We argue that the next generation of DGVMs should implement ideas derived from coexistence theory (Chesson, 2000) and community assembly theory (Keddy, 1992; Webb et al., 2010) into the process-based paradigm of dynamic global vegetation modelling. Yet, we wish to emphasize that while we can learn a lot from community ecology and coexistence theory, we should also appreciate that these disciplines do not have the same aims as dynamic global vegetation modelling. Community ecology primarily seeks to understand which traits determine fitness in which environmental settings. Much of this understanding can be gained using statistical methods (Shipley, 2010; Swenson & Weiser, 2010; Webb et al., 2010). Coexistence theory generally uses heuristic models to understand which processes and environmental settings promote coexistence (Chesson, 2000). DGVMs, on the other hand, seek to represent and understand the interplay between climate and vegetation. In the paragraphs that follow, we describe a conceptual scheme for a next-generation DGVM that is illustrated in Fig. 2.
Figure 2. Conceptual modelling framework for a next-generation dynamic global vegetation model (DGVM) as outlined in the section ‘Next-generation DGVMs’. Individuals are characterized by their traits that influence their carbon (C) status and phenotype. All individuals at a site form the community, which influences resources, environmental conditions and disturbances via engineering and modulating impacts. These conditions interact to influence growth of the individuals. Individuals, through reproduction, can add their traits to the community trait pool. Crossover and mutation of the community trait pool yield the community seed bank. PDF, probability density function.
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We propose that the key challenge for DGVMs is to move away from the fixed-PFT paradigm towards a more flexible trait-based approach, which allows communities to be assembled based on how plants with different trait combinations perform under a given set of environmental conditions. The primary object in such a model is the individual. An individual-based approach (DeAngelis & Mooij, 2005) allows a simulation run to consider many individual plants, each of which can potentially have a unique set of trait values (see Fig. 3 for traits of an individual plant that one could simulate in DGVMs). In this model structure, the traits describe how the rates of resource assimilation, growth, C allocation and respiration are influenced by the environment; these rates in turn determine the C balance and the state variables that define the phenotype of each individual plant (Fig. 2). Individuals with inappropriate trait values and poor C balance die, whereas individuals with sufficient C gain and trait values that allow seed production, reproduce. This model structure allows for variance in how individual plants respond to variable environmental conditions, which has been shown to promote species coexistence (Clark et al., 2004, 2010).
Figure 3. Traits and state variables of a single plant in a next-generation dynamic global vegetation model (DGVM). Arrows represent allocation of carbon produced by leaves to different biomass compartments of the plant. LAI, leaf area index; SLA, specific leaf area.
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Reproduction is a key element in next-generation DGVMs, as it transfers traits from one generation to the next (inheritance), allows transfer of traits between reproductive individuals (crossover) and allows novel trait values to enter through mutation. There are many ways that these processes can be modelled. A realistic modelling of these evolutionary processes (e.g. how dispersal, pollination processes or reproductive biology influences gene flow) is not warranted; rather we require an effective algorithm that rapidly generates and selects for individual trait combinations that are adapted to the abiotic and biotic environment at a site. A pragmatic approach, which we follow, is to use a genetic optimization algorithm to manage the transfer of traits between generations. Genetic optimization algorithms are general-purpose optimization routines that use the concepts of recombination and mutation to efficiently find quasi-optimal solutions to optimization problems (e.g. differential evolution, Storn & Price, 1997). In the context of DGVMs, the vectors that describe trait values of each reproducing individual are added to the community trait pool. Traits are mutated and recombined to produce a community seed bank of seeds that can potentially germinate (Fig. 4). Trait filtering occurs through the reproduction and mortality functions; trait combinations that do not produce offspring do not contribute their traits to the next generation, whereas those that produce many seeds dominate the community trait pool.
Figure 4. Seed bank model in a next-generation dynamic global vegetation model (DGVM). Each plant is characterized by a unique trait combination. Reproducing individuals add their seeds to the community trait pool. In the community trait pool, mutation and crossover of seeds generate new trait combinations, which constitute the community seed bank. Randomly selected seeds can germinate, which means that they are added to the plant community as seedlings.
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What emerges from trait filtering is a community of individuals at a site. The information on this community can be summarized in various ways: as a probability density function (PDF) of traits or a PDF of phenotypes – the phenotype can be used to classify individuals as belonging to a specific functional type, or the phenotypes at a site can be used to assign a site to a biome type (Fig. 2). The properties of individuals can additionally be used to calculate changes in resource availability (e.g. soil water, light environment) and environmental conditions (e.g. surface temperature). Hence, competitive effects are simulated by modelling the engineering and modulating effects of plants on their environment, which feeds back to influence plant growth (Fig. 2).
The community of individuals at a site additionally determines disturbance regimes (Fig. 2). While DGVMs have in recent years made great strides in improving the representation of fire disturbance (Thonicke et al., 2010), the individual-based approach we propose emphasizes the possibility to link traits and phenotypes to fuel properties and to the response of individual plants to fire (Pausas et al., 2004; Pausas & Verdu, 2008). One example of this link is the invasion of Norway spruce in northern Europe in the late-Holocene where it has been shown that the associated changes in the community structure had more impacts on fire regimes than climatic changes (Ohlson et al., 2011). Analogously, individual-level variance in the plant phenotype defines the value of vegetation to herbivores and how vegetation structure will respond to herbivory (Scheiter & Higgins, 2012).
The promiscuous nature of the way that such a genetic algorithm (Fig. 4) simulates reproduction has two major side-effects. First, the trait ‘evolution’ simulated by such a model cannot be compared with the trait evolution studied by evolutionary biologists. This is because the genetic algorithm will rapidly find optimal solutions to the ‘evolutionary’ problems posed by the modelled environment. However, reproduction could be constrained to individuals with similar traits or individuals with the same ‘species label’. This would restrict gene flow and thereby simulate reproductive isolation. The second side-effect is that the rampant and unconstrained evolution of trait combinations is likely to produce Darwinian demons (Law, 1979), individuals that simultaneously maximize all functions that contribute to fitness. Darwinian demons do not exist in the real world because allocation of resources, for instance, to reproduction ensures that fewer resources are available for other functions such as growth and survival. Identifying such tradeoffs is one of the major activities of life-history theory and of the growing literature on functional plant traits (Reich et al., 1997; Enquist, 2002; Wright et al., 2004; Shipley et al., 2006; Westoby & Wright, 2006; Chave et al., 2009). Process-based vegetation models that explicitly consider tradeoffs between traits are, however, rare (Kleidon & Mooney, 2000; Marks & Lechowicz, 2006; Reu et al., 2011; Pavlick et al., 2012).
The major task for the developer of the kind of DGVM we are proposing is to conceptualize and parameterize life-history tradeoffs. We envisage that there are three major types of tradeoff that need to be considered. The first are mass conservation tradeoffs – the amount of a resource allocated to candidate functions must sum to one. The consequences of these tradeoffs manifest themselves naturally as part of the model's dynamic. For example, allocating more C to bark might protect a tree from fire damage, but this might compromise its ability to grow tall and compete for light (Gignoux et al., 1997). The second kind of tradeoffs are engineering tradeoffs – certain plant structures or architectures are not mechanically feasible. For example, a minimum stem diameter is required to ensure the mechanical stability of a stem of a given height (Niklas, 1994). Similarly, a critical sapwood area is needed to supply foliage with water (Shinozaki et al., 1964). These first two kinds of tradeoffs can be addressed, respectively, by having a sound accounting system in the model and by using established principles of engineering. The third kind of tradeoffs are more diffuse to define and difficult to deal with. We will refer to them as empirical tradeoffs. Empirical tradeoffs are a result of processes not explicitly simulated by the model. For example, Shipley et al. (2006) argued that the tradeoff between leaf photosynthetic rates and leaf longevity is a consequence of cell anatomy. Yet, DGVMs do not explicitly model cell anatomy, meaning that this tradeoff cannot emerge as a result of the model's internal dynamics. We are forced to parameterize this tradeoff using empirically defined functions. We might use the empirical functions identified by Wright et al. (2004) to describe the tradeoff between photosynthetic rate and leaf longevity and refrain from attempting to model the mechanisms proposed by Shipley et al. (2006). The problem of which processes to model empirically and which to model mechanistically is, of course, a pervasive one in any kind of modelling endeavour.
The aDGVM2: a trait-based dynamic vegetation model
We now turn to the question of whether we can implement a model of the kind narrated in the previous section. In this section, we describe how we modify an existing DGVM (the aDGVM, Scheiter & Higgins, 2009) to realize aspects of the conceptual scheme illustrated in Fig. 2. The aDGVM2 is individual-based, which means that it simulates growth, reproduction and mortality of each individual plant and it keeps track of state variables such as biomass, height and LAI of each individual plant. In addition, each plant is characterized by an individual and potentially unique set of traits describing plant type (grass or tree), leaf characteristics, leaf phenology, C allocation to different plant compartments, allometry of plant architecture, re-sprouting response to fire, reproduction and mortality (Fig. 3). Each plant is tagged with a ‘species label’. These ‘species’ differ in the trait values used for the model initialization. Growth, reproduction and mortality of plants are influenced by both the plant-specific trait combination and the environmental conditions.
Plant traits are linked by tradeoffs to constrain overall plant performance. Mass conservation tradeoffs regulate allocation to roots, stems, leaves, bark, storage and reproduction. Engineering tradeoffs regulate plant architecture (Niklas & Spatz, 2010), while empirical functions define, for example, tradeoffs between specific leaf area (SLA) and leaf longevity (Reich et al., 1997) or between SLA and the capacity of a plant to extract water from the soil. The aDGVM2 simulates soil water competition and light competition via impacts of each individual plant on the resource base. Water uptake of single plants is defined by the fraction of root biomass in different soil layers, the moisture content of these soil layers and by the plant's capacity to extract water from the soil. The light available to a target plant is influenced by the height of neighbouring plants. Light availability and water availability influence the photosynthetic rate and thereby, via C status, the reproduction and mortality rates of each individual plant. Nutrient competition was not considered in this model version, even though it is important (Tilman, 1988).
Reproduction follows the scheme described in Fig. 4. Specifically, individual plants that allocate enough C to reproduction can produce seeds. Seeds of the same species label can exchange trait values, thereby allowing recombination of the community trait pool. Mutation adds new trait values to the community trait pool. Randomly selected seeds are drawn from the resulting community trait pool and are added to the plant population as seedlings. By simulating inheritance, mutation and crossover, the model generates a large variety of different trait combinations and iteratively, via mortality and reproduction, assembles a plant community that is adapted to and influences the environmental conditions, resource availability and the disturbance regime at a study site.