1. Different approaches to model forests
Different approaches have been developed to model forest ecosystems and
community dynamics, as well as forest cover and tree species
distributions. They range from basic theoretical models such as neutral
models (Hubbell 2001), through models of growth patterns of individual
trees, to forest stand or landscape models (Shifley et al. 2017), or
global vegetation models (Prentice et al. 2007). Depending on the
specific objectives of the developing scientists, the model
representation of biogeochemical processes, vegetation structure, or
biodiversity have been more or less detailed, by means of different
degrees of aggregation or abstraction or following various assumptions.
The three model types we briefly present here - SDMs, IBMs, DGVMs - have
been developed by different disciplines and cover a gradient from models
that initially focused on a detailed representation of individual
species to models that gave initial emphasis to the representation of
forest structure and tree demography, to others that focused on the
representation of biogeochemical processes. We chose these model types,
which have a long history and are all widely used, especially in the
context of global change, to illustrate the variety of modelling
approaches, but our general ideas also apply to other model types. In
the following, we present these three approaches by ordering them along
a gradient of decreasing resolution of biodiversity representation and
increasing resolution of biogeochemical process representation,
acknowledging other orders could have been used alternatively.
Species distribution
models
Species distribution models (SDMs; Booth et al. 2014; Guisan et al.
2017) focus on the spatial distribution of species and how it varies
with environmental drivers. SDMs have their origin in flora distribution
maps, which laid the concepts of biogeography (Humboldt 1849; Grisebach
1872). The development and increased usage of SDMs across a wide array
of taxa and environments have relied on several technical advances
(Guisan & Thuiller 2005; Elith & Leathwick 2009), namely statistical
approaches (e.g. MaxEnt), methods for physical environment mapping (e.g.
remote sensing techniques), and increased coordinational effort to
compile knowledge on species records. All these approaches have been
boosted by geographic information systems (GIS).
SDMs rely on the concept of ecological niche (Hutchinson 1957; Guisan &
Thuiller 2005; Soberón 2007), and can be described as a two-step process
as follows. First, the ecological niche representation of a species is
built in an environmental space, based on known records in places where
environmental conditions have been described. Then each geographic
location is assigned a probability of occurrence for the species, based
on the niche model (Elith & Leathwick 2009).
SDMs thus require little information on the processes from which species
distributions result. This can be an advantage, e.g. for poorly known
taxa in demand of conservation actions. Also, by looking for a best
model fit in species niche modelling, important environmental drivers of
spatial species patterns may be revealed (e.g. Thuiller et al. 2003;
Bertrand et al. 2012). SDMs have also been used to predict species
distributions under future environmental conditions, such as species
invasion or climate change (Thuiller 2003; Thuiller et al. 2005).
However, key assumptions of SDMs, mainly that species are at equilibrium
with their environment (Václavík & Meentemeyer 2019), and that the
species-environment relationships are valid beyond the range of model
calibration, may be violated under such applications (Svenning & Skov
2004; Araújo & Pearson 2005; Veloz et al. 2012). Classical SDMs are
further limited to a species-by-species approach, and thus typically
overlook the role of species interactions in shaping species
distributions (Dormann et al. 2018). Additionally, the inherent spatial
autocorrelation (SAC) of species distribution and environmental
variables can bias the estimated performance of SDMs (Bahn & McGill
2007; Fourcade et al. 2018), calling for care when using extrapolations
from SDMs (Sofaer et al. 2018). However, at the same time, accounting
for SAC in SDMs by various methods (Dormann et al. 2007; Václavík et al.
2012) can improve the accuracy of SDMs because SAC is often a result of
important ecological processes (e.g. dispersal limitation, colonization
time lag) that drive species distributions.
The integration of processes into SDMs is likely critical to infer
species distributions in novel environments or under no-present analogue
conditions (Kearney & Porter 2009; Dormann et al. 2012; Urban et al.
2016). Models that combine the traditional approach of SDMs with
process-based information (Morin & Lechowicz 2008; Thuiller et al.
2008), such as dispersal limitation or phenology, have been developed
(Stephenson 1990; Kleidon & Mooney 2000; Chuine & Beaubien 2001;
Bykova et al. 2012; Nobis & Normand 2014; Duputié et al. 2015).
Progress has also been made to integrate species competition as biotic
factors influencing species realized niche (Leathwick & Austin 2001;
Meier et al. 2011) and further extend these ideas to full ecological
communities (Ferrier & Guisan 2006).
Individual-based forest
models
There is a long tradition in ecology and forestry to use
individual-based forest models, to answer a broad range of scientific
questions. This type of models simulates the development of each
individual tree within a forest stand. A key component is the
interaction between single trees (e.g. by shading) which is crucial for
tree growth and influences community dynamics. The simulation of
individual trees allows to capture not only forest structure but also
tree species diversity. A widely known type of individual based forest
models is forest gap models (Shugart 1984; Huston et al. 1988). First
developed for forest stands in North America, they have since become
among the most used model types in ecology (Botkin et al. 1972; Shugart
& West 1977; Shugart et al. 2018).
In the gap model approach, a forest stand is described as a mosaic of
forest patches, (also named gaps). The dynamics of the forests emerges
from the growth, mortality, establishment and competition of individual
trees (Bugmann 2001; Porté & Bartelink 2002). Trees compete for light,
water and nutrients. The vertical distribution of leaves is used to
calculate the light availability for each tree, what affects growth and
mortality. For competition with neighbouring trees a competition range
has to be assumed (the patch size), wherein all trees compete with each
other (a large tree should also fit into a patch). Due to the
individual-based concept, these models are able to describe the
successional dynamics of forests (mosaic dynamics, e.g. Watt 1947) and
the natural heterogeneity of forest stands (Knapp et al. 2018). The
coupling of biogeochemical processes is modelled in an aggregated way in
forest gap models, using the concept of limiting factors (affecting tree
growth rates). Gap models can simulate the impact of temperature,
precipitation, CO2 and light on tree dynamics, and thus
on forest productivity, biomass and species composition (Solomon 1986;
Pastor & Post 1988; Overpeck et al. 1990). Some early studies also
included nutrient cycles (e.g. Pastor & Post 1986). Gap models can be
applied with daily time steps, but are typically used with monthly or
annual time steps.
Modules for forest management (e.g. Liu & Ashton 1995; Huth & Ditzer
2001; Mina et al. 2017) and disturbances like fire (Kercher & Axelrod
1984; Fischer 2013), browsing (Seagle & Liang 2001; Didion et al. 2009)
or wind through (Seidl et al. 2011, 2014a) have been included in
subsequent studies. Tree mortality can thus be described as an exogenous
process (e.g. by disturbances), but also as a growth-dependent and/or
intrinsic process (e.g. Keane et al. 2001). Although gap models were
first developed for temperate forests in the USA, they were soon applied
also for European temperate forests (Kienast 1987; Bugmann 1996) and
boreal forests (Leemans & Prentice 1989). Since the 90’s, forest gap
models for tropical forests have also been developed (Bossel & Krieger
1991; Köhler & Huth 1998; Fischer et al. 2016). To simplify the high
species richness of these forests, tropical gap models typically
simulate forest succession by grouping tree species that share similar
ecological features into several plant functional types (PFTs). The gap
model approach was also extended to grasslands (Smith & Huston 1990;
Taubert et al. 2012).
From the 1990s onwards, models that keep track of the positions of each
tree in a finer-grained grid (i.e. they are spatially-explicit) and thus
allow for a more detailed computation of tree light availability have
been developed (Pacala et al. 1996; Chave 1999; Pretzsch et al. 2002;
Maréchaux & Chave 2017). Other model developments have led to a more
explicit representation of processes, for example by including a more
detailed temperature and CO2 dependence of
photosynthesis and respiration, or a more detailed water and carbon
cycles or site fertility (Fischer et al. 2016; Maréchaux & Chave 2017).
Similarly, novel parameterizations have allowed to simulate hundreds of
species within communities (Maréchaux & Chave 2017; Rüger et al. 2019).
Other stand-based models were designed to describe forest stand
structure dynamics driven by ecophysiological processes in higher detail
and finer time scales (Kramer et al. 2002; Morales et al. 2005; Medlyn
et al. 2007), although often at the cost of simulation temporal or
spatial coverage. Individual-based forest models have since been used to
address a variety of basic and applied research questions (Bugmann &
Pfister 2000; Seidl et al. 2012; Bohn et al. 2014; Fischer et al. 2016;
Shugart et al. 2018). Modern extensions of these models allow also
simulations of forests at large spatial scales (e.g. for whole countries
or continents, Xiaodong & Shugart 2005; Sato et al. 2007; Scherstjanoi
et al. 2014; Rödig et al. 2017; Thom et al. 2017).
Dynamic global vegetation
models
DGVMs have their origin in four different modelling research areas that
were initially investigated separately: plant geography,
biogeochemistry, vegetation dynamics, and biophysics (Prentice et al.
2007), with HYBRID, LPJ and TRIFFID as being among the first DGVMs
(Cramer et al. 2001). DGVMs have been initially developed to represent
the interaction between vegetation and the global carbon cycle as
independent models, but also to represent vegetation dynamics in Global
Circulation Models.
DGVMs simulate vegetation dynamics on daily to monthly time steps at the
global scale, driven by climate, atmospheric CO2
concentration, and soil information, hence using plant physiology and
biogeochemistry to explain biogeography (Sitch et al. 2003; Krinner et
al. 2005). This approach results in calculating the large-scale
distribution of potential natural vegetation. Main components of each
DGVM are process-based representations of photosynthesis, respiration,
leaf transpiration, carbon allocation, mortality and disturbance. The
exchange of carbon and water fluxes is represented at the leaf level by
stomatal conductance (Ball et al. 1987; Collatz et al. 1991).
Describing vegetation dynamics at the global scale inevitably entails
strong model simplifications to represent vegetation. These models use
PFTs to aggregate functionally similar species to represent functional
properties at the biome scale. Usually global vegetation is described
with 5 to 14 PFTs by differentiating life form, leaf form, phenology, or
photosynthetic pathway, e.g. tropical broad-leaved raingreen tree or C3
grasses (Woodward & Cramer 1996; Prentice et al. 2007). Hence, these
PFTs represent a less detailed description of species diversity within
forest communities than the ones used in IMBs. Additionally, DGVMs often
conduct simulations using a relatively coarse-grained grid (typically of
0.5° lat/lon resolution) in which characteristics of each cell are
assumed to be homogenous, simulating average individuals per PFT, where
several of them can compete within one gridcell. Hence local competition
processes are oversimplified and the influence of spatial structure
within this coarse grid cell is neglected. Moreover, DGVMs typically
apply the ‘big-leaf’ approach, whereby photosynthesis of the PFTs is
simulated based on one photosynthetic surface throughout the grid cell.
Most stand-alone DGVMs are not initialized with any observed vegetation
distribution, nor with any values for the carbon and water pools. The
global PFT and carbon-pool distribution is therefore determined by the
given abiotic conditions and PFT-specific characteristics. Hence, each
change in abiotic conditions (e.g. climate change) results in a
non-prescribed reaction of the vegetation.
Although DGVMs were originally developed to simulate potential natural
vegetation, including fire disturbance (Lenihan et al. 1998; Thonicke et
al. 2001), they have been advanced by simulating land-use (Bondeau et
al. 2007; Boysen et al. 2016; Langerwisch et al. 2017; Rolinski et al.
2018), water management (Jägermeyr et al. 2015), and forest management
(Bellassen et al. 2010). In order to account for the role of nutrient
deposition in vegetation dynamics and its interaction with the global
carbon cycle, several DGVMs have further developed an explicit
representation of nitrogen and phosphorus cycles (Wang et al. 2010;
Smith et al. 2014; Reed et al. 2015; Goll et al. 2017; von Bloh et al.
2018). Similarly, a more explicit representation of tree hydraulics and
water flows has been developed in some DGVMs to better assess the effect
of climatic changes on evapotranspiration and drought-related mortality
(Hickler et al. 2006; Bonan et al. 2014; Langan et al. 2017; Joetzjer et
al. 2018). The need for a more realistic representation of vegetation
structure and biodiversity to improve the predictive power of DGVMs has
been highlighted to improve the predictive power of DGVMs (Quillet et
al. 2010; McMahon et al. 2011). To achieve this, several developments
have been made to include a finer representation of vegetation
demographic processes (Moorcroft et al. 2001; Smith et al. 2001; Hickler
et al. 2012; Fisher et al. 2018) and functional diversity (Pavlick et
al. 2013; Scheiter et al. 2013; Sakschewski et al. 2015; Verheijen et
al. 2015). Lately, also seed dispersal of trees and therefore the
ability for tree species migration has been implemented into hybrid
DGVMs (Snell & Cowling 2015; Lehsten et al. 2019).
In the following parts, we will henceforth use the terms “forest
models” and “forest modelling” to describe the variety of models that
have been used to simulate forest systems, among which the three
above-described model types are widely-used examples, acknowledging that
each model type is also used to simulate other ecological systems.