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Assessing uncertainties in a second-generation dynamic vegetation model due to
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ecological scale limitations
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Rosie Fisher1, Nate McDowell1, Drew Purves2, Paul Moorcroft3, Stephen Sitch4, Peter
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Cox5,6, Chris Huntingford7, Patrick Meir8, F. Ian Woodward9.
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1.
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Alamos, New Mexico, USA.
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2.
Microsoft Research, Cambridge, United Kingdom
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3.
Department of Organismic and Evolutionary Biology, Harvard University, 22 Divinity
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Avenue, Cambridge, MA 02138, USA
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4.
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5.
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Exeter EX4 4QF, UK.
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6.
Met Office Hadley Centre, Exeter EX1 3PB, UK .
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Centre for Ecology and Hydrology, Wallingford, Oxfordshire, OX10 8BB, UK
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8.
School of Geosciences, University of Edinburgh, Drummond Street, Edinburgh, UK.
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9.
Department of Animal & Plant Sciences, University of Sheffield, Sheffield, S10 2TN,
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UK
Earth and Environmental Science Division, Los Alamos National Laboratory, Los
Department of Geography, University of Leeds, Leeds, UK.
School of Engineering, Mathematics and Physical Sciences, University of Exeter,
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Word Count of main text = 7050
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ABSTRACT
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Second generation Dynamic Global Vegetation Models (DGVMs) have recently been
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developed that explicitly represent the ecological dynamics of disturbance, vertical
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competition for light, and succession. Here we introduce a modified second-generation
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DGVM and examine how the representation of demographic processes operating at two-
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dimensional spatial scales not represented by these models can influence predicted
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community structure, and responses of ecosystems to climate change. The key
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demographic processes we investigated were seed advection, seed mixing, sapling
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survival, competitive exclusion and plant mortality. We varied these parameters in the
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context of a simulated Amazon rainforest ecosystem containing seven plant functional
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types that varied along a trade-off surface between growth and the risk of starvation
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induced mortality. Varying the five unconstrained parameters generated community
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structures ranging from monocultures to equal co-dominance of the seven PFTs. When
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exposed to a climate change scenario, the competing impacts of CO2 fertilization and
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increasing plant mortality caused ecosystem biomass to diverge substantially between
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simulations, with mid-21st century biomass predictions ranging from 1.5 to 27.0 kgC m-2.
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Filtering the results using contemporary observation ranges of biomass, LAI, GPP and
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NPP did not substantially constrain the potential outcomes.
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demographic processes represent a large source of uncertainty in DGVM predictions.
We conclude that
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INTRODUCTION
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The terrestrial biosphere plays a critical role in regulating the Earth’s carbon cycle
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(Bonan 2008). There is concern that terrestrial ecosystems may be unable to maintain the
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current uptake of ~33% of anthropogenic emissions (Rodenbeck et al. 2003; Zeng et al.
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2005) because of the anticipated negative impact of heating and drying on photosynthesis
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and survival (Cox et al. 2000; Friedlingstein et al. 2006). For this reason, Dynamic
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Global Vegetation Models (DGVMs), are now recognized as a critical component of
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climate change prediction. DGVM models simulate a suite of ecosystem properties from
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half-hourly carbon and water exchange, through daily growth and tissue turnover, to
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longer term processes of reproduction, competition, and mortality. These models have
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become relatively advanced in their capability to simulate short-term surface gas and
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energy exchanges and atmospheric CO2 (Sellers et al. 1986; Hickler et al. 2008; Purves
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and Pacala 2008, Mercado et al. 2009; Randerson et al. 2009), but in contrast, DGVMs
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contain relatively simple and poorly tested representations of the processes driving long-
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term changes in vegetation composition – e.g. recruitment, competition and tree mortality
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(Moorcroft et al. 2006). The large structural and parametric uncertainty concerning these
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processes means that existing DGVMs produce a wide variety of predictions regarding
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the future strength and direction of the climate carbon-cycle feedback (Friedlingstein et
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al. 2006; Thornton et al. 2007; Sitch et al. 2008). For example, some models predict
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catastrophic declines in the Amazon and Boreal forests, while others predict relatively
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stable ecosystem composition and carbon storage, even with the same future climate
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drivers (as illustrated by Sitch et al. 2008). Model biases introduced by these
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uncertainties are not readily estimated because limited observations exist to constrain
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demographic processes under rapidly altering climates (Purves and Pacala 2008; Allen et
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al. 2010).
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In an attempt to increase ecological realism in DGVMs, more sophisticated models
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have recently been developed that explicitly represent the demographic processes of
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disturbance, recruitment, competition between plant types for light, and tree mortality
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(Friend et al, 2000; Moorcroft et al., 2001; Sato et al., 2007; Hickler et al., 2008; Scheiter
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and Higgins, 2008). This ‘second generation’ approach has numerous perceived benefits
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including the ability to 1) model re-growth after disturbance, 2) parameterise ecological
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dynamics directly using tree and plot scale data, and 3) to facilitate the representation of
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co-existence of different vegetation types by introducing different environmental niches,
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either along a successional gradient of light availability or vertical strata in the canopy
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(Smith et al. 2001; Moorcroft et al. 2001; Purves and Pacala 2008). The impact of this
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third property – the ability to simulate competition and co-existence of multiple plant
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types - is unclear. On one hand, successful co-existence of multiple plant functional
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types (PFTs) might buffer responses to climate change by preventing sudden switches
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between mono-dominant PFTs. On the other hand, relatively stable past climates might
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discourage the survival of those plant types which invest more resources in the tolerance
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of extreme climates, at the expense of PFTs with rapid growth rates, making ecosystems
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in general more susceptible to the effects of climate shifts.
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To resolve this issue, it is necessary to understand the processes that control
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community structure in second-generation models. In this paper, we present
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developments to a second-generation DGVM that facilitate the co-existence of plant
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functional types. We then identify several poorly constrained processes that
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fundamentally influence how community structure emerges from plant demography.
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These include seed advection, seed mixing, sapling mortality, competitive exclusion and
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stress-induced tree mortality. While representations of these ecological processes are
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typically present in current DGVMs, they all depend upon two-dimensional spatial scales
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not represented by these models. For example, rates of seed mixing and advection rates
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are properties of landscape heterogeneity, while the stochasticity or determinism of
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competitive exclusion and the rate of tree mortality under stress are both properties of
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multi-scale environmental heterogeneity (Clark et al. 2007). DGVMs are spatially one-
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dimensional, as they consider single points in space that do not interact with one-another.
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Therefore, it is not possible to explicitly represent these processes in the current
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modelling context, and instead their impact must be parameterised. In this paper, we
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identify five demographic processes whose outcome depends on the sub-grid spatial
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heterogeneity of a landscape, and investigate how the parameterisations affect the
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outcome of a one-dimensional dynamic vegetation model.
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In this paper, we use the Ecosystem Demography model (ED, Moorcroft et al.
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2001), a size and age structured DGVM that occupies a mid-point on the continuum from
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gap models (Sato et al. 2007; Hickler et al. 2008) that contain representations of
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individual trees, to area-based DGVMs, which model the fate of a single average
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individual for each PFT (Cox, 2001; Sitch et al. 2003, Bonan et al. 2003; Woodward and
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Lomas 2004). Because of this, ED is perceived as a promising template for a second
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generation of land surface models, appropriate for inclusion in large-scale climate
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simulations (Meir et al. 2006; Moorcroft 2006; Prentice et al. 2007; Purves and Pacala
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2008; Huntingford et al. 2008).
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MODEL DESCRIPTION AND DEVELOPMENTS
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Background
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In order to provide a realistic context for our study, we situate our hypothetical
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ecosystem in the eastern Amazon basin, and parameterise carbon fluxes and plant
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allocation using recently compiled data from three intensively studied forest plots (Malhi
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et al. 2009b). Further details are given in supplementary information and Table 2. A
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majority of Global Climate Models, (GCMs) predict that dry season rainfall over
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Amazonia will decline (Malhi et al. 2009a), and that temperatures will increase (Salazar
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et al. 2007). This makes the Amazon an ideal place to investigate the impact of
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alternative community structures on future vegetation structure and function. For a more
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complete review on prognoses for the Amazon rainforest see Cox et al. (2004, 2008),
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Huntingford et al. (2008), Malhi et al. (2008, 2009b), Meir et al. 2008, and Nepstad et al.
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(2008).
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ED model
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ED is a size-and-age structural approximation of a gap model, the state structure of
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which is a nested hierarchy of geographical grid cells, landscape age classes and cohorts
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of trees of different sizes and plant functional types. The landscape age classes are
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designed to capture horizontal biotic heterogeneity in canopy structure that arises from
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various forms of disturbance. Biotic heterogeneity does not include physical aspects of
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sub-grid heterogeneity such as variations in altitude, soils or aspect. These are not
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accounted for in the model structure. At each daily time-step, canopy tree mortality
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creates new areas of disturbed ground. To make the model computationally more
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efficient, the spatial locations of the disturbed areas are not specified, and thus can be
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tracked as a single landscape age class that represents the aggregation of canopy-gap
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sized areas within each grid cell that were disturbed at a similar time in the past. To
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minimize the proliferation of landscape age classes, the vertical structure and
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composition of model land classes are continually compared to each other and merged if
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they are sufficiently similar.
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New juvenile individuals of each PFT are recruited on a daily timestep, based on
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the reproductive output of existing individuals of the same PFT. Individuals located in the
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same landscape age class, PFT and size, are tracked as ‘cohorts’. Each cohort is defined
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by the number of individuals per unit area nc, and a single representative tree, defined by
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its structural biomass (bs) that is a function of tree diameter D (cm), and live biomass (ba)
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that consists of leaf (bl), fine root (br) and sapwood (bsw) (all in kg C individual-1 year-1).
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As with the landscape age classes, cohorts are continually compared and subsequently
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fused if they are in the same PFT, landscape age class and are close in size. Through this
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procedure, the ED model explicitly tracks horizontal and vertical heterogeneity in canopy
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structure.
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In the next section, we discuss model representations of recruitment, competition
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and mortality. Because these processes operate in two-dimensional spatial space, and
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therefore have no analogue in a one-dimensional model, parameterization from field
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observations is difficult. We introduce modifications to these processes, but unless
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otherwise stated, the model is the same as EDv1.0, as described by Moorcroft et al.
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(2001). Alterations made to the energy and gas exchange algorithms are described in the
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supplementary information.
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1. Modelling Sapling Recruitment
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Sapling recruitment is the sum of plant reproduction from local (internal) and
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non-local (external) sources. The smallest units considered by the model are 2.5m high
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saplings, we do not model the germination of seeds and early seedling development, but
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seed dispersal processes are nevertheless responsible for the location of the resultant
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saplings. External recruitment represents the advection of seeds from other geographical
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areas. Seed advection (As) from multiple directions, results in a point-specific sapling
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establishment rate measured in individuals m-2 PFT-1 year-1. As the distribution of
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different environmental conditions within a grid cell is not represented in the model, we
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use the null assumption that PFT advection is constant through time and that the number
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of saplings recruited per PFT is equal. For internal recruitment, a fixed fraction, frepro of
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the carbon available for growth (Cg , Equation 7) is partitioned into reproduction. The
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number of saplings per plant functional type is calculated from this carbon supply divided
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by the biomass required to make each 2.5m sapling. The internally generated saplings are
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distributed between landscape age classes. This requires an estimate of Xm: the
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probability that a propagule generated in one landscape age class establishes in a different
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landscape class from that of its parents. In other words, Xm represents how well mixed
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seeds are across a landscape with respect to the landscape age class gradient. Low levels
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of ‘seed mixing’ mean that seeds are likely to land near their parent tree, and vice-versa.
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Subsequently, a ‘sapling mortality’ is applied (Ms) the value of which represents the
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discrepancy between the maximum number of sapling and the number that are realised in
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the model. The total number of new established saplings in each time-step, Nsapling is
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therefore:
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Nsapling
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(1)
=
(As
+
Cg
(1-
Ms)/(freprob0)t
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Where t is the length of each daily time-step, in years (1/365) and b0 is the sapling
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biomass.
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The parameters As and Xm both depend upon the spatial structure of the landscape
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and the likelihood of ecosystems with different composition existing in close proximity.
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In a two-dimensional spatial model of interconnected patches (e.g. Kneitel and Chase
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2003; Leibold et al. 2006; Lischke et al. 2006) parameters representing the spatial
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movement of propagules would not be necessary, as they would be modelled with
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diffusion type equations, however, without this capacity, we must parameterise the
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processes of seed dispersal within a grid cell. Here we investigate how the
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parameterisation of seed advection and seed mixing affect community structure in a
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sensitivity analysis.
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2. Modelling canopy structure and co-existence.
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In the original EDv1.0 model (Moorcroft et al. 2001) there were no explicit spatial
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dimensions associated with each cohort, so the hypothetical leaf area of each tree
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extended across the entire surface of the landscape age class, effectively creating a steep
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vertical light profile that caused non-realistic levels of shade-induced competitive
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exclusion and reduced the capacity to simulate co-existence of plants within a
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successional age class. Resolving these issues requires representation of the physical
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dimension of tree crowns. We adopted and modified the Perfect Plasticity Approximation
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(PPA) of Purves et al., 2008. Based on the observation that tree crowns often occupy gaps
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in the canopy that are spatially dislocated from the base of the tree, PPA assumes that the
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horizontal plasticity of crown location and shape is infinite but that trees have realistic
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relationships between crown area and height. The end result is that; (1) when the total
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canopy area is greater than the total ground area, the canopy is considered to be ‘closed’
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and breaks into distinct layers, each consisting of those cohorts with heights within a
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particular range, such that each cohort occurs in only one layer; (2) in a situation with
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two layers, i.e. canopy and understory, the cohorts are assigned to the canopy or
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understory according to their height relative to a mean canopy intersection height ‘z*’; (3)
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trees within the same layer do not shade each other at all; (4) trees in a given layer are
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uniformly shaded according to the total LAI above the top height of that layer. This
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scheme means that a small increase in height of a cohort no longer confers a large
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competitive advantage, except where cohorts cross z*.
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The original version of the PPA model assumes that z* is spatially uniform within a
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stand, however, canopy intersection heights vary spatially such that a tree of height ‘h’
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might sometimes be in the canopy and sometimes be in the understory, depending on it’s
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circumstances. The assumption that z* is spatially uniform, exacerbated by the fact that
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ED typically aggregates the canopy into far fewer cohorts than the original PPA method
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of Purves et al. (2008), generates a highly deterministic model of competition, whereby a
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single cohort with a small height advantage might come to quickly and un-realistically
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dominate the entire canopy. It is therefore difficult to represent co-existence between
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similar PFTs without including some potential for z* to be heterogeneous. Clark et al.
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(2003, 2007) propose that deterministic models of co-existence often fail because they do
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not properly account for unobserved life history trade-offs, neglected genetic variation or
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spatial heterogeneity in topology, soil type, aspect and dispersal and recruitment
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processes, they term these factors ‘random individual effects’. In the context of the PPA
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model, this is analogous to the possibility that z* is spatially heterogenous.
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We introduced the potential influence of ‘random individual effects’ on community
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composition by aggregating all the processes that suppress the ability of the fastest
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growing PFTs to monopolise resources into a single ‘competitive exclusion’ parameter
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Ce.. Ce controls the probability that a tree of a given height will obtain a space in the
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canopy of a closed forest. The forest canopy is considered as closed when the total
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canopy area (Acanopy, m2), which is the sum of all the crown areas (Acrown, m2)
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Acanopy =∑Acrown,
(2)
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exceeds the ground area of the age class in question (Ap). Under these circumstances, the
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‘extra’ crown area Aloss, (Acanopy - Ap) is moved into the under-storey. For each cohort
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already in the canopy, we determine a fraction of trees that are lost from the canopy (Lc)
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and moved to the under-storey. Lc is calculated as
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Lc= Aloss wc/∑(wc)
(3),
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where wc is a weighting of each cohort determined by basal diameter D (cm) and the
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competitive exclusion coefficient Ce
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wc=DCe
(4).
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The higher the value of Ce, the greater the impact of tree diameter on the probability of a
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given tree obtaining a position in the canopy layer. That is, for high Ce values,
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competition is highly deterministic. Small average differences between cohorts are still
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significant because there is little randomness at the scale of individual trees. Therefore
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faster growing trees monopolise light resources more effectively, leading to competitive
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exclusion of slower growing trees. In contrast, low values of Ce imply that the outcome of
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competition is stochastic: small differences between cohorts do not matter very much,
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because randomness at the scale of individual trees is such that all cohorts suffer
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approximately equally from competition for canopy space. The smaller the value of Ce,
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the greater the influence of random factors on the competitive exclusion process, and the
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higher the probability that slower growing trees will get into the canopy. Appropriate
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values of Ce are poorly constrained (Clark et al. 2003, 2007) thus we investigated the
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impacts of a wide range Ce values on community structure and biomass predictions.
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3. Modelling Plant Mortality
Modelling community composition requires accurate simulation of the processes
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controlling mortality of different plant types. Mechanistic prediction of plant mortality is
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currently a developing field (e.g. McDowell et al. 2008) and the dominant mechanism of
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death remains unclear. Two potential physiological mechanisms underlying plant
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susceptibility to climate extremes and attack by biotic mortality agents include hydraulic
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failure caused by excessive xylem embolism, and carbon starvation due to stomatal
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closure and subsequent depletion of available carbohydrate reserves used for maintenance
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and defence. Though not yet understood sufficiently well to model, metabolic limitations
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induced by restrictions on phloem transport and tissue dehydration may exacerbate
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carbon starvation (Korner, 2003; McDowell and Sevanto 2010, Sala et al., 2010).
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Isohydric plants, which close their stomata during drought conditions, may be more likely
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to suffer carbon starvation than hydraulic failure (McDowell et al. 2008). Fisher et al.
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(2006) observed that leaf physiology was consistent with isohydric habit in Amazonian
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rainforest trees and Metcalfe et al. (this issue) provide evidence suggesting that the
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carbon budget and timing of death of artificially droughted rainforest trees is consistent
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with death from carbon starvation. Therefore, in this paper, we concentrate on carbon
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starvation as the likely mode of mortality. To simulate carbon starvation, we define a new
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‘stored carbon’ pool, bstore (kg C individual-1), and model allocation to this pool using the
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widespread observation that relative partitioning of photosynthate to storage increases
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during periods when photosynthesis is low (reviewed by McDowell and Sevanto 2010).
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Allocation to the store is thus altered according to the size of the existing pool and a
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‘target’ quantity S*, multiplied by leaf biomass, bl. S* is an indicator of the generic
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strategy plants undertake to avoid carbon starvation. The more carbon that is kept back
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for storage, the more likely it is that a plant can survive periods of negative carbon
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assimilation (McDowell et al. 2008). The carbon balance (Cb) available for storage,
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growth and reproduction is determined as
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Cb = NPP - md
(5)
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the balance of net primary productivity (NPP) and tissue turnover requirements (md, see
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Supplementary Information), both in kgC individual-1 year-1). The balance of stored
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carbon to target stored carbon fs:
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fs = bstore /(S*bl)
(6)
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is used to predict the flux of carbon to the storage pool as a fraction of the carbon balance
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(fstore)
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fstore= e-4fs
(7).
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The form of the above function depicts a situation whereby carbon allocation approaches
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1.0 when the store is low, and approaches zero when the store is higher than the target
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quantity. Flux to and from the store is calculated as:
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bstore = Cb. fstore
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Thus if Cb is negative (if NPP is less than maintenance demands, such as in winter or
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drought periods) carbon is removed from the store. Mortality increases as bstore declines
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below a threshold (see below), so negative bstore is avoided by gradual cohort death.
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Otherwise, the carbon remaining for growth and reproduction (Cg, kg C individual-1 year-
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1
) is what remains once allocation to the store has been removed.
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Cg = Cb (1.0- fstore)
(8).
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Because each cohort in ED represents the hypothetical means of a set trees with broadly
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similar but nonetheless variable genetic composition and environmental conditions, the
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prediction of mortality based on a single threshold carbon storage value is inappropriate.
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In this case, we model mortality rate M (fraction of trees dying per year) as a function of
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the ratio of bstore to leaf biomass where bstore<bl
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M=Bm+ Sm min(1.0,(bl-bstore)/bl
(9).
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Background mortality, Bm, (1.39% year-1, Chao et al. (2008) occurs irrespective of the
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stress on the carbon store. Sm is the mortality rate (fraction year-1) of a single cohort when
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mean cohort carbon storage is zero. The value of Sm is also affected by spatial
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heterogeneity. In the hypothetical ‘average’ stand modelled by a DGVM, an ‘average’
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tree may die (making it’s observed mortality 100%) because it’s carbon reserves fall to
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zero. In reality it is very unlikely that, across a whole grid cell, all of trees in of a given
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PFT and size class will die simultaneously. Because we can neither parameterise
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effectively nor simulate the sub-grid cell heterogeneities that lead to the discrepancy
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between stand level and landscape level mortality, it is necessary to parameterise the
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variable Sm as the impact of carbon deficit on mortality rates.
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Plant Functional Types
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Plant ecology models typically seek to explain the co-existence of species along
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functional “trade-offs” (Pacala et al. 1996; Moorcroft et al 2001; Kneitel and Chase 2003;
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Baraloto et al. 2005). These compromises in plant form and function mean that no species
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is the best competitor in all environments. We use variation in S* to represent an
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example of a growth vs. mortality risk trade-off surface (Hacke et al. 2006; Poorter et al.
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2009). We constrain S* using measurements of carbon storage from a rainforest in
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Panama (Würth et al. 2005), in which the average amount of carbon stored in trees was
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approximately the same as that required to replace all of the leaf and fine root biomass.
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Notably, variation between species was substantial. We calculated the range of carbon
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stored between species using the data on % carbon storage in different tissues, and the
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mean biomass of each tissue type (Würth et al. 2005) and found that carbon storage
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varied by a factor of 2.4 (or 3.7, if one species with extremely high levels of stem
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carbohydrate was taken into account). Reflecting this, we created an array of seven
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tropical, evergreen plant functional types (PFTs) which differed in S* from 1.0 for PFT2,
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to 2.5 for PFT7 (Table 1). The additional properties of these PFTs are described in Table
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2. Each PFT represents a class of species that is broadleaf, evergreen and tropical, but
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with a specific range of carbon storage behaviour.
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METHODS
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To develop a DGVM capable of predicting vegetation conditions under altered
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climate and CO2, we coupled the adapted ED model to the Met Office Surface Exchange
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Scheme (MOSES II, Essery et al. 2003), that has recently evolved into JULES (Mercado
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et al. 2007). JULES calculates the land surface gas exchange and provides fluxes of
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carbon to ED, which generates land surface and canopy structure to drive the land-
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atmosphere interactions in return. We term the coupled model JULES-ED.
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We drove JULES-ED using output from the IMOGEN analogue climate model
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(Huntingford and Cox 2000). IMOGEN utilizes pattern output from the Hadley Centre
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HADCM3-LC Global Circulation Model (Cox et al. 2000) to provide climatic anomalies
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between a baseline climate and a given climate change scenario. In this instance, we use
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the Climate Research Unit (CRU) 1900-1999 climatology as a baseline dataset onto
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which we superimpose these anomalies. In order to use both the historical climatology
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for spin-up, and the pattern output from the GCM to generate forward predictions, the
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simulations are not site specific. Instead, we utilize data from Malhi et al. (2009b) who
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synthesized observations of the carbon economy of three Amazonian sites (Manaus,
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Caxiuanã and Tapajòs) to parameterise the ecophysiology of rainforest ecosystems (see
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Supplementary Infomation). We use driving climatologies for a 3.25o x 2.5o grid cell, the
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South West corner of which is located at 56.25oW and –2.5oS, encompassing all three
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sites used by Malhi et al. (2009b).
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Model Sensitivity Tests
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To investigate how uncertainties in the parameterisation of demographic
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processes affect the development of community structure, we conducted a global
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sensitivity test to five parameters; seed advection As, seed mixing Xm, sapling mortality
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Ms, competitive exclusion Ce and stress-induced adult mortality rate Sm. For each
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parameter, we set high and low parameter boundaries and conducted a 200 member Latin
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Hypercube exploration (Iman and Conover, 1982) of the five-dimensional parameter
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space to identify how different combinations of these processes affect community
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structure. The parameter ranges for Xm, Ce, and Sm were between zero and one because
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these were the logical end points of these processes. For As the minimum input was 0 and
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the maximum upper limit was 50 individual hectare-1 year-1. For Ms the maximum rate
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was 1.0, while we set the minimum as 95%. The model results described later illustrate
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that the output appears to be insensitive beyond these ranges for As and Ms.
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For each ensemble member, we ran the model for 400 years, starting from bare
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ground in 1700. For the baseline climatology we use 100 years of CRU data randomised
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over these 400 years (except for the 20th century, where we use actual year numbers). To
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this we add climate anomalies generated by the IMOGEN model driven CO2
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concentrations from the HADCM3-LC coupled climate carbon-cycle model output (Cox
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et al. 2000; Frieldingstein et al. 2006; Sitch et al. 2008). This climate change scenario is
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among the most extreme for Amazonia (Malhi et al. 2009a), but appears consistent with
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recent climate variability in Amazonia (Cox et al. 2004; Cox et al. 2008, Jupp et al.,
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2010). The annual CO2, precipitation and temperature components of the model drivers
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are shown in Figure 1.
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RESULTS AND DISCUSSION
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Impact of parameter variation on ecosystem biomass responses to climate change.
413
Altering the five demographic parameters that control unconstrained spatially
414
mediated demographic processes had a profound influence on the predicted response of
415
ecosystem biomass to future CO2 and climate (Figure 2a). Biomass estimates in 2005
416
ranged from 6.6 to 22.1 KgC m-2 y-1. By 2050, the competing effects of increasing
417
mortality and productivity in the future scenarios create an even wider divergence in
418
biomass (3.25 to 27.0 KgC m-2 y-1). Some ensemble members are able to benefit from
419
CO2 fertilisation, while others are more rapidly affected by the increasingly severe
420
drought events (Figure 1). Between 2059 and 2060, there is a large drought event that
421
depleted the carbon store and caused mortality in even the most conservative plant
422
functional types. By 2100, plant biomass is heavily depleted in most scenarios, with the
423
most resilient scenario supporting 9.6 KgC m-2. The response of LAI to changing climate
424
and CO2 is both less extreme and less different between runs as LAI recovers more
425
quickly after disturbance and is therefore less affected by variations in ecosystem
426
demography. We emphasize that, owing to the random selection of baseline climate, this
14
427
illustration is not meant to be proscriptive of the actual future climate or vegetation in
428
particular years.
429
430
Filtering unrealistic ensemble members.
431
The parameter space exploration generated wide variation in ecosystem properties
432
for the present day (Figure 2a), however, many of the ensemble members generated
433
unrealistic predictions for ecosystem properties that can be constrained by current
434
observations. We filtered those ensemble members whose biomass, gross or net primary
435
productivity (GPP, NPP) or leaf area index (LAI) fell outside observed ranges (Malhi et
436
al. 2009b, Fisher et al. 2007, Brando et al. 2008). To account for measurement error in
437
the upper and lower boundaries of the observations, we extended the ranges by 10% on
438
either side. After the filtering process, 14 ensemble members remained whose estimates
439
of all four variables were inside the observed ranges (Figure 2b). Whilst there are many
440
fewer simulations in the filtered set, the spread of predictions is not substantially reduced,
441
with biomass in y2050 still ranging from 2.6 to 27.0 KgC m-2 y-1. Filtering with this
442
particular set of model metrics did not allow us to constrain the different model futures or
443
rule out either the extremely sensitive or extremely resistant scenarios. Therefore,
444
satisfactory approximation of contemporary ecosystem observations is not necessarily an
445
indicator that a model will produce accurate future predictions. Current efforts to
446
‘benchmark’ vegetation models with sets of basic ecosystem data, with the intention of
447
constraining the range of future predictions, should consider this possibility when
448
interpreting their results (e.g. Randerson et al. 2009). It is possible that additional filters
449
not used in this experiment, notably responses of forest to experimental drying (Fisher et
450
al. 2007, Brando et al. 2008) might provide more appropriate filtering data. These kinds
451
of plot-level observations are not yet considered in DGVM benchmarking exercises,
452
however, due to the difficulties involved in precisely replicating the experimental
453
conditions in DGVM models.
454
455
Community Structure and its relation to Ecosystem Biomass Predictions.
456
Figure 3 illustrates the different plant community structures found in the 14 runs
457
that met the filtering criteria. The panels are ordered according to their predicted
15
458
ecosystem biomass in 2050 (from low to high). Those runs where forest mortality events
459
were predicted to occur sooner and biomass in 2050 was consequentially lower (e.g.
460
Figure 3 - top two rows) were dominated by the fast growing plant functional type (PFT
461
#1, filled circles), while those runs where the ecosystem avoided biomass collapse for
462
longer tended to have a more equitable distribution of plant functional types (e.g. Figure
463
3 – bottom two rows). In this particular model scenario, prevailing conditions before
464
2000 typically favour the dominance of the fastest growing plant types. The persistence
465
of PFT1 as the dominant plant type in 2000 reflects the relatively benign climatic
466
conditions over the last century and is consistent with a small fitness cost associated with
467
low rates of carbon storage: NPP rarely falls enough to deplete stored carbon reserves
468
enough cause canopy tree mortality. In all cases, the fastest growing PFTs gain a slight
469
initial advantage via lower allocation to carbon storage. The eventual community
470
structure, however, depends upon the strength of processes that reinforce this initial
471
dominance, which is impacted substantially by varying the spatially mediated parameters
472
in this sensitivity test.
473
474
Impact of individual parameters on Community Structure and ecosystem properties.
475
Illustrating detailed ecosystem composition for every ensemble member was
476
impractical, so we reduced the dimensionality of the output by calculating a PFT range Rp
477
for each model run, as
478
479
Rp = Bf,1-Bf,7
(10)
480
481
where Bf,i is the fractional biomass of the i’th PFT in 2000. Fractional biomass is the total
482
of the total biomass accounted for by a given PFT. Values close to 1 indicate dominance
483
the fastest growing PFT and values close to zero indicate more equitable PFT
484
distribution. This metric of community structure provides a single value with which to
485
represent how much the community is dominated by fast growing plants. Figure 4
486
illustrates how this measure of community structure affects whole ecosystem properties
487
(GPP, NPP LAI, and biomass) used in the filtering process. Typically, those ecosystems
488
with a PFT range close to one had high values of GPP, NPP and LAI, that were often
16
489
outside the observational range.
Ecosystem biomass was highest for mid-range
490
community composition. Those ensemble members with highly equitable PFT
491
distribution tended to have very low biomass, below the acceptable range.
492
Figures 5-7 illustrate how the five demographic parameters that we investigated
493
were related to PFT range index (equation 9, Figure 5),. biomass predictions at 2050
494
(Figure 6) and LAI in 2005 (Figure 7). The impact of the different parameters on NPP,
495
GPP and biomass in 2005 and biomass in 2100 are included in the Supplementary
496
Information (S1-S4).
497
Of the five varied parameters, sapling mortality (Ms) had the largest impact on
498
community structure and ecosystem properties. To illustrate the impact of varying this
499
parameter on the model output, we shaded the points in Figures 4 to 7 according to their
500
value of Ms. Ms mediates the positive feedback between fast growth and sapling
501
production. Those trees with fast growth rates produce large numbers of saplings that
502
grow quickly during situations of low sapling mortality, increasing the tendency of fast
503
growing PFTs to become dominant. Low values of Ms encourage this positive feedback,
504
leading to mono-dominance and high PFT range. Simulations with high values of Ms
505
suppress this feedback and tended to have a more equitable PFT distribution with more
506
slow growing PFTs (Figure 5, panel d). These PFTs are less susceptible to drought
507
induced mortality (in the model), so the runs with high Ms have higher biomass in 2050
508
(Figure 6, panel d). In addition, a combination of higher allocation to storage, and less to
509
leaves, as well as lower overall under-storey recruitment rates, means that those
510
communities with high values of Ms have lower LAI estimates (Figure 7 panel d). The
511
first order impact of lower sapling mortality on biomass (more seeds = more biomass)
512
was not present in 2005 (Figure S3, panel d).
513
The seed mixing parameter (Xm) had a large impact on community structure.
514
Initial seeding conditions are an important control on community structure after canopy
515
closure. When large numbers of seeds are distributed to other patches, and Xm is high,
516
PFT1’s dominance of one age class makes it a source of PFT1 seed for other age classes,
517
increasing its share of the seed bank and thus its increasing ability to dominate newly
518
disturbed areas. Where most seeds land in their parent patch, and Xm is low, PFT1 wastes
519
most of its seed increasing competition with itself. Therefore, high Xm promotes both
17
520
dominance of PFT1 (Figure 5, panel c) and the development of communities with fast-
521
growing PFTs. These fast growing PFTs are at greater risk of dying under future
522
droughted conditions due to their lower carbon reserves, so forest biomass in 2050 is
523
lower for high Xm simulations (Figure 6 panel c). However, higher Xm allows faster
524
colonisation of recently disturbed gaps, facilitating faster regeneration and higher
525
spatially averaged leaf area index (Figure 7, panel c).
526
Seed advection (As) has a relatively minor impact on community structure and on
527
biomass in 2050 (Figure 5 and Figure 6, panel e). Increasing seed rain modulates the
528
dominance of the fast growing PFT for sapling recruitment, but also accelerates the rate
529
of canopy closure, enhancing the dominance of the faster growing plants (results not
530
shown).
531
consistent response from emerging. As did have a notable impact on the biomass in 2100
532
(Figure S2, panel e), as higher seed rain presumably promotes more rapid ecosystem
533
recovery from mortality events (Figure 7, panel e). Also higher seed advection promotes
534
higher LAI; the number of saplings present in the under-storey increases on account of
535
the shift in the equilibrium between recruitment and mortality.
536
There was little consistent impact of competitive exclusion (Ce, panel a) or stress-induced
537
mortality (Sm, panel b) on either PFT composition or biomass in 2050 (Figure 5 and
538
Figure 6, panels a and b). In isolation, these parameters can exert substantial control over
539
community structure (results not shown), but in the global sensitivity analysis (i.e.
540
varying all parameters simultaneously) their impact may well have been overridden by
541
large variations in the forcing caused by the other parameters. LAI is highest for low
542
values of Sm, as greater mortality rates of carbon starved plants in shade or drought
543
results in a lower equilibrium LAI (Figure 7, panel b).
The conflicting impact of these two mechanisms may well prevent any
544
545
Scale Limitations and Parameter Constraints.
546
Typically, vegetation modellers attempt to constrain model parameter values via
547
observations of the processes to which they apply. Unfortunately, the parameters we
548
investigate here are not amenable to observation because the scales at which they operate
549
are not represented in the spatially one-dimensional model environment. For example, the
18
550
rate of seed advection As of a given PFT is likely a function of (at least) the mean
551
distance in space to other areas of land containing that PFT. Landscape models that
552
include a two-dimensional spatial structure of inter-connected patches, with a
553
representation of both spatial arrangement and distance between patches, can simulate
554
this property, but not one-dimensional DGVM models (Neilson et al. 2005; Lischke et al.
555
2006).
556
Similar issues apply to the other three parameters.
Seed mixing, Xm, most
557
obviously, is the result of the unknown length scale of disturbance processes and patches
558
of land that ED represents via statistical aggregation. The length scale of ecosystem
559
patches in reality is controlled by the size of disturbance events. If most disturbance
560
events result from the death of single trees, this generates a matrix with a small length
561
scale and a consequentially high rate of inter-age class seed mixing. If mortality is
562
spatially aggregated because of blowdown events, pathogen outbreaks or fires, then the
563
length scale will be larger and mixing less likely. No DGVM at present tracks the two-
564
dimensional sub-grid variation in disturbance history. Tracking disturbance history is
565
only made computationally possible in the ED model by removing the spatial dimension
566
and tracking all patches of a common disturbance history together. This property must
567
therefore at present be parameterized. Here we illustrate, for the first time in the context
568
of a DGVM modelling study, how the values of this property affect model outcome.
569
Future studies must focus on resolving this issue either using top-down observational
570
constraints, by leveraging output from spatially explicit studies into the one-dimensional
571
model, or by converting the model framework to a substantially more computationally
572
intensive fine-mesh structure.
573
The degree of determinism and stochasticity of competitive exclusion, Ce, depends
574
upon smaller-scale spatial interactions between the crowns of adjacent trees. Simulation
575
of this process would require at least a branch-scale canopy simulation model, (e.g.
576
Williams, 1996), in addition to improved understanding of the genetic heterogeneity
577
between plants represented by a single PFT and the micro-variation in abiotic conditions.
578
It might be possible to estimate locally appropriate values of Ce from community
579
composition data using inverse Bayesian methods (Clark et al. 2003; Etienne and Olff,
580
2005).
19
581
Sapling mortality, Ms, which is an aggregate of seed number, seed germination, and
582
death of the germinated seedlings, is poorly understood and very complex to model
583
mechanistically. Inverse estimates of seed mortality from forest inventories might be
584
possible, but existing forest databases typically only measure trees greater than 10cm
585
diameter (Baker et al. 2004). Thus estimates of Ms are confounded with unobserved
586
under-storey growth and mortality processes. Also, sapling mortality is thought to be
587
influenced by dispersal distance via the influence of species-specific herbivores or
588
pathogens (Janzen 1970, Connell 1971) and by potential positive interactions between
589
parent trees and saplings, the interactive consequences of which are explored by Murrell
590
(2009).
591
Stress-induced mortality rates (Sm) appropriate for landscape scale models or
592
DGVMs are also very difficult to parameterise. Allen et al. (2010) illustrate the difficulty
593
of quantifying rates of vegetation mortality with observations made at multiple spatial
594
scales. High rates of observed stand level mortality typically translate into much lower
595
landscape level mortality rates, due to spatial variation in landscape properties, biotic
596
agents, species and weather (Allen et al. 2010). For a DGVM models, that scale linearly
597
from plot level simulations to landscape level prediction, the appropriate scale of
598
measurement of plant mortality rates is therefore contentious. Landscape level estimates
599
of tree mortality are very rare (Allen et al., 2010) but may be facilitated by vegetation
600
monitoring networks (Philips et al. 2008) in the future.
601
602
Spatial interactions in existing studies
603
The concept that spatial interactions are important for community structure is in no
604
way novel (Silvertown and Law 1987) but is infrequently considered by the DGVM
605
community (Neilson et al. 2005; Midgley et al. 2007). At present, no DGVMs represent
606
the movement of propagules in two dimensions, and no first-generation DGVMs
607
represent plant competition for light in a vertical profile (see Arora and Boer 2005, for a
608
detailed review of first generation DGVM plant competition algorithms). Literature from
609
forest gap models discusses possible conditions necessary for simulating co-existence and
610
the impact of competitive exclusion and spatial processes on community structure
611
(Adams et al. 2007; Lischke and Löffler, 2006; Kohyama and Takada 2009) but the
20
612
emerging literature on second generation DGVMs as yet provides little discussion on
613
how plant co-existence is generated along axes of variation other than early-to-late
614
successional plant traits.
615
biodiversity and species co-existence can potentially inform us on how best to proceed
616
from this point (McGill et al. 2006), and it seems likely that the possible limits on these
617
parameters may potentially be informed by the outcomes of more spatially explicit
618
models at various scales (Kneital and Chase 2004).
A vast literature on the assemblage of communities,
619
620
CONCLUSION
621
In this paper we introduce a series of modifications to the Ecosystem Demography
622
model that more readily allow the co-existence of plant types with similar growth rates.
623
We conclude that, despite major advances in dynamic global vegetation modelling, there
624
exist a number of processes pertaining to spatial plant ecology that are currently beyond
625
the capacity of even the most sophisticated dynamic global vegetation models to capture.
626
If we fail to appropriately represent or constrain the processes that control the emergence
627
of plant community structure in the new generation of global vegetation models, we risk
628
generating modelled communities of plants with erroneous responses to climatic and
629
atmospheric changes.
630
While we have endeavoured to create simulations that closely reflect the behaviour
631
of Amazonian rainforest ecosystems, we emphasize that our purpose was not to provide
632
definitive predictions of the future of the Amazon, but instead to illustrate the potential
633
importance of the representation of infrequently discussed plant demographic processes
634
of reproduction, competition, and mortality on the range of future predictions. We chose
635
to focus on one location to allow a detailed illustration of this high-dimension problem;
636
however it seems likely that the issues derived here may well be generically applicable,
637
in different modelling frameworks, and across multiple combinations of climate and
638
functional trade-off axes.
639
640
ACKNOWLEDGEMENTS
641
Funding was provided by the UK Natural Environment Research Council QUEST
642
‘Quantifying Ecosystem’s Role in the Carbon Cycle’ project (QUERCC), the
21
643
LANL/LDRD program and DOE-Office of Science (BER) Program for Ecosystem
644
Research. RF would like to thank Craig Allen, Doug Clark, Micheal Dietze, Manuel
645
Gloor, Heike Lischke, Jon Lloyd, Mark Lomas, Oliver Philips, Colin Prentice, Todd
646
Ringler, Allan Spessa, Ying-Ping Wang, Mark Westoby, Mat Williams and Ian Wright
647
for interesting discussions that help formulate the ideas in this manuscript.
648
22
649
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TABLES
1099
1100
Table 1 Value of S*, the ‘target’ carbon storage criteria between plant functional types.
1101
S* is the quantity of carbon targeted by the allocation scheme, in multiples of the total
1102
leaf biomass (bl). The range of values chosen is based on observations by Würth et al.
1103
(2005).
1104
PFT number
S*
1
1.0
2
1.25
3
1.5
4
1.75
5
2.0
6
2.25
7
2.5
1105
1106
33
1107
1108
Table 2. Model parameters obtained from literature sources.
1109
Parameter
Explanation
Units
Mb
Background Mortality
%
-3
Value
Source
1.39
Chao et al. 2008
D
Wood Density
gC cm
0.7
Chao et al. 2008
aleaf
Leaf Turnover
year -1
0.69
Wright et al. 2004
aroot
Fine root allocation
year -1
0.69
Malhi et al. 2009b
awood
Coarse wood turnover (branches & year-1
0.01
Malhi et al. 2009b
87
Carswell et al. 2000
145
Carswell et al. 2000
0.50
Malhi et al. 2009b
0.63
Malhi et al. 2009b
0.17
Mercado et al. 2007
coarse roots)
SLAc
Specific Leaf area (canopy)
cm2 g-1
2
-1
SLAu
Specific Leaf area (understory)
cm g
rr
Root respiration as a fraction of leaf fraction
respiration
rs
Stem respiration as a fraction of leaf fraction
respiration
KN
Exponent of change in nitrogen through canopy
N0
Nitrogen Concentration at canopy top
KgN KgC
0.046
Mercado et al. 2007
frepro
Fraction of growth carbon to respiration
fraction
0.37
Meir
et
unpublished
1110
34
al.
1111
FIGURE LEGENDS
1112
1113
Figure 1: Forcing data for model simulations; a) Carbon Dioxide concentrations, b)
1114
Temperature and c) Annual precipitation.
1115
1116
Figure 2: Response of the trajectory of total plant biomass to alterations in ecological
1117
parameterizations showing the last 150 years of the 400 year simulation. Panel a)
1118
includes all 200 members of the ensemble, and b) includes only those 14 ensemble
1119
members with acceptable biomass, LAI, GPP and NPP compared to observations. Grey
1120
shading on symbols indicates the sapling mortality (Ms) parameter for each run, and can
1121
be read from figure 5, panel d
1122
1123
Figure 3: Development of plant functional type community composition over 400 year
1124
model evaluation for each of 16 ensemble members with acceptable values of biomass,
1125
GPP, NPP and LAI. Panels are arranged according to the biomass predicted in 2050, to
1126
illustrate the impact of community composition on ecosystem prediction. Biomass in
1127
2050 for each run is shown in text on each figure. Symbols refer to different plant
1128
functional types as follows. Closed circles = PFT1, Open circles = PFT2, closed squares
1129
= PFT3, open squares = PFT4, closed triangles = PFT5, open triangles = PFT6, closed
1130
diamonds = PFT7, open diamonds = PFT8.
1131
1132
Figure 4: Relationship between a) GPP, b) NPP, c) LAI and d) Biomass in y2005, and
1133
ecosystem composition as expressed by the PFT range metric (equation 9). Shaded panel
1134
indicates the limits of observations. Grey shading on symbols indicates the sapling
1135
mortality parameter for each run, and can be read from Figure 5, panel d).
1136
1137
Figure 5: Response of modelled PFT range at y2005 to variation in a) competitive
1138
exclusion Ce, b) stress-induced adult mortality Sm, c) seed mixing Xm, d) sapling mortality
1139
Ms and e) seed advection As. Shaded area denotes limits of observations from Malhi et al.
1140
(2009). Square symbols denote members of the filtered ensemble with predictions of
1141
NPP, GPP, LAI and biomass within acceptable ranges. Grey shading on symbols
35
1142
indicates the sapling mortality parameter for each run, and can be read from panel d).
1143
1144
Figure 6: Response of predicted biomass at y2050 to variation in a) competitive exclusion
1145
Ce, b) stress-induced mortality Sm, c) seed mixing Xm, d) sapling mortality Ms and e) seed
1146
advection As. Square symbols denote members of the filtered ensemble with predictions
1147
of NPP, GPP, LAI and biomass within acceptable ranges. Grey shading on symbols
1148
indicates the sapling mortality parameter for each run, and can be read from panel d).
1149
1150
Figure 7: Response of modelled leaf area index at y2005 to variation in a) competitive
1151
exclusion Ce, b) stress-induced mortality Sm, c) seed mixing Xm, d) sapling mortality Ms
1152
and e) seed advection As. Shaded area denotes limits of observations from Brando et al.
1153
(2008) and Fisher et al. (2007). Square symbols denote members of the filtered ensemble
1154
with predictions of NPP, GPP, LAI and biomass within acceptable ranges. Grey shading
1155
on symbols indicates the sapling mortality parameter for each run, and can be read from
1156
panel d).
1157
1158
1159
1160
1161
36
1162
1163
Figure 1
1164
1165
1166
1167
37
1168
Figure 2
1169
38
1170
Figure 3
1171
1172
39
1173
Figure 4
1174
1175
1176
40
1177
1178
Figure 5
1179
1180
41
1181
Figure 6
1182
1183
1184
1185
42
1186
1187
Figure 7
1188
1189
43
1190
1191
1192
1193
44
1194
1195
1196
Supplementary Information
1197
1. Fluxes of water and carbon
1198
Cohort carbon fluxes are calculated by the JULES/MOSES MOSES (Cox et al.
1199
1999; Essery et al 2003) surface exchange scheme present in the IMOGEN model,
1200
modified to represent the updated canopy structure modifications and sub-grid tiling
1201
assumptions. The representation of tiling in the model was altered to replace the pre-
1202
existing system, where each tile represents a single plant functional type, to one where
1203
each tile represents an age-class or ED patch. Thus, we removed the existing DGVM
1204
present in the MOSES model, TRIFFID (Cox 2001) and replaced it with the ED model.
1205
This does not represent a large change in the conceptual model coupling, as the DGVM
1206
passes back the same information; tile areas, canopy LAI and height, to the land surface
1207
scheme. For some properties (albedo, root infiltration) plant type has an impact on the
1208
land exchange, and for these we generate a dominant plant functional type – that with the
1209
most biomass – used to drive these calculations. In the current implementation, the
1210
reflectance and infiltration properties are the same for all tree plant functional types, but
1211
this may be revisited for global applications.
1212
The new canopy scheme provides NPP at the cohort level by calculating the rate of
1213
net assimilation for each leaf layer in the canopy, and then disaggregating this to the
1214
cohorts according to their tree leaf area profile. We generate a matrix of net assimilation
1215
(A) with the dimensions (P,Y,FT,Z) where P is the patch level, Y is the canopy layer, FT
1216
is the functional type and Z is the leaf layer within the tree canopy.
1217
assimilation, A is derived from the model described by Cox (2001) and Mercado et al.
1218
(2007) that simulates photosynthesis based on the leaf photosynthesis models of from
1219
Collatz et al. (1991) ) and Collatz et al. (1992). These simulate potential leaf
1220
photosynthesis as the minimum of three limiting processes; Rubisco limited
1221
carboxylation, light limited photon conversion and rate of transport of photosynthetic
1222
products. Leaf dark respiration (Rd ) is simulated as a fraction of the maximum rate of
1223
carboxylation (Vmax ), both in (µmol m2 s1 ).
1224
photosynthesis via the soil moisture availability factor ø, (Anet = Aø ) where ø is a unitless
Leaf level
Moisture stress impacts on net leaf
45
1225
factor based on soil moisture in the four-layer soil model. In this model realisation,
1226
photosynthetic parameters for all PFTs are the same as those described by Cox (2001) for
1227
broadleaf trees, with the exception that we alter the light assimilation parameter alpha
1228
from the default suggested by Cox et al (1998) of 0.8, to that fitted to Amazonian forest
1229
data by Harris et al. (2004) of 0.6. We do not use the other parameters optimised by
1230
Harris et al. (2004), as these pertained to aspects of the model fundamentally altered by
1231
inclusion of the multi-layer canopy scheme. We also alter the depth of the bottom soil
1232
layer and the root system such that there are 7m of soil depth. This is to reflect the now
1233
widespread view that Amazon rainforest soils and root systems are substantially deeper
1234
than the 3m more typically used in models (the default value in JULES) (Jipp et al. 1998;
1235
Nepstad et al., 1994, Hodnett et al.,1995; da Rocha et al., 2004; Fisher et al. 2007).
1236
Estimates of the depth of root profiles in Amazon forests typically extend as deep as
1237
observations are made, up to 10m and beyond, but root abundance is very low in deeper
1238
soils (Fisher et al. 2007). The absence of an explicit water transport scheme in JULES
1239
means that the impact of this low root density on the difficulty of extracting water is
1240
difficult to estimate mechanistically (e.g. Sperry et al. 1998), thus we use a value of 7m
1241
here as a compromise between these two conflicting factors.
1242
In the original version of MOSES (Cox et al. 1999), leaf level photosynthesis is
1243
scaled up to canopy level using a ‘big leaf approach’ (Sellers et al. 1992). Here, we
1244
introduced a multi-layer canopy model, whereby incoming light (I) declines
1245
exponentially through the canopy according to Beer’s Law (I = Ie-0.5L.). Light attenuation
1246
to the top leaf layer of each canopy layer (Z=1) is controlled by the leaf area index L
1247
averaged over the whole land surface in the canopy layers above (or 0, in the case of the
1248
top canopy layer). Leaf layers within canopies then exist under light condition attenuated
1249
by an LAI of 1.0 for each leaf layer. The cohort level photosynthesis is calculated using
1250
the Anet matrix. Each cohort has a value of P, FT and Y, and integrates photosynthesis
1251
over the different leaf layers according to its tree leaf area index, tlai, which is determined
1252
by the ratio of leaf area to ground area.
1253
1254
tlai=Aleaf/ Acanopy
(s1)
1255
46
1256
Where Aleaf is the total leaf area of a single tree and Acrown is the ground area occupied by
1257
the crown. Tree leaf area index is different to the leaf area index averaged over the
1258
ground area, as the area occupied by trees might be less than the total ground area.
1259
Therefore, by implicitly including the leaf area of individual trees, we allow for the
1260
likelihood that leaf area occurs in clumps related to individual trees, and for the
1261
possibility that different cohorts maybe exhibit independently varying leaf area. Note that
1262
the JULES canopy radiation model has since been significantly upgraded to include a
1263
two-stream model and diffuse radiation effects (Mercado et al. 2007; Mercado et al.
1264
2009), but this version was not available for this study.
1265
1266
1267
1268
Maintenance Demands
Once NPP (KgC individual-1 year-1) for each cohort is calculated, the cost of
maintaining live tissues, md, is removed the give the remaining carbon balance Cb.
1269
1270
Cb=NPP-md
(s11)
1271
1272
md is the sum of the requirements for leaf and root turnover.
1273
1274
md=braroot+blaleaf.
(s12)
1275
1276
Because br is assumed to be the same as bl, and because Malhi et al. (2009b) determined
1277
that the total cost of leaf turnover to be similar to that of root turnover (once reproductive
1278
structures are removed from the fine litter estimates, Meir et al. (unpublished) for tropical
1279
forests, the turnover of roots is also assumed to be similar to that of leaves (determined as
1280
the mean of the average value for tropical forests in a leaf trait database, 0.68 (Reich et al.
1281
2001). From the carbon balance, the allocation of carbon to storage compounds is
1282
removed to give the carbon available for growth and reproduction. The fraction going to
1283
reproduction was calculated as 0.37, from estimates of reproductive structures collected
1284
in litter traps (Meir et al. unpublished) and estimate of wood biomass increment
1285
generated by Malhi et al. (2009b).
1286
47
1287
1288
1289
Control of Leaf Area Index
Aleaf is calculated from leaf biomass bl (kgC individual-1) and specific leaf area
(SLA, m2 kgC-1)
1290
1291
Aleaf = bl,SLA
(s2)
1292
1293
For a given tree allometry, leaf biomass is determined from basal area using the function
1294
used by Moorcroft et al. (2001) where dw is wood density in g cm-3.
1295
1296
bl = 0.0419D1.56 dw0.55
(s3)
1297
1298
Crown area, Acrown, is defined as
1299
1300
Acrown = π(Cs Sc)1.56
(s4)
1301
1302
Here we follow the methodology of Purves et al., by specifying a ‘canopy spread’ scaling
1303
parameter ‘Sc’, the value of which is discussed in the ‘Control of Canopy Area’ section
1304
below. In contrast to Purves et al., we use an exponent, identical to that for leaf biomass,
1305
of 1.56, not 2.0, to maintain a constant LAI under changing diameter for mature trees.
1306
However, using this model, where leaf area and crown area are both fixed functions of
1307
diameter, then the leaf area index of the tree is the same, irrespective of the growth
1308
conditions.
1309
methodology for ‘trimming’ those leaves in the canopy that exist in negative carbon
1310
balance. That is, their total annual assimilation rate is insufficient to pay for the turnover
1311
and maintenance costs associated with their supportive root and stem tissue, plus the
1312
costs of growing the leaf. The tissue turnover maintenance cost per m2 of leaf is
To allow greater plasticity in tree canopy structure, we implemented a
1313
1314
Lcost = md/( blSLA)
(s5)
1315
1316
The net uptake Unet (taking into account stem and root respiration required to support that
1317
leaf as well) is
48
1318
1319
Unet = g-rd(1+rr+rs)
(s6)
1320
1321
where g is the GPP of the bottom layer of leaves in each tree (KgC m-2 year-1), rd is the
1322
rate of leaf dark respiration (also KgC m-2 year-1), and rr and rs are the rates of root and
1323
shoot respiration, relative to leaf respiration.
1324
1325
We use an iterative scheme to define the cohort specific canopy trimming fraction
Ctrim, on an annual time-step, where
1326
1327
bl = Ctrim0.0419D1.56 dw0.55
(s7)
1328
1329
1330
If the annual maintenance cost of the bottom layer of leaves (KgC m-2 year-1) is less than
then the canopy is trimmed by an increment ‘i’ (0.01).
1331
1332
for Lcost > Unet
; Ctrim,t+1 = max(Ctrim,t-i,1.0)
1333
for Lcost < Unet
; Ctrim,t+1 = min(Ctrim,t+i,0.5)
(s8)
1334
1335
We define an arbitrary minimum value on the scope of canopy trimming of 0.5. If plants
1336
are able simply to drop all of their canopy in times of stress, with no consequences, then
1337
tree mortality from carbon starvation is much less likely to occur because of the greatly
1338
reduced maintenance and turnover requirements.
1339
1340
Control of Canopy Area
1341
Using the scheme described above under good growth conditions (i.e. if Ctrim is
1342
equal to 1.0) the tree leaf area index will remain at it’s maximum theoretical value, again
1343
irrespective of conditions. Given that the ED model has the capacity to model open
1344
canopies, this model property means that, even if there is no competition between trees
1345
for light, some of the leaves will be in relatively deep shade, on account of the perceived
1346
spatial limitation in canopy space. In an open canopy, plants are able to position a larger
1347
fraction of their leaves in full sunlight, both because there are fewer spatial constraints
1348
mediated by neighbouring trees, and because light can enter the tree canopy from the side
49
1349
as well as from the top. We do not attempt to model the 3D light environment explicitly,
1350
but instead modulate the canopy spread co-efficient such that prior to canopy closure, the
1351
effective leaf are index is <1.0 and all the leaves are in full sunlight. To achieve this we
1352
determined the ‘spread’ of the canopy (Sc), iteratively each daily time-step as the canopy
1353
area relative to ground area changes. In an open canopy, Sc is equal to the maximum
1354
value Smax, is gradually decreased to the minimum value Smin as the canopy closes. This
1355
process starts once the total canopy area is above a nominal threshold where the trees
1356
interfere with each other (St=0.8). Should this occur, Sc is decremented, again by
1357
increment I
1358
1359
for Acanopy > ApSt ; Sc,t+1 = max(Sc,t-i,Smin)
1360
for Acanopy < ApSt ; Sc,t+1 = min(Sc,t+i,Smax)
(s9)
1361
1362
This algorithm generates a circularity whereby the canopy area is a function of canopy
1363
spread, which is a function of canopy area. However, the iterative scheme converges on
1364
an equilibrium point where the canopy covered fraction area is just less than St, until the
1365
minimum canopy packing density is reached, and no more spatial condensing of canopy
1366
foliage is possible. The maximum tree leaf area is thus a function of the minimum crown
1367
aerial extent. In this case, the minimum parameter Smin =0.1 means that the maximum
1368
leaf area index of any canopy tree is 3.8. Any additional leaf area index exists in the
1369
understorey.
1370
1371
Gradients within the canopy.
1372
In a model that determines leaf area index based on the physiological principles
1373
outlined above (that the lowest leaf layer must pay for it’s own construction and
1374
maintenance costs) the variation in photosynthetic and growth parameters through the
1375
canopy has a critical impact on both gas exchange and the maximum achievable leaf area
1376
index. Firstly, leaf nitrogen concentrations are known to vary through the canopy,
1377
Mercado et al. (2007) define a nitrogen allocation coefficient, Kn, using data generated by
1378
Carswell et al. (2000) and we employ this value here to scale Nitrogen through the
1379
canopy in a manner which is not, as many ‘big leaf’ models of photosynthesis have
50
1380
assumed, proportional to light level. We employ this value of Kn (0.17) here to model the
1381
decline in photosynthetic capacity with canopy depth,
1382
1383
N=N0-Lkn
(s10)
1384
1385
where N is leaf Nitrogen content, N0 is leaf Nitrogen content of the top leaf surface (also
1386
defined from observations by Mercado et al. 2007), L is integrated leaf area above the
1387
leaf in question. The optimal scaling of canopy properties with depth is discussed at
1388
length by Lloyd et al. (2009) who derive a model which demonstrates that, where there
1389
are genetic limits on the nitrogen content of leaves at the canopy top, and where the use
1390
of nitrogen incurs respiratory costs, a nitrogen profile which is shallower than the decline
1391
in light availability is in fact more optimal.
1392
Secondly, specific leaf area (SLA), typically defined as a constant, is known to
1393
change markedly through the canopy between sun and shade leaves. Carswell et al.
1394
(2000) observed an increase in SLA through the tree canopy at the Caxiuanã site from 87
1395
to 145 cm g-1 (8.7-14.5 m2 kg-1, or 115 –69 g m-2). Lloyd et al. (2009) report a similar
1396
increase in SLA through the canopy using information from 204 different vertical profiles
1397
within the Amazon. For the top of the canopy, these values of SLA are similar to the
1398
average for broadleaf evergreen trees of 79 cm2 g-1 reported by Reich et al. (2007).
1399
However, the values for the lower canopy are substantially higher (this is not surprising,
1400
as the data used by Wright et al. 2004 and Reich et al. 2007 used sun leaves wherever
1401
possible). Between plant types, decreases in SLA are typically partially offset by
1402
increases in leaf lifespan owing to changes in leaf toughness and resistance to herbivory
1403
and decay (Wright et al. 2004).
1404
However, this relationship does not necessarily persist when applied to variation of
1405
traits within a canopy. Selaya et al. (2008) found no correlation between leaf lifespan and
1406
specific leaf area in the Bolivian Amazon and several studies have shown that leaf
1407
lifespan is negatively correlated with irradiance within tropical canopies (Osada et al.
1408
2003; Hikosaka 2005).
1409
canopy, then the modelled leaf area index is low, compared to observations. One
1410
approach to rectifying this is to introduce a function varying SLA with canopy light
If the cost of leaf area is assumed to be constant through the
51
1411
environment such that shading increases SLA according to observed behaviour.
1412
However, mathematically, the dependence of light environment on LAI and therefore
1413
SLA generates a circularity. Instead, we introduce a fixed variation in the SLA between
1414
the overstory (87 cm g-1) and the understory (145 cm g-1), such that trees in the upper
1415
canopy have thicker leaves than those in the understorey. There is some error induced
1416
here by not simultaneously changing the leaf lifespan, owing to a lack of information on
1417
how these properties scale to one another, but this will likely only have a large impact on
1418
LAI, as biomass and gas exchange fluxes are more heavily influenced by the properties
1419
of the top leaf layers.
1420
Gradients in transpiration demand with height are also likely due to changes in
1421
relative humidity from the canopy to the understory (an average change of 10% being
1422
observed by Fisher and Lobo do Vale, unpublished data, at Caxiuana) but are generally
1423
not represented in land surface models. In the JULES model, leaf temperature is also
1424
constant with canopy depth, so it is likely that impacts of drought stress will be
1425
asymmetric through the canopy, again affecting the cost-benefit analysis of leaves at
1426
different canopy layers.
1427
52
1428
1429
Supplementary Figures
1430
Figure S1. Response of predicted biomass at y2005 to variation in a) competitive
1431
exclusion Ce, b) stress-induced mortality Sm, c) seed mixing Xm, d) sapling mortality Ms
1432
and e) seed advection As. Shaded area denotes limits of observations from Malhi et al.
1433
(2009). Square symbols denote members of the filtered ensemble with predictions of
1434
NPP, GPP, LAI and biomass within acceptable ranges. Grey shading on symbols
1435
indicates the sapling mortality parameter for each run, and can be read from panel d).
1436
1437
Figure S2. Response of predicted biomass at y2100 to variation in a) competitive
1438
exclusion Ce, b) stress-induced mortality Sm, c) seed mixing Xm, d) sapling mortality Ms
1439
and e) seed advection As. Legend as for figure S1.
1440
1441
Figure S3. Response of predicted GPP at y2100 to variation in a) competitive exclusion
1442
Ce, b) stress-induced mortality Sm, c) seed mixing Xm, d) sapling mortality Ms and e) seed
1443
advection As. Legend as for figure S1.
1444
1445
Figure S4. Response of predicted NPP at y2100 to variation in a) competitive exclusion
1446
Ce, b) stress-induced mortality Sm, c) seed mixing Xm, d) sapling mortality Ms and e) seed
1447
advection As. Legend as for figure S1.
1448
53
1449
1450
1451
Figure S1
1452
1453
1454
1455
54
1456
1457
Figure S2
1458
1459
1460
1461
1462
55
1463
1464
Figure S3
1465
1466
1467
1468
1469
1470
56
1471
1472
Figure S4
1473
1474
1475
1476
1477
57