling waves in ecology have become increasingly recognized and in any field study, their origin is unknown (Sherratt & Smith 2008), although theory predicts some causes. One theory concerns ‘reaction-diffusion’ models, named owing to the combination of ‘reactions’; in this case being the trophic interactions (e.g. predator-prey or herbivore-plant), with ‘diffusion’, the spatial movement of reactants (individuals) (e.g. (Bjørnstad, Ims & Lambin 1999; Sherratt & Smith 2008). Such models produce scenarios that may lead to waves (for a review, see Sherratt & Smith 2008). One is the generation of waves of prey-predators (or host–parasitoid, plant–herbivore) by boundaries with hostile environments. These mechanisms have the ‘potential to generate large-scale regions with a single periodic travelling wave, and thus provide possible explanations for the waves seen in ecological field data’ (Sherratt & Smith 2008). An approach involving a Z. diniana–parasitoid interaction, predicts directional waves if dispersal is unidirectional or habitat productivity varies across the landscape (Bjørnstad et al. 2002). For the same system, a tri-trophic model demonstrated that landscape gradients in favourable habitats alone could induce waves from epicentres (Johnson, Bjørnstad & Liebhold 2004). Both are applicable to the flighted Z. diniana (Baltensweiler & Fischlin 1988) but not to the flightless O. brumata.

The distribution of populations of the early-season guild and particularly that of O. brumata as well as of their hosts is patchy on a local scale. However, on the scale of Europe or regionally, with many potential hosts, one may assume it to be approximately uniform. On this large scale, the vast conifer-covered area in NE Russia and the forest-sparse Siberia/NW Kazakhstan, with regularly occurring low winter air temperature (AgroAtlas 2003-2009) should be a hostile environment to O. brumata. Climate has not prevented outbreaks in east and south-east European Russia. Why then did outbreaks there deviate from the western ones (Fig. 2b)? Vegetation there is distinctly zoned (Figs 1 and S4). Outbreak localities in this part have been in isolated broadleaved stands on the steppe (EuroVegMap) or close to the border between the steppe and the forest-steppe zones (Rubtsov & Utkina 2011). In the latter zone, host occurrence gradually changes westward from small and widely separated stands to large and nearby stands until stands merge into the zone of broadleaved forests (Fig. S4).

Because O. brumata has a limited capacity to disperse, stand isolation should impede exchange of individuals between subpopulations. The spatial distribution of O. brumata is negatively associated with stand isolation in terms of distance and positively with stand area (Dongen van et al. 1994). Theoretically, short-distance dispersal may synchronize entire meta-populations if within-patch dynamic is cyclic (Fox et al. 2010). Hence, there seem to be two critical zones for O. brumata occurrence: one climatic at the Europe-Asia border beyond which outbreaks cannot occur (see 'Materials and methods') and one in E/SE Europe where broadleaved stands thin out eastward until the prospect for O. brumata to disperse is low or nil. Interestingly, the distance of the forest-steppe zone from the western baseline and the distance from where the waves seem to start concord approximately (Figs 1 and 2a). In addition, the ENE–WSW extension of the zone concords with the ENE–WSW extension of where the waves seem to start (Fig. 4c). Accordingly, we hypothesize that increasing stand isolation eastward within and beyond the forest-steppe zone creates a ‘hostile’ environment to the dispersal of O. brumata. West of this gradient, or in the western part of it, within-patch outbreaks are synchronized by delayed density-dependent factors, for example, parasitism, and meta-population outbreaks by short-distance dispersal. From there, then, waves travel westward across Europe. East of the gradient, outbreaks may instead have been synchronized by years of favourable climate (Fig. 2a). Potential hostile environments, like the European Alps, the English Channel and the Baltic, may have delayed but have not prevented the passage of waves (Fig. 4c). A traverse of Scandinavia from NE to SW, as indicated in Fig. 4c, should agree with the findings by Klemola, Huitu & Ruohomäki (2006) that the four E. autumnata outbreak waves in 1970–2004 on average have passed Fennoscandia from NE/E to SW/W.

Delayed density-dependent parasitism is assumed to drive geometrid cycles (e.g. Klemola et al. 2010; i.e. E. autumnata) as are host plant defences (for a discussion, see Klemola et al. 2010 and references therein). We consider both. Högstedt, Seldal & Breistøl (2005) found that periodically oscillating herbivores feeding on long-lived hosts tend to fluctuate in long cycles (≥6 years). For host plants to drive such cycles, it is required that grazed hosts can mobilize a delayed induced resistance that has a relaxation time of several years (Högstedt, Seldal & Breistøl 2005; Ruuhola et al. 2007). In the same mode, the mechanistic model by Hunter (1994) for cyclic outbreaks on drought-tolerant plants may apply.

Neither the North Atlantic Oscillation (NAO) nor sunspot activity should be able to create travelling waves (Nilssen, Tenow & Bylund 2007). While one cannot rule out that climatic phenomena were somehow involved in the initiation or spreading of these waves, the nature of any climatic phenomenon with a spatio-temporal behaviour of this kind is not obvious (M. Rummukainen, pers. comm.). The limited mobility of early-season geometrids is incompatible with the high speed of the waves (>300 km year−1). Wind transported parasitoids may disperse far and fast; however, to affect the population dynamics of their hosts, they have to find the hosts within the short phenological time when these are open to parasitism. Because this is unlikely at long-distance dispersal, parasitoids seem not to be the main factor that drives the waves. Two recent studies have addressed the regulatory importance of larval parasitoids. Both concern early-season geometrid hosts that defoliate mountain birch in northern Fennoscandia. The result of a parasitoid exclosure experiment (Klemola et al. 2010) supports the hypothesis that delayed density-dependent parasitism locally contributes to generate E. autumnata population cycles. Another study (Hagen et al. 2010) tested the interaction between larval parasitism and the rate of larval population crashes in E. autumnata and O. brumata along a 60-km long transect. It showed that larval parasitoids were not able to explain the distinct spatially patterned crashes of the two host populations (Hagen et al. 2010). It is likely, therefore, that the other agents shape the spatio-temporal dynamics of the two moths and future studies should focus on the interactions between the moths, their host plant and enemies acting on other moth life stages (Hagen et al. 2010).

Referring to the reaction-diffusion models, one can speculate about the origin of the waves as follows. Along the forest-steppe zone, the size of discrete broadleaved stands gradually increases westward until stands merge. Here, where stands have reached the necessary degree of connectivity, epicentral populations (cf. the Netherlands example) peak synchronized every 9th and 10th year. Outbreaks induce a resistance of a long-lasting relaxation time in defoliated trees that interact with delayed larval parasitism. This causes a deep decline in geometrid populations. Hence, because of parasitism and a slowly relaxing resistance of host trees, it will take 9–10 years until geometrid populations along the attacked forests are released to peak again. On the other hand, deciduous trees growing west of the outbreak zone and parallel to it have now, on average, a fully relaxed defence since outbreaks 9–10 years ago. During the later part of this period, O. brumata populations there have had time to increase. Parasitism rate is low and populations are now prone to peak in forests that are again susceptible to outbreaks. By such successive spatially directed transformation of susceptible forests west of outbreaks to resistant forests east of them, a periodic wave travelling westward is created. However, the enigmatic rapid movement of the waves has to be explained.

Often, population increases are terminated at levels too low to trigger an induced defence. In general, however, recorded peaks should have been revealed by severe defoliations and should therefore mostly represent outbreaks that cause long-lasting resistance. We find that some hostile boundary variant of the reaction-diffusion models (Sherratt & Smith 2008) is a good candidate to explain the outbreak waves of O. brumata that travel westward across Europe. In such models, the connectivity of stands and resistance of host plants irrespective of species, interplaying with defoliator enemies, should be key interactants in creating both the 9- to 10-year cyclicity and the travelling waves. Our study demonstrates two findings: neither can local outbreaks be understood without knowledge of the waves nor can isolated local or even regional studies fully explain the large-scale spatio-temporal dynamics of outbreaks. Essential for an understanding of the underlying mechanisms are continentally, multidisciplinary coordinated studies.


We thank Veijo Kaitala for his comments on an earlier version of the manuscript and Markku Rummukainen for his comment on the involvement of climate in the origin of the periodic outbreak waves. We thank Stephan Hennekens for introducing us to EuroVegMap and for producing the vegetation map used in Fig. S4. Finn Williams kindly read our manuscript and corrected the English. Critics and suggestions by Matthew Smith and two anonymous reviewers greatly improved the manuscript.