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Ecological Modelling 300 (2015) 89–101

Contents lists available at ScienceDirect

Ecological Modelling

journa l h om epa ge: www.elsev ier .com/ locate /eco lmodel

he site-scale processes affect species distribution predictionsf forest landscape models

u Lianga, Hong S. Heb,c, Wen J. Wangc, Jacob S. Fraserc, ZhiWei Wua, Jiawei Xub,∗

State Key Laboratory of Forest and Soil Ecology, Institute of Applied Ecology, Chinese Academy of Sciences, Shenyang 110016, ChinaSchool of Geographical Science, Northeast Normal University, Changchun 130024, ChinaSchool of Natural Resources, University of Missouri, 203m Anheuser-Busch Natural Resources Building, Columbia, MO 65211-7270, USA

r t i c l e i n f o

rticle history:eceived 24 April 2014eceived in revised form 6 January 2015ccepted 10 January 2015

eywords:orest landscape models (FLMs)ite-scale processestand-scale processesANDISpecies distribution predictionspatial pattern

a b s t r a c t

Forest landscape models (FLMs) are important tools for testing basic ecological theory and for exploringforest changes at landscape and regional scales. However, the ability of these models to accurately pre-dict changes in tree species’ distributions and their spatial pattern may be significantly affected by theformulation of site-scale processes that simulate gap-level succession including seedling establishment,tree growth, competition, and mortality. Thus, the objective of this study is to evaluate the effects ofsite-scale processes on landscape-scale predictions of tree species’ distributions and spatial patterns.

We compared the deviations and similarity in species distribution (quantified by species’ percent cover)as well as its spatial pattern derived from two FLMs: (1) an age cohort model with simplified site-scaleprocesses based on the presence or absence of age cohorts (a representative version: LANDIS 6.0), and(2) a stand density model with detailed site-scale processes based on stand density (a representativeversion: LANDIS PRO 7.0), which have the same framework but different site-scale process formulations.

We found that site-scale processes affected the simulated species’ percent cover and spatial pattern.The importance of site-scale processes to individual species’ predictions depended on species’ ecologi-cal traits such as shade tolerance, growth rate, seed dispersal, and other factors. For early-successionalspecies, simulated distributions were insensitive to the formulation of site-scale processes. Conversely,for shade-tolerant, middle-to late-successional species simulated distributions were highly sensitive tothe formulation of site-scale processes. Species’ shade tolerance may accentuate this simulation sensitiv-ity. In addition, because the stand density model incorporated additional quantitative information, theirsimulation results had a higher year-to-year variation than those from the age cohort model. The degree

of spatial aggregation of species’ distributions was insensitive to the formulation of site-scale processes,whereas patch size and arrangement (landscape composition) for the species distribution were sensi-tive. Results from this study revealed the differences in simulation results between these two modelswith different site-scale process formulations, which may help narrow down prediction uncertaintiesand point to areas where representations of site-scale processes need to be enhanced in the future.

© 2015 Elsevier B.V. All rights reserved.

. Introduction

Forest landscape models (FLMs) are important tools for testingasic ecological theory and for exploring forest changes at land-cape and regional scales. They simulate forest change includingite-scale and forest landscape-scale processes (He, 2008; Keane

t al., 2004; Perry and Enright, 2006; Scheller and Mladenoff,007; Taylor et al., 2009). Site-scale processes include growth,ortality, and competition, which are represented in FLMs to be

∗ Corresponding author. Tel.: +86 15840498505.E-mail addresses: liangysts@gmail.com (Y. Liang), xujw634@nenu.edu.cn (J. Xu).

ttp://dx.doi.org/10.1016/j.ecolmodel.2015.01.007304-3800/© 2015 Elsevier B.V. All rights reserved.

non-spatial and occur at each individual site (cell), whereas forestlandscape-scale processes include seed dispersal and forest dis-turbance, which are spatial and stochastic (He, 2008). Both typesof processes affect forest change at landscape to regional scales(Araújo and Luoto, 2007; Dawson et al., 2011; Gustafson et al.,2010).

Because of their spatially explicit and interactive nature, com-putational loads for FLMs may be intractable when the site-scaleprocesses simulated become too complex. Thus, FLMs typically

simplify these processes in order to simulate relatively large land-scapes (Mladenoff, 2004). Information tracked at each site in earlyFLMs is either aggregated as the presence or absence of species’age cohorts (e.g., in LANDIS) (Mladenoff and He, 1999) or forest

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ype (e.g., in LANDSUM and SIMMPPLE) (Chew et al., 2004; Keanet al., 2002). Consequently, tree growth in these FLMs is simplifieds age increment (Li and Barclay, 2001; Mladenoff and He, 1999)ather than DBH and crown increment as simulated in forest standodels (e.g., Pacala et al., 1996). Resource competition at site scales

s either simplified by comparing species shade tolerance classeso that shade-tolerant species successionally replace shade intol-rant species (e.g. in LANDIS) or simplified by using successionalathways so that late-successional forest types replace early- andiddle- successional types determined by predefined transition

robabilities (Chew et al., 2004; Keane et al., 2004; Roberts, 1996).tand structure in these FLMs is also greatly simplified as the pres-nce or absence of defined age cohorts or simply forest types (He,008). The simplified formulations of vegetation dynamics in earlyLMs may be sufficient for landscapes where forest landscape-scalerocesses such as fire or harvest can override site-scale processesSchumacher et al., 2004; Turner, 2010). However, the FLMs withimplified site-scale processes omit tree density and size metricshat are key mechanisms determining site-scale resource compe-ition (Bohlman and Pacala, 2012; Moorcroft et al., 2001; Wangt al., 2013). Thus, the FLMs with simplified site-scale processesay not produce realistic predictions for forest landscapes where

ffects of disturbance do not predominate and where site-scale pro-esses largely drive forest landscape change (Schumacher et al.,004; Wang et al., 2013).

Recent FLMs have improved the formulation of site-scale pro-esses by adding quantitative information (e.g. tree numbers andiomass) at each site. For example, LANDIS II adds biomass to eachpecies’ age cohort and uses a ratio of actual biomass to poten-ial biomass to quantify resource availability at each site, assumingge-cohort biomass by species implicitly incorporates tree densitynformation (Scheller et al., 2007, 2011). LANDCLIM also replaceshe presence/absence of species’ cohorts in the LANDIS modelith species’ biomass dynamics, which tracks numbers of trees

nd biomass by species’ age cohort. Site-scale resource competi-ion is determined by growth- and density-dependent mortalityriven by maximum stand biomass (Schumacher et al., 2004). InreeMig, reproduction is modeled in a detailed way, including seedroduction by adult trees, seed dispersal, seed bank dynamics, ger-ination, and sapling development. Moreover, TreeMig accounts

or within-cell structure in terms of horizontal and vertical hetero-eneity within the forest stand (Lischke et al., 2006). In addition,ANDMOD is scaled up from a gap model to accelerate the com-utation efficiency (Garman, 2004), where growth and mortalityunctions and bioclimatic values are fitted by meta-modeling to

odel gap simulations (Urban et al., 1999).Studies have shown that simulated forest change is highly

ensitive to the formulation of site-scale processes (Araújo anduoto, 2007; Dawson et al., 2011; Elkin et al., 2012; McMahont al., 2011; Purves and Pacala, 2008; Tylianakis et al., 2008). Forxample, different formulations of tree growth rates at the site-cale lead to different FLMs simulation results when more detailedesponse variables are considered, such as species compositionalhanges associated with elevation. In contrast, such effects are notccounted for when results are assessed at larger spatial (land-cape) scales and when coarse-scale response variables (e.g., totalorest biomass) are considered (Elkin et al., 2012; Liang et al.,013). Other studies also have shown that different formulationsf site-scale processes in FLMs affect the mechanisms used to sim-late inter-specific competition, which consequently can lead toonflicting simulation results (Kellomäki et al., 2008; Spittlehousend Stewart, 2004). For example, LANDCLIM includes only the

resence or absence of seeds and does not link seed numbers todult tree density and maturity. Applying LANDCLIM thus mayesult in the domination of long lived, shade tolerant species inhe long run (Schumacher et al., 2004). In addition, some FLMs

lling 300 (2015) 89–101

limit seed numbers of shade intolerant species (Pennanen andKuuluvainen, 2002). This limitation is modeled by rules that forcethese species to establish only in open gaps (Pennanen et al., 2004),leading to biased estimation of the distribution of shade-intolerantspecies.

Despite many attempts, it remains a challenge to determinethe effects of site-scale processes on predicting forest landscapechange. This is because differences in FLMs design and formulationmake it difficult to identify and separate the effects of site-levelprocesses. Comparing models with the same framework but differ-ent site-scale process formulations thus might overcome some ofthese problems.

In our study, we chose two FLMs, variants from the LANDISmodel family: (1) a model with simplified site-scale processesbased on the presence or absence of age cohorts (the age cohortmodel) (He et al., 2005; Mladenoff and He, 1999; Yang et al.,2011), and (2) a model with detailed site-scale processes basedon stand density (the stand density model) that includes consid-eration of gap level succession (Wang et al., 2013) for evaluatingeffects of site-scale processes on landscape-scale predictions of treespecies distribution and spatial pattern. Specifically, we examined(1) the deviations in species distribution (quantified by species rel-ative abundance) as well as spatial pattern derived from the twomodels; (2) the similarity of overall and year-to-year variation inspecies distribution and pattern derived from the two models; and(3) whether the response of spatial pattern predictions to site-scale processes was similar to predictions of species distribution.Our study also examined how the drivers of site-scale dynamics,species’ ecological traits such as shade tolerance, growth rate, andseed dispersal, influenced individual species’ predictions.

2. Methods

2.1. Case study landscape

Our study area (4.1 × 105 ha) was located in the Changbai Moun-tain National Natural Reserve (CMNNR) and the 8 km surroundingarea at 41◦62′–42◦49′N, 127◦59′–128◦38′E. CMNNR lies within thehighest mountain range in northeastern China and protects oneof the largest natural temperate forests in the world (Shao, 1996;Stone, 2006). There are four vertical vegetation/elevation zonesranging from 740 m at the lowest elevation to 2691 m at the sum-mit of the Changbai Mountains. Elevations from 740 to 1100 m arepredominantly a mixed Korean pine-hardwood forest zone, includ-ing Korean pine (Pinus koraiensis Siebold & Zucc.), basswood (Tiliaamuresis Rupr), Asian white birch (Betula platyphylla Suk), aspen(Poplus davidiana Dode), ash (Fraxinus mandshurica), Mongolian oak(Quercus mongolica [Fisch] Ledeb.), maple (Acer mono Maxim) andelm (Ulmus propingua). From 1100 to 1700 m lies the evergreenconiferous forest zone dominated by jezo spruce (Picea jezoensisSiebold & Zucc.) and Manchurian fir (Abies nephrolepis [Trautv.]Maxim), with characteristics typical of boreal forests. From 1700 to2000 m lies the subalpine forest zone dominated by mountain birch(Betula ermanii Cham) and Olga Bay larch (Larix olgensis A. Henry).Elevations above 2000 m include tundra, bare rock and a volcaniclake (Shao, 1996). Hardwood forests extend 8 km outside the naturereserve (lower than 750 m elevation) where human activities havetransformed the pine–hardwood forests into those mainly com-prising hardwoods. The Changbai Mountains is also comprisedof azonal vegetation types and other types such as larch forests,aspen-birch forests, alpine meadows, sparse forests, windthrow

areas, abandoned forests, as well as cut-over sites and other areassubject to human use. Along with the zonal vegetation types, thereare 20 land cover types distributed mainly along elevational gradi-ents.

Y. Liang et al. / Ecological Modelling 300 (2015) 89–101 91

F of sites

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ig. 1. Comparison of the age cohort model and the stand density models. Comparisonpecies- and stand-scale competitive succession and dispersal.

.2. Model description

LANDIS is a spatially explicit, raster-based stochastic FLMhat has evolved over the past two decades (He and Mladenoff,999a,b; He et al., 1999; Mladenoff, 2004; Mladenoff and He, 1999;ladenoff et al., 1996). In the original LANDIS model, simplified

ite-scale processes were implemented based on only presence orbsence of defined species’ age cohorts, and succession was simu-ated as a competitive process driven by species vital attributes (e.g.,ongevity, maturity, and shade tolerance). Over the years, incre-

ental improvements were made to simulate wind, fire, harvest,uel management and biological disturbance agent (BDA) in laterersions of the model (versions 1.0–6.0) (Gustafson et al., 2000; Hend Mladenoff, 1999a; Mladenoff and He, 1999; Sturtevant et al.,004; Yang et al., 2004). However, the model’s core structure ofsing age cohort succession remained unchanged.

.2.1. The model with simplified site-scale processes (the ageohort model)

In the age cohort LANDIS model (a representative ver-ion: LANDIS 6.0, download link: http://landis.missouri.edu/andis60dlform.php), succession is driven by species vital attributesncluding longevity, age of sexual maturity, shade tolerance class,

inimum age of vegetative reproduction, and seed dispersal dis-ance. Tree birth, sprouting, growth, and mortality processes act onpecies age cohorts by generating the birth of the youngest age

ohort, increasing the age of existing cohorts (through growth),nd removing existing age cohorts (through mortality). Standevel processes, such as competition, are simplified by comparingpecies shade tolerances so that species of a lower shade-tolerance

-scale processes for the age cohort model and the stand density models, including

cannot establish on a site where more shade tolerant and maturespecies are present (Mladenoff and He, 1999). On the other hand,the occupancy of the most shade-tolerant species on an open site isdelayed until a specified period of occupancy by intolerant specieshas been met. Species with age cohorts younger than the minimumseed-producing age are ignored in this shade-checking algorithm,which serves as a surrogate for crown closure. Without disturbance,shade-tolerant species will tend to dominate the landscape whenother attributes are not limiting.

Seed dispersal is modeled as a function of species effective andmaximum seeding distances (He and Mladenoff, 1999b). A sitewithin the effective seeding distance of a species has a higher prob-ability (e.g., p > 0.95) of establishing a new age cohort than one lyingbeyond that distance (He and Mladenoff, 1999b). The maximumseed-dispersal distance is that distance beyond which a seed hasnear zero probability (e.g., p < 0.001) of reaching. Seed-dispersalprobability (p) between the effective (ED) and maximum seedingdistance (MD) follows a negative exponential distribution:

p = e−b(x/MD) (1)

where x is a given distance from the seed source (MD > x > ED) andb is an adjustable coefficient (b > 0) (b = 1 in the current version ofLANDIS), which can change the shape of the exponential curve cor-responding to various seed-dispersal patterns when information isavailable.

When a seed successfully arrives at a site, the shade tolerance

rule described above is used to determine elegibility for seedlingestablishment (Fig. 1a). Once a seed is determined elegible, environ-mental suitability for the seed is checked by comparing the species’establishment probability (SEP) with a uniformly drawn random

92 Y. Liang et al. / Ecological Modelling 300 (2015) 89–101

Fig. 2. Stand initiation and stem exclusion stages in the stand density model. Seedling establishment scenarios during stand initiation and stem exclusion stages in relationt ity mos pointo

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o species’ shade tolerance and growing space occupied (GSO) for the stand denstands exceed Maximum GSO, they thereby attain the stem exclusion stage. At thatld-growth stages, respectively.

umber (0–1). This procedure captures the stochasticity of speciesstablishment and ensures that species with high SEPs have higherrobabilities of establishment (Mladenoff and He, 1999) (Fig. 1a).

.2.2. The model with detailed site-scale processes (the standensity model)

The stand density LANDIS model (a representative ver-ion: LANDIS PRO 7.0, download link: http://landis.missouri.edu/andis70dlform.php) adds number of trees and diameter at breasteight (DBH) for each species’ age cohort and implements a treeensity-based successional module (Wang et al., 2013). Succes-ional models based on tree density are executed in addition toge-based succession, which thus facilitates comparing the twoypes of models. In the stand density model, new attributes (max-mum DBH, maximum stand density index, and potential annualumber of viable seeds) are added to improve representation oftand-scale processes, which include stand density and tree sizeactors that regulate self-thinning and seedling establishment. Treerowth is simulated as both DBH and age increment, which is exe-uted as species growth rate (a curve of DBH increment with agey species). Stand-scale competition is regulated by the amount ofrowing space occupied (GSO) (Oliver and Larson, 1996). GSO, inurn, is derived from stand density index, which is a relative mea-ure of stand density by species based on the relation between tree

ensity and average tree diameter (Wang et al., 2013).

Stand development patterns are governed by GSO and simu-ated to follow the well documented stand development stages:tand initiation, stem exclusion, understory reinitiation, and

del. There are four defined ranges of GSO within the stand initiation stage. Once, self-thinning is initiated and continues to subsequent understory reinitiation and

old-growth stages (Wang et al., 2013). At stand initiation and stemexclusion stages, four threshold classes of GSO are used to regu-late seedling establishment (Fig. 2): (1) open grown (0–GSO1), (2)partially occupied (GSO1–GSO2), (3) crown closure (GSO2–GSO3),and (4) fully occupied (GSO3–MGSO) (Fig. 2). MGSO represents themaximum growing space that can be occupied. When GSO becomesfully occupied, stands enter the stem exclusion stage of develop-ment. Trees that are small, shade intolerant, or approaching theirspecies’ longevity limits are typically those that first succumb toself-thinning (Coomes and Allen, 2007; Reynolds and Ford, 2005).After that, stand development continues on to the understory reini-tiation and old-growth stages, respectively (Wang et al., 2013).

Similar to the age cohort model, seed dispersal is modeled usinga negative exponential decay function but with counting of num-bers of seeds. The total number of seeds of each species reachinga given site is accumulated from all available mature trees withinthe dispersal kernel, which is the product of dispersal probabilityand potential annual number of viable seeds. Unlike the age cohortmodel, seedling establishment in the stand density model is reg-ulated by potential annual number of viable seeds, GSO, speciesshade tolerance, and SEP (Fig. 1b).

2.3. Model initiation

The age cohort and stand density models share two spatial datalayers (raster maps of land type and forest composition) in addi-tion to other non-spatial parameters (e.g., species’ vital attributes,SEPs). In LANDIS, a heterogeneous landscape can be differentiated

Modelling 300 (2015) 89–101 93

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nto various land types based on characterizations of environmen-al heterogeneity. The land type map in our study was derived fromlevation zones and Landsat imagery (Shao, 1996), which classifiedhe study area into 20 major land cover types. The forest composi-ion map contains age cohort information by species for each rasterell, which was derived by integrating classified remote sensingmagery and the stand map including forest composition informa-ion (Shao, 1996). Species’ vital attributes (Table 1) and SEPs forach land type were compiled from previous studies (He et al.,005; Liang et al., 2011a,b).

Besides the above parameters, the stand density model addsome new parameters, such as number of trees by species ageohort in each cell, GSO thresholds for each land type, and addi-ional species’ vital attributes (such as maximum DBH, maximumtand density index and potential annual number of viable seeds,able 1). We calculated the number of trees by species age cohortor the cell size based on National Forest Inventory data, whichecorded total numbers of trees, stand age and species compositionn various forest stands, and previous studies (Liang et al., 2011a,012; Hao et al., 2002; Wang et al., 2009, 2011). We estimate GSOy summing the total minimum growing space required to sup-ort all trees within each raster cell. The minimum growing spaceequired for each tree at a given species and size is derived fromhe Reineke stand density index and maximum stand density index.eineke’s stand density index (Reineke, 1933) is a widely acknowl-dged stand density index, which is representative of the degree ofompetition in the stand. Maximum stand density index is defineds the maximum number of 10-in. diameter trees per hectare, andas already been reported for many species (Long, 1985; Reineke,933). Potential annual number of viable seeds, which is derivedrom Burns and Honkala (1990) and other empirical studies, can bealibrated to ensure the predicted density and basal area match theorest Inventory data (Burns and Honkala, 1990). In addition, Max-mum DBH and species growth rates were derived from the forestnventory data.

.4. Model calibration

Simulation results for the stand density model include speciesomposition, stand density, basal area, stocking, and importancealue by species for each cell. They can be directly compared withorest inventory data, which makes full utilization of such dataossible to construct initial forest conditions and calibrate modelarameters. Thus, in this study, we first parameterized and cali-rated the stand density model using forest inventory data, andhen parameterized the age cohort model based on the calibratedarameters of the stand density model since the age cohort modelhares some parameters with the stand density model, whichequired additional model parameters. This treatment ensured thathe shared sets of model parameters were identical for the two

odels and different modeling outcomes were attributable to dif-erent model designs.

We initialized the stand density model using forest inventoryata from year 2000, simulated the model to 2010 at five yearime step, and then compared the simulated data with the 2010nventory data. To ensure the initialized landscape matched forestnventory data from the year 2000, we iteratively adjusted speciesrowth rates (DBH-age relationship) until the initialized speciesasal area derived from the stand density model matched the sum-arized forest inventory data from the year 2000 at the landscape

cale. We then used the year 2000 initial landscape as the start-ng point and simulated forest succession without disturbance to

010 to calibrate potential annual number of viable seeds per par-nt tree. Potential annual number of viable seeds was calibratedteratively until the simulated number of trees and basal area bypecies closely matched the observed changes in forest inventory Ta

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or the same time period (Wang et al., 2013). The adjustment pro-ess was analogues to sensitivity analysis because the adjustmentsere incremental. To establish the credibility of model predictions,e compared the predicted forest succession trajectories with the

ld-growth forests in our study area, because, in absence of disturb-nce, our model is meant to predict potential natural succession.

.5. Model simulation

We used the age cohort and stand density models to simulatehe 12 most common tree species (Korean pine, spruce, fir, moun-ain birch, white birch, larch, oak, ash, maple, aspen, basswood, andlm) from years 2000 to 2200 using five-year steps. All spatial dataere initialized at a resolution of 100 × 100 m, which is compat-

ble with previous simulation studies; this yielded 960 rows and47 columns (He et al., 2005; Liang et al., 2013). Disturbances suchs forest harvesting, fire, and wind were not simulated becauseur objective was to evaluate natural successional trajectories ofhe most abundant dominant species in relation to different site-cale processes. Simulations for all scenarios were replicated fiveimes. The model replications started with the same input param-ters with the exception of the randomly generated seed numberssed to simulate stochastic processes such as seed dispersal andeedling establishment.

LandStat, an ancillary program of LANDIS, was used to pro-ess simulation results. These results were summarized as species’ercent cover (the number of pixels in which a species occurredivided by the total number of pixels). To quantify species’ spa-ial patterns, largest patch index (LPI), aggregation index (AI), andnterspersion and juxtaposition index (IJI) were calculated by usinghe landscape statistical software, FRAGSTATS (McGarigal et al.,012). These indices were calculated based on maps of species pres-nce/absence at different age cohorts, since these maps were theommon outputs of both models. For an age cohort map, a pixel waslassified as “0” if the species was absent in this pixel; a pixel waslassified as “1” if the age of the species was within 0–5 years; a pixelas classified as “2” if the age of the species was between 6 and 10

ears, and so forth. LPI measures percentage of the landscape com-osed of the largest patch. Larger LPIs indicate more large patches.I measures the share of possible edges of corresponding patch

ype, which provided an indicator of connections among patchesf the same type (He et al., 2000). Larger AIs indicate higher levelsf aggregation. IJI was used to assess the arrangement of species’istribution patches in the landscape (landscape composition). IJIpproaches 0 when the distribution of adjacencies among patchypes becomes increasingly uneven (heterogeneous); it equals 100hen all patch types are equally adjacent to all other patch types.

.6. Data analysis

Comparisons of simulation results (species’ percent cover andpatial pattern) between the age cohort model and the stand den-ity model were based on trajectories of species’ percent cover andpatial pattern index across the simulation period (2000–2200).or each model, the simulation result in a given simulation yearas mean of five model replicates in the given simulation year. Werst assess the oscillation of trajectories of species’ percent covernd spatial pattern index across the simulation period for eachodel and calculate average deviations of trajectories of simulation

esults during the entire simulation period (2000–2200) betweenhe two models. We then calculated the raw and detrendedorrelation coefficients to examine the similarity of overall and

ear-to-year variation of two trajectories simulated by the twoodels.The oscillation of a time series can be assessed by the combi-

ation of mean, variance and first order autocorrelation (Box and

lling 300 (2015) 89–101

Jenkins, 1976; Strackee and Jansma, 1992). Thus, we calculatedmeans (standard errors), variation, and the first order autocorre-lation coefficients of trajectories of species relative abundance aswell as spatial pattern index for each of these two models, andcompared their differences between the two models. Mean andvariation are the average value and variation range of the trajectoryacross the simulation period for each model. Standard error is thestandard error of five model replicates for each model. First orderautocorrelation coefficient, calculated based on trajectory acrossthe simulation period for each model, is symmetric on [−1, +1],where larger absolute values indicate higher autocorrelation.

The average deviation of trajectories of simulation results dur-ing the entire simulation period (2000–2200) between the twomodels was calculated using the following formula (Vanclay andSkovsgaard, 1997).

AD =n∑

i=1

(Di − Ai) /n (2)

where AD is average deviation, Di is the simulation result (meanof five model replicates) for year i derived from the stand densitymodel, Ai is the simulation result for year i derived from the agecohort model, and n is the number of years within the simulationperiod. The t-test for paired simulation results (mean of five repli-cates) from the two models was used to test whether AD differsfrom zero.

The raw correlation coefficients were used to show overallsimilarity of two trajectories simulated by the two models. Thedetrended correlation coefficients were calculated to comparetrajectories simulated by the two models only in respect of itsyear-to-year variation, which were based on trajectories of thedetrended index across the simulation period. The detrended cor-relation coefficients were calculated based on the following foursteps. We first evaluated trends in the simulated trajectories foreach model using linear regression with the simulation result asdependent and the year as independent variable. The trajectorywas considered to be trended if the slope of the regression rela-tion significantly differed from zero. We then calculated linearlydetrended simulations by time step, which were determined bythe regression relation. Specifically, linearly detrended simulationresult in a given simulation year was calculated by the regressionrelation with the given simulation year as independent variable. Atthe third step, we calculated the detrended index for each year iwithin the simulation period for each model using the formula:

Ii = SIiSDJi

(3)

where Ii is the detrended index, SIi is the simulation result foryear i and SDJi is the linearly detrended simulation result for yeari. At the fourth step, we calculated the correlation coefficient ofthe detrended index between the two models. Both the raw anddetrended correlation coefficients were investigated directly byPearson product-moment correlation coefficients.

All of the above statistical tests were carried out for bothspecies’ percent cover and spatial pattern index. Besides that, wedid Cohen’s Kappa statistic (Congalton and Green, 1999) to directlymeasure the agreement in spatial patterns simulated by these twomodels in the simulated short term (the year 2050), medium term(the year 2100) and long term (the year 2200) period. Overall Kappacoefficient (k) derived from Cohen’s Kappa statistic was symmetricon [0,1]: 0≤ k <0.2 implies slight agreement; 0.2 ≤ k < 0.4 implies fairagreement; 0.4 ≤ k < 0.6 implies moderate agreement; 0.6 ≤ k < 0.8

implies substantial agreement, and 0.8 ≤ k < 1 implies almost per-fect agreement (Landis and Koch, 1997).

We used the language and environment R (R DevelopmentCore Team, 2011) for all of the above statistical tests. After

Y. Liang et al. / Ecological Modelling 300 (2015) 89–101 95

F abuns

csrt

3

3

awfsTsddsiTofiaat(s(tc

t

ig. 3. The trajectory of species relative abundance. The trajectory of species relativeimulation period.

ompleting these analyses, we found that six species (fir, basswood,pruce, Korean pine, mountain birch and white birch) captured theesponse patterns of all 12 species. Thus, we present below onlyhe results of those six species.

. Results

.1. Relative abundance

Our results showed that the mean relative abundance of fircross the simulation period simulated by the stand density modelere larger than those simulated by the age cohort model, whereas

or basswood, spruce and Korean pine, the mean relative abundanceimulated by the stand density model were smaller (Fig. 3, Table 2).he average deviation in relative abundance of fir, basswood,pruce and Korean pine between the two models significantlyiffered from zero (p ≤ 0.001, Table 3). For example, relative abun-ance of spruce simulated by the age cohort model increasedlightly from 61.6 to 62.4%, whereas relative abundance of sprucen the stand density model did not show a similar trend (Fig. 3).he relative abundance of fir in the stand density model fluctuatednly slightly during the simulation period. In the age cohort model,r abundance was similar to the stand density model until 2140,fter which it significantly decreased (Fig. 3). In contrast, the rel-tive abundance of both mountain birch and white birch betweenhe age cohort and stand density models did not differ significantlyFig. 3, Table 3). Moreover, for both species the two models showedignificantly positive correlations in relative abundance trajectoriesp ≤ 0.001, Table 3). Similarly, the detrended trajectories of moun-

ain birch and white birch for the two models were also positivelyorrelated (p ≤ 0.001, Table 3).

For most species (fir, basswood, spruce, Korean pine and moun-ain birch), absolute values of first order autocorrelation coefficient

dance simulated by the age cohort model and the stand density model across the

for the age cohort model were larger than those for the standdensity model (Fig. 4), suggesting higher autocorrelations simu-lated by the age cohort model than those simulated by the standdensity model.

3.2. Spatial pattern

For most species (fir, basswood, spruce, Korean pine and moun-tain birch), LPI’s derived from the age cohort model were largerthan those from the stand density model (Fig. 5). For example, LPIof fir derived from the age cohort model was 43.69 ± 1.52, whichwas larger than that from the stand density model (39.32 ± 0.14).In addition, for basswood, spruce, Korean pine and mountain birch,IJI’s derived from the age cohort model were larger than those fromthe stand density model; larger values of IJI for the stand densitymodel were attained only by fir and white birch (Fig. 5). In con-trast, the AI’s from the age cohort model for basswood, spruce andKorean pine were larger than those from the stand density model,whereas the AI’s of fir, mountain birch and white birch from thestand density model were larger than those from the age cohortmodel (Fig. 5). For almost all species, absolute values of first orderautocorrelation coefficient of trajectories for LPI, AI and IJI derivedfrom the age cohort model were larger than those from the standdensity model (Fig. 6).

Most of our results for deviation and correlation in spatialpattern were similar to those we observed for species relative abun-dance. However, there were some spatial pattern results that didnot follow this trend. For example, a significant correlation betweenthe age cohort and stand density models occurred in LPI for all

species (p ≤ 0.001), whereas in IJI there were no significant cor-relations for these species (Table 4). For AI, a significant correlationoccurred only in spruce and Korean pine. In addition, significantcorrelations in detrended trajectories of LPI occurred in basswood,

96 Y. Liang et al. / Ecological Modelling 300 (2015) 89–101

Table 2Mean and variation of the relative abundance trajectories for the entire simulation period (2000–2200) for the age cohort and stand density models.

Mean (%) ± standard errorsof model replicates

Variation of abundance trajectoriesacross the simulation period

Fir The age cohort model 48.149 ± 0.012 21.854The stand density model 59.817 ± 0.016 1.018

Basswood The age cohort model 76.368 ± 0.008 0.245The stand density model 56.886 ± 0.027 9.507

Spruce The age cohort model 62.270 ± 0.005 0.592The stand density model 59.495 ± 0.020 1.022

Korean pine The age cohort model 66.530 ± 0.007 0.166The stand density model 66.087 ± 0.006 0.592

Mountain birch The age cohort model 18.977 ± 0.014 11.177The stand density model 19.900 ± 0.015 9.956

White birch The age cohort model 27.451 ± 0.007 19.237The stand density model 28.690 ± 0.006 17.907

Table 3Statistical comparisons by species for differences and correlations between the age cohort and stand density models. The average deviation and correlation coefficient (raw)refer to the relative abundance trajectories shown in Fig. 3. The correlation coefficient (detrended) refers to the detrended index trajectories. The p-values given for theaverage deviation and the correlation coefficients represent type-I errors for the null hypothesis that the two models do not differ based on t-tests.

Average deviation Correlation coefficient (raw) Correlation coefficient (detrended)

Fir 11.668** −0.137ns 0.007ns

Basswood −19.482*** −0.973*** −0.760***

Spruce −2.852*** −0.559*** 0.205ns

Korean pine −0.443*** 0.672*** −0.620***

Mountain birch 0.923ns 0.956*** 0.549***

White birch 1.239ns 0.963*** 0.836***

*** p ≤ 0.001.** p ≤ 0.01.

*

n

swpc(

utIsas

Ft

p ≤ 0.05.s non-significant.

pruce, Korean pine, mountain birch and white birch (p ≤ 0.001),hereas a significant correlation in IJI was observed only in Koreanine and mountain birch. For detrended trajectories of AI, signifi-ant correlations occurred only in Korean pine and mountain birchTable 4).

For all of the simulated species, k value decreased with the sim-lation period (Fig. 7), which was illustrated by a lower k value inhe simulated long term than those in the early and medium terms.n addition, for basswood, spruce and Korean pine in the simulated

hort, medium and long terms, as well as fir in the simulated shortnd medium terms, k values were larger than 0.6, which illustratedubstantial agreement between these two models.

ig. 4. Differences in first order autocorrelation coefficients of species relative abundance trajhe upper, estimated, and lower value, respectively.

4. Discussion

Our results showed that site-scale processes such as tree growth,stand density, and tree size-related resource competition impactsspecies percent cover and its spatial distribution pattern modeledwith FLMs. This is consistent with results from a previous study onthe sensitivity of FLMs to small-grain processes. When assessingforest state on a species-specific basis, different formulations of treegrowth had a strong impact on simulation results (Elkin et al., 2012).

Furthermore, we found that the relative importance of site-scaleprocesses on species distribution prediction is likely to depend onspecies’ ecological traits.

ectories between the age cohort model and the stand density model. Box plot presents

Y. Liang et al. / Ecological Mode

Fig. 5. The mean values and standard errors of spatial pattern index. The mean val-ui

ssgsccsMbico

staoltpio

a larger relative abundance than the age cohort model, whereas

es and standard errors of largest patch index (LPI), aggregation index (AI) andnterspersion and juxtaposition index (IJI).

Shade-tolerant, middle- to late-successional species was highlyensitive to the formulation of site-scale processes. Moreover,pecies’ shade tolerance may accentuate this sensitivity as sug-ested by our study. For example, the moderately shade tolerantpruce and the highly shade tolerant fir both displayed signifi-ant deviations in their distribution trajectories between the ageohort and stand density models; concomitantly, there was noignificant positive correlation in raw and year-to-year variation.oreover, the larger deviation in fir compared to spruce may have

een related to differences in their relative competitiveness, whichn turn leads to a consideration of the formulation of site-scale pro-esses such as those regulating stand density and growing spaceccupied (GSO).

In this study, seedling establishment modeled with the detailedite-scale processes was largely determined by species’ shadeolerance (reflecting early-, middle- or late-successional species)nd GSO. Moreover, thresholds of GSO at various stand devel-pment stages affect the establishment of early-, middle- andate-successional species differently. For example, the stand initia-ion stage (GSO ) is characterized by widespread establishment of

1rimarily shade-intolerant early-successional species; as the stand

s progressively filled and occupied (GSO2 and GSO3), only seedlingsf shade-tolerant middle- to late-successional species can become

lling 300 (2015) 89–101 97

established; when the growing space becomes fully occupiedthrough a combination of tree establishment and growth, the standis considered fully stocked (GSO4), thereby, only late-successionalspecies with the highest shade tolerance class can establish. Otherstudies have similarly found that formulating site-scale processesin more details can influence the relative competitive ability ofspecies including their seed production and dispersal. In turn,those factors may importantly influence the distribution of shade-tolerant species (Gross, 1984; Howe et al., 1985; Paz et al., 1999;Tripathi and Khan, 1990; Turnbull et al., 1999). We accordinglysuggest that model applications aimed at evaluating species’ inter-actions or simulating the distribution of shade-tolerant speciesshould consider site-scale processes (Fekedulegn et al., 1999; Heet al., 2011). In future research, we can relax the GSO threshold ofcrown closure stage (GSO4) by essentially making it converge tothe GSO thresholds of open growth (GSO1) and partially occupiedstand development stages (GSO2 and GSO3). This would essentiallysimplify the stand development processes. By doing so, we can testwhether the simplified site-scale processes can achieve the similaroutcome for the middle- and late-successional species as those sim-ulated under the original design. The results can help us simplifymodel parameterization.

Conversely, early successional species was insensitive to the for-mulation of site-scale processes. This results from the relatively fastgrowth and high seed dispersal rates of early successional speciesthat preferentially confer to them an advantage of resource utiliza-tion. Those traits thus may override low establishment probabilitiesby allowing those species to establish in less suitable areas (He andMladenoff, 1999b). Thus, for early successional species, simulateddistribution is robust with respect to different site-scale processessuch as resource competition. In our study, this phenomenon isreflected in species such as white birch, an early successional andexpanding species (He et al., 2005). Other observational studiesalso found no apparent effects of site-scale processes such as seedmass on the growth and distribution of early successional species(Dalling and Hubbell, 2002).

Our results also showed that for some species the mean abun-dance simulated by the stand density model was generally largerthan that simulated by the age cohort model. The stand densitymodel incorporated quantitative details at stand scale includingtree density and size related resource competition as well as num-bers of seed. Seedlings accumulate from the seed dispersal of allavailable parent trees within the dispersal kernel (Wang et al.,2013). Increasing seed numbers (compared to presence or absenceof seed in the age cohort model) increases the chance of a viableseed successfully arriving at a site and developing into a seedling.Thus, species distribution simulated by the stand density modelshould, at least theoretically, always is larger than that simu-lated by the age cohort model. Studies using other FLMs, such asTreeMig, produced similar findings (Lischke et al., 2006). Contin-uously increasing seed supply therefore depends on numbers ofseed-producing parent trees sufficient to produce a positive feed-back loop of “more seeds-more seed producers-more seeds.” Thisfeedback process continues as long as the numbers of seeds pro-duced remain below some maximum carrying capacity of seedlings(Lischke and Loffler, 2006).

In the stand density model, a larger distribution of the mostshade-tolerant species may have a negative effect on the distri-bution of moderately shade-tolerant species. Thus, for the standdensity model as applied in our study, the distribution of mod-erately shade tolerant species was smaller than that for the agecohort model. For example, the stand density model for fir revealed

that relation was reversed for spruce. The relative abandance offir decreased dramatically in the age cohort model after simu-lated 140 years. This is because the age cohort model does not

98 Y. Liang et al. / Ecological Modelling 300 (2015) 89–101

F IJI) bee

ivssaficsa

Fc2

ig. 6. Differences in first order autocorrelation coefficients of pattern index (LPI, AI andstimated, and lower value, respectively.

ncorporate number of seeds, which reduces the chance of aiable seed successfully arriving at a site and developing into aeedling, and consequently may affect the regeneration of the mosthade tolerance species. Thus, fir decreased significantly when theypproach their maximum lifespan. In the stand density model,r did not decrease in relative abundance as it did in the age

ohort model, but rather maintained its abundance with onlylight fluctuations. This self-maintenance of fir thereby produced

decrease in spruce abundance associated with its lower shade

ig. 7. The agreement in spatial patterns simulated by these two models. Overall Kappaoefficient (k) in the simulated short term (the year 2050), medium term (the year100) and long term (the year 2200) period.

tween the age cohort model and the stand density model. Box plot presents the upper,

tolerance than fir. This outcome also was confirmed by a three-decade forest inventory of late-successional hemlock-hardwoodforests in Michigan, USA. There, very shade-tolerant species suchas hemlock (Tsuga Canadensis) increased or fluctuated in abun-dance, whereas moderately shade-tolerant species such as spruceover time greatly declined in abundance albeit sporadically (Wood,2000).

As expected, when more site-scale processes are incorporated inthe stand density model, simulation results of species distributionand its spatial pattern have a lower autocorrelation of year-to-yearvariation (generally exhibit a higher year-to-year variation) thanthat in the age cohort model. This is because succession in the standdensity model was affected by formulations of various processes,including site-scale processes (e.g., tree growth, stand density, andtree size-related resource competition) and landscape processes(e.g., seed dispersal). In contrast, the age cohort models neitherexplicitly simulate tree growth nor account for inter-specific com-petition effects during stand development. Instead, they reflectthe assumption that establishment probabilities were determinedby factors affecting species’ performance during succession. Onceestablished, trees died only because of large-scale disturbances, or

when they approach their maximum lifespan (He and Mladenoff,1999a). Thus, the autocorrelation of year-to-year variations in agecohort models are often high except when trees experience dis-turbance and death.

Y. Liang et al. / Ecological Modelling 300 (2015) 89–101 99

Table 4Statistics comparing spatial patterns simulated by the age cohort model versus the stand density model. Average deviation and the correlation coefficient (raw) refer to thespatial pattern index shown in Fig. 5. The correlation coefficient (detrended) refers to the detrended index of spatial pattern. The p-values given for the average deviationand the correlation coefficients represent type-I errors for the null hypothesis that the two models do not differ based on t-tests.

Indexa Average deviation Correlation coefficient (raw) Correlation coefficient (detrended)

Fir LPI −4.372** 0.974*** −0.006ns

AI 2.028* 0.030ns −0.091ns

IJI 7.251* 0.015ns −0.241ns

Basswood LPI −14.089*** −0.974*** −0.871***

AI −5.246*** 0.103ns 0.013ns

IJI −23.934*** 0.028ns 0.199ns

Spruce LPI −2.074*** −0.945*** −0.412**

AI −0.495*** −0.568*** −0.167ns

IJI −5.089*** 0.022ns −0.062ns

Korean pine LPI −1.072*** −0.997*** −0.584***

AI −0.255*** −0.963*** −0.796***

IJI −3.574*** 0.012ns −0.761***

Mountain birch LPI −1.167ns 0.962*** 0.924***

AI 0.117ns −0.043ns 0.711***

IJI −8.092*** 0.268ns 0.734***

White birch LPI 0.006ns −0.603*** 0.966***

AI 1.108ns −0.009ns 0.196ns

IJI 3.241ns 0.040ns 0.139ns

ns non-significant.*** p ≤ 0.001.

ion in

msltircsts

Fsm

** p ≤ 0.01.* p ≤ 0.05.a LPI: largest patch index; AI: aggregation index; IJI: interspersion and juxtaposit

Our results showed that for all simulated species, the agree-ents in spatial patterns from the two models in the simulated

hort and medium terms were higher than that in the simulatedong term. In addition, our results showed that the degree of spa-ial aggregation of species’ distributions (as quantified by AI) wasnsensitive to the formulation of site-scale processes, but wereelated with species’ percent cover. Larger species’ percent coverorresponded to more aggregated distributions. In contrast, patch

ize and arrangement (landscape composition) for the species dis-ribution across the landscape (as quantified by LPI and IJI) wereensitive to the formulation of site-scale processes. LPI and IJI

ig. 8. Comparison of spruce distribution patterns derived from the age cohort model and thpruce distribution simulated by the two models at year 2200. Spruce distributions at lowodel.

dex.

values for the stand density model also were smaller than for theage cohort model. These relations thus substantiate that the standdensity model is capable of creating relatively small patches andsimulating high forest heterogeneity. The simulations with highheterogeneity are especially important where steep environmentalgradients prevail such as in mountainous landscapes where micro-scale conditions control tree species establishment and growth(Ott et al., 1997). Such landscapes are generally characterized by

complex spatial vegetation patterns. Spatial patterns of species’distributions simulated by the stand density model thereforemay better approximate distributional patterns in mountainous

e stand density model for the study area. The green part of the map represents theer and higher elevations in the age cohort model are larger than in the stand density

1 Mode

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sBacosstneid(bm

5

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A

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00 Y. Liang et al. / Ecological

andscapes. This further suggests that site-scale processes also maye important in shaping distributional patterns through their effectn interspecific competition. For example, spruce is not normallyery competitive with fir at lower and higher elevations, which isupported by our stand density model (Fig. 8).

Disturbances have the potential to substantially alter land-cape properties and influence forest dynamics (Schumacher andugmann, 2006; Reyes and Kneeshaw, 2008), which may medi-te the sensitivity of site-scale processes. In boreal and westernoniferous forests where stand replacing fire and clearcut haveverwhelming effects on forest succession, disturbances can over-hadow site-scale processes and make site-scale processes lessensitive in these systems. Previous studies also confirmed thathe sensitivity of simulation results to site-scale processes wasot substantially increased or decreased by disturbances (Elkint al., 2012). Therefore, the age cohort model would be adequaten capturing forest landscape dynamics. In deciduous and mixedeciduous and coniferous forests where large-scale disturbancese.g., stand-replacing fire and clearcut) are rare, site-scale processesecome more sensitive in these system. Therefore the stand densityodel would be adequate.

. Conclusion

The age cohort model incorporated only presence/absence dataf tree age cohorts, and thus provided little quantitative detailsbout stand composition or stand structure at the scale of thendividual raster cell, whereas the stand density model incorpo-ated quantitative details at stand scale including tree density andize related resource competition as well as numbers of seed. Foriddle- or late-successional species, both species percent cover

nd its spatial distribution pattern simulated by the age cohortnd stand density models were different because during standevelopment these successional states were sensitive to site-scalerocesses such as competition. Conversely, for early successionalpecies, the simulation results from these two models were sim-lar because these species were insensitive to the formulation ofite-scale processes. We accordingly suggest that model applica-ions aimed at evaluating species’ interactions or simulating theistribution of shade-tolerant species should consider site-scalerocesses. In addition, due to incorporating additional quantita-ive information, the simulation results from the stand density

odel had a lower autocorrelation of year-to-year variation thanhat from the age cohort model. The degree of spatial aggrega-ion of species’ distributions was insensitive to the formulation ofite-scale processes, whereas patch size and arrangement (land-cape composition) for the species distribution were sensitive. Thistudy did not aim to verify whether the detailed site-scale pro-esses enhanced model predictive ability. However, results fromhis study revealed the differences in simulation results betweenhese two models with different site-scale process formulations,hich may help narrow down prediction uncertainties and point

o areas where representations of site-scale processes need to benhanced in the future.

cknowledgements

Funding for this research was provided by the scienctific andechnological support project (2012BAD22B04), “the 973 project”2011CB403206), Chinese National Science Foundational Project31300404) and the project of State Key Laboratory of Forest andoil Ecology (LFSE2013-12).

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