Integrating dynamic plant growth models and microclimates for species distribution modelling
Introduction
The relationship between the growth and distribution of plants and environmental drivers is a fundamental concern of ecology (Billings, 1952). Modern tools and datasets enable modelling of the dynamic interactions between organisms and the environment at the scale of the individual organism. This capability can be used to develop insights and hypotheses about the mechanistic drivers of plant growth and stresses that limit the distribution of plant species. The use of such a physiological approach may assist the prediction of species distributions in future climates, or novel conditions (Bozinovic, Pörtner, 2015, Kearney, Porter, 2009).
Species distribution models (SDMs) are often developed using correlative techniques, with coarse-grained environmental predictors. However, there is a growing consensus that ecological models need to incorporate more structural realism (Grimm and Berger, 2016). For this reason process-based, mechanistic and hybrid models have been proposed as a more realistic alternative to correlative SDMs (Connolly, Keith, Colwell, Rahbek, 2017, Dormann, Schymanski, Cabral, Chuine, Graham, Hartig, Kearney, Morin, Römermann, Schröder, Singer, 2012, Kearney, Wintle, Porter, 2010, Postma, Kuppe, Owen, Mellor, Griffiths, Bennett, Lynch, Watt, 2017, Smith, Germino, Johnson, Reinhardt, 2009). Practically, correlative and mechanistic models exist on a spectrum of increasing causal detail (Dormann et al., 2012), where mechanistic models include explicit biophysical and physiological processes (Connolly et al., 2017).
However, choosing mechanistic models over correlative models is not simply a question of theoretical value, but also one of economy: mechanistic models are more difficult to construct, and more computationally intensive than correlative models (Dormann, Schymanski, Cabral, Chuine, Graham, Hartig, Kearney, Morin, Römermann, Schröder, Singer, 2012, Kearney, Maino, 2018). Improvements to mechanistic species distribution modelling require simultaneous development of theory and the practical tools for applying it efficiently (Briscoe et al., 2019).
Mechanistic SDMs have become more common for animals (Kearney and Porter, 2009). Although mechanistic modelling has a longer history in plant biology (Grimm and Berger, 2016), mechanistic SDMs remain less well-developed for plants. We follow Connolly et al. (2017) and distinguish mechanistic models from process-based models (PBMs), ignoring those that include only dispersal processes without specifying the components of plant growth (Merow et al., 2011).
A range of mechanistic models have been used to predict plant species distributions. These include phenological models that integrate environmental stress factors (Chapman, Haynes, Beal, Essl, Bullock, 2014, Chuine, Beaubien, 2001, Morin, Viner, Chuine, 2008) and models of environmental interactions with growth processes based on tree growth rings (Sanchez-Salguero et al., 2016). Other models have incorporated plant growth and C/N allocation in response to environmental drivers, to produce maps of relative growth potential (Higgins, O’Hara, Bykova, Cramer, Chuine, Gerstner, Hickler, Morin, Kearney, Midgley, Scheiter, 2012, Higgins, Richardson, 2014, Moncrieff, Scheiter, Langan, Trabucco, Higgins, 2016, Nabout, Caetano, Ferreira, Teixeira, Alves, 2012, Stratonovitch, Storkey, Semenov, 2012). Mechanistic growth models provide the most scope for capturing the interactions between plant ontogeny and the environment, as plant stresses can co-occur in sequential patterns with different effects across plant ontogeny (Niinemets, 2010). They can also provide a base model that can integrate phenological components, or be used for truly mechanistic demographic and distribution models.
A key example of a mechanistic growth model used for SDMs is the Thornley Transport Resistance model (TTR) (Thornley, 1972a), that tracks carbon and nitrogen budgets for roots and shoots. It has been used in hybrid mechanistic/fitted plant SDMs (Higgins, O’Hara, Bykova, Cramer, Chuine, Gerstner, Hickler, Morin, Kearney, Midgley, Scheiter, 2012, Higgins, Richardson, 2014, Moncrieff, Scheiter, Langan, Trabucco, Higgins, 2016). Additionally, Nabout et al. (2012) applied the Plantgro model to maize distribution, which uses growth response curves tuned to monthly conditions. Stratonovitch et al. (2012) and Storkey et al. (2014) used climatic data with daily time-steps and incorporated ontogeny in a sophisticated plant SDM. However, the Sirius model (Jamieson et al., 1998) used in Storkey et al. (2014) is focused on agricultural plants, and its formulation was not made available.
Realism in growth models can be increased by modelling causal processes more explicitly. It can also be improved by using finer gained environmental variables, because the responses of organisms to changes at the macroclimate scale actually occur at the microclimate scale (Harwood et al., 2014).
Animals usually exercise some choice over the microclimates they are exposed to, but the life of a plant occurs in a fixed location: they must tolerate all environmental conditions that occur there over their lifespan. However, at a finer scale plants grow through vertical climatic gradients over their ontogeny. They experience different conditions at different life-stages, and these differences can be critical in growth process (Niinemets, 2010) and in constraining the boundaries of their distribution (Smith et al., 2009). To establish at a particular location, plants must experience a favourable sequence of microclimatic conditions that match the needs of all life stages – not simply favourable climatic averages.
Growth based plant SDMs have generally used long time-steps (i.e. monthly) and climatic, rather than microclimatic data (Higgins, O’Hara, Bykova, Cramer, Chuine, Gerstner, Hickler, Morin, Kearney, Midgley, Scheiter, 2012, Higgins, Richardson, 2014, Moncrieff, Scheiter, Langan, Trabucco, Higgins, 2016, Nabout, Caetano, Ferreira, Teixeira, Alves, 2012). A general plant model suitable for SDMs – that can simulate complete plant ontogeny with realistic combinations of environmental stresses – remains to be demonstrated. Dynamic energy budget (DEB) growth models, coupled to mass and energy exchange between organisms and their microclimates, have achieved this for animal SDMs (Kearney, 2012; Kearney et al., 2018).
Dynamic Energy Budget theory (DEB) generalises growth processes for all organisms and symbioses (Kooijman, 2010). It is frequently used to model the transition from juvenile to adult in animals and bacteria (Jager, Martin, Zimmer, 2013, Singer, Johst, Banitz, Fowler, Groeneveld, Gutiérrez, Hartig, Krug, Liess, Matlack, Meyer, Pe’er, Radchuk, Voinopol-Sassu, Travis, 2016) and can capture complete organismal ontogeny. It has been used to model animal species distributions ( Kearney, 2012; Kearney et al., 2018), and has been suggested as an alternative growth model for plant SDMs (Higgins et al., 2012).
DEB theory simplifies the metabolism of organisms to material fluxes of substrates in processes of assimilation, growth and dissipation (Lorena et al., 2010). From simple rules and feedbacks it can capture complex growth dynamics while being explicit about matter, energy and entropy balances (Sousa et al., 2010).
DEB models focus on the interactions of different abstract categories of biomass, namely: structure (V), that is produced by the growth process and requires ongoing maintenance, and reserve (E), that represents the pool into which assimilates flow, and does not require maintenance. An additional type is product (P), representing byproducts of the growth process. In animals these are often excreted, but in plants may be included in measured biomass as bark and heartwood. The simplifying assumption of this framework is that each category has fixed proportion of chemical constituents. This enables the closure of both mass and energy balances (Sousa et al., 2010).
For models with multiple reserve substrates, such as separate carbon and nitrogen reserves, “synthesizing units” (SUs) are used to model enzyme dynamics for reserve combination, giving smooth transitions between limiting resources ((Kooijman, 2016, Ledder, Russo, Muller, Peace, Nisbet, 2019), pp.99–105). Synthesizing units bind multiple substrates to synthesize compounds, depending on their availability. Using an SU, carbon and nitrogen pools can be combined into a general reserve to be used in growth and maintenance. Reserve mobilised in each simulation time-step is calculated from the ratio of reserve to structure, adjusting growth rates to match available resources.
A useful outcome of the reserve-structure dynamics of a DEB model that tracks nutrient state is the ability to model growth from embryo to mature organism, by initially allocating high reserve/structure ratios and small structural mass. This can produce smooth transitions from the embryo phase, dependent primarily on stored nutrients, to later phases where nutrients are assimilated from the environment. Previous models of plant ontogeny often start with a seedling (Levy et al., 2000). In DEB models, growth rates vary with temperature but also with the dynamics of the root and shoot reserves, the growth rate being proportional to the density of the limiting reserve. This captures transient dynamics that drive, for example, rapid growth of seedlings or rapid shoot growth after a sudden loss of biomass from e.g. grazing events or fire.
The intrinsic generality and modularity of DEB theory means that, in principle, any number of structures can interact to exchange substrates, allowing simulations of single-celled heterotrophs, complex autotrophs, and even symbioses. This ability allows us to construct a DEB plant model, where at least root and shoot structures must be considered explicitly to model asynchronous nutrient assimilation. It also means that a DEB model has the open-ended potential to model more or less complex dynamics, by adding or removing structures. We could represent stems, leaves and roots separately, or include substrate exchange between fine roots and soil symbionts – requiring few additional formulations or parameters.
While the DEB model was proposed as a framework for modelling all organisms, the majority of published DEB models have focused on heterotrophs. The literature for autotrophs remains sparse: (Kooijman, 2016, Kooijman, Andersen, Kooi, 2004, Lorena, Marques, Kooijman, Sousa, 2010, Munné-Bosch, Alegre, 2004). Livanou et al. (2018) and Ledder et al. (2019) are notable contributions. A simple, single-structure microalgae model was presented in Lorena et al. (2010), contrasting with most animal models by tracking separate reserves for carbon and nitrogen to model temporally separated uptake dynamics. The symbiosis of a simple heterotroph and photo-autotroph was also modeled by Muller et al. (2009).
Modelling plants requires multiple structures to capture the additional spatial separation of nutrient and carbon uptake that occurs in roots and shoots (Kooijman, 2010), pp.201–206). Such a plant model was demonstrated by Kooijman (2010). However, it has not been widely tested or peer-reviewed and uses a large number of parameters. Recently Ledder et al. (2019) explored the dynamics of a simplified two-structured plant model, proposing “The local control theory of resource allocation”. In this formulation, resource sharing between plant structures is similar to resource sharing in a holobiont: roots and shoots only translocate unused metabolites, without centralised coordination or fixed allocations to translocation. This simple formulation achieves optimal growth rates, while maintaining dynamic growth behaviour. It also requires fewer parameters and causal processes than either globally-optimised resource sharing or the fixed-proportion local control used in Kooijman (2010) and in the well known Thornley Transport Resistance plant growth model (TTR) (Thornley, 1972a).
There are some differences in the strategies used to track carbon, nitrogen and general reserve state in DEB autotroph models. Kooijman (2010) tracked carbon reserve (C), nitrogen reserve (N) and general reserve (E), while Ledder et al. (2019) did not track reserves at all, instead generating general reserve from assimilated C and N for each time-step. Lorena et al. (2010) track C and N reserves. Despite structural differences, these models invariably track reserve and structure as abstract, but stoichiometrically fixed compounds measured in C moles and N moles.
Improvements in climatic datasets and downscaling methods have enabled detailed modelling of microclimate at the scale of individual organisms in any location. NicheMapR (Kearney and. Porter, 2017) and the microclimate datasets (Kearney, 2018) generated by it are tools that make detailed site-specific microclimates accessible over multiple decades, with the hourly resolution for multiple heights and depths at reasonable accuracy. They provide soil water potential (Kearney and Maino, 2018), soil temperature (Kearney et al., 2014), incident radiation, air temperature, snow cover, relative humidity and wind-speed, enabling the modelling of finely detailed organism-environment interactions. Microclimate data are provided as hourly sequences of environmental variables in discrete spatial layers.
DEB models do not represent organism growth spatially, besides simple surface area/mass relationships. But microclimates are fundamentally spatial. Water availability and soil temperature both vary with depth, while air temperature varies with height above ground. This means that a spatially-explicit model is required to integrate a DEB growth model with microclimate data.
The interactions of plant growth and microclimate could be most accurately modelled with three-dimensional models of root and shoot architecture (Vrugt et al., 2001). However, producing mapped species distributions imposes a number of practical constraints. There are limits to computing power when models may run over 8000 times for a year of growth at a single point. This can translate to the order of a billion runs to produce continent-scale maps on decennial timescales. Further, our ability to easily construct complex models and determine their parameters is limited by the availability of easily assembled modelling tools and data. The dimensionality and accuracy of the spatial transformation used must be some compromise between these factors.
There are a number of requirements for our plant growth model. Generally, a plant model should to some extent balance the growth of roots and shoots to align with their relative needs for substrate assimilation. To enable the modelling of growth throughout life-stages, it should capture growth trajectories from seed to plant, switching smoothly between stored and assimilated resources.
Optimal partitioning theory (McCarthy and Enquist, 2007a; Thornley, 1972a) describes how resources are optimally allocated between plant organs depending on relative availability; plants with adequate N supplies preferentially grow more shoots, instead of roots. This dynamic is a central component of many plant models (Cheeseman, 1993, Ledder, Russo, Muller, Peace, Nisbet, 2019), although it is not without criticism (Lambers, 1983, Muller, Kooijman, Edmunds, Doyle, Nisbet, 2009).
There are multiple methods for modelling optimal root/shoot ratios. Two alternatives are central (Perrin, 1992) and local (Cheeseman, 1993, Ledder, Russo, Muller, Peace, Nisbet, 2019) control of translocation. Cheeseman (1993) showed that simple local rules can lead to the emergence of balancing at the scale of the whole plant, without the need to invoke signalling or centralised control of allocation. However, they use fitted polynomial functions for growth rates, rather than bottom-up methods that could respond to hourly microclimate conditions. Ledder et al. (2019) recently demonstrated a local control model in a context of dynamic growth using the synthesising units of a two-substrate DEB model, where translocation of excess metabolites achieves optimal balanced growth.
Shoots low in C translocate less or no excess to roots, leading to more shoot growth than root growth, until balance is achieved. The inverse happens for N in roots. With parallel complementary SUs a proportion of each substrate is always translocated, and effectively cycled between structures. These dynamics can be fine-tuned by using k-family synthesizing units, where the overall proportions of used and rejected metabolites can be adjusted (Ledder et al., 2019).
One difference between local control theory and functional-balance theory is that root growth is not affected by low water availability in the version of local control presented in Ledder et al. (2019). Optimisation of water uptake is not always supported by experimental results (Metcalfe, Meir, Aragão, da Costa, Braga, Gonçalves, de Athaydes Silva Junior, de Almeida, Dawson, Malhi, Williams, 2008, McConnaughay, Coleman) and root/shoot ratios may be unaffected by water availability (McConnaughay and Coleman, 1999b). However, other studies cite both water and nutrients as factors in optimal root/shoot scaling. (Mccarthy and Enquist, 2007b). In local control theory (Ledder et al., 2019) only substrate availability (generally C and N) affect root/shoot ratios. Water shortages may have indirect effects by limiting assimilation.
Modelling complete plant ontogeny and changes in relation to microclimatic stresses requires a smooth transition between seed and plant life-stages. However, this transition is not commonly modelled. Seeds are largely composed of reserves such as carbohydrate and lipids, and rapid initial growth can be driven by the high ratio of reserve to structural tissue. DEB theory is well suited to modelling these processes, because the reserve concept links the embryo to the life cycle through the transition from use of initial reserve to assimilation of additional reserve (Kooijman, 1986). Periods of slowdown and readjustment of growth rates may occur in the transition between seed reserve and assimilated reserve when resources are limiting (Kitajima, 2002). These can be captured by a DEB model.
In this paper, we aim to explore the potential for modelling plant distributions based on limits to plant growth caused by the specific sequence of stresses a plant experiences during its ontogeny. There are three components of this approach. First, developing practical modelling tools that support both our current aims and future research in the field; second, developing methods to a connect a mechanistic model of plant ontogeny to microclimate models; and third, assessing the behaviour of the model across plant ontogeny and varying environmental conditions and scenarios, up to the scale of continental distribution. Ultimately, these components are intended to collectively enable the parametrisation of species distribution models of plant species and functional groups.
To model plant ontogeny with fine spatial and temporal resolution, we use a DEB model and connect assimilation, growth and maintenance processes to the microclimOz microclimate data set (Kearney, 2018) using temperature response curves and a photosynthesis/transpiration model. We develop model components as separate libraries that enable future adaption for use in a wide variety of SDMs, and in ecological models more generally.
Section snippets
Methods
We modelled a simple, generalised C3 grass or herb-like plant using a two-structure two-reserve DEB model. The DEB model is based on the plant model provided in Kooijman (2016) and Kooijman (2010) with simplifications outlined by Ledder et al. (2019) and Lorena et al. (2010). While the plant model in Kooijman (2016) specifies a photosynthesis component for C assimilation, it does not integrate environmental variables, stomatal conductance or the role of soil moisture in C uptake. Instead we use
Results
The model smoothly simulated the early stages or plant ontogeny against a background of microclimatic variation (Fig. 2), transitioning from dependence on stored seed reserves to assimilated reserves. A period of stalled growth and rebalancing was visible in mid September when seed reserves became depleted, and low soil water potential limited assimilation and growth until late September. As N uptake is not mediated by soil water potential in the model, but C assimilation is, N assimilation was
Discussion
In this paper we have demonstrated a proof of concept for a mechanistic, ontogenetically-explicit plant species distribution model. A simple DEB model of plant ontogeny, coupled to microclimatic drivers, can produce realistic plant growth dynamics from seed to maturity that respond to multiple environmental stresses and generate plausible spatial distributions.
Fundamental to the development of this model was component-based design methodology for mechanistic modelling. We have defined modular
Conclusions
In this paper we have shown that integrating mechanistic plant growth models with fine-grained microclimate data is a practical option for predicting environmentally forced plant growth dynamics, and ultimately distributions.
We have demonstrated methods for connecting dynamic energy budget growth models to microclimate datasets across plant ontogeny. This formulation can produce complex, realistic growth dynamics in response to multiple environmental stresses, and can be scaled up to produce
CRediT authorship contribution statement
Rafael Schouten: Conceptualization, Methodology, Software, Visualization, Writing - review & editing. Peter A. Vesk: Conceptualization, Supervision, Writing - review & editing. Michael R. Kearney: Conceptualization, Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We would like to thank James Maino, Jian Yen, Bas Kooijman, and Daniel Falster for feedback during the development of this manuscript, as well as Roger Nisbet and an anonymous reviewer for the detailed feedback provided.
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