Alternative stable states and tipping points of ecosystems

doi:10.17520/biods.2020233

Abstract

Abstract:

Many ecosystems may experience abrupt shifts at certain tipping points subject to gradual environmental changes or small perturbations. The theory of alternative stable states has been applied to explain a wide range of observed ecosystem tipping points. In recent years, alternative ecosystem states and tipping points have received increasing attention among both researchers and the public. Here, we reviewed the theoretical basis of alternative stable states, the approaches for detecting the existence of alternative stable states, and a set of “generic early warning indicators” for anticipating the transitions between alternative stable states. We also reviewed typical cases to demonstrate how the alternative stable states theory is linked to real-world ecosystems. and discuss the potential misuse and controversy with respect to the concept and applications of this theory. We expect to provide useful references to Chinese audiences in the fields of nonlinear ecosystem dynamics, ecosystem management and biodiversity conservation in a changing world.

Key words: regime shift, critical transition, bifurcation, early warning signal, resilience, self-organization

Chi Xu, Haijun Wang, Quanxing Liu, Bo Wang. Alternative stable states and tipping points of ecosystems[J]. Biodiv Sci, 2020, 28(11): 1417-1430.

Add to citation manager EndNote|Ris|BibTeX

URL: https://www.biodiversity-science.net/EN/10.17520/biods.2020233

https://www.biodiversity-science.net/EN/Y2020/V28/I11/1417

Figures/Tables 5

References 91

[1]	Abis B, Brovkin V (2019) Alternative tree-cover states of the boreal ecosystem: A conceptual model. Global Ecology and Biogeography, 28, 612-627.
[2]	Beisner BE, Haydon DT, Cuddington K (2003) Alternative stable states in ecology. Frontiers in Ecology and the Environment, 1, 376-382.
[3]	Berdugo M, Kéfi S, Soliveres S, Maestre FT (2017) Plant spatial patterns identify alternative ecosystem multifunctionality states in global drylands. Nature Ecology and Evolution, 1, 0003.
[4]	Bertness MD, Trussell GC, Ewanchuk PJ, Silliman BR (2002) Do alternate stable community states exist in the Gulf of Maine rocky intertidal zone? Ecology, 83, 3434-3448.
[5]	Carpenter SR, Cole JJ, Pace ML, Batt R, Brock WA, Cline T, Coloso J, Hodgson JR, Kitchell JF, Seekell DA, Smith L, Weidel B (2011) Early warnings of regime shifts: A whole-ecosystem experiment. Science, 332, 1079-1082.
[6]	Chen N, Jayaprakash C, Yu KL, Guttal V (2018) Rising variability, not slowing down, as a leading indicator of a stochastically driven abrupt transition in a dryland ecosystem. The American Naturalist, 191, E1-E14. URL PMID
[7]	Cooper GS, Willcock S, Dearing JA (2020) Regime shifts occur disproportionately faster in larger ecosystems. Nature Communications, 11, 1175. DOI URL PMID
[8]	D’Odorico P, Caylor K, Okin GS, Scanlon TM (2007) On soil moisture-vegetation feedbacks and their possible effects on the dynamics of dryland ecosystems. Journal of Geophysical Research: Biogeosciences, 112, G04010.
[9]	Dai L, Korolev KS, Gore J (2013) Slower recovery in space before collapse of connected populations. Nature, 496, 355-358. DOI URL PMID
[10]	Dai L, Vorselen D, Korolev KS, Gore J (2012) Generic indicators for loss of resilience before a tipping point leading to population collapse. Science, 336, 1175-1177.
[11]	Dakos V, Carpenter SR, van Nes EH, Scheffer M (2015) Resilience indicators: Prospects and limitations for early warnings of regime shifts. Philosophical Transactions of the Royal Society B: Biological Sciences, 370, 20130263.
[12]	Dantas VL, Batalha M, Pausas JG (2013) Fire drives functional thresholds on the savanna-forest transition. Ecology, 94, 2454-2463.
[13]	Dantas VL, Hirota M, Oliveira RS, Pausas JG (2016) Disturbance maintains alternative biome states. Ecology Letters, 19, 12-19. URL PMID
[14]	DeAngelis DL, Post WM, Travis CC (1986) Positive Feedback in Natural Systems. Springer-Verlag, Berlin.
[15]	Drake JM, Griffen BD (2010) Early warning signals of extinction in deteriorating environments. Nature, 467, 456-459. DOI URL PMID
[16]	Feng JF, Wang HL, Zhu L (2009) Review on alternative stable states in ecosystems. Ecology and Environmental Sciences, 18, 1553-1559. (in Chinese with English abstract)
	[ 冯剑丰, 王洪礼, 朱琳 (2009) 生态系统多稳态研究进展. 生态环境学报, 18, 1553-1559.]
[17]	Flores BM, Fagoaga R, Nelson BW, Holmgren M (2016) Repeated fires trap Amazonian blackwater floodplains in an open vegetation state. Journal of Applied Ecology, 53, 1597-1603.
[18]	Flores BM, Holmgren M, Xu C, van Nes EH, Jakovac CC, Mesquita RCG, Scheffer M (2017) Floodplains as an Achilles’ heel of Amazonian forest resilience. Proceedings of the National Academy of Sciences, USA, 114, 4442-4446.
[19]	Fukami T (2015) Historical contingency in community assembly: Integrating niches, species pools, and priority effects. Annual Review of Ecology, Evolution, and Systematics, 46, 1-23.
[20]	Fukami T, Nakajima M (2011) Community assembly: Alternative stable states or alternative transient states? Ecology Letters, 14, 973-984. URL PMID
[21]	Ge ZP, Liu QX (2020) More than the sum of its parts: Self-organized patterns and emergent properties in ecosystems. Biodiversity Science, 28, 1431-1443. (in Chinese with English abstract)
	[ 葛振鹏, 刘权兴 (2020) 整体大于部分之和: 生态自组织斑图及其涌现属性. 生物多样性, 28, 1431-1443.]
[22]	Hantson S, Scheffer M, Pueyo S, Xu C, Lasslop G, van Nes EH, Holmgren M, Mendelsohn J (2017) Rare, intense, big fires dominate the global tropics under drier conditions. Scientific Reports, 7, 14374.
[23]	Hirota M, Holmgren M, van Nes EH, Scheffer M (2011) Global resilience of tropical forest and savanna to critical transitions. Science, 334, 232-235. DOI URL PMID
[24]	Holmgren M, Scheffer M (2001) El Niño as a window of opportunity for the restoration of degraded arid ecosystems. Ecosystems, 4, 151-159.
[25]	Holmgren M, Scheffer M (2010) Strong facilitation in mild environments: The stress gradient hypothesis revisited. Journal of Ecology, 98, 1269-1275.
[26]	Holmgren M, Scheffer M, Huston MA (1997) The interplay of facilitation and competition in plant communities. Ecology, 78, 1966-1975.
[27]	Jensen M, Liu ZW, Zhang XF, Reitzel K, Jensen HS (2017) The effect of biomanipulation on phosphorus exchange between sediment and water in shallow, tropical Huizhou West Lake, China. Limnologica, 63, 65-73.
[28]	Jeppesen E, Søndergaard M, Lauridsen TL, Davidson TA, Liu ZW, Mazzeo N, Trochine C, Özkan K, Jensen HS, Trolle D, Starling F, Lazzaro X, Johansson LS, Bjerring R, Liboriussen L, Larsen SE, Landkildehus F, Egemose S, Meerhoff M (2012) Biomanipulation as a restoration tool to combat eutrophication: Recent advances and future challenges. Advances in Ecological Research, 47, 411-488.
[29]	Joshi AA, Ratnam J, Sankaran M (2020) Frost maintains forests and grasslands as alternate states in a montane tropical forest-grassland mosaic; but alien tree invasion and warming can disrupt this balance. Journal of Ecology, 108, 122-132.
[30]	Kéfi S, Dakos V, Scheffer M, van Nes EH, Rietkerk M (2013) Early warning signals also precede non-catastrophic transitions. Oikos, 122, 641-648. DOI URL
[31]	Kéfi S, Holmgren M, Scheffer M (2016) When can positive interactions cause alternative stable states in ecosystems? Functional Ecology, 30, 88-97.
[32]	Levin SA, Carpenter SR, Godfray HCJ, Kinzig AP, Loreau M, Losos JB, Walker B, Wilcove DS (2012) The Princeton Guide to Ecology. Princeton University Press, Princeton.
[33]	Li H, Yuan L, Zhang LQ, Li W, Li SH, Zhao ZY (2017) Alternative stable states in coastal intertidal wetland ecosystems of Yangtze estuary, China. Chinese Journal of Applied Ecology, 28, 327-336. (in Chinese with English abstract) URL PMID
	[ 李蕙, 袁琳, 张利权, 李伟, 李诗华, 赵志远 (2017) 长江口滨海湿地潮间带生态系统的多稳态特征. 应用生态学报, 28, 327-336.] PMID
[34]	Li XR, Xiao HL, Zhang JG, Wang XP (2004) Long-term ecosystem effects of sand-binding vegetation in the Tengger Desert, northern China. Restoration Ecology, 12, 376-390.
[35]	Li YZ, Liu Y, Zhao L, Zou R, Wang CY, Guo HC (2013) Survey on threshold detection methods of regime shift in shallow lake ecosystem. Acta Ecologica Sinica, 33, 3280-3290. (in Chinese with English abstract)
	[ 李玉照, 刘永, 赵磊, 邹锐, 王翠榆, 郭怀成 (2013) 浅水湖泊生态系统稳态转换的阈值判定方法. 生态学报, 33, 3280-3290.]
[36]	Liautaud K, van Nes EH, Barbier M, Scheffer M, Loreau M (2019) Superorganisms or loose collections of species? A unifying theory of community patterns along environmental gradients. Ecology Letters, 22, 1243-1252. DOI URL PMID
[37]	Liu QX, Herman PMJ, Mooij WM, Huisman J, Scheffer M, Olff H, van de Koppel J (2014) Pattern formation at multiple spatial scales drives the resilience of mussel bed ecosystems. Nature Communications, 5, 5234. DOI URL PMID
[38]	Livina VN, Kwasniok F, Lenton TM (2010) Potential analysis reveals changing number of climate states during the last 60 kyr. Climate of the Past, 6, 77-82.
[39]	Mouquet N, Lagadeuc Y, Devictor V, Doyen L, Duputié A, Eveillard D, Faure D, Garnier E, Gimenez O, Huneman P, Jabot F, Jarne P, Joly D, Julliard R, Kéfi S, Kergoat GJ, Lavorel S, Le Gall L, Meslin L, Morand S, Morin X, Morlon H, Pinay G, Pradel R, Schurr FM, Thuiller W, Loreau M (2015) Review: Predictive ecology in a changing world. Journal of Applied Ecology, 52, 1293-1310.
[40]	Nolting BC, Abbott KC (2016) Balls, cups, and quasi-potentials: Quantifying stability in stochastic systems. Ecology, 97, 850-864. DOI URL PMID
[41]	Noy-Meir I (1975) Stability of grazing systems: An application of predator-prey graphs. Journal of Ecology, 63, 459-481. DOI URL
[42]	Pan BZ, Wang HZ, Pusch MT, Wang HJ (2015) Macroinvertebrate responses to regime shifts caused by eutrophication in subtropical shallow lakes. Freshwater Science, 34, 942-952.
[43]	Petraitis PS, Dudgeon SR (2005) Divergent succession and implications for alternative states on rocky intertidal shores. Journal of Experimental Marine Biology and Ecology, 326, 14-26.
[44]	Rietkerk M, Dekker SC, de Ruiter PC, van de Koppel J (2004) Self-organized patchiness and catastrophic shifts in ecosystems. Science, 305, 1926-1929. DOI URL PMID
[45]	Rocha JC, Peterson G, Bodin Ö, Levin S (2018) Cascading regime shifts within and across scales. Science, 362, 1379-1383. URL PMID
[46]	Scheffer M (1997) Ecology of Shallow Lakes. Chapman and Hall, London.
[47]	Scheffer M (2009) Critical Transitions in Nature and Society. Princeton University Press, Princeton.
[48]	Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR, Dakos V, Held H, van Nes EH, Rietkerk M, Sugihara G (2009) Early-warning signals for critical transitions. Nature, 461, 53-59. DOI URL PMID
[49]	Scheffer M, Carpenter SR (2003) Catastrophic regime shifts in ecosystems: Linking theory to observation. Trends in Ecology and Evolution, 18, 648-656.
[50]	Scheffer M, Carpenter SR, Dakos V, van Nes EH (2015a) Generic indicators of ecological resilience: Inferring the chance of a critical transition. Annual Review of Ecology, Evolution, and Systematics, 46, 145-167.
[51]	Scheffer M, Carpenter SR, Lenton TM, Bascompte J, Brock W, Dakos V, van de Koppel J, van de Leemput IA, Levin SA, van Nes EH, Pascual M, Vandermeer J (2012a) Anticipating critical transitions. Science, 338, 344-348. DOI URL PMID
[52]	Scheffer M, Carpenter S, Foley JA, Folke C, Walker B (2001) Catastrophic shifts in ecosystems. Nature, 413, 591-596.
[53]	Scheffer M, Hirota M, Holmgren M, van Nes EH, Chapin FS III (2012b) Thresholds for boreal biome transitions. Proceedings of the National Academy of Sciences, USA, 109, 21384-21389.
[54]	Scheffer M, Hosper SH, Meijer ML, Moss B, Jeppesen E (1993) Alternative equilibria in shallow lakes. Trends in Ecology and Evolution, 8, 275-279.
[55]	Scheffer M, van Nes EH (2007) Shallow lakes theory revisited: Various alternative regimes driven by climate, nutrients, depth and lake size. Hydrobiologia, 584, 455-466.
[56]	Scheffer M, Vergnon R, Cornelissen JHC, Hantson S, Holmgren M, van Nes EH, Xu C (2014) Why trees and shrubs but rarely trubs? Trends in Ecology and Evolution, 29, 433-434. DOI URL PMID
[57]	Scheffer M, Vergnon R, Cornelissen JHC, Hantson S, Holmgren M, van Nes EH, Xu C (2015b) The mystery of missing trubs revisited: A response to McGlone et al and Qian and Ricklefs. Trends in Ecology and Evolution, 30, 7-8. DOI URL PMID
[58]	Scheffer M, Xu C, Hantson S, Holmgren M, Los SO, van Nes EH (2018) A global climate niche for giant trees. Global Change Biology, 24, 2875-2883. DOI URL PMID
[59]	Schröder A, Persson L, de Roos AM (2005) Direct experimental evidence for alternative stable states: A review. Oikos, 110, 3-19.
[60]	Staal A, Flores BM (2015) Sharp ecotones spark sharp ideas: comment on “Structural, physiognomic and above-ground biomass variation in savanna-forest transition zones on three continents-how different are co-occurring savanna and forest formations?” by Veenendaal et al (2015). Biogeosciences, 12, 5563-5566.
[61]	Staal A, Flores BM, Aguiar APD, Bosmans JHC, Fetzer I, Tuinenburg OA (2020) Feedback between drought and deforestation in the Amazon. Environmental Research Letters, 15, 044024.
[62]	Staal A, Dekker SC, Xu C, van Nes EH (2016) Bistability, spatial interaction, and the distribution of tropical forests and savannas. Ecosystems, 19, 1080-1091.
[63]	Staal A, Tuinenburg OA, Bosmans JHC, Holmgren M, van Nes EH, Scheffer M, Zemp DC, Dekker SC (2018a) Forest-rainfall cascades buffer against drought across the Amazon. Nature Climate Change, 8, 539-543.
[64]	Staal A, van Nes EH, Hantson S, Holmgren M, Dekker SC, Pueyo S, Xu C, Scheffer M (2018b) Resilience of tropical tree cover: The roles of climate, fire, and herbivory. Global Change Biology, 24, 5096-5109.
[65]	Staver AC, Archibald S, Levin SA (2011) The global extent and determinants of savanna and forest as alternative biome states. Science, 334, 230-232. URL PMID
[66]	Steffen W, Crutzen PJ, McNeill JR (2007) The Anthropocene: are humans now overwhelming the great forces of nature. Ambio, 36, 614-621. DOI URL PMID
[67]	Strogatz SH (2018) Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edn. CRC Press, Boca Raton.
[68]	Su HJ, Chen J, Wu Y, Chen JF, Guo XC, Yan ZB, Tian D, Fang JY, Xie P (2019a) Morphological traits of submerged macrophytes reveal specific positive feedbacks to water clarity in freshwater ecosystems. Science of the Total Environment, 684, 578-586.
[69]	Su HJ, Wu Y, Xia WL, Yang L, Chen JF, Han WX, Fang JY, Xie P (2019b) Stoichiometric mechanisms of regime shifts in freshwater ecosystem. Water Research, 149, 302-310.
[70]	Suding KN, Gross KL, Houseman GR (2004) Alternative states and positive feedbacks in restoration ecology. Trends in Ecology and Evolution, 19, 46-53. DOI URL PMID
[71]	Sutherland WJ, Freckleton RP, Godfray HCJ, Beissinger SR, Benton T, Cameron DD, Carmel Y, Coomes DA, Coulson T, Emmerson MC, Hails RS, Hays GC, Hodgson DJ, Hutchings MJ, Johnson D, Jones JPG, Keeling MJ, Kokko H, Kunin WE, Lambin X, Lewis OT, Malhi Y, Mieszkowska N, Milner-Gulland EJ, Norris K, Phillimore AB, Purves DW, Reid JM, Reuman DC, Thompson K, Travis JMJ, Turnbull LA, Wardle DA, Wiegand T (2013) Identification of 100 fundamental ecological questions. Journal of Ecology, 101, 58-67.
[72]	van de Koppel J, Crain CM (2006) Scale-dependent inhibition drives regular tussock spacing in a freshwater marsh. The American Naturalist, 168, E136-E147. DOI URL PMID
[73]	van de Koppel J, Rietkerk M, Weissing FJ (1997) Catastrophic vegetation shifts and soil degradation in terrestrial grazing systems. Trends in Ecology and Evolution, 12, 352-356. DOI URL PMID
[74]	van Langevelde F, van de Vijver CADM, Kumar L, van de Koppel J, de Ridder N, van Andel J, Skidmore AK, Hearne JW, Stroosnijder L, Bond WJ, Prins HHT, Rietkerk M (2003) Effects of fire and herbivory on the stability of savanna ecosystems. Ecology, 84, 337-350.
[75]	van Nes EH, Arani BMS, Staal A, van der Bolt B, Flores BM, Bathiany S, Scheffer M (2016) What do you mean, ‘tipping point’? Trends in Ecology and Evolution, 31, 902-904. DOI URL PMID
[76]	van Nes EH, Staal A, Hantson S, Holmgren M, Pueyo S, Bernardi RE, Flores BM, Xu C, Scheffer M (2018) Fire forbids fifty-fifty forest. PLoS ONE, 13, e0191027. URL PMID
[77]	Veraart AJ, Faassen EJ, Dakos V, van Nes EH, Lürling M, Scheffer M (2012) Recovery rates reflect distance to a tipping point in a living system. Nature, 481, 357-359. DOI URL PMID
[78]	Wang HJ (2007) Predictive Limnological Researches on Small- to Medium-sized Lakes Along the Mid-lower Yangtze River. PhD dissertation, Institute of Hydrobiology, Chinese Academy of Sciences, Wuhan. (in Chinese with English abstract)
	[ 王海军 (2007) 长江中下游中小型湖泊预测湖沼学研究. 博士学位论文, 中国科学院水生生物研究所, 武汉.]
[79]	Wang HJ, Wang HZ, Liang XM, Wu, SK (2014) Total phosphorus thresholds for regime shifts are nearly equal in subtropical and temperate shallow lakes with moderate depths and areas. Freshwater Biology, 59, 1659-1671.
[80]	Wu QL, Xing P, Li HB, Zeng J (2013) Impacts of regime shift between phytoplankton and macrophyte on the microbial community structure and its carbon cycling in lakes. Microbiology China, 40, 87-97. (in Chinese with English abstract)
	[ 吴庆龙, 邢鹏, 李化炳, 曾巾 (2013) 草藻型稳态转换对湖泊微生物结构及其碳循环功能的影响. 微生物学通报, 40, 87-97.]
[81]	Xu C, van Nes EH, Holmgren M, Kéfi S, Scheffer M (2015a) Local facilitation may cause tipping points on a landscape level preceded by early-warning indicators. The American Naturalist, 186, E81-E90. URL PMID
[82]	Xu C, Hantson S, Holmgren M, van Nes EH, Staal A, Scheffer M (2016) Remotely sensed canopy height reveals three pantropical ecosystem states. Ecology, 97, 2518-2521.
[83]	Xu C, Holmgren M, van Nes EH, Hirota M, Chapin FS III, Scheffer M (2015b) A changing number of alternative states in the boreal biome: Reproducibility risks of replacing remote sensing products. PLoS ONE, 10, e0143014. DOI URL PMID
[84]	Xu C, Holmgren M, van Nes EH, Maestre FT, Soliveres S, Berdugo M, Kéfi S, Marquet PA, Abades S, Scheffer M (2015c) Can we infer plant facilitation from remote sensing? A test across global drylands. Ecological Applications, 25, 1456-1462. DOI URL PMID
[85]	Xu C, Li EH, Yang J, Ma Y, Zhang M, Feng WS, Liang XM, Wang HJ (2020) Integrating underwater light condition and seed bank to indicate submersed macrophyte restoration zone: Lake Jinhu as a case. Acta Hydrobiologica Sinica, 44, 1111-1118. (in Chinese with English abstract)
	[ 徐超, 厉恩华, 杨娇, 马雨, 张苗, 冯伟松, 梁小民, 王海军 (2020) 基于水下光照条件和种子库分布指示沉水植物恢复区: 以金湖为例. 水生生物学报, 44, 1111-1118.]
[86]	Xu C, Staal A, Hantson S, Holmgren M, van Nes EH, Scheffer M (2018) Remotely sensed canopy height reveals three pantropical ecosystem states: Reply. Ecology, 99, 235-237.
[87]	Xu C, Vergnon R, Cornelissen JHC, Hantson S, Holmgren M, van Nes EH, Scheffer M (2015d) Temperate forest and open landscapes are distinct alternative states as reflected in canopy height and tree cover. Trends in Ecology and Evolution, 30, 501-502. DOI URL PMID
[88]	Xu Z, Mason JA, Xu C, Yi S, Bathiany S, Yizhaq H, Zhou Y, Cheng J, Holmgren M, Lu H (2020) Critical transitions in Chinese dunes during the past 12,000 years. Science Advances, 6, eaay8020. DOI URL PMID
[89]	Zhao L, Liu Y, Li YZ, Zhu X, Zou R (2014) Survey on theory and driving factors of regime shifts on lake ecosystems. Ecology and Environmental Sciences, 23, 1697-1707. (in Chinese with English abstract)
	[ 赵磊, 刘永, 李玉照, 朱翔, 邹锐 (2014) 湖泊生态系统稳态转换理论与驱动因子研究进展. 生态环境学报, 23, 1697-1707.]
[90]	Zhao LX, Xu C, Ge ZM, van de Koppel J, Liu QX (2019) The shaping role of self-organization: Linking vegetation patterning, plant traits and ecosystem functioning. Proceedings of the Royal Society B-Biological Sciences, 286, 20182859.
[91]	Zhao YJ, Wang R, Yang XD, Dong XH, Xu M (2016) Regime shifts revealed by paleoecological records in Lake Taibai’s ecosystem in the middle and lower Yangtze River Basin during the last century. Journal of Lake Sciences, 28, 1381-1390. (in Chinese with English abstract)
	[ 赵雁捷, 王荣, 羊向东, 董旭辉, 徐敏 (2016) 古生态记录揭示的长江中下游太白湖生态系统稳态转换过程. 湖泊科学, 28, 1381-1390.]

	模型方程	反馈机制
植被生物量模型1 Vegetation biomass model 1	$\frac{\partial P}{\partial t}=P\left( 1-P \right)-iWP-sP+{{D}_{P}}\Delta P$	抑制 Inhibition
植被生物量模型2 Vegetation biomass model 2	$\frac{\partial P}{\partial t}=P\left( 1-P \right)\frac{P}{P+{{k}_{2}}}-iWP-sP+{{D}_{P}}\Delta P$	促进 + 抑制 Facilitation + inhibition
植被生物量模型3 Vegetation biomass model 3	$\frac{\partial P}{\partial t}=P\left( 1-P \right)-\frac{{{k}_{3}}}{P+{{k}_{3}}}iWP-sP+{{D}_{P}}\Delta P$	促进 + 抑制 Facilitation + inhibition
枯落物生物量 Wrack biomass	$\frac{\partial W}{\partial t}=sP-bW+{{D}_{W}}\Delta W$

	模型方程	反馈机制
植被生物量模型1 Vegetation biomass model 1	$\frac{\partial P}{\partial t}=P\left( 1-P \right)-iWP-sP+{{D}_{P}}\Delta P$	抑制 Inhibition
植被生物量模型2 Vegetation biomass model 2	$\frac{\partial P}{\partial t}=P\left( 1-P \right)\frac{P}{P+{{k}_{2}}}-iWP-sP+{{D}_{P}}\Delta P$	促进 + 抑制 Facilitation + inhibition
植被生物量模型3 Vegetation biomass model 3	$\frac{\partial P}{\partial t}=P\left( 1-P \right)-\frac{{{k}_{3}}}{P+{{k}_{3}}}iWP-sP+{{D}_{P}}\Delta P$	促进 + 抑制 Facilitation + inhibition
枯落物生物量 Wrack biomass	$\frac{\partial W}{\partial t}=sP-bW+{{D}_{W}}\Delta W$