Dispersal of allergenic pollen from Cryptomeria japonica and Chamaecyparis obtusa: characteristic annual fluctuation patterns caused by intermittent phase synchronisations

Trees produce pollen during specific times of the year. Pollen can induce pollinosis, a type of allergic rhinitis, in humans. In Japan, allergenic pollen is mainly dispersed from February to May. Using data collected at 120 observation sites managed by the Japanese Ministry of the Environment, we studied the annual patterns of airborne allergenic pollen. The allergenic pollen showed an alternating ON–OFF cycle, but the length of the cycle differed among regions. We used an in-phase/out-of-phase analysis to quantify two characteristic features of the synchronisation. The degrees of phase synchronisation were strong in eastern and weak in western Japan. The pattern of allergenic pollen dispersal throughout Japan is typical intermittent synchronisation. This is the first study to evaluate allergenic pollen’s distribution from a phase synchronisation viewpoint.

The amounts of flowers or fruits vary from year to year in forest trees such as beech 5 and oak 6 . Moreover, some forest trees show masting, the phenomenon in which the production of reproductive organs is synchronised within a population 7 . In Finland, the annual allergenic pollen distributions can be synchronised among various species (including Betula, Alnus, Corylus, Salix, and Populus) at several locations 8 . The degree of spatial synchronisation of annual pollen production has been studied 9 .
Previous studies on sugi pollen in Japan have mainly focused on its biological characteristics and how to predict the total annual pollen amount. In terms of biological characteristics, the mean temperature in July of the previous year is positively correlated with the amount of male flowers 10 , and a high mean temperature in summer promotes their differentiation. Therefore, the weather conditions in summer and an index of the amount of male flowers have been used to estimate the amount of airborne pollen [11][12][13] . It is also empirically known that the dispersal rhythms of sugi and hinoki pollen have alternate cycles of ON-(abundant amount) and OFF-(small amount) years. Conventionally, this alternate dispersal rhythm has been incorporated as a dummy variable in the regression analysis of the total pollen count 14 . In this paper, we assumed that the alternate dispersal rhythm correlated with nonlinear dynamics. Although many researchers have studied the pollen of these trees, almost all the studies have been conducted using limited nearby sites. Therefore, to date, it is unclear how allergenic pollen production is spatially synchronised in Japan. Beginning in 2003, the Japanese Ministry of the Environment launched the pollen observation system "Hanako-san", which is available for public use. This system has recorded the dispersal of sugi pollen each year at 120 sites located throughout Japan. In this paper, we used the data supplied by this system to investigate the spatial distribution of synchronisations. The overall aim of this study was to obtain new fundamental knowledge regarding the dispersal of allergenic pollen (such as sugi and hinoki) in terms of phase synchronisation. In particular, we employed an in-phase and out-of-phase analysis to quantify the characteristic features of nationwide synchronisations of allergenic pollen. The results obtained here will be useful for the accurate prediction of airborne allergenic pollen levels. Numerical forecasts of allergenic pollen abundance are essential for both allergic individuals and clinicians 14 . Earlier predictions of nationwide pollen distribution patterns may contribute to the more effective prevention of pollinosis.
Pollen observation system "Hanako-san". The pollen observation system "Hanako-san" is managed by the Japanese Ministry of the Environment 15 . The data are collected at 120 observation sites located in all the Japanese prefectures, except for Okinawa. Figure 1 illustrates the locations of the 120 sites, and the annual measurement times (months) and measurement periods (  Locations of 120 observation sites for data collection. These sites were located in eight regions, covering 1,400 km north-south and 1,200 km east-west in the Japanese islands, excluding Okinawa prefecture. The longest distance among the 120 sites is 1,613 km between site 3 (lat. 43.807783, lon. 142.439397) and site 120 (lat. 43.807783, lon. 142.439397). The shape file for the map was downloaded from Geospatial Information Authority of Japan (https://www.gsi.go.jp/kankyochiri/gm_jpn.html#gm_jpn_dl) and processed with QGIS 2.18 31 .
The "Hanako-san" system employs KH-3000 (Yamatronics, Japan) automatic pollen monitors and locates them at all the observation sites. There are two types of airborne pollen measurement methods, the Duraham (gravitational) and the Burkard (volumetric). KH-3000 was designed based on the volumetric method; therefore, it can measure hourly variations in airborne pollen concentration for 24 h a day. Kawashima et al. described the principle and algorithm of the KH-3000 in detail 16 . They also conducted validations by comparisons with the Burkard (Hirst-type) pollen sampler and revealed high correlation coefficients between the two methods.
The accuracy verification of KH-3000 has continued to be carried out nationwide from before the system was operational in 2003 in the Kanto area until present day. The Duraham method has been mainly adopted as a reference method [17][18][19][20][21][22][23][24]  In addition to sugi, the atmosphere absorbed by automatic measurement equipment contains another important tree, hinoki (C. obtusa). The Japanese Forest Agency reported that the sugi forest area was 4.5 million hectares, while the hinoki forest area was 2.6 million hectares in 2012. Hinoki pollen is also allergenic. The sugi forest area is 1.7 times greater than that of hinoki forests in Japan. However, the measured values do not always reflect only sugi and hinoki pollen because the measured values are based on a particle size of approximately 30 µm in diameter. Therefore, we set the period as February1 st to April 30 th for the analysis. Consequently, the data reflected mainly sugi and then hinoki pollen, and minimised the effects of other plant species, such as rice.

Results and Discussion
Patterns of annual variation. To see the collective behaviours of 120 x i (t) more comprehensively, we used a time-space diagram as shown in Fig. 2(b). Three states are defined as below, for each term over two successive years in the [t − t + 1] term: Increased state: , and Unchanged state: Fig. 2(b), we hypothesised that the two-year cycle is a base of the collective behaviours of 120 x i (t). However Correlation analysis. Pearson's correlation coefficient is a conventional method to investigate synchronisation between two sites [25][26][27] . Here, r ij denotes Pearson's correlation coefficient between site i and site j. Based on the correlation matrix, the mean of the correlation coefficients was defined, as follows, using Eq. (1) to indicate the strength of nationwide synchrony [25][26][27] : where r ij represents the Pearson's correlation coefficient between sites i and j, and N represents the number of observation sites. The calculated value of S for the whole of Japan (i.e., all eight regions, N = 120) was 0.361. We defined two types of mean correlation coefficients, S w (within a region) and S b (between two regions), as follows for region (l) and region (m): The diagonal and non-diagonal components of the regional correlation matrix in Fig. 3 in Kansai. This result is inconsistent with the behaviours exhibited in Fig. 2, in which Kanto was more synchronised than Kansai. Figure 3(c) represents the column averages of the matrices for each region; however, it is difficult to distinguish the differences between eastern and western regions. www.nature.com/scientificreports www.nature.com/scientificreports/ In-phase and out-of-phase analysis. We introduced an in-phase and out-of-phase analysis to explore phase synchronisation, because this technique is useful for two-cyclic (alternating ON-OFF) collective behaviours, as seen in Fig. 2. Prasad et al. 28 expressed phase differences as in-phase and out-of-phase to quantify the extent of phase synchronisation. Fist, ∅ i j t ( , , ) is defined as follows;  The time averaged in-phase fraction between sites i and j during T years was defined as follows: Based on the in-phase fraction, we defined F IN (t) as the degree of in-phase synchronisation throughout Japan for successive years, t and t + 1. N represents the total number of observation sites (N = 120). Thus: The inner-regional in-phase fraction within region (l) was as follows:  Fig. 4(a). Inner-regional synchronisations were strong in eastern regions, such as Hokkaido, Tohoku, Kanto, and Chubu. Tohoku and Chubu also showed significant inter-regional synchronisations. In contrast, the degrees of synchronisation in the western regions were weaker than in the eastern regions. Figure 4(b) shows regional synchronisations with FIN w l as diagonal components and FIN b l m , as non-diagonal components for the eight regions and all 28 combinations. The inner-regional in-phase synchronisations (represented by the diagonal www.nature.com/scientificreports www.nature.com/scientificreports/ components) were very high in the four eastern regions (A-D), with Kanto showing the highest degree (FIN w C = 0.888). This result is consistent with those shown in Fig. 2.
The inter-regional synchronisations FIN b l m , were highest in the eastern regions. All of them were greater than 0.7, especially the following four regional combinations that had very high degrees of synchrony: . In the western regions, only Shikoku's inner-regional synchronisation was greater than 0.7 = .
. The inter-regional synchronisations between all pairs in the western regions (E-H) were less than 0.7. The eight regional averages of in-phase matrices are illustrated in Fig. 4(c). Regional synchronisations in the eastern regions (A-D) were very strong, while those in the western regions (E-H) were less synchronised. A comparison of Figs 3(c) and 4(c) indicated that the in-phase and out-of-phase analysis was more appropriate than a correlation analysis for the two-cycle-based fluctuations.
To show the time evolution of spatial synchrony, Fig. 5(a)   Concluding remarks. Using an in-phase and out-of-phase analysis, we found two important features of nationwide synchronisations of allergenic pollen coming mainly from sugi (C. japonica) and hinoki (C. obtusa) in Japan.
First, there was the difference in the degree of phase synchronisations between eastern and western Japan. In the four eastern regions, both inner-and inter-regional synchronisations were significant. In the four western regions, no significant synchronisation was identified.
Second, the nationwide synchronisation pattern was "intermittent synchronisation", because there were yearly changes in the degree of in-phase synchronisation. Besides the perfect in-phase synchronisation in 2009-2010 and the almost perfect desynchronisation in 2015-2016, the other measurement periods demonstrated mixed in-phase and out-of-phase synchronisations, reflecting chimera-like states 29,30 .
The mechanism causing regional differences in the degree of synchronisation and nationwide intermittent synchronisation is still unknown. However, based on masting and/or alternate bearing, we hypothesise that the pollen synchronisation patterns are spatially distributed collective dynamics driven by pollen coupling and the Moran effect 27 . To clarify their causes, a comparison of the data and collective dynamics models should be conducted using an in-phase and out-of-phase analysis.