Process-based models outcompete correlative models in projecting spring phenology of trees in a future warmer climate

Highlights

• Process-based phenology models were more robust than correlative models.

• Robustness of process-based models increase when their calibration could rely on forward estimation.

• Process-based models projected a reduction in the phenological cline along the elevation gradient by the end of the 21^st century.

Abstract

Many phenology models have been developed to explain historical trends in plant phenology and to forecast future ones. Two main types of model can be distinguished: correlative models, that statistically relate descriptors of climate to the date of occurrence of a phenological event, and process-based models that build upon explicit causal relationships determined experimentally. While process-based models are believed to provide more robust projections in novel conditions, it is still unclear whether this assertion always holds true and why. In addition, the efficiency and robustness of the two model categories have rarely been compared. Here we aimed at comparing the efficiency and the robustness of correlative and process-based phenology models with contrasting levels of complexity in both historical and future climatic conditions. Models were calibrated, validated and compared using budburst dates of five tree species across the French Alps collected during 8 years by a citizen-science program. Process-based models were less efficient, yet more robust than correlative models, even when their parameter estimates relied entirely on inverse modeling, i.e. parameter values estimated using observed budburst dates and optimization algorithms. Their robustness further slightly increased when their parameter estimates relied on forward estimation, i.e. parameter values measured experimentally. Our results therefore suggest that the robustness of process-based models comes both from the fact that they describe causal relationships and the fact that their parameters can be directly measured. Process-based models projected a reduction in the phenological cline along the elevation gradient for all species by the end of the 21^st century. This was due to a delaying effect of winter warming at low elevation where conditions will move away from optimal chilling conditions that break bud dormancy vs an advancing effect of spring warming at high elevation where optimal chilling conditions for dormancy release will persist even under the most pessimistic emissions scenario RCP 8.5. These results advocate for increasing efforts in developing process-based phenology models as well as forward modelling, in order to provide accurate projections in future climatic conditions.

Introduction

Phenology is a key aspect of plant and animal life strategies because it determines the timing of growth and reproduction. Life cycle of species must be adapted to the local weather conditions and resources. As a consequence, phenology is one of the top controls of crop yield (Olesen et al., 2011; Nissanka et al., 2015), population dynamics (Anderson et al., 2013), species distribution (Chuine, 2010) and evolutionary dynamics (Duputié et al., 2015; Burghardt et al., 2015). Phenology also ultimately regulates many functions of ecosystems such as productivity (Richardson et al., 2012), ecosystem carbon cycling (Delpierre et al., 2009), water (Hogg et al., 2000) and nutriment cycling (Cooke and Weih, 2005).

Since the 1970s, spring phenology has been reported to advance in response to warming (Walther et al. 2002; Parmesan and Yohe, 2003; Menzel et al. 2006; Fu et al. 2014). For instance, it has been shown that the apparent response of leaf unfolding to temperature was –3.4 days per °C between 1980 and 2013 in temperate Europe (Fu et al., 2015). This advance in spring phenology events is due to the warming of springs as bud growth rate is positively and strongly related to temperature (see for review Chuine and Régnière, 2017). However, this trend has been slowing down by about 40% after 2000 (Fu et al., 2015). One of the most likely hypotheses to explain this slowdown is the warming of winters (Asse et al., 2018). Indeed, most of temperate and boreal trees have developed a key adaptation to winter cold: the inability to resume growth despite transient favorable growing conditions in terms of temperature (Howe et al., 2000). This particular physiological state, called endodormancy (Lang et al., 1987), establishes in fall and disappears in early to late winter after a certain exposure to cold temperatures. Therefore, the warming of winters is suspected to delay endodormancy release and be responsible for the apparent decrease in the response of leaf unfolding to warming after 2000. Ultimately, this lack of chilling temperatures might compromise budburst itself at some point if warming continues (Chuine et al., 2016). Such a situation is more likely to occur in populations inhabiting the warm edge of a species range and/or lower elevations in mountain regions, where species are already in suboptimal chilling conditions (Benmoussa et al., 2018; Guo et al., 2015). More than ever there is a need for more accurate projections of tree phenology for the upcoming decades to remove the large uncertainties that still remains.

Two main categories of predictive phenology models exist although there can be a continuum in-between: correlative and process-based models (for review see (Chuine et al., 2013; Chuine and Régnière, 2017). Correlative models statistically relate descriptors of climate to phenological variables (i.e. usually the occurrence dates of a phenological phase such as bud break or flowering). In correlative models, parameters have no a priori defined ecological meaning and processes can be implicit (process-implicit) (Lebourgeois et al., 2010). In contrast, process-based models are built around explicitly stated mechanisms and parameters have a clear ecological interpretation that is defined a priori. In this category of model, response curves are often obtained directly from experiments, contrasting with empirical relationships of correlative models. Consequently, process-based models often require a larger number of parameters to be estimated or measured, with the consequence of a higher level of complexity than correlative models. However, they provide greater insights into how precisely each driver affects the trait, and they are expected to provide more robust projections in new climatic conditions corresponding either to other geographical areas or other time periods (Chuine et al., 2016).

Among the most widely used process-based phenology models, are the so-called one-phase models that describe solely the ecodormancy phase, which follows the endodormancy phase. During the ecodormancy phase, bud cell elongation can take place whenever temperatures are appropriate, and the higher the temperature is, the higher is the rate of cell elongation during this phase. This category of models has been shown to be efficient in predicting accurately budburst date under historical climate (Vitasse et al., 2011; Basler, 2016). Another category of models, called two-phase models, describes additionally the endodormancy phase, and take into account the possible negative effect of winter warming on endodormancy release. This category of models is thus considered to provide more accurate projections in future climatic conditions (Chuine, 2010; Vitasse et al., 2011). However, it has been shown recently that this second type of models might suffer from flawed parameter estimation when dates of endodormancy release have not been used for their calibration (Chuine et al., 2016). Unfortunately, observations of endodormancy release date are very rare because they are very difficult to determine (Jones et al., 2013; Chuine et al., 2016). Models are thus usually calibrated using solely bud break or flowering dates (Chuine, 2000; Caffarra et al., 2011; Luedeling et al., 2009; but see Chuine et al., 2016). Some other models go further in the description of the processes by integrating a photoperiod cue (Schaber and Badeck, 2003; Gaüzere et al., 2017). Some studies indeed support the hypothesis that in photosensitive species, which might represent about 30% of temperate tree species (Zohner et al., 2016), long photoperiod might compensate for insufficient chilling (Caffarra et al., 2011a; Gaüzere et al. 2017).

There is now a large number of phenology models that differ in their level of complexity and in the types of response function to environmental cues they use (see for review Chuine et al., 2013; Basler, 2016; Chuine and Régnière, 2017). However, very few studies aimed at comparing their efficiency and robustness so far (Basler, 2016), especially in future climatic conditions (but see Vitasse et al., 2011; Chuine et al., 2016; Gaüzere et al., 2017), while this has been done multiple times for species distribution models (e.g. Cheaib et al., 2012; Higgins et al., 2012; Morin and Thuiller, 2009; Kearney et al., 2010) and crop models (Lobell and Burke, 2010) for example. By efficiency, we mean here the ability of the model to provide accurate predictions in conditions that have been used to calibrate the model (Janssen and Heuberger, 1995); and by robustness, we mean here the ability of the model to provide accurate predictions in external conditions (Janssen and Heuberger, 1995), i.e. other conditions than those used to calibrate the model. Model's robustness determines its transferability in time and space.

Process-based models are usually expected to provide more accurate projections for the future than correlative models because they describe causal relationships. The effect of each driver identified as affecting a particular trait value can be described by a causal relationship, sometimes involving other drivers as well (interaction between drivers). For this reason, process-based models have also an expected greater potential to deal with non-analog situations. However, the putative higher robustness of process-based models could also come from the fact that parameter values describing the causal relationships, or at least some of them, can be measured directly (forward estimation of parameter values) instead of being inferred statistically through inverse modelling techniques and data assimilation (backward estimation of parameter values). Yet, there has been no attempt so far to validate this widely accepted expectation.

Here, we aimed at comparing the efficiency and robustness of correlative vs process-based phenology models with contrasting levels of complexity, both in space and time. More precisely, we aimed at answering the following questions: (1) Are process-based phenology models more robust than correlative models? (2) If so, is it because they describe causal relationships or because they can be less dependent on statistical inference (i.e. back estimation of parameter values) and rely more on experimental measurements (i.e. forward estimation of parameter values)? (3) How do projections of both types of model differ in future climatic conditions?

Using observations of budburst dates collected over the Western Alps by a citizen science program during 8 years, and experimental data, we calibrated correlative and process-based phenology models with three levels of complexity for five major tree species: Corylus avellana (L.), Fraxinus excelsior (L.), Betula pendula (Roth), Larix decidua (Mill.) and Picea abies (L.). We then compared their predictions and projections over the Western Alps in historical climate and in future climate respectively.

The Western Alps are particularly interesting to evaluate phenology models because the elevation gradient provides a wide temperature range on a very short distance. In addition, the southern part of the Western Alps is nearly located at the warmest edge of the geographic range of the five studied species, where it has been shown that winter warming is already affecting endodormancy release and budburst Asse et al., 2018). Finally, temperature has already increased in the Western Alps twice as fast as in the northern hemisphere during the 20^th century (Rebetez and Reinhard, 2008) and recent evidence indicates that the current warming rate increases with increasing elevation (Mountain Research Initiative EDW Working Group, 2015). Consequently, mountain summits might warm faster than lower elevation sites, so that the response of mountain ecosystems to climate change might be non-linear along elevation gradients. Therefore, ultimately, we aimed at answering a fourth question: ((4) How will climate change alter the budburst date of alpine species?