2.1 Study species and flowering phenology

We used flowering data from five Shorea species (Dipterocarpaceae) in the 50-ha forest dynamics plot at the center of the Pasoh Forest Reserve in Negeri Sembilan, Malaysia (2° 58′ 47′′ N, 102° 18′ 29′′ E) between 2002 and 2014 (Chen et al., 2018). S. macroptera, S. parvifolia, S. acuminata, and S. leprosula are in section Mutica, and the final species, S. maxwelliana, is in section Shorea. We calculated flowering intensity as the proportion of adult trees flowering each week. Sample sizes were 10, 10, 13, 35, and 23 individuals for S. macroptera, S. parvifolia, S. acuminata, S. leprosula, and S. maxwelliana, respectively. Data collection methods are as per Chen et al. (2018).

2.2 Meteorological measurements

We used the same weather data as in Chen et al. (2018). Daily mean air temperature and daily rainfall data were collected from a weather station fixed to the top of a 52 m observation tower extending above the local forest canopy, 2 km from the 50-ha plot, from September 2001 to October 2014 (Chen et al., 2018; Kosugi et al., 2012). As diel temperature profiles at different vertical levels (1, 5, 10, 20, 30, 40, 45, and 53 m) were similar (Ohkubo et al., 2008), data at the height of 52 m were used as representative values.

2.3 Environmental triggers for flowering

We adopted the same models of Chen et al. (2018) that environmental triggers needed for floral induction accumulate for n_i days prior to the onset of floral induction (Figure 1). Flowers then develop for n_d days before opening and falling (Figure 1). A previous study that monitored expression levels of flowering-time genes over four years showed that the onset of floral induction occurs at least one month before anthesis in Shorea species (Yeoh et al., 2017). Then, the cool unit at time t, CU(t), is calculated as:

(1)

where and x(t) are the threshold temperature and temperature at time t, respectively. max(x₁, x₂) is a function that returns a larger value for the two arguments. Drought unit at time t, DU(t), is defined as the difference between the mean daily accumulation of rainfall over n_i days and a threshold level of rainfall (). This drought unit is given as:

(2)

where and y(t) are the threshold level of rainfall and rainfall at time t, respectively. max(x₁, x₂) is defined similarly as in Equation (1). We generated time series for CU(t), DU(t) and a synergistic trigger of cool and drought unit (CU(t)×DU(t)) using estimated parameter values for n_d, n_i, and for each of the five Shorea species in a previous study (Chen et al., 2018).

2.4 Causality test using Empirical Dynamic Modeling (EDM)

We tested the environmental prediction hypothesis by two steps. Step 1: we first examined a causality from each environmental trigger of flowering (CU(t), DU(t) and CU(t)×DU(t)) to flowering. Step 2: for each environmental trigger that is estimated to be a causal factor of flowering, we examined whether there is a causal relationship from the environmental trigger of flowering to future rainfall. Future rainfall was defined as the cumulative sum of rainfall over n₄ days calculated from n₃ days after all census dates (Figure 1). n₃ and n₄ represent periods for seed development and rainfall accumulation during the time of seed germination and early seedling establishment, respectively. To test the environmental prediction hypothesis, we examined all combinations of n₃ and n₄ within the range of 1–150 and 1–50 by integers, respectively.

For causal inference, we used the framework of EDM. EDM is based on the theories of state-space reconstruction (SSR) (Deyle & Sugihara, 2011; Sauer et al., 1991; Takens, 1981). A multivariate dynamical system forms an attractor (i.e., a set of states and their trajectories) in a multidimensional state space where each coordinate corresponds to each system variable. The SSR theories prove that the original attractor can be reconstructed with time-delayed coordinates of an observed time series even without information of all system states (Deyle & Sugihara, 2011; Sauer et al., 1991; Takens, 1981). The EDM framework builds on the SSR theories and enables us to identify the causal relationship between different variables and measure the effect sizes of detected causality from an observed time series.

To infer causal relationships between variables, Convergent Cross Mapping (CCM), one of the EDM methods, is adopted. CCM has been used for causality testing by leveraging a dynamical property so that the univariate embedding of an affected variable contains information of the affecting variable (Sugihara et al., 2012). Specifically, a causality test is performed by checking the predictive skill (also called cross-mapping skill), which is measured by Pearson's correlation coefficient ρ between observed values of a tentative causal variable and its predicted (cross-mapped) values (Sugihara et al., 2012; Figure 2). The predicted values are calculated using the information of the nearest neighbors on the SSR attractor of the affected variable with an optimal time-delayed dimension (Sugihara et al., 2012; Figure 2). This method has been increasingly used in ecological studies (Kawatsu & Kishi, 2018; Sugihara et al., 2012; Ushio et al., 2018) as well as earth system sciences (Runge et al., 2019) and brain sciences (Hirata et al., 2016) to dissect complex interaction networks among variables. Using this approach, we assumed no specific functional relationship between flowering cues and flowering phenomenon. This allows the inclusion of any possible nonlinear influence of flowering cues on water availability during seedling establishment. For Step 1, the affected variable is flowering phenology of each Shorea species and the affecting variable is each environmental trigger of flowering. For Step 2, the affected variable is future rainfall and the affecting variable is each environmental trigger that causes flowering (Table S1).

Our CCM analysis took three steps in accordance with the standard protocol of EDM (Chang et al., 2017; Figure 2): (a) We determined the optimal embedding dimension E for the state space reconstruction using simplex projection (Sugihara & May, 1990; Sugihara et al., 2012) of affected variable, (b) we tested the nonlinearity of the SSR attractor constructed from time series data of affected variable, and (c) we performed causality tests by calculating the predictive skill of affected variable cross-mapping affecting variable. To cover biological processes of flowering initiation and to avoid overestimation of the analysis, we set time lag τ as 1 week and searched for the embedding dimension up to 30 weeks. To evaluate convergence of predictive skill, we calculated the predictive skill with the maximum library length (462 weeks both for flowering data and environmental trigger) and those with the minimum library length (=E + 1) using 1,000 bootstrap samples (ρ_max and ρ_min, respectively). Convergence is based on the fact that the longer the time series length, the smaller the distance between the trajectories on the manifold. When Y causally influences X, it leads to an increase of predictive skill with increasing time series length, converging to a plateau (Figure 2). Additionally, to check the false high predictive skill owing to seasonality for Step 1, we generated 1,000 twin surrogate data that preserve the nonlinearity and seasonality of the original affected time series but lose the causal relationship with the affecting variable (Thiel et al., 2006; Ushio et al., 2018). The predictive skill of the library variable cross-mapping surrogate (ρ_surr) was then calculated. We evaluated the causality significance using two criteria (Figure 2): (a) The 95% lower confidence limit of the difference between ρ_max and ρ_min (ρ_max–ρ_min) is greater than zero, and (b) mean of ρ_max is larger than the 95% upper confidence limit of ρ_surr. Optimal embedding dimension and nonlinearity parameters for Step 1 and Step 2 are listed in Tables S2 and S3, respectively.

2.5 Measuring interaction strength from affecting to affected variables

To evaluate the interaction strength from the affecting to affected variables, we measured the strength and sign of effect from each affecting variable to affected variable listed in Table S1 using the S-map (sequential locally weighted global linear map) method (Chang et al., 2017; Sugihara, 1994). In the S-map method, partial derivatives of affected variable X by affecting (causal) variable Y (i.e., Jacobian ∂X/∂Y (Deyle et al., 2016)) are calculated in a multivariate state space at each time point, yielding coefficients that are a good approximation of the interaction strength from Y to X.

To calculate partial derivatives of affected variable by affecting variable, we created a multivariate SSR attractor as follows. First, we reconstructed a univariate attractor with dimension E with a time series of affected variable. Then, the last coordinate of the univariate embedding was replaced by an affected variable. Based on the multivariate attractor, the strength and sign of effect from affecting to affected variables were calculated using the S-map.

R version 3.5.1 (R Core Team 2018) was used for all EDM analyses with the EDM package (rEDM version 0.7.3) for R. We normalized each time series to have mean = 0 and sd = 1 so that Euclidian distance in the multivariate embedding is scale-free.

3.1 Causality from potential proximate cues of flowering to actual flowering

The causality of cool unit (CU) on flowering was not detected in all four species in section Mutica (Table S4). In S. maxwelliana, the only species in section Shorea, flowering was causally influenced by CU (Table S4). On the contrary, we found significant causality of drought unit (DU) and the combination of cool and drought units (CU × DU) on flowering in all five species (Table S4). The predictive skills of flowering phenology cross-mapping for CU × DU were highest among all environmental signals for all Shorea species (Table S4).

We next examined the effect of causal proximate cues (DU and CU × DU) on flowering by multivariate S-map analyses. In two species (S. acuminata and S. maxwelliana), the effect of DU on flowering was positive over almost all monitoring periods (Figure 3c,e). In the other three species, the effect of DU on flowering was a mix of positive or negative even during flowering (Figure 3a,b,d). Conversely, a positive effect from CU × DU on flowering was detected in all species, especially during flowering events (Figure 3). The effect of CU × DU on flowering was elevated when flowering happened in most of species, except for S. macroptera (Figure 3a). This result suggests that CU × DU is a more stable causal cue of flowering than the sole use of DU.

3.2 Predicting future rainfall with proximate cues

Both DU and CU × DU causally influenced future rainfall for diverse parameter values for seed development period (n₃) in all species when the accumulation period of rainfall (n₄) is greater than 30 days (Figure 4). The parameter ranges where causality was detected were similar between DU and CU × DU, but varied slightly among species. In the three early flowering species in section Mutica, the means of the fruit development period with causality were relatively long (93, 77, and 67 days for S. macroptera, S. parvifolia, and S. acuminata, respectively), while it was shortest in S. leprosula which has the latest flowering of all species studied (64 days; Figure S1a). The differences in values of n₃ reflect the order of sequential flowering among these species (Chan & Appanah, 1980; Chen et al., 2018). The means of the accumulation period of rainfall (n₄) with causality were not different between species (Figure S1b).

The effect of causal cues of flowering (DU and CU × DU) on the availability of rainfall during seedling established was estimated by S-map analyses. We set the fruit development period (n₃) as the observed peak of fruiting for each species (22, 18, 17, 16, and 15 weeks after the time of flower peak for S. macroptera, S. parvifolia, S. acuminata, S. leprosula, and S. maxwelliana, respectively; Hosaka et al., 2017). The accumulation period of rainfall (n₄) was set as 45–50 days for all species because strong causality from the environmental cue to future rainfall was detected (Figure 4). The effect of DU on rainfall availability at the peak of fruiting was significantly positive for most of accumulation periods of rainfall in all species (Figure 5a–e). Similarly, all species showed the significantly positive effect from CU × DU to rainfall availability at the peak of fruiting (Figure 5f–j), except for the accumulation period of 50 days in S. maxweliana (Figure 5j).

Lastly, we compared the predictive skill of future rainfall by DU and CU × DU. Although the predictive skill was not significantly different between DU and CU × DU in S. macroptera (Figure 6a), for the rest of four species, predictive skill was significantly higher in CU × DU than in DU (Figure 6b–e). The predictive skill of future rainfall by CU × DU varied among species, revealing relatively high predictive skill in S. parvifolia and S. leprosula (mean of ρ_max > 0.4), while it was low in S. maxwelliana (mean of ρ_max < 0.2). These results suggest that the combination of chilling and drought is a more effective signal for environmental prediction than drought alone, and species-specific flowering cues would result in differential skills to predict favorable environment conditions during seedling establishment. The mean of seed fall peak was 127 days after flowering. The cumulative sum of 50-day rainfall after 127 days from flowering revealed highly variable profiles with distinct peaks and valleys (Figure 6f). Projection of observed general flowering events on the plot showed that general flowering always coincided with an increasing phase of rainfall (Figure 6f). This consistency would be the result of optimizing flowering time in response to environmental signals that associate with rainfall during seed fall, namely the combination of cool temperature and drought.