Forecasting seed production in perennial plants:
identifying challenges and charting a path forward

Valentin Journé<fnref n="1" />, Andrew Hacket-Pain<fnref n="2" />, Iris Oberklammer<fnref n="3" />, Mario B. Pesendorfer<fnref n="3" />, Michał Bogdziewicz<fnref n="1" />

keywords: masting | forecasting | resource | climate | seed production

Corresponding authors: michalbogdziewicz@gmail.com & journe.valentin@gmail.com

ORCID:

Valentin Journé: https://orcid.org/0000-0001-7324-7002

Andrew Hacket-Pain: https://orcid.org/0000-0003-3676-1568

Iris Oberklammer: https://orcid.org/0000-0002-6518-271X

Mario B. Pesendorfer: https://orcid.org/0000-0002-7994-7090

Michał Bogdziewicz: https://orcid.org/0000-0002-6777-9034

Twitter:

Valentin Journé: @Valentin_Journe; Iris Oberklammer: @I_Uppercanyon; Mario B. Pesendorfer: @MBPesendorfer; Michał Bogdziewicz: @mic_bog

<footnote n="1">¹Forest Biology Center, Faculty of Biology, Adam Mickiewicz University, Uniwersytetu Poznańskiego 6, 61-614 Poznan, Poland.</footnote>

<footnote n="2">²Department of Geography and Planning, School of Environmental Sciences, University of Liverpool, Liverpool, United Kingdom.</footnote>

<footnote n="3">³Institute of Forest Ecology, Department of Forest and Soil Sciences, University of Natural Resources and Life Sciences, Vienna, Peter-Jordan-Strasse 82, A-1190 Austria</footnote>
## Abstract

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Interannual variability of seed production, known as masting, has far-reaching ecological impacts including effects on forest regeneration and the population dynamics of seed consumers. Because the relative timing of management and conservation efforts in ecosystems dominated by masting species often determines their success, there is a need to study masting mechanisms and develop forecasting tools for seed production. Here, we aim to establish seed production forecasting as a new branch of the discipline. We evaluate the predictive capabilities of three models - *foreMast*, ΔT, and a sequential model - designed to predict seed production in trees using a pan-European dataset of *Fagus sylvatica* seed production. The models are moderately successful in recreating seed production dynamics. The availability of high-quality data on prior seed production improved the sequential model's predictive power, suggesting that effective seed production monitoring methods are crucial for creating forecasting tools. In terms of extreme events, the models are better at predicting crop failures than bumper crops, likely because the factors preventing seed production are better understood than the processes leading to large reproductive events. We summarize the current challenges and provide a roadmap to help advance the discipline and encourage the further development of mast forecasting.

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## Introduction

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Mast seeding or masting, highly variable and synchronized annual reproduction, is common in perennial plants (Kelly & Sork, 2002). Central to plant population dynamics, masting provides foundational but unstable resources for seed consumers, creating cycles of feast and famine in food webs (Schmidt & Ostfeld, 2008; Clark et al., 2019). The pulsed nature of masting influences the success of management and conservation actions, thus making short-term predictions of seed production a powerful potential tool for practitioners (Pearse et al., 2021). For instance, planning of forest regeneration actions, such as soil scarification or prescribed fires, must be timed with seed crops (Girona et al., 2018), and the timing of masting in relation to disturbance may influence forest recovery, shaping management responses (Rammig et al., 2007). Masting may also lead to multiyear seed scarcity that may challenge the timeframe of funded restoration projects (Woolsey et al., 2018). In some species, bumper crops of seeds are extremely rare (e.g. once in several years), and seeds cannot be stored, resulting in a mismatch of planned activities and seed availability (Kettle et al., 2010, 2011). Anticipatory forecasting of seed production with several-months notice, "mast cast", would therefore prepare forest agencies, managers, and other stakeholders to utilize the rare and short windows of opportunities for restoration (Kettle et al., 2010, 2011). Similarly, to manage animal populations that rely on masting plants, the timing of reintroduction efforts and other interventions needs to be timed in relation to annual variation in plant reproduction (Fidler et al., 2008). This includes the removal of pest species that are part of the trophic chain anchored by seeds, so that the efficacy of eradication efforts can be maximized (Köhnke et al., 2020). Finally, masting affects public health near forests, as it can determine the annual pollen load for tree species, and, through indirect effects on trophic chains, the transmission of zoonotic diseases to humans (Tseng et al., 2020; Bregnard et al., 2021). The development of forecasts of plant reproduction and subsequent trophic cascades would thus give conservationists, land managers, and public health officials advance notice of upcoming bumper crops or crop failures. While ecological forecasting is slowly starting to enter the mainstream of the discipline (Lewis et al., 2022), surprisingly sparse information exists on the current state of the art in forecasting plant reproduction (Holland & James, 2015a; Chiavetta & Marzini, 2021; Pesendorfer et al., 2021; Pearse et al., 2021).

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Accurate modeling of reproduction in perennial plants has long been challenging due to the large interannual and inter-individual variability inherent to masting (Vacchiano et al., 2018; Clark et al., 2021; Journé et al., 2022). This problem was further compounded by limited data availability (Koenig, 2021; Clark et al., 2021). However, with the recent advancement of global coordination in monitoring and data synthesis, we now have access to broad taxonomic data sets for plant reproduction time series (Pearse et al., 2020; Clark et al., 2021; Hacket-Pain et al., 2022). With this opportunity, we aim to develop mast forecasting ("mast cast") as a new branch of the discipline. Masting may offer high potential for ecological forecasting, as the data consists of extended time series with well-established abiotic drivers, potentially providing high intrinsic predictability (Pennekamp et al., 2019; Pearse et al., 2016, 2021). Additionally, the efforts to develop mast forecasting will lead to wider benefits for the discipline, as it will require the formulation of quantitative predictions and challenge researchers to compare the explanatory power of empirical and process-based models across different geographic regions and ecological contexts (Lewis et al., 2022). To take the first steps in mast forecasting, we use European beech (Fagus sylvatica) masting across Europe as a case study to discuss the current state of the art and outline a roadmap for future development. European beech is a suitable model species due to its broad distribution, forest-forming nature, well-studied seed production mechanisms, and exceptional data availability (Hacket-Pain et al., 2022). Although our focus is on this particular species, the sources of uncertainty and ways to improve masting prediction discussed in this study are generalizable. Our goal is to motivate new efforts that will enhance our understanding of seed production ecology and provide the tools that land managers urgently need.

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What determines masting and how predictable is it? Currently, we understand masting as a result of the interplay between weather and the internal resource dynamics of plants, and their combined impact on flower and seed development (Pearse et al., 2016; Pesendorfer et al., 2021; Bogdziewicz et al., 2020a; Roncé et al., 2023). Weather, as an external factor, has been demonstrated to impact various stages of the reproductive process, including flower initiation, pollination, and seed abortion (Kon & Noda, 2007; Koenig et al., 2015; Nussbaumer et al., 2020; Satake & Kelly, 2021). On the other hand, the endogenous effects of resource depletion (e.g. carbon or nitrogen) limit seed production after large seed crops (Crone et al., 2009; Sala et al., 2012; Han & Kabeya, 2017). Thus, predictions of masting mainly rely on our understanding of the links between weather and seed production, the sensitivity of masting to weather and resource depletion, and the uncertainty of these drivers.

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To understand the current state of seed production models for *F. sylvatica*, we compare two published tools for predicting masting based on empirical relationships between seed production and weather, the ΔT model and *foreMast*, with a mechanism-based model (hereafter "sequential model") that includes additive weather effects along a sequence of phenological steps involved in seed production. The ΔT model predicts seed production based on the difference in summer weather between the two years leading up to seed fall (Kelly *et al.*, 2013). It does not include the impact of resource availability, instead relying on the idea of an epigenetic weather memory that results in elevated flower production if hot summers follow cold ones (large ΔT values) (Samarth *et al.*, 2020, 2021). The ΔT forecast is utilized by New Zealand's National Predator Control Program, for example in forecasting Southern beech masting at sites where native species are vulnerable to the effects of mast-induced increases in the abundance of invasive predators (Holland *et al.*, 2018), but it can also be applied to *F. sylvatica* (Vacchiano *et al.*, 2017). The second tool, *foreMast* (Chiavetta & Marzini, 2021), is an R package developed specifically for *F. sylvatica*, using data from a global time series database (Ascoli *et al.*, 2017) to forecast mast events based on summer temperatures of the two years leading up to seed fall. Previous work has shown that when a cold summer is followed by a hot one, beech is likely to produce a
bumper crop (Vacchiano *et al.*, 2017). Additionally, *foreMast* indirectly accounts for the effects of resource depletion on seed production through a parameter that decreases the probability of consecutive mast years.

In addition to the two existing models, we constructed the *sequential model*, which takes into account the previous year's seed production as well as a series of weather drivers of seed production in *F. sylvatica*. Unlike ΔT and *foreMast*, the *sequential model* explicitly includes the direct relationship between sequential years of seed production, a crucial factor in mast seeding (Knops *et al.*, 2007; Crone & Rapp, 2014; Miyazaki *et al.*, 2014). Additionally, *F. sylvatica* seed production is not only correlated with temperatures in the past two summers (Vacchiano *et al.*, 2017), but also with the weather during pollination in spring (Mund *et al.*, 2020), late spring frosts (Allevato *et al.*, 2019; Journé *et al.*, 2021), and summer drought (Nussbaumer *et al.*, 2020) (see Table 1 for a model summary). By including predictors from various time periods before the seed fall event, we hope to gain an initial understanding of the potential forecast horizon for *F. sylvatica* seed production. This approach should provide insights into which data to collect, how future models should be structured, and what experiments should be prioritized to enhance the forecasting ability of masting in this species and beyond (Dietze, 2017).

<table><caption>**Table 1:** Overview of the three models used to hindcast seed production in *Fagus sylvatica*. † *T0* is the seed fall year, *T1* is the year preceding the seed fall, *T2* two years preceding the seed fall.</caption><thead><tr><th>Model</th><th>Coefficient type</th><th>List of predictors used</th></tr></thead><tbody><tr><td>foreMast</td><td>Inherited from foreMast package</td><td>Summer precipitation (T1, T2), summer temperature (T1, T2), auto-correlation term that helps to avoid two consecutive high-seed production years.</td></tr><tr><td>ΔT</td><td>Site specific estimation</td><td>Summer temperature difference T1-T2.</td></tr><tr><td>Sequential</td><td>Site specific estimation</td><td>Summer temperature (T1, T2), seed production T1, late spring frost (T0), spring temperature (T0) and summer moisture deficit (T0).</td></tr></tbody></table>

## Where are we?

How good are current models at predicting seed production? Which parameters have the strongest impact on predictions? How does data quality matter? To start addressing these questions, we compared the *foreMast*, ΔT, and sequential models by performing a hindcast analysis to assess their ability to recreate past seed production (Petchey *et al.*, 2015; Holland & James, 2015a). In addition to traditional metrics of model fit such as $R^2$, the proportion of the explained variance, and *RMSE*, the root-mean-square error, we evaluated how well the predicted values align with observed values across the range of mast production and whether they accurately capture the interannual variability (CV - coefficient of variation) of mast production in beech populations. Finally, to investigate the effect of data quality on forecasting ability, we explored the relationship between prediction errors and site-specific covariates, such as the seed production monitoring method. With this analysis, we aim to lay the foundation for mast forecasting by exploring the potential of current models to recreate past seed production in European beech (Dietze, 2017).
<figure><img src="image_1.png" /><figcaption>**Figure 1:** Goodness-of fit metrics for ΔT, *foreMast*, and the sequential model. a) Predicted vs. observed values in the three models for each site-year observation and predictions. Black dotted lines indicate a 1:1 relationship, while blue lines are regressions between predicted and observed values. b) Models *R*², and c) Root-mean-square error (*RMSE*). We computed *R*², i.e. the proportion of variance in the dependent variable that can be explained by the independent variables, and *RMSE*, i.e. the average difference between values predicted by a model and the actual values, for each site and combined them for each model to determine boxplot size. The asterisks show the statistical difference between each group tested with a t-test and adjusted *P* (**** for *P* < 0.0001, *** for *P* < 0.001, ** *P* < for 0.01, * *P* < for 0.05, and n.s. for *P* > 0.05). Further metrics comparisons between the three models are presented in Figure S2 and S3.</figcaption></figure>

To assess our ability to predict seed production in beech populations, we used 94 time series of seed production data with at least 8 years of observations from the MASTREE+ database (see Supporting Information Methods S1) (Hacket-Pain *et al.*, 2022). These data were combined with weather data for each location, starting in 1980. The *foreMast* algorithm provides masting forecasts for any given set of coordinates, while the coefficients for the ΔT and sequential models were estimated by fitting each model to each time series, yielding site-specific values for coefficients (Fig. S1). We then compared observed and predicted values for seed production in each time series. To accommodate among-site variation in methods of seed production monitoring, we scaled seed production for each site between 0 and 1 by dividing all values by the highest recorded value in the time series.

Models tend to over-predict seed production in years of poor seed production, and also under-predict seed production in large seeding years (Fig. 1 a). The sequential model showed higher accuracy in recreating seed production compared to the simpler *foreMast* and ΔT models (Fig. 1). The median *R*² for the sequential model was 0.65 [95% CI = 0.47, 0.82]. The median
$R^2$ for the other two models were lower, with $\Delta T$ equal to 0.26 [0.12; 0.36] and *foreMast* = 0.25 [0.13; 0.35]. The *RMSE* values further indicate the sequential model performed best, and indicate that the $\Delta T$ model performed better than *foreMast* (Fig. 1c). The median *RMSE* for the sequential model was 0.18 [95% CI = 0.12, 0.22]. The median *RMSE* for the other two models were higher, with $\Delta T$ equal to 0.27 [0.24; 0.30] and *foreMast* = 0.39 [0.35; 0.44]. The lower performance of the *foreMast* model was expected, as the other models were fitted locally to individual time series. Meanwhile, the higher $R^2$ for the sequential model is associated with its higher complexity, as it includes six parameters compared to only one in the $\Delta T$ model. However, our goal here is not necessarily to find the most parsimonious model, but one that will provide the most useful prediction of masting given the data available and the requirements of the user. The weather parameters used in the sequential model are easily accessible, so the increase in accuracy may come at a low cost. Still, monitoring seed production is logistically challenging and some predictors in the sequential model occur during seed maturation, which could reduce the potential forecast horizon (Petchey *et al.*, 2015; Pearse *et al.*, 2021). Thus, we next evaluated the impact of each predictor on the performance of the sequential model.

To determine the impact of each parameter on the predictive power and potential forecast horizon of the sequential model, we employed two approaches. First, we dropped individual variables, re-fit the model, and evaluated its performance to assess the relative importance of each variable. Second, we added the parameters to the model in the phenological order of their occurrence, which provides information on the time frame when meaningful predictions of seed production may be possible (i.e. the potential forecast horizon). Our analysis showed that the previous year's summer temperature and seed production are the most significant predictors of model performance (Fig. 2a,b, Fig. S4). This implies that beech seed production can be predicted with good accuracy with one year's lead time, but it requires monitoring of seed production (Fig. 2b). Including information on weather conditions during flowering and seed maturation (spring temperature, summer drought, frost) can further improve model predictive power (Fig. 2b), but it comes at the cost of a reduced forecast horizon, which may limit its usefulness for certain management activities.

Given limited research time and resources, it is crucial to focus on factors that bring the greatest improvement in predictive power. Generally, the most impactful factors on the predictability of ecological processes are those that the process is highly sensitive to and those characterized by high uncertainty (Dietze, 2017). As past studies and our analysis indicate, masting is impacted by weather (low input uncertainty and high sensitivity) and past seed production (high input uncertainty and high sensitivity). This combination implies that reliable forecasts depend on the availability of high-quality seed production monitoring. To test this, we analyzed the effect of different seed crop monitoring methods which vary in their accuracy on the $R^2$ of the models.

In the MASTREE+ dataset, annual seed production is estimated at the population level using various methods, including seed counts - ground-counting within a certain time frame (Bogdziewicz *et al.*, 2020b), seed traps (Bajocco *et al.*, 2021), and visual crop assessment - a population-level estimate of the year's crop, such as the proportion of reproducing individuals. Visual assessments are often used over large areas by foresters, e.g. by Polish State Forests (Pesendorfer *et al.*, 2020). Of these methods, seed traps are expected to provide the lowest input uncertainty in terms of past seed production, which leads to higher model predictive power, as demonstrated by our model (Fig. S5). The median $R^2$ for the sequential model trained on time series based on seed traps (0.74 [95% CI = 0.45, 0.87]) was much higher than those of visual crop assessment (0.51, 95% CI = 0.44, 0.60) and the seed count method (0.58, 95% CI = 0.49, 0.65). It is worth noting that all "seed count" time series in our data come from trees in the UK beech monitoring program (Fig. S5), which was severely affected by climate change
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 2:** Effects of focal predictors on the sequential model performance ($R^2$). a) Each boxplot shows the sequential model $R^2$ with one predictor removed, b) predictors added in phenological order. We determined $R^2$ for each site and computed them together to determine boxplot size. An analogous figure with *RMSE* is in Fig. S4</figcaption></figure>

(Bogdziewicz *et al.*, 2020b). It is therefore uncertain whether the low $R^2$ values are due to the method's accuracy (Koenig *et al.*, 1994; Touzot *et al.*, 2018; Tattoni *et al.*, 2021) or due to changes in the climate that altered the masting processes at these sites, which merits further investigation (Bogdziewicz, 2022).

Forecasting large mast years and crop failures is crucial due to their extensive impact on ecosystem functioning (Pearse *et al.*, 2021). Therefore, we examined whether the models predict the data well at the extreme ends (mast and failure years). To this end, we evaluated whether the predicted values are low enough (in failure years) or high enough (in mast years). We defined
<figure><img src="image_4.png" /><figcaption>**Figure 3:** Effects of seed production estimation method on the sequential model *R*². The methods are seed count (ground counting within a given time frame), monitoring with seed traps, and visual crop assessment. The asterisks represent significant differences between each group tested with a t-test (**** for *P* < 0.0001, *** for *P* < 0.001, ** *P* < for 0.01, * *P* < for 0.05, and n.s. for *P* > 0.05). An analogous figure with *RMSE* is in Fig. S6.</figcaption></figure>

mast years as years when seed production was higher than the site-specific 80th centile (9.64%±5.19 SD site-years), and failure years as below the 20th centile (62.8%±17.5 SD site-years). Importantly, that categorization was done only once the predictions of the models were obtained, not for fitting the models. We note that dividing seed production into mast and non-mast is an ecologically false dichotomy in the sense that the distribution of seed production is not binomial, and the "mast year" definition is subjective. Nonetheless, such categorization can be useful from the forecasting/management perspective and is often used in forestry (Pearse *et al.*, 2021).

Our evaluation revealed that the three models had limited success in accurately predicting extreme seeding events. In our dataset, large mast years occurred in 9.64% of the years. The ΔT model correctly predicted these years in only 0.19% of cases, but got false negative in 9.45% of the observed mast years. Equivalent performance for *foreMast* was 4.68% true positive and 4.97% false negative, and for the sequential model it was 3.63% true positive and 6.01% false negative. On the other hand, the models performed better in predicting crop failures (defined as seed production below 0.2), although still far from satisfactory (Fig. 4a). In our dataset, crop failures occurred in 62.8% of the years. The ΔT model correctly predicted these failures in 19.9% of the years and predicted 42.9% of false negatives. Similar results were observed for the *foreMast* model, with correct predictions of 17.4% and failed predictions with 45.4% of false negative. The sequential model performed the best in this aspect, with correct predictions of 42.8% and failed predictions with false negatives in 20.0% (Table 2).

Interannual variation of seed production is the defining feature of masting. Thus, we further examined how the interannual variation of predicted values recreates the observed variation. Despite the better performance in predicting low seed production years, the overall poor ability of the models to predict large seed crops leads to low estimates of the variability of masting time series (Fig. 4b). A similar finding was reported in a study of seed production in valley oaks (*Quercus lobata*), where historical crop failures were accurately modeled, but the extent of seed production in mast years was not well captured (Pesendorfer *et al.*, 2016).

Assessing the ability of the models to predict extreme seeding events (large mast and failure years) in addition to their performance based on *R*² provides valuable insights into models' effectiveness. Both mast and failure years are underpredicted, with especially poor performance
<table><caption>**Table 2:** Prediction of mast and failure years by the three evaluated models. For each time series, we scaled seed production to a range of 0 - 1, and defined mast years as years when seed production was above 0.8, whereas failures as below 0.2. Based on this arbitrary threshold, mast years occurred in ~ 9.64%, and failure years occurred in ~ 62.8% of years. We reported average values with standard deviation (SD) in percent.</caption><thead><tr><th></th><th>Mast years</th><th>Failure years</th></tr></thead><tbody><tr><td><em>True positive (hit)</em></td><td></td><td></td></tr><tr><td>ΔT</td><td>0.19% ± 1.33</td><td>19.9% ± 17.9</td></tr><tr><td><em>foreMast</em></td><td>4.68% ± 4.42</td><td>17.4% ± 5.55</td></tr><tr><td>Sequential</td><td>3.63% ± 5.78</td><td>42.8% ± 21.6</td></tr><tr><td><em>False positive (type one error)</em></td><td></td><td></td></tr><tr><td>ΔT</td><td>0% ± 0</td><td>1.18% ± 3.05</td></tr><tr><td><em>foreMast</em></td><td>14.0% ± 6.1</td><td>1.92% ± 3.97</td></tr><tr><td>Sequential</td><td>0.42% ± 1.52</td><td>1.94% ± 3.71</td></tr><tr><td><em>False negative (type two error)</em></td><td></td><td></td></tr><tr><td>ΔT</td><td>9.45% ± 5.17</td><td>42.9% ± 16.6</td></tr><tr><td><em>foreMast</em></td><td>4.97% ± 4.74</td><td>45.4% ± 15.7</td></tr><tr><td>Sequential</td><td>6.01% ± 5.10</td><td>20.0% ± 15.0</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 4:** Distribution and variation of observed and predicted seed production. a) Histograms with density curves of all observed and predicted annual seed production. b) Coefficient of variation (CV) calculated based on observed and predicted values of annual seed production at each site. We computed CV by dividing standard deviation (SD) by the mean value of seed production of the time series for each site. Predictions are based on the three evaluated models, i.e. ΔT, *foreMast*, and sequential model. We computed CV based on annual seed predictions, and from scaled observations, for each sites (Sequential, $R^2$ = 0.29; *foreMast*, $R^2$ = 0.02; ΔT, $R^2$ = 0.05). For the three models in b) we fitted a loess regression to visualize trends.</figcaption></figure>

in the prediction of mast years. The sequential model predicts failure years better, partially due to its inclusion of the previous year's seed production. That model accuracy in predicting failures decreases when the previous year's seed production is removed (correctly predicted true positive failure years: 37.2%). The sequential model also performs better in predicting failure years when trained solely on seed trap data, which is associated with lower uncertainty (correctly

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predicted true positive failure years: 47.2%). These findings support the idea that resource
depletion plays an important role in seed production, making seed failure after high-seed years
predictable (Crone et al., 2009; Abe et al., 2016), while the mechanisms driving high-seed years
are less clear or more stochastic (Schermer et al., 2020), highlighting this as a priority for future
research (Bogdziewicz, 2022).
**Box 1: Hindcasting vs forecasting.**

Analysis in our study is based on hindcast analysis that assessed models' ability to recreate past seed production. Actual forecasting will require models to be trained on existing data and predict unobserved future seed production, which will likely result in reduced performance. To illustrate that, we used a cross-validation procedure with the sequential model, based on a random data-split (Yates et al., 2023). For each site, we trained the model with 70% of randomly selected observations, and repeated this process five times. The $R^2$ was evaluated with the remaining 30% of observations across the 10-fold block selection for a model trained on 70% of the observations. With cross-validation, observations can be used for training or validation only, whereas a model trained with the full dataset would include these 30% of observations for both model training and validation. Training data on a subset reduces the sequential model accuracy in predicting both failure and mast years (Fig. 5). On average, the models trained with split data achieved a lower mean $R^2$ at 0.41 [CI 97.5% = 0.12, 0.65] compared to a model trained with all observations ($R^2$ = 0.65 [0.42, 0.94], Fig. 5b). The take-home message is that forecasting masting shows great early promise, but substantial efforts will be required before we can predict masting with satisfying accuracy.

<figure><img src="image_6.png" /><figcaption>**Figure 5:** Comparison between cross-validation (data-split) and full data for model training. Predicted vs observed values for a model with (a) data-split and (b) a model trained on full data. Black dotted lines indicate a 1:1 relationship, while blue lines are regressions between predicted and observed values, each dot is a site-year. c) The $R^2$ from the model trained on 70% of the dataset or trained on the full dataset; an analogous figure with *RMSE* is given in Fig S7. d) Histogram and density of observed values, values predicted in cross-validation (70% of the data used for calibration, 30% for the validation), and values predicted by the model trained on the full data. Note that we used 30% of the observations for each site randomly sampled ten times, which resulted in a different sample compared to Fig. 1.</figcaption></figure>
What is next?

Our results, based on one of the best-studied systems in the field, suggest that much work is needed to develop reliable tools for forecasting seed production in masting plants. The abilities of models to recreate past seeding were limited, even in predicting the data on which they were trained (Box 1). However, the path forward has become clearer. The sequential model, which considers a broader range of factors affecting seed production compared to the other two models, shows promising accuracy. Despite this, the models' inability to accurately predict bumper crops remains a crucial limitation. One potential solution could be to transition the sequential model from an additive to an interactive configuration (Kelly et al., 2013; Vacchiano et al., 2017). On the other hand, the ability to predict crop failures is much improved compared to other models, likely due to the deterministic impact of seed production on future reproductive investment.

Forecasting in ecology depends on our ability to identify key parameters that drive the system and how accurately we can measure these parameters (uncertainty) (Dietze, 2017). To achieve accurate forecasts, it is crucial to identify the right parameters and fine-tune them effectively. For instance, enhancing our understanding of how weather variability influences seed production can lead to substantial improvement in the quality of masting forecasts. Currently, correlations between masting and weather are often based on fixed time frames, such as mean maximum temperatures in June-July (Vacchiano et al., 2017). However, the timing of these effects can vary depending on local climates and current year conditions, similar to other phenological events like bud burst or flowering (Fu et al., 2015; Zohner et al., 2018; Nussbaumer et al., 2018). Using a site-specific moving window analysis can help pinpoint the right weather correlate and its timing (Bogdziewicz et al., 2023). While in European beech the cues change little among populations (Vacchiano et al., 2017; Bogdziewicz et al., 2023), in other species the weather correlates and underlying mechanisms can vary much more among populations (Bogdziewicz et al., 2020c; Fleurot et al., 2023). The challenge ahead lies in developing general rules that can connect local variation to a global model.

A related problem are the unknown mechanisms that connect masting and weather variation, as these links are often only assumed after the correlations are established (Crone & Rapp, 2014; Bogdziewicz et al., 2020a). The phenological synchrony hypothesis stands out compared to other weather cues with a developed theory and experiments on how weather affects seed crops through pollination efficiency (Koenig et al., 2015). However, even in this case, the exact mechanism behind flowering synchrony, a key factor in pollination efficiency, remains unclear. Different theories propose different temperature sensitivities, with the photoperiod-sensitivity hypothesis suggesting temperature affects flowering months before it occurs (Chuine, 2010; Bogdziewicz et al., 2020c), while the micro-climatic hypothesis posits that temperature during flowering is crucial (Koenig et al., 2015). The effects of warm spring weather on seed production can be also explained by higher pollen dispersal in such conditions (Schermer et al., 2019). This disagreement on the relevant period makes it difficult to identify the timing of maximum sensitivity, adding complexity to the task of constructing reliable masting forecasting tools.

Improving the accuracy of forecasts can also be achieved by reducing uncertainty in parameters. The uncertainty of weather parameters is generally low as past measurements are mainly used. However, for parameters with high sensitivity, which increases the cost of uncertainty, weather can be measured directly at the focal site instead of relying on data from nearby meteorological stations. To assess the benefits of local measurements, case studies are needed. Another important source of uncertainty is the impact of past seed production on current-year reproductive investment. Therefore, determining the most effective method of seed monitoring
at relevant spatial scales is a priority. The method chosen can vary based on factors such as plant species (e.g. the spatial scale of seed production synchrony, the importance of post-seeding resource depletion on next year's seed production) (Touzot et al., 2018; Tattoni et al., 2021), and the objective of the forecast. Further research into the physiology of resource depletion following seed production holds promise for improvement, including examining how stand age/mean size or local factors (soil type, competition) affect the limiting role of post-mast resource depletion on subsequent year's seed production (Pesendorfer et al., 2020; Wion et al., 2023), or whether extreme mast years can result in two consecutive mast failures.

## Conclusions

The vast array of masting strategies across species, and potentially even within species (Fleurot et al., 2023), may make it difficult to develop a universal model of masting. To address this challenge, stakeholders, including experts on masting and those who use such information, should collaborate to design research projects that focus on specific goals, rather than relying solely on lessons learned from other systems (Dietze, 2017). However, a general understanding of masting is crucial in providing a framework to work toward specific applications. To facilitate this, we summarize the key points in Box 2.

It is worth mentioning that although the sequential model outperformed in our analysis, this does not necessarily render other models ineffective. For instance, our analysis was focused on European beech, but the ΔT model has already proven successful in forecasting seed production in Southern beech (Holland & James, 2015a). Our intention is not to suggest that certain models are superior or inferior, but rather to emphasize that existing models show potential, require enhancements in key areas, and their effectiveness will depend on specific applications.

A crucial priority is to determine the intrinsic predictability of seed production time series. In other words, how predictable is masting, and what is the achievable level of accuracy for the models? It is important to understand if the system is inherently predictable to evaluate the quality of the chosen model (Pennekamp et al., 2019). The impact of chaotic dynamics, the effect of changing initial conditions on model results, should also be considered when assessing the models (Rogers et al., 2022). Improving our understanding of what can be predicted and how to improve those predictions is essential for making ecology more relevant to policy, management, and decision-making (Clark et al., 2001; Dietze, 2017).
Box 2 :

The Next Steps: A Roadmap for Masting Forecasting. To advance masting forecasting
the following research areas are identified as essential or promising. This roadmap aims
to provide guidance for future efforts in this field and to help advance our understanding
of masting dynamics and its predictability.

* **Predicting mast years and failures.** Classifying seed production into mast and non-mast years is subjective and does not accurately represent the complex ecological processes involved. However, extreme events play a significant role in management decisions. The limitations of current models in accurately forecasting these stochastic large events highlight the need for further research into the mechanisms that drive mast years.

*   **Physiology of seed production.** Promising results have been achieved using sequential models, which are based on established correlative mechanisms. This suggests that a deeper understanding of the mechanisms behind seed production and weather correlations, as well as the factors that limit post-mast seed production (such as the resource allocation to flowering and identification of resources that actually limit reproduction), could further improve the effectiveness of these models.

*   **Model types.** The development of models for masting forecasting should follow an iterative process, in which model performance is constantly evaluated, refined, and re-evaluated (Dietze *et al.*, 2018). The selection and validation of models are crucial steps in this process and can be improved by identifying and separating sources of uncertainty in the forecast. For example, Heilman *et al.* (2022) separately evaluated the uncertainty from initial conditions, parameters, drivers, and processes. Within the iterative cycle, comparing the explanatory power and predictive ability of both mechanism-based and empirical models (Lewis *et al.*, 2022), as well as artificial intelligence approaches such as deep learning (Christin *et al.*, 2019), can be a promising approach. Our sequential model showcases the advantage of a mechanism-informed empirical approach, which adds complexity but significantly improves hindcasting accuracy. Alternative routes include other mechanism-based models, such as the resource budget model of masting (Satake & Iwasa, 2000; Holland & James, 2015b; Schermer *et al.*, 2020), or phenomenological models (Lebourgeois *et al.*, 2018).

*   **Identifying and incorporating rare veto factors.** Incorporating rare and difficult-to-quantify veto events presents a challenge in masting forecasting. Such events, such as late spring frosts or extreme droughts, can have significant localized impacts by killing flowers or causing fruit abortion (i.e. high sensitivity). However, these events are rare and only have significance if the masting process has already been initiated (i.e. previous processes in the phenological sequence that leads to large mast years have happened). Measuring their effects on masting is challenging due to the limited data available and their non-linear, threshold-based nature. Despite these difficulties, the predicted increase in the frequency of such events in the future suggests they may play an increasingly important role in driving masting.

*   **Intrinsic vs. extrinsic drivers of masting** Certain species show bimodal seed produc-
tion patterns, which are only altered due to vetoes. For example, silver fir *Abies alba*
shows strong biannual reproduction unless a late frost acts as a veto (Owens & Morris,
1998). Thus, by investigating the cyclicity and autocorrelation of reproduction across
species in different ecological contexts, we may learn more about the role of intrinsic
and extrinsic drivers of reproductive variation.

* **Informed model selection by users.** Different models have varying strengths when it comes to forecasting masting, and the ideal model may depend on the specific needs and requirements of the user. For instance, the relative significance of incorrectly predicted mast events (false positives) compared to missed mast years (false negatives) can influence the choice of a model. To facilitate informed decision-making, it is crucial to establish a stakeholder-driven framework for evaluating models, which will allow users to choose the best model for their specific needs.

* **Non-stationarity and predictability of seed production.** To determine the realistic level of forecast accuracy of the models, it is important to assess the intrinsic predictability of the seed production time series. This includes determining the extent to which the masting system is inherently predictable, and evaluating the chosen model quality in relation to the system's intrinsic predictability (Pennekamp *et al.*, 2019). Comparing the intrinsic predictability across different masting species would provide valuable insights and be a fascinating research endeavor.

* **Climate change.** The changing climate is having a significant impact on seed production patterns (Bogdziewicz, 2022) and therefore on masting forecasting. For instance, the sensitivity of seed production in European beech to summer weather temperatures is declining, educating the sensitivity of masting to a key predictor (Bogdziewicz *et al.*, 2021). It is crucial to understand the consequences of these changes in climate on other parameters and how they translate into the predictability of masting. This will help to improve the forecasting of production patterns in the face of ongoing climate change.

* **Data quality, parameters uncertainty, seed production monitoring.** Determining the measurement of seed production is crucial for future masting forecasting efforts. The question arises as to what spatial scale seed production should be measured and how many individuals should be included in the measurement. With the presence of spatial synchrony in seed production (LaMontagne *et al.*, 2020; Wion *et al.*, 2020), forecasts may not necessarily rely on direct observations from the targeted population. It is imperative to conduct studies that will establish a cost-effective seed production monitoring program, one that will strike a balance between the logistical challenges of monitoring and the management objectives.

* **Temporal vs spatial prediction.** The analysis presented here is largely focused on temporal predictions, i.e. forecasting future seed production. Another potentially relevant approach is spatial prediction, i.e. predicting seed production at sites where observations are missing. The efficacy of such prediction will hinge on the degree of spatial synchrony in seed production exhibited by the species under scrutiny (Bogdziewicz *et al.*, 2023), but perhaps also on stand characteristics such as soils or topography.

* **Rapid data access.** To develop accurate forecasts, timely and accessible seed production data is essential. Platforms such as the Ecological Forecasting Initiative (https://ecoforecast.org/), which focuses on fine-tuning ecological forecasting through rapid data sharing, can serve as a model for seed production research. The establishment of similar platforms will greatly benefit the development and evaluation of masting forecasting.
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# Acknowledgements

We thank Ian Pearse for his helpful comments on the earlier version of this manuscript, and Andreas Wion, Samuel Venner, and an anonymous reviewer for their constructive comments that helped us improve the text. VJ was supported by project No. 2021/43/P/NZ8/01209 co-funded by the Polish National Science Centre and the EU H2020 research and innovation programme under the MSCA GA No. 945339. For the purpose of Open Access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. MB was supported by the European Union (ERC, ForestFuture, 101039066). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. MBP and IO were supported by the Waldfonds project FORSEE, funded by the Austrian Federal Ministry of Agriculture, Regions and Tourism. The development of MASTREE+ was supported by the UK Natural Environment Research Council grant no. NE/S007857. AHP received funding from Defra through a UKRI Future of UK Treescapes programme Fellowship. We acknowledge the organizers and contributors of the British Ecological Society-Royal Meteorological Society symposium "Climate Science for Ecological Forecasting", London, May 2022.

## Author contributions

All authors designed and developed the study. Analysis was performed by VJ. MB and VJ led the writing of the manuscript with contributions from AHP, IO and MBP.

## Competing interests

None declared.

## Data availability statement

Data used are available at : https://doi.org/10.17605/OSF.IO/RKN8A.
New Phytologist Supporting Information

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**Article title:** Forecasting seed production in perennial plants: identifying challenges and chart-
ing a path forward

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**Authors:** Valentin Journé, Andrew Hacket-Pain, Iris Oberklammer, Mario B. Pesendorfer, Michał Bogdziewicz

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**Article acceptance date:** 12-04-2023

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Methods S1

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Seed production data

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We used data from MASTREE+ database (Hacket-Pain et al., 2022) and extracted seed produc-
tion data for European beech *Fagus sylvatica*. We only used records measured on a continuous
scale that covered more than 8 years of observations after 1980, and excluded records of annual
flowering, pollen production, and tree-ring-based mast year reconstructions (Fig. A1a) (n = 94
MASTREE+ sites; 1,929 site-years). We scaled seed production for each site to between 0 and
1 by dividing all values by the highest recorded value in the time series (Fig. A1b). This was
done to accommodate among-site variation in methods of seed production monitoring among
various datasets included in MASTREE+.

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<figure><img src="image_7.png" /><figcaption>**Figure A1:** a) Map of sites used in the analysis (n=94). b) Seed production patterns for each site are shown in grey with an average value from all sites in black.</figcaption></figure>

Models : ΔT, *foreMast*, and sequential model

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We used three different models to predict masting in beech: ΔT (Kelly *et al.*, 2013), *foreMast* (Chiavetta & Marzini, 2021), and the sequential model. The ΔT model is based on the difference in temperature between two past consecutive summers (*T1* and *T2*) (Kelly *et al.*, 2013). The

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`foreMast` model is based on an R package that predicts the probability of seed production in a given year (Chiavetta & Marzini, 2021). This model includes both previous (T1 and T2) summer temperature and summer precipitation but also an auto-correlation term that helps to avoid two consecutive high-seed production years. The sequential model includes several weather variables known to affect seed production in beech, from pollination to fruit maturation, and the previous year's seed production: past summer temperature (T1 and T2), spring temperature of the year of seed fall (T0), late frost and summer moisture deficit of the year of seed fall; all defined below.

The *foreMast* algorithm provides masting forecasts for any given set of coordinates, while the coefficients for the ΔT and sequential models were estimated by fitting separate models to each time series (i.e. each unique site). We have fitted site-specific models, instead of for example a hierarchical model, as we were interested in site-specific coefficients for predictions. We used beta regression to fit the ΔT and sequential model (Grün *et al.*, 2012; Brooks *et al.*, 2017). As the beta distribution allows only values above zero and below one, and re-scaled our data for each site using the equation (Smithson & Verkuilen, 2006; Grün *et al.*, 2012):

$$Y_s = \frac{(y_s * (n_s - 1) + 0.5)}{n_s} \quad (1)$$

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the $y_s$ is the observation value of seed production for the site $s$ (previously scaled to $0 \le y_s \le 1$) and $n_s$ is the number of observation per site. This method involves the addition of minute values to observations that possess a value of 0, while simultaneously subtracting negligible values from observations that possess a value of 1.

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For ΔT and the sequential model, we extracted daily minimal, maximal, and average temperature, and precipitation used for the moisture deficit, for each site using EOS-obs (v22.0e, Cornes *et al.* 2018, 0.1° x 0.1°). Summer temperature was defined as the average of June-July-August max temperature. Spring temperature was April-May mean average temperature. We defined late spring frost based on cumulative growing degree days calculated for each year and MASTREE+ site as the sum of daily mean air temperature above 5°C from the 1st of January to the date of the last frost day (<-2°C) (Vitasse *et al.*, 2018). A high value of cumulative degree days indicates a high risk of frost injury (Vitasse *et al.*, 2018). The summer moisture deficit was defined as $P - PET$, with P for precipitation and PET for evapotranspiration, summed from June 1st to August 31st. Evapotranspiration (PET) was calculated with the Thornthwaite equation (Thornthwaite, 1948), by using the R package SPEI (Beguería & Vicente-Serrano, 2017). Distribution and correlation between climate variables are reported in Figure S8. Covariates included in the sequential model were standardized and centered before being included in the model.

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The *foreMast* package includes a function to extract climate from each location starting from 1981 based on ERA5-Land (Chiavetta & Marzini, 2021). Both monthly-year average temperature and precipitation, coming from EOS-obs and *foreMast* climate extraction present robust correlation (Figure S9).

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To evaluate the effects of focal predictors on the sequential model predictive power, we fitted several sub-models. This included two approaches: in one, we excluded one variable at a time (e.g. spring temperature in year T0), refitted the model, and evaluated its performance. In the second, we added variables in their phenological order of occurrence, starting with a model with only summer T2 (i.e. only one predictor), next added model summer T1 (two predictors), previous year seed production (tree predictors), late spring frost (four predictors), spring temperature (five predictors), and lastly summer moisture deficit (six predictors).

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We assessed the ability of models to re-create past seed production by using two main metrics: the *R-squared* ($R^2$) and the *Root Mean Squared Error* (RMSE). The objective is to
compare predictions of yearly seed production to the observed yearly seed production. The $R^2$ is the square of the correlation, which gives the proportion of the variation in the dependent variable that is predictable from the independent variables. An $R^2$ of 1 means that predictions perfectly match the observations. The *RMSE* provides the standard deviation of the prediction; smaller values indicate better model performance. Models were fitted on the site level, site-specific parameter coefficients were used to back-cast seed production, and $R^2$ and *RMSE* were computed for each site.

We also conducted cross-validation on the sequential model by using a cross-validation procedure (Arlot & Celisse, 2010). We randomly sampled 70% of the data in each time series to train the model and validate it based on the remaining 30% (by computing $R^2$ and *RMSE* for each site). We repeated this random sampling 10 times for each site and then computed the $R^2$ for each site.

## References

Arlot, S. & Celisse, A. (2010). A survey of cross-validation procedures for model selection. *Statistics Surveys*, 4, 40–79.

Beguería, S. & Vicente-Serrano, S.M. (2017). *SPEI: Calculation of the Standardised Precipitation-Evapotranspiration Index*. R package version 1.7.

Brooks, M.E., Kristensen, K., van Benthem, K.J., Magnusson, A., Berg, C.W., Nielsen, A. *et al.* (2017). glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. *The R Journal*, 9, 378–400.

Chiavetta, U. & Marzini, S. (2021). *foreMast: an R package for predicting beech (Fagus sylvatica L.) masting events in European countries*. *Annals of Forest Science*, 78, 1–10.

Cornes, R.C., van der Schrier, G., van den Besselaar, E.J. & Jones, P.D. (2018). An ensemble version of the E-OBS temperature and precipitation data sets. *Journal of Geophysical Research: Atmospheres*, 123, 9391–9409.

Grün, B., Kosmidis, I. & Zeileis, A. (2012). Extended beta regression in R: Shaken, stirred, mixed, and partitioned. *Journal of Statistical Software*, 48, 1–25.

Hacket-Pain, A., Foest, J.J., Pearse, I.S., LaMontagne, J.M., Koenig, W.D., Vacchiano, G. *et al.* (2022). MASTREE+: Time-series of plant reproductive effort from six continents. *Global Change Biology*, 28, 3066–3082.

Kelly, D., Geldenhuis, A., James, A., Penelope Holland, E., Plank, M.J., Brockie, R.E. *et al.* (2013). Of mast and mean: Differential-temperature cue makes mast seeding insensitive to climate change. *Ecology Letters*, 16, 90–98.

Smithson, M. & Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. *Psychological Methods*, 11, 54–71.

Thornthwaite, C. (1948). An approach toward a rational classification of climate. *Geographical Review*, 38, 55–94.

Vitasse, Y., Schneider, L., Rixen, C., Christen, D. & Rebetez, M. (2018). Increase in the risk of exposure of forest and fruit trees to spring frosts at higher elevations in switzerland over the last four decades. *Agricultural and Forest Meteorology*, 248, 60–69.
<figure><img src="image_8.png" /><figcaption>**Figure S1:** Standardized coefficients from the sequential model coming from MASTREE+ sites. Coefficient values have been extracted for each covariate and from each site where the beta regression models have been run. Grey dots represent the coefficient values of the site. The dot size above the boxplots is scaled to the number of observations that have been used to run beta regression models at the focal site.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Figure S2:** *R*² comparisons among the three models: scatter plots of *R*², *R*² distributions, and their correlation. For correlations, we used Pearson correlation with *** for *P*-values <0.001, ** for 0.001, * for 0.01. The range of x-axis (*R*²) differs between the three models. The lower panel presents kernel density estimation of *R*², from dark to yellow for higher density, and each dots represent *R*² of each sites.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Figure S3:** *RMSE* comparisons among the three models: scatter plots, *RMSE* distributions, and their correlation. For correlations, we used Pearson correlation with *** for *P*-values <0.001, ** for 0.001, * for 0.01. The range of x-axis metric (*RMSE*) differs between the three models. The lower panel presents kernel density estimation of *RMSE*, from dark to yellow for higher density, and where each dots represent *RMSE* of each site.</figcaption></figure>
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

**Figure S4:** Effects of focal predictors on the sequential model performance evaluated with *RMSE*. a) Each boxplot shows sequential model *RMSE* with one predictor removed, b) predictors added in phenological order.
<figure><img src="image_13.png" /></figure>

**Figure S5:** Goodness-of-fit of the sequential model presented with a) *R*² and b) *RMSE*. The yellow background represents the species distribution of *Fagus sylvatica* extracted from EUFORGEN (https://www.euforgen.org/species/). The dots represent each site, color-coded by the collection method. The size of the dots varies according to goodness-of-fit. The "other" category follows MASTREE+ and gathers collection methods that did not fit any other categories presented.
<figure><img src="image_14.png" /><figcaption>**Figure S6:** Effects of seed production estimation method on the sequential model *RMSE*. The methods are seed count (ground counting within a given time frame), monitoring with seed traps, and visual crop assessment. The asterisks represent significant differences between each group tested with a t-test (**** for *P* < 0.0001, *** for *P* < 0.001, ** *P* < 0.01, * *P* < 0.05, and n.s. for *P* > 0.05)</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure S7:** Boxplot of the *RMSE* from the model trained on 70% of the dataset or trained on the full dataset.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

**Figure S8:** Bivariate relationships and distribution of climatic variables. The upper panels show correlations, and the lower panels bivariate relationships using the loess function. Dots represent each site-yearly observations. For correlation between scaled climate variables, we used Pearson correlation with *** for *P*-values <0.001, ** for <0.001, * for <0.01
<figure><img src="image_17.png" /><figcaption>**Figure S9:** Correlation between climate obtained from EOS-obs and *foreMast* package (based on ERA5-Land). a) Correlation between average monthly temperature and b) Correlation between average monthly precipitation. Each dot represents a value for a month-year from our sites. Linear model summary is reported with slope, intercept and *P*-values at the bottom right.</figcaption></figure>