Ecography 37: 001–005, 2014
doi: 10.1111/j.1600-0587.2013.00495.x
© 2014 The Authors. Ecography © 2014 Nordic Society Oikos
Subject Editor: Thiago Rangel. Accepted 18 October 2013
LANDIS PRO: a landscape model that predicts forest composition
and structure changes at regional scales
Wen J. Wang, Hong S. He, Jacob S. Fraser, Frank R. Thompson III, Stephen R. Shifley
and Martin A. Spetich
W. J. Wang, H. S. He (heh@missouri.edu) and J. S. Fraser, School of Natural Resources, Univ. of Missouri, 203 ABNR Bldg, Columbia, MO
65211, USA. – F. R. Thompson III and S. R. Shifley, USDA Forest Service, Northern Research Station, 202 ABNR Bldg, Columbia, MO 65211,
USA. – M. A. Spetich, Arkansas Forestry Sciences Laboratory, USDA Forest Service, Southern Research Station, PO Box 1270, Hot Spring,
AR 71902, USA.
LANDIS PRO predicts forest composition and structure changes incorporating species-, stand-, and landscape-scales
processes at regional scales. Species-scale processes include tree growth, establishment, and mortality. Stand-scale processes
contain density- and size-related resource competition that regulates self-thinning and seedling establishment. Landscapescale processes include seed dispersal and disturbances. LANDIS PRO is designed to be compatible with forest inventory
data, thus extensive inventory data can be directly utilized to initialize and calibrate model parameters before predicting
future forest changes. LANDIS PRO allows for exploring the effects of disturbances, management, climate change, and
modeling the spread of invasive species. We demonstrate that LANDIS PRO successfully predicts forest successional trajectories and stand development patterns in the Central Hardwood Forest region in U.S.
Niche- and biogeochemical/ecophysiographical process-based
models are the primary tools used to predict forest
change at regional scales ( 108 ha) (Morin and Thuiller
2009). Both types of models have limitations in their
abilities to incorporate site- and forest landscape-scale
processes (but see Engler et al. 2009, Boulangeat et al.
2012). Site-scale processes include growth, mortality, competition, and other stand-scale processes, which are critical in
shaping species ranges and influencing biomass predictions
at regional scales (Araújo and Luoto 2007, Tylianakis et al.
2008). Forest landscape scale processes are a set of spatial and
stochastic processes that include seed dispersal and disturbances (He 2008). They play an important role in shaping
forest change at regional scales (Dawson et al. 2011) and
may exert greater effects than the direct effects of climate
warming (Gustafson et al. 2010). Most niche-based models do not include site- and forest landscape-scale processes
(but see Engler et al. 2009), whereas processed-based models
typically simplify the effects of disturbances as removal of
a fixed portion of biomass at specified time (Scheiter and
Higgins 2009). Without adequately accounting for the siteand forest landscape-scale processes, regional-scale forest
change predictions made by niche- and process-based models may be subject to high uncertainties (Purves and Pacala
2008, McMahon et al. 2011).
Forest landscape models (FLMs) are explicitly designed
to incorporate site- and forest landscape-scale processes to
predict forest change at landscape scales (He 2008). To date,
FLMs have contributed relatively little to regional-scale
forest change predictions due to the immense computational loads required (Supplementary material Appendix 1).
The maximum simulation capacity (number of pixels) of
FLMs is currently in the range of 106–107 cells (He 2008).
Even at such a simulation capacity, site-scale processes are
simplified omitting tree density and size metrics, which are
key for determining stand-scale competition for resources
(e.g. light) (Bohlman and Pacala 2012). Here we present LANDIS PRO, a variant from LANDIS FLM family
designed to overcome these challenges confronting FLMs.
Conceptual design of LANDIS PRO
LANDIS PRO is a raster-based FLM that evolved over 15
yr of development and applications of the original LANDIS
model (ver. 6.0 and older) (He and Mladenoff 1999,
Mladenoff and He 1999, Yang et al. 2011, Wang et al.
2013a). Within each raster cell, the model records number of trees by species age cohort. It uses a sorted linked
list to store trees and age information in a sequential order
(Fig. 1a). A lookup table for indexing data value for a given
key (hash table) and a new algorithm for compressing data
of adjacent raster cells (run-length compression) are used
to enhance computational efficiency and memory usage in
LANDIS PRO (Yang et al. 2011), thus presenting a computational solution to regional-scale simulation.
Early View (EV): 1-EV
Figure 1. (a) LANDIS PRO uses a sorted linked list to store number of trees occurring by species age cohort in sequential order in
each raster cell; (b) the conceptual design of LANDIS PRO that simulates forest change incorporating species-, stand-, and landscapescale processes.
Size (diameter at breast height or DBH) for each species
age cohort is derived from empirical age-DBH relationships.
With both tree density and size information, LANDIS
PRO derives key stand parameters including density, basal
area, stocking, and biomass by species for each raster cell.
LANDIS PRO simulation results allow for straightforward comparisons with forest inventory data, thus making
it possible to fully utilize such data to construct the initial
forest conditions and calibrate model parameters.
LANDIS PRO simulates forest composition and structure
changes incorporating species-, stand-, and landscape-scale
processes at regional scales (Fig. 1b). Species-scale processes
include tree growth, establishment, resprouting, and mortality and are simulated using species’ vital attributes as in
previous versions of LANDIS (He and Mladenoff 1999) and
LANDIS II (Scheller et al. 2007), but with new functionalities. For example, tree growth is simulated as DBH increment (species growth curves) in addition to age increment.
DBH increment is simulated using empirical log-normal
relationships of DBH to age or calibrated locally using forest
inventory data by landtype, which accounts for the effects of
varying resource availabilities and species establishment.
2-EV
Stand-scale processes contain density- and size-related
resource competition that regulates self-thinning and seedling establishment. The competition intensity is quantified
by growing space occupied (GSO), which is estimated by
summing the total growing space required to support all trees
within each raster cell. The growing space is derived from the
stand density index (Reineke 1933) using tree density and
size information. Stand development patterns are governed
by GSO and simulated to follow stand initiation, stem exclusion, understory reinitiation, and old-growth stages (Oliver
and Larson 1996) (Fig. 2). Four GSO thresholds are defined
to regulate seedling establishment in the stand initiation
stage, where seedlings can only become established before
stands reach fully occupied: 1) open grown (0-GSO1), 2)
partially occupied (GSO1-GSO2), 3) crown closure (GSO2GSO3), 4) fully occupied (GSO3-MGSO) (maximum growing space occupied) (Fig. 3). These GSO thresholds can vary
by ecological section and can be modeled outside LANDIS
PRO platform to incorporate the effects of varying MGSO
resulting from nitrogen or CO2 fertilization under climate
change that is similar to the concept of maximum aboveground net primary productivity (ANPP) in LANDIS II
Figure 2. The Reineke density diagrams (Reineke 1933) and
Yoda’s 23/2 self-thinning rule (Yoda et. al 1963) are combined
to display the stand development patterns was governed by GSO.
Reineke density diagrams plots the log of quadratic mean diameter
against log of stem density (trees per hectare). The maximum size
density lines represents 100% growing space and other size-density
combinations express as a percentage of the maximum resource
availability at different stand development stages: 1) stand initiation stage, 2) stem exclusion stage, 3) understory reinitiation stage,
and 4) old-growth stage (Oliver and Larson 1996). In four substages are defined based on GSO to regulate seeding establishment
in stand initiation stage: open grown, partially occupied, crown
closure, fully occupied. Seedling can only become established
before stands reach fully occupied depending on species shade tolerance and SEPs. Once stands exceed MGSO, stands are presumed
to reach stem exclusion stage, meanwhile, self-thinning is initiated
and continues to the following understory reinitiaion and oldgrowth stages. Self-thinning associated tree mortality is characterized by a decrease in the number of trees with increasing average
tree size in the stand and follows the –3/2 rule. Stand development
trajectories converge with the self-thinning line and moved along
the self-thing line from lower right to upper left.
(Scheller et al. 2012). They can also be defined for a variety
of ecosystems. For example, a woodland system may never
reach the crown closure stage and have low GSO1 and GSO2
values. Once stands exceed MGSO, stands reach stem exclusion stage; meanwhile, self-thinning is initiated and continues to the following understory reinitiaion and old-growth
stages (Oliver and Larson 1996) (Fig. 2). LANDIS PRO
implements self-thinning, where tree mortality is characterized by a decrease in the number of trees with increasing
average tree size in the stand and follows the –3/2 Yoda’s
self-thinning line (Yoda et al. 1963). Trees that are small,
shade intolerant, or approaching their longevity can be outcompeted first via self-thinning. Such design enables stand
development trajectories to converge with the self-thinning
line and move along the line from lower right to upper left
(Fig. 2). During the understory reinitiaion stage, seedlings
with higher shade tolerance can establish. Continued tree
growth and mortality in the absence of exogenous disturbance moves the stand into the old-growth stage, where old
trees die as they reach their longevity, creating large canopy
gaps that promote tree regeneration and move the stand into
uneven-aged condition.
LANDIS PRO simulates landscape-scale processes
including seed dispersal (exotic species invasion), fire, wind,
insects and diseases, forest harvesting, and fuel treatments
in independent modules (Fig. 1b). Seed dispersal is simulated using a dispersal kernel determined by species-specific
maximum dispersal distances, where the probability of seed
dispersal to every cell is calculated using a negative exponential decay function (Mladenoff and He 1999). The total
number of potential germination seeds (NPGS) for each
species reaching a given raster cell are accumulated from all
available mature trees within the dispersal kernel. The NPGS
can be derived from Burns and Honkala (1990) and calibrated to ensure the predicted species density and basal area
are consistent with forest inventory data. Thus, LANDIS
PRO accounts for dispersal limitation and seed availability
that can constrain species distributions under rapidly changing environment. Further information on the disturbance
modules can be found elsewhere (Fraser et al. 2013, Wang
et al. 2013b).
A heterogeneous landscape is stratified into landtypes in
LANDIS PRO (also called ecoregions for broad-scale studies), which capture the coarse-level (coarse grain) spatial
heterogeneity in resource availabilities (MGSO) and species
assemblages (species establishment probability). Seed dispersal
and disturbances result in the intermediate-level (fine grain,
within or between landtype) heterogeneity in forest composition and structure. Finally, site-scale processes (e.g. competition, establishment) result in the fine-level (within raster cell)
heterogeneity in forest composition and structure.
LANDIS PRO is a 32- or 64-bit computer model that
runs on Windows XP and Windows 7, whose software
package and a detaile user’s guide can be downloaded from
http://landis.missouri.edu.
Case study
To demonstrate the capabilities of LANDIS PRO, we
applied the model to the Central Hardwood Forest Region
(CHFR) in U.S. covering 98 million ha (Fig. 3a). The area
was dominated by broadleaf deciduous hardwood forests.
Forests in CHFR regenerated following extensive timber
harvesting in the early 1900s and at or near maturity and
thus self-thinning was a key process in driving stand development. We restricted our analyses to the most prominent
16 tree species, which included oaks (Quercus spp.), hickories (Carya spp.), and maples (Acer spp.) and accounted for
95% of the total forest biomass.
The initial forest species compositions map (Fig. 3b1)
included the number of trees by species age cohort for each
raster cell for the entire CHFR and was directly derived from
U.S. Forest Service Inventory and Analysis (FIA) data for
1980. All the input maps were gridded to 90 m resolution,
which yielded about 100 million cells. We iteratively adjusted
species growth curves and NPGS following 30 yr (1980 to
2010) of simulation by statistically comparing the simulated
species density and basal area with the observed values of FIA
data in the same period for each ecological section until the
calibrated results passed chi-square test. Finally, we used the
constrained initial forest conditions and calibrated parameters to project forest changes from 1980 to 2130 at five-year
time steps without any disturbance. To evaluate the model
projections, we compared the projected forest succession trajectories with characteristics of old-growth forests from field
3-EV
Figure 3. (a) The study area is U.S. Central Hardwood Forest Region (CHFR) covering 98 million ha; (b) the projected age, density, basal
area, and biomass for white oak at 1980 and 2130 for the entire CHFR and show decrease indensity, increase in age, basal area and biomass,
and white oak range expansion; (c) the projected density, basal area, and biomass summarized by six species group and total carbon for the
Ozark Highlands ecological section; and (d) the evaluation of stand development trajectories for mean stand conditions using Gingrich
(1967) stocking charts from 1980 to 2130 for the Ozark Highlands ecological section.
studies, because our model was meant to project the potential natural succession in the time frame we simulated.
We presented white oak projections for the entire CHFR to
illustrate model results (Fig. 3b). White oak decreased in density and increased in basal area, biomass, and age due to selfthinning and tree growth. White oak range expanded due to
seed dispersal. Because of space restrictions, we only presented
results from one of ecological sections – Ozark Highlands ecological section to illustrate the model calibration and evaluation
processes (Fig. 3c, d). Overall, the initial forest composition of
the Ozark Highlands for 1980 captured the historical conditions in 1980 reasonably well (density: c2 1.93, DF 5,
4-EV
p 0.86; basal area: c2 1.40, DF 5, p 0.92). There were
also no significant differences in density and basal area by species between the simulated and FIA data for 2010 (density:
c2 1.85, DF 5, p 0.87, basal area: c2 2.61, DF 5,
p 0.76). Thus, the calibrated model parameters predicted
reasonable outcomes for the Ozark Highlands ecological section. The projected density of oaks, hickories, and pines in
the Ozark Highlands decreased while the projected basal area
increased over the 150 simulation years. The projected density
and basal area of maples gradually increased over the next 150
yr, because a lack of disturbances favored the establishment of
shade tolerant species. These projected successional trajectories
were consistent with studies of oak-dominated forest: oak forests typically transition to a greater proportion of longer-lived
white oak species and shade-tolerant species such as maple
in absence of disturbance (Johnson et al. 2009). We plotted
the increases in mean stocking percentage and mean diameter
and decreases in density as results of tree growth and mortality on Gingrich (1967) stocking charts (Fig. 2d). These resultant stocking percentages were consistent with the 75–90%
stocking percentages reported for mature and old-growth oak
forests in CHFR (Johnson et al. 2009). Therefore, LANDIS
PRO projected the credible stand development patterns from
1980 to 2130.
Conclusions
LANDIS PRO achieves the regional-scale predictions while
incorporating site- and forest landscape-scale processes. Such
regional-scale predictions allow for comparisons with predictions made from niche-and process-based models to reveal the
effects of forest landscape scale processes, thus reducing the
prediction uncertainties. Since LANDIS PRO is designed to
be compatible with field inventory data, it enables the model
to fully utilize these data for model initialization, calibration,
and evaluation. With number of trees and DBH by species age
cohort, LANDIS PRO is able to simulate tree-based mortality
and more realistically simulate forest disturbances and management. With the design of stand-scale processes, LANDIS
PRO predictions can be directly linked to stand density management diagrams, thus making model predictions more relevant to forest management and planning. LANDIS PRO has
the potential to explore the effects the spread of invasive species and climate change on species’ range shift, forest composition, structure, and biomass at regional scales.
To cite LANDIS PRO or acknowledge its use, cite this
Software note as follows, substituting the version of the
application that you used for ‘version 0’:
Wang, W. J., He, H. S., Fraser, J. S., Thompson III, F. R., Shifley,
S. R. and Spetich, M. A. 2014. LANDIS PRO: a landscape
model that predicts forest composition and structure changes
at regional scales. – Ecography 37: 000–000 (ver. 0).
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Supplementary material (Appendix ECOG-00495 at www.
oikosoffice.lu.se/appendix). Appendix 1.
5-EV