relationships between regional primary production and vegetation patterns

Ecological Modelling 172 (2004) 1–12

Relationships between regional primary productionand vegetation patterns

Qiong Gaoa,∗, Mei Yub, Junhua Wanga, Haikun Jiaa, Kun Wanga

a MOE Key Lab of Environmental Change and Natural Disaster, Institute of Resources Science, Beijing Normal University,Beijing 100875, PR China

b Institute of Botany, Chinese Academy of Sciences, Beijing 100093, PR China

Received 24 July 2002; received in revised form 7 May 2003; accepted 10 June 2003

Abstract

Linear relationships between increases in regional primary productivity to possible future climate change and vegetationpatterns are derived. These relationships are applied to the simulated productivities and vegetation distributions in China underaltered climate scenarios projected by seven general circulation models (GCM). The results of analysis indicate that the relation-ships hold valid for different resolution of analysis. Patchiness of vegetation distribution can explain more than 50% of changesin vegetation distribution and changes in structural responses of primary production, and thus is an important index to quantifyvegetation responses to possible future climate change. Patchiness can accelerate either degradation or recovery of a vegetationtype, depending on whether altered climate conditions are adverse or favorable for the vegetation type.© 2003 Elsevier B.V. All rights reserved.

Keywords:Patchiness; Patterns and processes; Terrestrial ecosystems; Vegetation distribution

1. Introduction

Simulation models have been used as importantmeans to investigate the responses and feedbackof regional and global terrestrial ecosystems to cli-matic changes (Lauenroth et al., 1986, 1993; Kinget al., 1989; Lauenroth and Sala, 1992; Muller, 1992;Krapivin, 1993; Gote et al., 1994; Ludeke et al.,1994; Denning et al., 1996; Fitz et al., 1996; Friendet al., 1997; Kohlmaier et al., 1997, for example).Biogeochemical models address the problems of pri-mary productivity responses (Running and Coughlan,1988; Running and Nemani, 1988; Raich et al., 1991;

∗ Corresponding author. Tel.:+86-10-6220-6050;fax: +86-10-6220-6050.

E-mail addresses:[email protected], [email protected] (Q. Gao).

Melillo et al., 1993, 1995; Parton et al., 1993; Foley,1994, 1995; Running, 1994), whereas biogeographymodels simulate vegetation distribution under differ-ent climate scenarios (Woodward and McKee, 1991;Prentice et al., 1992; Neilson, 1995). Global or re-gional simulation models for terrestrial ecosystemsusually include a large number of state variablesdefined over large spatiotemporal domains, and com-plex mathematical relationships are used to quantifyvarious ecosystem processes such as assimilation,distribution of the assimilated materials, hydrologicaland biogeochemical cycles, competition, and migra-tion of plants and communities. Numerical outputs ofthese simulation models usually include spatiotem-poral distribution patterns of net primary produc-tivity and vegetation types under various climaticscenarios.

0304-3800/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0304-3800(03)00250-3

2 Q. Gao et al. / Ecological Modelling 172 (2004) 1–12

Efficient and reliable methods are needed to analyzelarge volumes of output data from these simulationmodels in order to draw correct conclusions aboutresponses of regional ecosystems processes to cli-mate changes and to investigate relationships betweenthese responses and vegetation distribution patterns(Melillo et al., 1995; Baker, 1996; Gao et al., 2000b).Two important questions in post-simulation analysesof the large volume of simulation output are: (1) howprimary production processes are related to vegeta-tion distribution pattern at regional or global scalesand (2) how the relationship between primary pro-duction processes and vegetation distribution patterninterplay with climate in the projected future terres-trial ecosystem states under various climate-changescenarios. These questions exemplify a more generalissue of relationships between patterns and processes(Turner, 1989; Walker and Walker, 1991; Gao andYang, 1997). It is not difficult to understand that therecertainly exist implicit relationships between primaryproduction processes and vegetation patterns becausethe latter governs many spatial processes such as lat-eral movement of water and nutrients (run-off/run-onand sub-surface flow) and plant migration within alandscape or region, which strongly affect the primaryproduction (Aguiar and Sola, 1999). Given that thesespatial processes are considered and implemented atsite scale (grid cells) in regional/global simulationmodels by defining the interactions between any twoadjacent grid cells with different ecological types, ourquestion is what explicit and quantitative conclusionsabout the relationships between primary productionand vegetation patterns at regional/global scales canbe drawn from the large amount of output of thenumerical simulations. Statistical approaches are themost commonly used means for the purposes (Gaoand Zhang, 1997). However, the empirical nature ofstatistics made it difficult to arrive at general conclu-sions beyond the simulated ecosystems.

Our objective in this study is to develop a moremechanistic approach to explore large volumes ofoutputs of regional and global ecosystem simulations.Theoretical relationships between vegetation patternsand primary production at regional scales are derived.The relationships are applied to simulated vegeta-tion and net primary productivity of Chinese terres-trial ecosystems generated with a regional terrestrialecosystem model to provide a preliminary validation.

2. Theory

We start with an assumption that vegetation in a re-gion can be classified inton classes, and each class oc-cupies multiple number of sub-domainsΩij, enclosedby curve Cij, where i = 1, 2, . . . , n, and j = 1,2, . . . , mi (mi is the number of sub-domains occu-pied by classi). Total annual net primary productionof vegetation classi at equilibrium state, denoted byQi, can be computed by integrating the unit area pro-duction or productivity,qi, over all the sub-domains,or

Qi =mi∑j=1

∫Ωij

qi dAi (1)

where dAi stands for infinitesimal area element.Gauss’s mean value theorem allowed us to writeEq. (1) as Qi = ∑mi

j=1qijAij = qiAi, where qij is

the mean value ofqi in Ωij, Ai = ∑mi

j=1Aij and

qi = ∑mi

j=1qijAij/Ai.When external driving factors such as climate and

atmospheric CO2 concentration change, both produc-tivity qi and sub-domainΩij will change. As illus-trated inFig. 1, Ωij and its boundaryCij shrink/expandand move toΩ′

ij and C′ij . If the changes are small

enough, changes in total production, denoted asQi,

Fig. 1. Geometric relationship between the baseline and altereddistributions of a vegetation class.Ωij is the jth sub-area occupiedby vegetation classi and Cij is the boundary ofΩij . Ω′

ij andC′ij

are the distorted (moving and expansion/shrink)Ωij and Cij byaltered climate, respectively.

Q. Gao et al. / Ecological Modelling 172 (2004) 1–12 3

at the new equilibrium state can be computed as

Qi =mi∑j=1

[∫Ωij

(qi) dAi +∫

Cij

qi(vi) · ds

](2)

where ds is the infinitesimal vector with magnitudeequal to the length of the infinitesimal arc on the curveand pointing to the out-normal direction ofCij. vi

is a vector pointing to the moving direction of themiddle point of ds. The magnitude ofvi, denoted by|vi|, is the distance travelled by the middle point ofds whenCij changed toC′

ij .We can further writevi · ds = |vi| · |ds|cosγ =

dai, whereγ is the angle betweenvi and ds and dai

is the infinitesimal area swept by ds (the area enclosed

by︷︸︸︷wxyzin Fig. 1). The first relationship we can derive

from Eq. (2) is

Qi =mi∑j=1

[∫Ωij

(qi)dAi +∫

Ωij

qi dai

]

=mi∑j=1

qijAij +mi∑j=1

qijbAij (3)

where Ωij is the changed part ofΩij, Aij =∫Cij

vi · ds, and qijb is the value ofqi at a point onthe boundary ofΩij, according to Gauss’s mean valuetheorem. Substitutingqi = ∑mi

j=1qijAij/Ai, qib =∑mi

j=1qijbAij/Ai, and Ai = ∑mi

j=1Aij intoEq. (3), and dividing the result byQi = qiAi, we have

Qi = Qif + Qis = qi

qi

+ qib

qi

· Ai

Ai

= qi

qi

+ qib

qi

· Ai = qi

qi

+ kbi · Ai (4)

whereQi is thetotal responses of primary productioncalculated as the relative increase in total primary pro-duction of vegetation classi; Qif = qi/qi is therelative increase in productivity that can be attributedto the direct effects of altered functional processes,such as assimilation and respiration, by external driv-ing factors, and thus is calledfunctional productionresponse; Qis = (qib/qi) · (Ai/Ai) = kbi · Ai isproportional to the relative increase in area occupiedby the vegetation class due to changes in competitionwith all other vegetation classes, and is thus calledstructural production response; Ai = Ai/Ai is the

relative increase in area occupied by vegetation classi;andkbi = qib/qi. Hence, thetotal response of primaryproduction of a vegetation class can be partitionedinto a functional responseand astructural response.

To relate thestructural responseto the vegetationpatterns, we can write it as the following

Qis = 1

qiAi

mi∑j=1

∫Cij

qi(vi) · ds = 1

qiAi

mi∑j=1

qijcSij

(5)

whereSij is the length ofCij andqijc = qi(s)|v(s)|cosγ(s) is the increase in primary production per unitlength at some points along the boundary ofΩij.qijc can either be positive or negative, dependingon γ(s). Gauss’s mean value theorem of integrationwas used in the last step ofEq. (5). Letting qic =∑mi

j=1qijcSij/Si, whereSi = ∑mi

j=1Sij is the totalboundary length of vegetation classi, we now have

Qi = Qif + Qis = qi

qi

+ qic

qi

· Si

Ai

= qi

qi

+ qic

qi

· Psi = qi

qi

+ ksiPsi (6)

wherePsi = Si/Ai is the boundary length per unit areaandksi = qic/qi. As Si is directly proportional to thepartial patchiness defined byGao and Yang (1997), Psi

is calledspecific patchiness,or partial patchiness perunit area. Psi is larger for a vegetation class with manysmall, irregularly shaped sub-areas than a vegetationclass with a few large, round sub-areas. ComparingEqs. (4)–(6), we can have a third relationship

Ai = kaiPsi (7)

wherekai = ksi/kbi = qic/qib. Eq. (7)states that therelative increase in distribution area is proportional tothe specific patchiness for a vegetation class.

3. Application of the derived relationships tothe simulation outputs of a Chinese terrestrialecosystem model

The model used to simulate responses of Chineseterrestrial ecosystems to climatic changes used cou-pled vegetation dynamics and primary production pro-cesses (Gao and Zhang, 1997; Gao and Yu, 1998; Gao


et al., 2000a; Yu et al., 2001, 2002). For given climatescenarios, the model simulates equilibrium spatialdistribution of green and non-green biomass, primaryproductivity, and nitrogen concentrations of a num-ber of different vegetation classes in a given region.Simultaneously, soil moisture and total and availablenitrogen contents were also computed as functionsof space and time. Primary production was coupledwith water and nitrogen cycles, and spatiotemporalvariation of vegetation distribution was simulated asa result of the competition change in altered climate.Detailed model description can be found in (Yu et al.,2002). The application of this model to China conti-nent and two largest islands involved simulation runsfor 8 equilibrium scenarios for a total of 19 vegeta-tion classes in the spatial domain (Yu et al., 2001).Equilibrium outputs of seven general circulation mod-els (GCM), including GFDL for Geographical FluidDynamics laboratory, GISS for Goddard Institute forSpace Studies, OSU for Oregon State University,LLNL for Lawrence Livemore National Laboratory,MPI for Max Planck Institute (Geostrophic ocean),UKML for UK Meteorological Office-low resolution,and UKMH for UK Meteorological Office-high res-olution, under doubled atmospheric CO2 concentra-tions, plus contemporary climate, were used to drivethe model to equilibrium. Sixteen natural vegetationclasses, deciduous conifer forests (DCNF), tempo-ral evergreen conifer forests (TGCN), sub-tropicalevergreen forests (SGCN), sub-tropical mountainousforests (SMCN), deciduous broadleaf and evergreenconifer mixed forests (DBGC), deciduous broadleafforests (DBRD), evergreen broadleaf forests (GBRD),deciduous shrubs (DSHB), evergreen shrubs (GSHB),shrubs and meadows (SHMD), short shrub deserts(SHDS), cold short shrub deserts (CSSD), typical drygraminal steppes (GSTP), graminal grass and shortshrubs (CRSS), cold graminal meadows (CMDS), andmeadows and wetlands (MDWT) and 3 agriculturallands, 1CRP, 2CRP, and 3CRP for 1, 2, and 3 crops,

Fig. 2. Simulated vegetation distribution in China by a regional dynamic vegetation model (Gao et al., 2000a). Scenario code:PRES—Contemporary climate, GFDL—Geographical Fluid Dynamics laboratory, GISS—Goddard Institute for Space Studies, OSU—OregonState University, LLNL—Lawrence Livemore National Laboratory, MPI—Max Planck Institute, UKML—UK Meteorological Office-lowresolution, and UKMH—UK Meteorological Office-high resolution. Vegetation code: DCNF—Deciduous conifer forests, GCNF -Evergreenconifer forests, DBRD—Deciduous broadleaf forests, GBRD—Evergreen broadleaf forests, SHRB—Shrubs, DEST—Desert vegetation,GRAS—Grasslands, CROP—Agricultural crops. Note GCNF includes TGCN, SGCN, SMCN and DBGC of simulated vegetation classes.Similarly, SHRB includes GSHB and DSHB, DEST includes SHDS and CSSD, GRAS includes GSTP, GRSS, CMDS, SHMD and MDWT,and CROP includes 1CRP, 2CRP and 3CRP. Refer to the text for codes of simulated vegetation classes.

respectively, were involved in the application. Thespatial resolution was 20′×20′ (latitude by longitude).The simulation grid had 105 rows from 53.3333N(north) to 18.6667N (south) and 183 columns from73.6667E (west) to 134.3333E (east), with eachgrid cell representing 1/3N by 1/3E. Figs. 2 and 3illustrate the simulated equilibrium distribution ofvegetation and net primary productivity, respectively.

To apply the relationship developed in the previoussection to the simulation results, we did two aggrega-tions of the simulation grid as the following. Aggrega-tion 1 had 7 rows from north to south and 12 columnsfrom west to east, with each aggregation row repre-senting 5N and including 15 consecutive rows of thesimulation grid, and each aggregation column (exceptthe right most one) representing 5E and including 15consecutive columns of the simulation grid. The lastcolumn of aggregation 1 was mapped into the 16 mosteast columns of the simulation grid. Similarly, aggre-gation 2 had 4 rows from north to south and 6 columnsfrom west to east. Each of the first 3 rows of aggre-gation 2 represented 8.667N and was mapped with26 consecutive rows of the simulation grid, whereasthe last row of aggregation 2 in the most south wasmapped with the 27 rows in the south most of simu-lation grid. Each column of aggregation 2 except thelast one represented 10E and was mapped into 30consecutive columns of the simulation grid, whereasthe last column of aggregation 2 was mapped with themost east 31 columns of the simulation grid. Thus,each cell in the two aggregated grids represented rect-angular sub-area (in geographic coordinates) that con-tains a number of cells in the simulation grid. For eachvegetation classi in each of the rectangular sub-area(I, J) at row I and columnJ in an aggregation grid,specific patchiness,Psi (I, J), was calculated from thesimulated vegetation with contemporary climate con-ditions. At the same time, the following calculationswere performed for each of the seven altered climatescenarios.


Fig. 3. Simulated net primary productivity in China by a regional dynamic vegetation model. Climate scenario codes are the same asFig. 2. The units in the legend bars are (t hm−2 a−1).


(1) Total production of classi and total area oc-cupied by classi, in the sub-area (I, J) underscenarioa, denoted byQi,a(I, J) and Ai,a(I, J)respectively, were calculated for alli, a, I, andJ.Relative increase in total primary production ofvegetation classi at sub-area (I, J) in responseto altered scenarioa, denoted byQi,a(I, J), andthe corresponding relative increase in occupiedareaAi,a(I, J), were computed by subtractingthe primary production and occupied area for thecontemporary climate from those for the alteredclimate scenarios, respectively, and then dividingthe results by respective quantities for contempo-rary climate, for alli, I, J, anda.

(2) Functional production response of vegetationclassi to an altered climate scenarioa in a sub-areaof the aggregations (I, J), denoted byQif,a(I,J), was calculated asQif,a(I, J) = [Qi,a(I, J)/

Ai,a(I, J) − Qi,0(I, J)/Ai,0(I, J)]/[Qi,0(I, J)/

Ai,0(I, J)] for all i, I, J, and a, where subscript‘0’ denotes quantities under the contemporaryclimate scenario.

(3) Structural production response of vegetation classi to an altered climate scenarioa in sub-area (I,J), denoted byQis,a(I, J), was calculated bysubtractingQif,a(I, J) from Qi,a(I, J), for alli, I, J, anda, i.e.,Qis,a = Qi,a − Qif,a.

The results of the above calculations for all veg-etation classes, all sub-areas, and all altered climatescenarios were pooled together to produce three ar-rays for each of the two aggregations,Qs, A,and Ps, for pooled relative structural production re-sponse, pooled relative changes in occupied area,and pooled specific patchiness, respectively. Caseswith A > 4.0 were excluded to ensure that theassumption of ’small change’ was satisfied. Thethree arrays were then separated into two groups,one of which was a positive-increase group withA > 0, and the other a negative-increase groupwith A ≤ 0. Statistical regressions were conductedfor the following three models for each of the twogroups:

Qs = kbA (8)

A = kaPs (9)

Qs = ksPs (10)

wherekb, ka, andks are three constants to be estimatedin the regression analyses.Eqs. (8)–(10)are pooledand simplified versions ofEqs. (4), (6), and (7), re-spectively. If the regression analyses are statisticallysignificant, we can conclude that our model for ana-lyzing the relationships between primary productionand vegetation structure holds correct.

4. Results and discussion

Fig. 4illustrates the relationship between the pooledstructural production responses to altered climate sce-narios and the pooled relative increases in occupiedareas of Chinese vegetation classes in response toaltered climate scenarios. Panels (a) and (b) are forcases with positive increases in distribution (occu-pied areas), whereas (c) and (d) are for cases withnegative increases, or decreases, in distribution. Theregression estimatedkb is 0.5478 for aggregation 1and 0.5543 for aggregation 2 for the positive-increasegroup, whereas those for negative-increase groupchanged from 1.163 for aggregation 1 to 1.674 foraggregation 2. More than 72% of the variation instructural production responses can be explained byrelative changes in occupied areas. The significant re-gressions indicated that the derived relationship heldfor both positive- and negative-increase groups in allclimate scenarios. The relationship also held for bothaggregations, showing that the significance of therelationship was invariant for spatial resolution. Thelinearity of the relationship is especially evident for−0.5 < A < 1.0, because the model was derivedfrom the assumption of ’small changes’. The result isnot a surprise for increases in total primary produc-tion of any vegetation class, which should be directlyproportional to its distributed area, as demonstrated inEq. (8).

The relationship between the pooled relative in-creases in occupied area in response to the alteredclimate scenarios and the pooled specific patchinessunder contemporary climate was shown inFig. 5.Fig. 5a and bshow cases with positive increases,whereasFig. 5c and dare for cases with the corre-sponding negative increases (decreases) in the areasfor the two aggregations, respectively. Even thoughthe distribution of the points are more scattered thanFig. 4, the regressions were shown to be significant


Fig. 4. Relationships between relative changes in structural primary production and relative changes in distribution areas in response toaltered GCM climate scenarios. Panels (a) and (c) are for positive-increase groups and panels (b) and (d) for negative-increase groups in5 × 5 and 8.667× 10 (latitude× longitude) aggregation resolutions, respectively.

for all the four groups. The absolute values of regres-sion coefficients (estimates ofka) decrease from 0.76to 0.67 for the positive-increase group and from 0.44to 0.29 for the negative-increase group, as the gridcell sizes of aggregation increased from 5× 5 to8.667× 10 (latitude× longitude). More than 50% ofthe variations in the positive-increase group and morethan 75% of the variations in the negative-increasegroup can be explained by the specific patchiness.The linear relationship between relative changes inoccupied areas and the specific patchiness impliedthat patchiness was a double-edged blessing: In thepositive-increase group, the expansion of occupiedarea by a vegetation class was proportional to specificpatchiness; thus patchiness helped a vegetation class toinvade into areas previously occupied by other classes.On the other hand, in the negative-increase group,the shrink of the area occupied by a vegetation classwas also proportional to specific patchiness. Hence,patchiness made a vegetation class more vulnerable to

be invaded by other vegetation classes. Hence, patch-iness can accelerate either degradation or recovery ofa region or landscape, depending on whether the ex-ternal driving forces or environmental conditions arefavorable or adverse for the major vegetation classesin the region or landscape. The result is not difficult tounderstand. For any given vegetation class occupyinga certain area at the baseline scenario (the contem-porary climate in our case), a larger patchiness ingeneral means a longer boundary enclosing the areaand hence more exposure to neighborhood vegetationclasses. When an altered climate scenario is appliedto drive the vegetation system, one should expect thata longer boundary can either help the vegetation classto invade the neighborhood vegetation classes whenthe altered scenario is more favorable for the vegeta-tion class than the baseline scenario, or accelerate theinvasion by neighborhood vegetation classes into thearea when the altered scenario is more adverse for thevegetation classes than the baseline scenario.


Fig. 5. Relationships between relative changes in distribution area in response to altered climate as projected by GCMs and specificpatchiness of vegetation distribution under contemporary climate. Panels (a) and (c) are for positive-increase groups and panels (b) and(d) are for negative-increase groups in 5× 5 and 8.667× 10 (latitude× longitude) aggregation resolutions, respectively.

Fig. 6 illustrates the relationship between thepooled structural production responses of vegetationclasses to altered climate scenarios and the specificpatchiness of vegetation distribution under contem-porary climate. The regression coefficient (estimatesof ks) decreased from 0.76 to 0.67 for the positive-increase groups, but increased from−0.44 to−0.29for the negative-increase groups, as the aggregationresolution decreased from 5× 5 to 8.667 × 10(latitude× longitude). More than 50 and 75% of vari-ations in the structural primary production increasescan be explained by the specific patchiness for thepositive- and negative-increase groups, respectively.From the theoretical derivation of the relationshipsamong primary production responses, vegetation dis-tribution responses, and specific patchiness, we can in-fer thatks = kakb. This equality is checked inTable 1for both positive- and negative-increase groups for thetwo aggregation resolutions. The differences betweenks andka kb varied from 2.6 to 11.4%. We could seehere again that the structural production response of

vegetation classes to external environmental changewas linearly related to specific patchiness for bothpositive- and negative-increase groups for both aggre-gation resolutions. Thus, patchiness can either increaseor decrease the primary production of a vegetationclass, depending on whether the altered environmentis more favorable or adverse for the vegetation classthan the baseline environmental conditions.

In their review of ecological process and vegeta-tion patterns for arid regions,Aguiar and Sola (1999)

Table 1Relationships among regression coefficients of the model

5 × 5 aggregation 8.667× 10 aggregation

Positiveincrease

Negativeincrease

Positiveincrease

Negativeincrease

ka 0.763 −0.443 0.675 −0.292kb 0.548 1.163 0.544 1.674ka kb 0.418 −0.515 0.367 −0.489ks 0.438 −0.529 0.414 −0.523


Fig. 6. Relationships between relative changes in structural primary production in response to altered climate as projected by GCMs andspecific patchiness of vegetation distribution under contemporary climate. Panels (a) and (c) are for positive-increase groups and panels(b) and (d) are for negative-increase groups in 5× 5 and 8.667× 10 aggregation resolutions, respectively.

proposed a conceptual model relating production todistribution heterogeneity. They concluded that patch-iness of vegetation patterns, in general, increasesoverall primary production in a two-phase vegetationmosaic (densely-vegetated patches and lower-covermatrix). Their argument, however, is based on the’static’ patchiness. The production they referred to isthe functional production in our case. In other words,they did not consider the increases in production thatresulted from shrink and expansion of the dense vege-tation patches, i.e., the structural production responsesin our terms.

5. Summary and conclusions

We derived a theoretical linear relationship betweenrelative increases in a component of primary produc-tion and relative increases in distribution (occupied

area) of vegetation classes in responses to changesin external environmental conditions. Linear relation-ships between these responses and vegetation dis-tribution patterns quantified by a specific patchinessindex are also derived. The relationships were appliedto simulated vegetation and primary productivity dis-tributions of Chinese terrestrial ecosystems by meansof a regional dynamic vegetation model driven by cli-mate scenarios from seven general circulation models.The results indicate that all the relationships hold validfor a wide range of relative changes in distribution andfor different spatial resolutions of calculation. Morethan 70 and 55% of structural production responses ofvegetation classes to altered climate conditions can beexplained by changes in vegetation distribution andby specific patchiness, respectively, and more than50% of changes in distribution of vegetation classescan be explained by the specific patchiness. Hence,vegetation pattern is an important index to quantify


vegetation responses to possible future climate and en-vironmental changes. Patchiness can increase primaryproduction and facilitate recovery of a vegetation classfrom degradation when the changed environment ismore favorable for the vegetation class than the base-line environment. On the other hand, patchiness canalso decrease primary production and accelerate thedegradation of a vegetation class if the changed ex-ternal environment is more adverse for the vegetationclass than the baseline environmental conditions.

Acknowledgements

This research was supported by National Sci-ence Function of China under grants #90202008 and#90211002.

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relationships between regional primary production and vegetation patterns

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