1 Introduction

Phenology is the study of the timing of certain periodical biological events (life stages such as flowering, fruiting and bird arrival) and the influence of climate as well as other abiotic factors on these [1]. Timing and the interaction with climate [1, 2] underpins or influences many different ecological processes [3–5] and as a consequence plays a significant role in many sectors of society (e.g. human health, biodiversity, forestry, agriculture and tourism [6, 7]).

Determining phenological trends in relation to long-term climate, however, is not easy as they can be confounded by short-term interannual trends [8–10]. Hence, not only are long-term records required but also methods which can deal with this confounding factor [11, 12]. By necessary, this has led to additional mathematical and statistical methods for examining phenological time series being introduced (e.g. [13–17]).

Singular spectrum analysis (SSA) is an analytical method that has been applied to many branches of scientific study: such as gene expression research, environmental science and bio-geosciences [18–20]. It is essentially a linear approach which can decompose a time series into its underlying components (e.g. trends, oscillatory modes or seasonalities, change points and noise) and is useful for short, noisy time series [21] of which many phenological datasets are. We are motivated to use SSA because it is a nonparametric technique that works with arbitrary statistical processes, whether linear or nonlinear, stationary or nonstationary, Gaussian or non-Gaussian. Moreover, contrary to the traditional methods of time series analysis, SSA makes no prior assumptions about the data [22].

The primary aim of this research is to demonstrate the utility of SSA techniques and their ease of implementation in phenology by examining the relationship between flowering intensity and temperature and rainfall since temperature is a major climatic influence on phenological events such as flowering [23, 24] as is rainfall [25, 26] but often to a somewhat lesser extent. By using eucalypt species, this work also contributes significantly to our understanding of the interplay between climate and Eucalyptus flowering—a major southern hemisphere genus which contributes significantly to the character and diversity of the Australian flora [27]. Additionally, the species examined in this study have been recognised as an important resource for preserving eucalypt phylogenetic diversity [28].

2 Methods

2.1 Phenological Data

Monthly observations of the flowering and budding of eucalypts were recorded within plots by the former Forests Commission of Victoria in the forests near Maryborough, Victoria. The timing and distribution of flowering of eight species of Eucalyptus were collected on a monthly basis usually on the 15th (and sometimes 16th) day of each month. Whilst the monthly data limits the sensitivity of the analysis, no data of greater temporal resolution are currently known to be available in Australia for this period. It should also be noted that the mean flowering for each of the species studied is greater than 3 months.

This study extends the work in Hudson and Keatley [29] from four to eight eucalypt species with the examination of flowering intensity in E. camaldulensis, E. goniocalyx (January 1940–May 1970), E. macrorhyncha (January 1940–December 1969) and E. melliodora (January 1940 to March 1972) and additional data for E. leucoxylon, E. microcarpa, E. polyanthemos and E. tricarpa (January 1940 to March 1972).

Flowering was recorded as a categorical measure, defined by both quantity and distribution. The categories are such that the highest rank was given to the ‘heavy flowering’ with ‘general’ distribution. Keatley and Hudson [30] formulated a rank value to calculate an intensity measure in the range 0 to 5, and from these, categorised quantities and distributions were determined. The rank allows the flowering characteristics of these species to be determined—commencement and cessation of flowering, most probable month of flowering, peak flowering and duration of flowering. The intensity of flowering measure is a simple sum of assigned values for the quantity and distribution that produces a continuous time series. The monthly flowering intensities time series profiles for the eucalypt species are shown in Fig. S1. The mean and median flowering duration for the eight species, in addition to the most probable month of flowering start and cessation of flowering per flowering year, is given in Table S1.

2.2 Climate Data

Daily minimum and maximum temperature along with daily rainfall were obtained from the Bureau of Meteorology, for the closest weather station (approximately 3.5 km away), Maryborough, Victoria (37° 03′ 22″ S, 143° 43′ 55″ E, 249.3 m elevation). Monthly means for minimum, maximum, temperature and rainfall were used in the analyses.

2.3 Analyses

Singular spectrum analysis (Caterpillar SSA 3.40 Professional M edition http://www.gistatgroup.com/cat/A R package by the same authors is also available https://cran.r-project.org/web/packages/Rssa/Rssa.pdf [31]) with a window length of 120 (equivalent to 10 years and approximately one third of the series) was used to analyse both the flowering and climate series. This window length was chosen as it allows comparison with previous work on eucalypt flowering using SSA [29]. It also meets the criterion of not being greater than half the length of the time series. The root mean square error of the residuals is reduced when a window length between N/3 and N/2 is used. Further, as there is a known seasonal component in the time series (i.e. flowering usually occurred annually), a window length that was proportional to seasonal component was used [32, 33] A thorough description of the theoretical and practical foundations of the Caterpillar SSA technique (with several examples) can be found in Golyandina and Zhigljavsky [21].

SSA involves four steps: embedding, singular value decomposition (SVD), eigentriple (ET) grouping and diagonal averaging. Summing of each SSA decomposed structure is carried out before diagonal averaging to obtain the reconstructed structures (Fig. 1). The series used in the reconstruction were chosen using a combination of a scree diagram of the eigenvalues’ logarithms [29, 33] (Fig. S2). Trends were identified as the slowly varying component of the series which did not contain oscillatory components [21, 33]. Eigenvalues which have the same amplitude and are harmonic (or almost) are considered oscillatory pairs and may be grouped [34]. Hence, the shape of the paired eigentriples (e.g. Fig. S3) which reflects the harmonic and their periodograms (Fig. S4) as well the weighted correlations matrix of the reconstructed series (Fig. S5) were also considered [21, 33].

Fig. 1
figure 1

Schema of the mathematical and computational approach of SSA using E. polyanthemos as the example

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The resulting SSA-reconstructed series were also cross-correlated to determine whether significant contemporaneous or lagged relationships between flowering and climate exist (following the approach of Hudson and Keatley [29]). Cross-correlations between SSA-reconstructed flowering and rainfall and the temperature variants were lagged from 1 to 12 months prior to the species-specific peak flowering month.

To illustrate further the utility of SSA, ARIMAX models were fitted to E. leucoxylon flowering to check the bivariate correlations and to establish causal relationships between flowering and lagged climate (monthly mean minimum temperature, mean monthly maximum temperature and mean monthly rain) and flowering intensities with lags up to p months. ARIMAX models are equivalent to the transfer function models of Box et al. [35] and also known as Var(p) models (see Chapter 5 of [36]).

Var(p) was performed via the astsa package (applied statistical time series analysis) in R version 3.0.2 [37]. The optimal number of lags p was obtained via the selection criteria AIC [38] and Final Prediction Error (FPE) [39].

3 Results

3.1 SSA Climate Results

The significant SSA sub-components of the climate variables are given in Table S2. The first reconstructed series (RS 1) for monthly mean minimum, maximum and daily temperature (1940–1972) for Maryborough, Victoria, account for 83.8, 91.9 and 90.0 % of the signal (Table S2, Fig. S6A–C), respectively. Typically, the first component indicates the trend in the climate series, as is the case here. The first RS in rainfall accounts for 69.9 % of the signal (trend) (Table S2, Fig. S6 D). The RS 2–3s represent the annual cycle also for each of the weather variables (see [29]). The final SSA-reconstructed series, obtained by combining all sub-components (as delineated in Table S2), account for 99.6 to 72.6 % of the variance for maximum and temperature and rainfall profiles, respectively.

3.2 SSA Results on Flowering Series

3.2.1 Reconstructed Series 1 (RS 1): Trend

As with the climate RSs, the first RS of each eucalypt species reflects its trend and accounts for the maximum amount of variation in three of the eight species examined: E. leucoxylon (62.3 %), E. tricarpa (36.6 %) and E. macrorhyncha (35.7 %) (Table 1, Fig. 2a, b, g). In the remaining species, E. camaldulensis, E. melliodora, E. polyanthemos, E. goniocalyx and E. microcarpa, the second RS (annual flowering cycle) accounts for the majority of the variance compared to the trend (RS 1) (Table 1).

Table 1 SSA reconstructed series, characteristics and variance accounted for species
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Fig. 2
figure 2

First reconstructed series (RS1). a E. leucoxylon, b E. tricarpa, c E. microcarpa, d E. polyanthemos, e E. melliodora, f E. camaldulensis, g E. macrorhyncha and h E. goniocalyx

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Although occurring at different times, there is a clear decrease in flowering intensity over the observation period in each species except for E. camaldulensis and E. goniocalyx (Fig. 2f, h). The track of this decrease appears most similar in E. leucoxylon, E. tricarpa and E. macrorhyncha (Fig. 2a, b, g). For E. microcarpa and E. polyanthemos (Fig. 2c, d), there is an increasing trend prior to a stable period (October 1951 to August 1953 and November 1945 to January 1947, respectively) before the decrease in flowering intensity commences. Eucalyptus camaldulensis also increases in flowering intensity reaching a peak in December 1953 and January 1954 prior to decreasing in intensity until July 1966 after which a sharp increase occurs. Eucalyptus goniocalyx is the most variable in its trend (Fig. 2h). There is a decrease in its flowering intensity between April 1940 and January 1956 where flowering intensity remains steady until May. After this flowering, intensity increases reaching the same commencement value in March 1.

3.2.2 Reconstructed Series 2 and 3: Annual Flowering Peaks

For all species, the RS 2–3s (Fig. 3a–g) represent the annual flowering cycle with the peaks indicative of the time of peak flowering. The agreement between the annual peaks from RS 2–3 and the original time series varies from weak in E. tricarpa (37.5.0 %) to moderate (66.7 %) in E. camaldulensis (Table 2). The most probable peak months are January for E. camaldulensis, E. macrorhyncha and E. melliodora; March for E. goniocalyx and E. microcarpa; July for E. tricarpa; September for E. leucoxylon and E. polyanthemos peaks in November (Tables 3 and S1). Agreement in all species is improved (range from 6.0 to 34.4 %) if the month, either side of the peak month, is included (Table 2).

Fig. 3
figure 3

Second and third reconstructed series (RS 2–3) for a E. leucoxylon, b E. tricarpa, c E. microcarpa, d E. polyanthemos, e E. melliodora, f E. camaldulensis, g E. macrorhyncha and h E. goniocalyx

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Table 2 Agreement between annual peaks in the original time series and RS 2–3 and RS 4–5
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Table 3 Cross correlations of the reconstructed series between species and climate: shorter [<6 months] and longer lags [≥6 months] prior to peak flowering intensity
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3.2.3 Reconstructed Flowering Series 4 and 5

The R4–5 series show the first difference in the flowering signal between the eight species (i.e. the previous RSs were similar across all species) but also point to where grouping of species occurs based on flowering commencement (Tables 1 and S1). Eucalyptus leucoxylon and E. tricarpa which commence flowering in autumn exhibit a quasi-biennial cycle (Fig. 4a, b, Table 1). The strength of agreement of these biennial peaks and the original time series is similar to that of the annual peaks (Table 2).

Fig. 4
figure 4

Fourth and fifth reconstructed series (RS 4–5) for a E. leucoxylon, b E. tricarpa, c E. microcarpa, d E. polyanthemos, e E. melliodora, f E. camaldulensis, g E. macrorhyncha and h E. goniocalyx

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Eucalyptus camaldulensis, E. melliodora and E. polyanthemos which commence flowering in spring (Table S1) exhibit a 6-monthly cycle (Fig. 4d–f). For each of these species, the R4–5 series is detecting the annual flowering peak (e.g. January for E. camaldulensis) (Table 2) with a similar strength as for the RS 2–3 series. However, it is not clear why peaks are detected at the other times as no flowering occurs.

The remaining three species, E. goniocalyx, E. macrorhyncha and E. microcarpa, commence flowering in summer. In this group, there is no similarity between the reconstructed series: E. goniocalyx has an approximate biennial cycle which ranges from 15 to 26 months (Fig. 4h, Table 1), E. macrorhyncha displays an approximate 4-year cycle (average of 49.2 months with range of 41 to 55 months) (Fig. 4g, Table 1) and E. microcarpa has a 6-monthly cycle (Fig. 4c, Table 1). Both E. goniocalyx and E. microcarpa have strong agreement with respect to their RS 2–3 series; however, in E. macrorhyncha the strength of agreement in percentage terms is lower.

3.2.4 Higher-Order (RS 6–7 and above) Reconstructed Flowering Series: Change Points and Sub-cycles

This set of RSs is where differences between all species occur. Eucalyptus camaldulensis did not have any discernible higher-order series. Eucalyptus leucoxylon has an average cycle of 20.5 months with a range of 23 months (1940 to 1942) to 18 months (1945 to 1947) compared to E. tricarpa which has on average a 4.4-year cycle with a range of 4.0 to 4.6 years.

Both E. microcarpa and E. polyanthemos exhibit a quasi-biennial cycle (mean 22.9 and 23.8 months, respectively) (Fig. S8 C, D). For E. goniocalyx, RS 6–7 represents a 6-monthly sub-cycle (Fig. S8 G) with some agreement with the annual peak (33.3 %). RS 8–9 for E. macrorhyncha represents a 10-year cycle (Table 1). RS 8–9 for E. melliodora’s biennial cycle is 24.2 months in duration, but ranges from 22 to 26 months.

These higher-order RSs also represent change point years: the quasi-biennial cycle (RS 4–5) of E. leucoxylon changes from aligning with the even years to the odd years in 1951. This cycle in E. tricarpa also changes to odd years in 1957. These also represent change point years for E. goniocalyx (RS 4–5) and E. melliodora (RS 8–9). These years (1951/1957) align with a drier El Niño period [40].

Figure 5 shows the leading higher-order SSA sub-components of flowering for E. leucoxylon, E. tricarpa and E. polyanthemos. Additionally, Fig. 5 shows the annual temperature and rainfall anomalies indicating wetter periods and years of maximum/minimum temperature extremes for the observation period. The final SSA-reconstructed series per species is obtained by summing up the significant subcomponents (RSs). Figure S9 gives the final reconstruction of E. melliodora’s flowering series.

Fig. 5
figure 5

Significant underlying SSA sub-components RS 2–3, RS 4–5 and RS 6–7 of flowering for a E. leucoxylon, b E. tricarpa, c E. polyanthemos and d anomalies compared to the standard reference period (1961–1990) for temperature (annual mean maximum and minimum) and annual rainfall

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3.2.5 Correlation Between Flowering and Weather: Main Drivers of Current Peak Flowering

The relationship between the reconstructed annual cycle of flowering (RS 2–3) and current climate variables were examined via correlational analysis (Table 4). Significant relationships (P ≤ 0.005) were found for both temperature and rainfall for all eight species. For E. leucoxylon and E. tricarpa there were negative correlations of peak flowering with each temperature variant (−0.895 < ρ < −0.693), in contrast to a positive relationship with rainfall (0.539 < ρ < 0.642). These relationships were reversed in the remaining species; hence, for these species, warmer and drier periods result in greater flowering intensity. In contrast, cooler and wetter periods lead to increased flowering in E. leucoxylon and E. tricarpa.

Table 4 Correlation of SSA reconstructed peak flowering intensity and SSA reconstructed climate variables (no lag)
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At an individual species level, SSA identified which of the climate variables were the main drivers of flowering. For E. leucoxylon, the main (negative) relationship with flowering intensity was with minimum temperature (ρ = −0.742) and for E. tricarpa with maximum temperature (ρ = −0.895) (Table 4). Minimum temperature was also indicated as the main temperature driver of flowering for E. goniocalyx (ρ = 0.270) and E. microcarpa (ρ = 0.383), but the strength of these values are weak so they should be viewed with some caution. In contrast, for E. camaldulensis (ρ = 0.802), E. melliodora (ρ = 0.851) and E. polyanthemos (ρ = 0.674), there was a significant positive relationship, with maximum temperature exerting a greater influence (Table 4). Flowering intensity in E. macrorhyncha was also influenced positively by all three temperature variants, with mean temperature being the most significant (ρ = 0.412).

3.2.6 Cross-correlations Between Flowering and Weather

SSA-reconstructed flowering and weather series were lagged from 1 to 12 months prior to the species-specific peak flowering month. The resultant SSA cross-correlation functions (SSA-CCFs) were sinusoidal signatures or profiles whether for temperature or rainfall (e.g. E. camaldulensis, E. goniocalyx, E. macrorhyncha and E. melliodora in Fig. 6). For all species, significant cross-correlational relationships (P ≤ 0.005) were found between flowering and both temperature and rainfall. Table 3 reports the highest absolute value of the SSA-based cross-correlations, for lags either in the short term (≤6 months) to peak flowering intensity, or the long term (>6 months). The number of months at which either lag occurs prior to peak flowering intensity differs across species. The SSA-CCFs show points of maximum positive and negative cross-correlation and that these occur systematically apart for each species (see the delta (∆) values, Table 3).

Fig. 6
figure 6

Resultant SSA cross-correlation functions of E. camaldulensis, E. goniocalyx, E. macrorhyncha and E. melliodora: a mean temperature and b rainfall

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The cross-correlation analysis highlights that the species which commence in the austral spring, E. camaldulensis, E. melliodora and E. polyanthemos, are similarly influenced by temperature with a difference in rainfall: both E. melliodora and E. polyanthemos are more strongly influenced by the short-term (negative) rainfall lag whereas in E. camaldulensis the long-term (positive) rainfall lag is slightly more influential (Table 3).

The triple, E. goniocalyx, E. microcarpa and E. macrorhyncha, which commence flowering in the summer, have the opposite directionality, with a positive short-term and negative long-term influence of rainfall. For E. macrorhyncha, the long-term influence of rainfall is slightly stronger than that of short term (Table 3). Likewise, this group has cross-correlations with temperature, which are negative in the short term (<6 months) and positive in the long term (>6 months) (Table 3).

This analysis also revealed that although E. tricarpa and E. leucoxylon both commence flowering in autumn and are similarly influenced at the time of peak flowering by temperature and rainfall (Table 4), they are, however, influenced differently throughout the year (Table 3). Specifically, the short-term lags of E. tricarpa (−1 month) were associated with negative cross-correlations with temperature and its long-term lags (−7 months) associated positively with temperature. By contrast, the short-term lags of E. leucoxylon were associated positively with temperature (−5 months) and its long-term lags (−10 months) associated negatively with temperature. Hence, for approximately 6 months before peak flowering, the influence of any temperature variable is positive for E. leucoxylon; which favours increased flowering intensity, but this would be moderated by the negative influence of rainfall. However, for E. tricarpa, 4 months prior to and including the peak flowering month, the influence of temperature is negative. This would result in a lower flowering intensity, with the positive influence of rainfall once again being a moderating factor. For all species, rainfall is shown to exert a negative influence when temperature is positive (Table 3).

To support the correlative results of SSA, the results of the optimal Var(4) model and the Var(12) model as the second best model are reported for E. leucoxylon.

The Var(4) model of E. leucoxylon flowering allows lags up to 4 months for three climate variables (minimum temperature, maximum temperature and rain) along with previous flowering intensity up to lag 4 months. A causal relationship between flowering and climate was established as follows. Overall, the mean level of E. leucoxylon flowering was 2.22 (t = 2.667, P < 0.009). After adjusting for the highly significant positive relationship between current E. leucoxylon flowering and its flowering 1 month earlier (β = 0.61, t = 9.68, P < 0.000001), flowering is significantly and positively related to minimum temperature at lag 4 (β = 0.19, t = 3.09, P < 0.003) and negatively related to rainfall 4 months earlier (β = −0.005, t = −2.23, P < 0.03). The model fits well with a multiple R 2 of 0.69 and an adjusted R 2 of 0.66.

The Var(12) models of E. leucoxylon flowering allow lags up to 12 months. In this model, the mean level of flowering in E. leucoxylon was 2.88. As with the Var(4) model, after adjusting for the highly significant and positive relationship between current E. leucoxylon flowering and flowering 1 month earlier (β = 0.57, t = 8.19, P < 0.000001), flowering is significantly and positively related to minimum temperature also at lag 4 (β = 0.15, t = 2.12, P < 0.04), but positively related to rainfall 12 months earlier (β = 0.005, t = 2.09, P < 0.04) (the negative trend at lag 4 with rain is not significant). The Var(12) model fits well with a multiple R 2 of 0.76 and an adjusted R 2 of 0.69. The effects of lag 12 temperature although negative for both temperature variants were found not to be significant; however, rain was.

4 Discussion

4.1 Trends and Cycles

SSA has separated out the trend and cycles in the climate variables with trend accounting for more than 69 % in each variable. It has also delineated the trend, annual and other cycles in flowering intensity in each of the species. The results of SSA analysis of trends in flowering over the period of study, for the four species previously studied, agree with recent wavelets results [25]. For E. melliodora and E. macrorhyncha, an overall decreasing trend in flowering was also detected. In E. camaldulensis and E. goniocalyx, this was not the case with each showing an overall variable flowering.

The annual cycle has been clearly delineated by subcomponent RS 2–3, with the mean month of peak intensity, therefore identified by its peaks (e.g. E. leucoxylon: September, E. tricarpa: July, E. melliodora: January, E. goniocalyx: March). For five of the species (E. leucoxylon, E. tricarpa, E. melliodora, E. polyanthemos and E. microcarpa), this is in agreement with those identified by other analytic methods (the mean flowering intensity in a flowering year and/or by wavelets [25]).

Biennial cycles or ‘on/off’ years have been noted by apiarists in each of the species studies from at least the early 1900s [41, 42] but often with the caveat of being location dependent. In this study, all species except E. camaldulensis and E. macrorhyncha were identified as having biennial cycles. Eucalyptus leucoxylon was the only species, which flowered each year over the observation period. Hence, the cycles observed in each of the remaining are in part probably attributable to years of no flowering (i.e. flowering intensity = 0). In E. leucoxylon, flowering generally alternates between a quasi-biennial (1950 to 1952, 1955 until 1963) and an annual cycle. It is the only species in this study, where the biennial cycle is associated solely with low (<2) intensity.

Eucalyptus tricarpa and E. macrorhyncha had an extended cycle of 4 years detected. A 4-year cycle in E. tricarpa has also been found earlier using auto-correlograms [43] but not by wavelet analysis [12]. Eucalyptus macrorhyncha was the only species to have a 10-year cycle detected. These longer-term cycles have also been noted previously by apiarists [44].

With the exception of E. leucoxylon, E. macrorhyncha and E. tricarpa, each species was found to have an approximately 6-month flowering cycle. Determining the biological significance of this is difficult, but confirmation remains the topic of future research.

The reconstruction of E. melliodora’s flowering series (Fig. S9) showed that the period 1958–1959 of no flowering is not optimally estimated by SSA. Spurious oscillations/values below zeros could be cancelled by higher-frequency harmonics and also would gradually disappear if more SSA terms were included in the reconstruction [45]. However, the number of terms (series) we used in the SSA reconstruction was chosen using a combination of the following: a scree diagram of the eigenvalues’ logarithms [29, 33] (Fig. S2); trends being identified as the slowly varying component of the series which did not contain oscillatory components [21, 33]; and eigenvalues which have the same amplitude and are harmonic (or almost) being considered to be oscillatory pairs and hence grouped [34]. Hence, the shape of the paired eigentriples (e.g. Fig. S3) which reflects the harmonic and their periodograms (Fig. S4) as well the matrix of w-correlations (Fig. S5) were also considered [21, 33]. Thereby, we have limited the number series used in our SSA reconstruction. This may be considered a current limitation of SSA, but future refinements to SSA will generalise SSA theory to better accommodate flat stretches and/or zeros and missing values [41–43], which are common features within multivariate phenological time series. A possible further limitation is that these spurious oscillations may artificially increase the correlation between flowering and climate time series, thus providing overestimated results.

4.2 SSA-Based Cross-correlation and Correlation Functions

SSA cross-correlations provide insight into the dynamic, changing relationship between climate and peak flowering intensity over the year for each species. The Var(4) and Var(12) models for E. leucoxylon indicate that there is a causative basis to the SSA cross-correlations and mirror the results of wavelet analysis [25]. They highlight, as in SSA, that the main temperature predictor and rain do not act in concert. Further, the Var(p) models support earlier findings that the influence of rainfall varies throughout the year. Wavelet analysis found that the long-term lags (from 8 to 12 months) prior to flowering for rainfall in E. leucoxylon were a negative and short-term lags (from two to seven months) were positive [25].

SSA correlations also highlighted similarities among species based on when they start flowering. There are three clear groupings with similar SSA-CCFs, namely, (1) E. leucoxylon and E. tricarpa; (2) E. camaldulensis, E. melliodora and E. polyanthemos and (3) E. goniocalyx, E. microcarpa and E. macrorhyncha. This is apparent if one examines the whole 12-month pattern of the SSA-CCF signatures (Fig. 6 and wavelet CCF Fig. S10), in relation to flowering duration and cessation, and 12 months back (note the vertical line in Fig. S10 delineates 12 months prior to peak flowering and the horizontal line depicts flowering duration), rather than on focusing on the signs of the CCFs at months of maximum positive/negative cross-correlation (Table 3).

Recently, the species within each of these groupings have also been clustered based on Self-Organising Maps (SOMs) [46] and wavelets patterns [45] underlying the flowering series, along with similar influences of climate [47]. In this study, for example, E. goniocalyx and E. microcarpa which both commence flowering in summer (Table S1) prefer a drier and warmer autumn and winter to be followed by a cooler and wetter spring, summer prior to flowering. Correspondingly, an upper threshold temperature of approximately 16 °C (mean temperature) has been demonstrated for E. microcarpa [47]. Additionally, Rawal et al. [48] have also recently demonstrated the negative influence of temperature (mean annual) 3 months prior to peak flowering in E. microcarpa. For the other species that commence in summer, E. macrorhyncha, the optimal conditions for increased flowering are a warm middle summer (January) though to early winter (June) with a cooler and wetter winter until late spring (November). There are some differences as flowering failed in each species on a number of occasions; however, on no occasion did they fail in the same year [30, 49].

For E. camaldulensis and E. melliodora, which in this study commence flowering in late spring (Table S1), increased peak flowering is aligned with a warmer and drier middle spring (October) and summer and a cooler and wetter middle autumn, winter and early spring. In some locations, apiarists have long regarded that these two species flower synchronously [41]. Overall, in our study location this is supported, as the climate influences are very similar and their flowering period is, on average, the same. Flowering in the other spring commencement species, E. polyanthemos, is enhanced by warm, dry conditions coinciding with peak flowering in November, preceded by a warm, dry middle winter (July) and spring, a cool, wet middle summer (January) remaining so until early winter (June). As with the summer flowering species, there are some differences: flowering in E. microcarpa failed in 5 years, E. camaldulensis failed to flower in 4 years, whereas E. melliodora failed only once over the study period [30, 49].

In the species which commence flowering in autumn (Table S1)—more intense peak flowering is likely to occur in E. leucoxylon when cool, wet conditions coincide with its peak flowering. However, peak flowering would be further enhanced if the preceding period from late summer (February) to middle winter (July) were warm and dry, and the previous spring (September) through to middle summer (January) cool and wet. Eucalyptus tricarpa requires the identical conditions at peak flowering month (i.e. cool and wet), but more or less the reverse conditions to E. leucoxylon in the months leading up to flowering, except in February and March, when flowering in both is enhanced by warm and dry conditions. This also agrees with the results of Rawal et al. [48] for E. tricarpa.

Correlation analysis of the SSA-reconstructed flowering and climate series show the same contemporaneous effects of temperature on E. tricarpa and E. leucoxylon’s flowering, with significantly increased flowering with decreased temperature, the main drivers for each species being different: maximum temperature for E. tricarpa and minimum temperature for E. leucoxylon. Additionally, both these species had a positive and significant relationship with rainfall. This negative influence of temperature and positive influence of rain in E. tricarpa were reported by Porter [50].

For E. camaldulensis, E. melliodora and E. polyanthemos, the reverse directionality was demonstrated—likewise for E. goniocalyx, E. microcarpa and E. macrorhyncha. Thus, flowering intensity in all species, except E. leucoxylon and E. tricarpa, is enhanced by warmer, drier conditions (at peak flowering time). Broadly speaking, at the time of peak flowering, a negative relationship with temperature implies that as these temperature variants increase during the observation period, flowering intensity decreased, with the positive influence of rainfall moderating flowering in wetter periods.

The SSA-CCFs show that for all species there is on average 6 months when temperature positively influences flowering and 6 months when the influence of temperature is negative. Additionally, the influence of rainfall is always opposite to that of temperature. That is, within a given species, if the cross-correlation with temperature is positive, at a particular time of year, then the relationship with rainfall is negative and vice versa. Until now, this phenomenon of 6-monthly cycling has been also confirmed in the wavelet study of Hudson et al. [25] (see Table S4 and Fig. S10 which report the wavelet-based cross-correlations and sinusoids) and is now formalised quantitatively in this SSA study. A mixed transition distribution (MTD) analysis [51] of four of the eight species studied here (E. leucoxylon, E. microcarpa E. polyanthemos and E. tricarpa) also established species-specific short-term and long-term cyclic lags and opposing signed profiles, relating flowering with climate states. These likewise indicated characteristic climatic signatures between specific species groupings and that on average there was a 6-month difference between short- and long-term climate effects.

There is some evidence of this 6-month cycling phenomenon between flowering and climate in earlier research—it can be observed in the reported tables and/or figures of the following studies: Fitter et al. [52] (Fig. 4), Sparks and Carey [53] (Table 2) and Roberts [54] (Fig. 3). As a consequence of the 6-month cycling, seasonal change points from negative/positive short-term to positive/negative long-term temperature and rainfall lags and vice-versa.

Finally, there appears, as such, to be at a very broad level a seasonal influence which points to a similar combination of climatic drivers, as established by synchronisation studies of Hudson et al. [46, 55]. Table S1 shows the eight species grouped into three clusters, with similarities in the seasons of the clusters’ phenophases highlighted in grey.

4.3 Other Influences on Flowering

The relationships between phenophases and climatic variables may be considered to be physiologically and/or statistically based [56]. Wavelet analysis [12] has found a so-called off phase sub-component (d2) which coincides with other reproductive phases (e.g. budding, seeding) in eucalypts. Earlier, House [57] suggested that whilst flowering time seems to be under the control of climatic conditions, it is during bud formation and development that there may be genetic control of the actual flowering periods in local (sub-)populations. Bud development rate influences the timing and quantity of flowering [58–60]. This relationship has rarely been examined for eucalypt [58, 61, 62]. In eucalypts, the development of buds often commences in a different season or, if in the same season, can occur in different years [63–65]. Additionally, eucalypts have been observed to have multiple cohorts of buds [66, 67]. As such, climate influences on budding may differ to flowering. Recently, Hudson and Keatley [61] investigated the influence of climate on budding, and additionally the effects of current and past budding (up to 3 months prior), and of climate on peak flowering for two of the eight species (E. tricarpa and E. leucoxylon). It was shown that for these two species, the commencement of the budding and the flowering phenophases were generally 4 months apart. Also, minimum temperature positively influenced bud development (above a minimum temperature threshold) and maximum temperature negatively influenced budding (below an upper threshold) [51]. The influence of rainfall on E. leucoxylon’s budding was nonlinear and benign until a threshold of 40 mm was reached, after which rainfall had a significant negative influence; no significant rain effect on budding was shown for E. tricarpa. Hence, unravelling the additional role of budding in all eight species will be a focus for future research.

Hudson and Keatley [61] also established that for both species (E. tricarpa and E. leucoxylon) flowering increased with budding intensity above a certain threshold, and the effect of the climate variables was opposite to their influences on budding in that flowering increased with lower minimum temperatures and with elevated rainfall (maximum temperature had a positive, though nonsignificant effect). The 4-month separation between the commencement of the two phenophases, the need for budding to have reached a particular maturity before flowering commenced and the opposing climate impacts on the phenophases may provide some insights into the 6-month cycling in the SSA-CCFs. Further examination of the budding-climate-flowering interplay is needed to confirm this postulate.

5 Conclusion

This study used SSA to analyse long-term records of the flowering of eight eucalypt species, E. camaldulensis, E. goniocalyx, E. leucoxylon, E. macrorhyncha, E. melliodora, E. microcarpa, E. polyanthemos and E. tricarpa. At an individual species level, SSA decomposition and reconstruction, in addition to (cross-)correlation analysis, (i) determined the strength, directionality and lagged nature of the relationship between climate and flowering; (ii) identified the primary climatic drivers at peak flowering intensity and earlier and (iii) confirmed the dynamic nature of the relationship between peak flowering and climate over the year. This study adds further understanding about the interplay between climate and flowering of eight eucalypt species—recognised as a major southern hemisphere genus. The results suggest a physiological foundation for this interplay. Species-specific SSA correlation and cross-correlation signatures were found relating flowering intensity with climate and indicating climatic impacts and signatures for synchronisation between specific species groups, in agreement to those recently identified. SSA methods are shown to be valuable tools for the investigation of phenological time series, in studies which aim to detect and understand local interacting climatic impacts on phenological phases and possibly of global climate change. Change point years for flowering based on SSA sub-components seem to generally align with some years of major shift in global ENSO signal as indicated by the extended multivariate ENSO index of Wolter and Timlin [40]. SSA gives results that are comparable to recent wavelet analyses of the same eight species. This supports the work of Bozzo et al. [68] who showed formally, via asymptotic properties of the eigenvalues of Toeplitz matrices, that SSA is related to Fourier analysis, as is wavelet analysis. Future refinements to SSA as discussed by Golyandina and Zhigljavsky [21] and Zhigljavsky [69] will generalise SSA theory to better accommodate flat stretches and/or zeros and missing values [70–72]—common features within multivariate phenological time series.