Skip to main content

Tree Structure Revisited: Eco-Evolutionary Models

  • Chapter
  • First Online:
Book cover Models of Tree and Stand Dynamics

Abstract

In this chapter we introduce the eco-evolutionary approach to modelling and review its applications for determining carbon allocation to tree structure in different environments. We begin with an introduction to optimisation ideas and a discussion of how they relate to the theory of evolution, and how such models should be used and interpreted. We then present some examples of models that utilise the eco-evolutionary approach to derive plant structure and carbon allocation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ågren GI, Franklin O (2003) Root:shoot ratios, optimization and nitrogen productivity. Ann Bot 92:795–800

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ågren GI, Axelsson B, Flower-Ellis JGK, Linder S, Persson H, Staaf H, Troeng E (1980) Annual carbon budget for a young scots pine. Ecol Bull 32:307–313

    Google Scholar 

  • Ahl V, Allen TFH (1996) Hierarchy theory, a vision, vocabulary and epistemology. Columbia University Press, New York

    Google Scholar 

  • Bar-Yam Y (2012) Dynamics of complex systems. Perseus Books, Dordrecht/London/New York

    Google Scholar 

  • Borchert F, Slade NA (1981) Bifurcation ratios and the adaptive geopmetry of trees. Bot Gaz 142:394–401

    Article  Google Scholar 

  • Bossel H (1996) TREEDYN3 forest simulation model. Ecol Modell 90:187–227

    Article  Google Scholar 

  • Brännström Å, Johansson J, von Festenberg N (2013) The hitchhiker’s guide to adaptive dynamics. Games 4:304–328

    Article  Google Scholar 

  • Brouwer R (1962) Distribution of dry matter in the plant. Neth J Agric Sci 10:361–376

    Google Scholar 

  • Bruning EF (1976) Tree forms in relation to environmental conditions. An ecological viewpoint. In: Cannell MGR, Last FT (eds) Tree physiology and yield improvement. Academic Press, New York, pp 139–156

    Google Scholar 

  • Cannell MGR, Dewar RC (1994) Carbon allocation in trees: a review of concepts for modelling. Adv Ecol Res 25:59–104

    Article  Google Scholar 

  • Cowan IR, Farquhar GD (1977) Stomatal function in relation to leaf metabolism and environment. In: Jennings DH (ed) Integration of activity in the higher plant. Cambridge University Press, Cambridge, pp 471–505

    Google Scholar 

  • Davidson RL (1969) Effect of root/leaf temperature differentials on root/shoot ratios in some pasture grasses and clover. Ann Bot 33:561–569

    Article  Google Scholar 

  • Dewar RC (1996) The correlation between plant growth and intercepted radiation: an interpretation in terms of optimal plant nitrogen content. Ann Bot 78:125–136

    Article  Google Scholar 

  • Dewar RC (2001) A model of the coupling between respiration, active processes and passive transport. Ann Bot 86:279–286

    Article  CAS  Google Scholar 

  • Dewar RC, Franklin O, Mäkelä A, McMurtrie RE, Valentine HT (2009) Optimal function explains forest response to global change. BioScience 59:127–139

    Article  Google Scholar 

  • Dewar R, Mauranen A, Mäkelä A, Hölttä T, Medlyn B, Vesala T (2018) New insights into the covariation of stomatal, mesophyll and hydraulic conductances from optimization models incorporating nonstomatal limitations to photosynthesis. New Phytol 217:571–585

    Article  CAS  PubMed  Google Scholar 

  • Duursma RA, Mäkelä A, Reid DEB, Jokela EJ, Porté A, Roberts SD (2010) Branching networks in gymnosperm trees: implications for metabolic scaling. Funct Ecol 24:723–730

    Article  Google Scholar 

  • Dybzinski R, Farrior C, Wolf A, Reich PB, Pacala SW (2011) Evolutionary stable strategy carbon allocation to foliage, wood, and fine roots in trees competing for light and nitrogen: an analytically tractable, individual-based model and quantitative comparisons to data. Am Nat 177:153–166

    Article  PubMed  Google Scholar 

  • Fontes L, Bontemps J, Bugmann H, van Oijen M, Gracia C, Kramer K, Lindner M, Rötzer T, Skovsgaard JP (2010) Models for supporting forest management in a changing environment. For Syst 19(Specia):8–29

    Google Scholar 

  • Ford ED (1992) The control of tree structure and productivity through the interaction of morphological development and physiological processes. Int J Plant Sci 153:S147–S162

    Article  Google Scholar 

  • Franklin O (2007) Optimal nitrogen allocation controls tree responses to elevated CO2. New Phytol 174:811–822

    Article  CAS  PubMed  Google Scholar 

  • Franklin O, Ågren GI (2002) Leaf senescence and resorption as mechanisms of maximizing photosynthetic production during canopy development at n limitation. Funct Ecol 16(6): 727–733

    Article  Google Scholar 

  • Franklin O, Johansson J, Dewar RC, Dieckmann U, McMurtrie RE, Brännström Å, Dybzinski R (2012) Modeling carbon allocation in trees: a search for principles. Tree Physiol 32(6):648–666

    Article  CAS  PubMed  Google Scholar 

  • Franklin O, Näsholm T, Högberg P, Högberg MN (2014) Forests trapped in nitrogen limitation: an ecological market perspective on ectomycorrhizal symbiosis. New Phytol 203:657–666

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Franklin O, Harrison SP, Dewar R, Farrior CE, Brännström Å, Dieckmann U, Pietsch S, Falster D, Cramer W, Loreau M, Wang H, Mäkelä A, Rebel KT, Meron E, Schymanski SJ, Rovenskaya E, Stocker BD, Zaehle S, Manzoni S, Van Oijen M, Wright IJ, Ciais P, van Bodegom PM, Peñuelas J, Hofhansl F, Terrer C, Soudzilovskaia NA, Midgley G, Prentice CI (2020) Organizing principles for vegetation dynamics. Manuscript accepted for publication in Nature Plants

    Google Scholar 

  • Geritz SAH, Kisdi É, Meszéna G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12:35–57

    Article  Google Scholar 

  • Gersani M, Brown JS, O’Brien EE, Maina GM, Abramsky Z (2001) Tragedy of the commons as a result of root competition. J Ecol 89:660–669

    Article  Google Scholar 

  • Gray HR (1956) The form and taper of forest-tree stems. Institute paper 32, Imperial Forestry Institute, University of Oxford

    Google Scholar 

  • Hari P, Kulmala Le (2008) Boreal forest and climate change. Advances in global change research, vol 34. Springer, Berlin

    Book  Google Scholar 

  • Hari P, Mäkelä A, Korpilahti E, Holmberg M (1986) Optimal control of gas exchange. Tree Physiol 2:169–175

    Article  PubMed  Google Scholar 

  • Hilbert DW (1990) Optimization of plant root:shoot ratios and internal nitrogen concentration. Ann Bot 66:91–99

    Article  CAS  Google Scholar 

  • Honda H, Fisher JB (1978) Tree branch angle: maximizing effective leaf area. Science 199: 888–890

    Article  CAS  PubMed  Google Scholar 

  • Horn HS (1971) The adaptive geometry of trees. Princeton University Press, Princeton

    Google Scholar 

  • Ilomäki S, Nikinmaa E, Mäkelä A (2003) Crown rise due to competition drives biomass allocation in silver birch (Betula pendula l.). Can J For Res 33:2395–2404

    Article  Google Scholar 

  • Ingestad T (1980) Growth, nutrition and nitrogen fixation in grey alder at varied rate of nitrogen addition. Physiol Plant 50:353–364

    Article  CAS  Google Scholar 

  • Ingestad T, Ågren GI (1992) Theories and methods on plant nutrition and growth. Physiol Plant 84:177–184

    Article  CAS  Google Scholar 

  • Ingestad T, Aronsson A, Ågren GI (1981) Nutrient flux density model of mineral nutrition in conifer ecosystems. Studia Forestalia Suecica 160:61–72

    Google Scholar 

  • Iwasa Y, Cohen D, León JA (1985) Tree height and crown shape, as results of competitive games. J Theor Biol 112:279–297

    Article  Google Scholar 

  • Johnson IR, Thornley JHM (1987) A model of shoot:root partitioning with optimal growth. Ann Bot 60:133–142

    Article  Google Scholar 

  • Kantola A, Mäkelä A (2006) Development of biomass proportions in Norway spruce (Picea abies [l.] Karst.). Trees 20:111–121

    Article  Google Scholar 

  • King DA (1990) The adaptive significance of tree height. Am Nat 135:809–828

    Article  Google Scholar 

  • King DA (1993) A model analysis of the influence of root and foliage allocation on forest production and competition between trees. Tree Physiol 12:119–135

    Article  CAS  PubMed  Google Scholar 

  • Landsberg JJ (1986) Physiological ecology of forest production. Academic Press, London

    Google Scholar 

  • Landsberg JJ, Waring RH (1997) A generalised model of forest productivity using simplified concepts of radiation use efficiency, carbon balance and partitioning. For Ecol Manage 95: 209–228

    Article  Google Scholar 

  • Le Roux X, Lacointe A, Escobar-Gutiérrez A, Le Dizès S (2001) Carbon-based models of individual tree growth: a critical appraisal. Ann For Sci 58(5):469–506

    Article  Google Scholar 

  • Lindh M (2016) Evolution of plants. A mathematical perspective. Umea University, Umea

    Google Scholar 

  • Lindh M, Zhang L, Falster D, Franklin O, Brännström Å (2014) Plant diversity and drought: the role of deep roots. Ecol Modell 290:85–93

    Article  Google Scholar 

  • Litton CJ, Raich JW, Ryan MG (2007) Carbon allocation in forest ecosystems. Glob Change Biol 13:2089–2109

    Article  Google Scholar 

  • Luenberger DG (1979) Introduction to dynamic systems. John Wiley & Sons, New York

    Google Scholar 

  • Mäkelä A (1985) Differential games in evolutionary theory: height growth strategies of trees. Theor Popul Biol 27:239–267

    Article  Google Scholar 

  • Mäkelä A (1986) Implications of the pipe model theory on dry matter partitioning and height growth in trees. J Theor Biol 123(1):103–120

    Article  Google Scholar 

  • Mäkelä A, Sievänen R (1987) Comparison of two shoot-root partitioning models with respect to substrate utilization and functional balance. Ann Bot 59:129–140

    Article  Google Scholar 

  • Mäkelä A, Sievänen R (1992) Height-growth strategies in opengrown trees. J Theor Biol 159: 443–467

    Article  Google Scholar 

  • Mäkelä A, Valentine HT (2001) The ratio of NPP to GPP: evidence of change over the course of stand development. Tree Physiol 21:1015–1030

    Article  PubMed  Google Scholar 

  • Mäkelä A, Vanninen P (1998) Impacts of size and competition on tree form and distribution of aboveground biomass in Scots pine. Can J For Res 28:216–227

    Article  Google Scholar 

  • Mäkelä A, Berninger F, Hari P (1996) Optimal control of gas exchange during drought: theoretical analysis. Ann Bot 77:461–467

    Article  Google Scholar 

  • Mäkelä A, Givnish TJ, Berninger F, Buckley TN, Farquhar GD, Hari P (2002) Challenges and opportunities of the optimality approach in plant ecology. Silva Fenn 36:605–614

    Article  Google Scholar 

  • Mäkelä A, Valentine HT, Helmisaari H (2008b) Optimal co-allocation of carbon and nitrogen in a forest stand at steady state. New Phytol 180:114–123

    Article  CAS  PubMed  Google Scholar 

  • Maynard-Smith J, Price GR (1973) The logic of animal conflict. Nature 246:15–18

    Article  Google Scholar 

  • Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • McMurtrie RE (1991) Relationship of forest productivity to nutrient and carbon supply: a modeling analysis. Tree Physiol 9:87–99

    Article  PubMed  Google Scholar 

  • McMurtrie R, Wolf L (1983) Above- and below-ground growth of forest stands: a carbon budget model. Ann Bot 52(4):437–448

    Article  Google Scholar 

  • McMurtrie RE, Norby RJ, Medlyn BE, Dewar RC, Pepper DA, Reich PB, Barton CVM (2008) Why is plant-growth response to elevated CO2 amplified when water is limiting, but reduced when nitrogen is limiting? a growth-optimization hypothesis. Funct Plant Biol 35:521–534

    Article  CAS  PubMed  Google Scholar 

  • Merganičová K, Merganič J, Lehtonen A, Vacchiano G, Zorana Ostrogović Sever M, Augustynczik A, Grote R, Kyselová I, Mäkelä A, Yousefpour R, Krejza J, Collalti A, Reyer C (2019) Forest carbon allocation modelling under climate change. Tree Physiol 11:11–12

    Google Scholar 

  • Newnham RM (1965) Stem form and the variation of taper with age and thinning regime. Forestry 38(2):218–224

    Article  Google Scholar 

  • Niklas KJ, Kerchner V (1984) Mechanical and photosynthetic constraints on the evolution of plant shape. Paleobiology 10(1):79–101

    Article  Google Scholar 

  • Oker-Blom P, Kellomäki S (1982) Theoretical computations on the role of crown shape in the absorption of light by forest trees. Math Biosci 59:291–311

    Article  Google Scholar 

  • Pigliucci M (2005) Evolution of phenotypic plasticity: where are we going now? Trends Ecol Evol 20:481–486

    Article  PubMed  Google Scholar 

  • Poorter H, Niklas KJ, Reich PB, Oleksyn J, Pooti P, Mommer L (2011) Biomass allocation to leaves, stems and roots: meta-analyses of interspecific variation and environmental control. New Phytol 193:30–50

    Article  CAS  PubMed  Google Scholar 

  • Pretzsch H, Grote R, Reineking B, Rötzer TH, Steifert ST (2008) Models for forest ecosystem management: a European perspective. Ann Bot 101:1065–1087

    Article  CAS  PubMed  Google Scholar 

  • Reynolds JF, Chen J (1996) Modelling whole-plant allocation in relation to carbon and nitrogen supply: coordination versus optimization: opinion. Plant Soil 185(1):65–74

    Article  CAS  Google Scholar 

  • Rose MR (1978) Cheating in evolutionary games. J Theor Biol 75:21–34

    Article  CAS  PubMed  Google Scholar 

  • Running SW, Coughlan JC (1988) A general model of forest ecosystem processes for regional applications I. Hydrological balance, canopy gas exchange and primary production processes. Ecol Modell 42:125–154

    Article  CAS  Google Scholar 

  • Running SW, Gower ST (1991) A general model of forest ecosystem processes for regional applications II. Dynamic carbon allocation and nitrogen budgets. Tree Physiol 9:147–160

    Article  CAS  PubMed  Google Scholar 

  • Ryan MG (1991) A simple method for estimating gross carbon budgets for vegetation in forest ecosystems. Tree Physiol 9:255–266

    Article  PubMed  Google Scholar 

  • Ryan MG (1995) Foliar maintenance respiration of subalpine and boreal trees and shrubs in relation to nitrogen content. Plant Cell Environ 18:765–772

    Article  CAS  Google Scholar 

  • Shinozaki K, Yoda K, Hozumi K, Kira T (1964a) A quantitative analysis of plant form – the pipe model theory. I. Basic analysis. Jap J Ecol 14:97–105

    Google Scholar 

  • Starr AW, Ho YC (1969) Nonzero-sum differential games. J Optim Theory Appl 3:184–206

    Article  Google Scholar 

  • Sterck FJ, Schieving F (2007) 3-D growth patterns of trees: effects of carbon economy, meristem activity, and selection. Ecol Monogr 77:405–420

    Article  Google Scholar 

  • Strigul N, Pristinski D, Purves D, Dushoff J, Pacala S (2008) Scaling from trees to forests: tractable macroscopic equations for forest dynamics. Ecol Monogr 78:523–545

    Article  Google Scholar 

  • Valentine HT (1985) Tree-growth models: derivations employing the pipe-model theory. J Theor Biol 117(4):579–585

    Article  Google Scholar 

  • Valentine HT (1997) Height growth, site index, and carbon metabolism. Silva Fenn 31(3):251–263

    Article  Google Scholar 

  • Valentine HT, Mäkelä A (2005) Bridging process-based and empirical approaches to modeling tree growth. Tree Physiol 25:769–779

    Article  PubMed  Google Scholar 

  • Valentine HT, Mäkelä A (2012) Modeling forest stand dynamics from optimal balances of carbon and nitrogen. New Phytol 194:961–971

    Article  CAS  PubMed  Google Scholar 

  • Valentine HT, Green EJ, Mäkelä A, Amateis RL, Mäkinen H, Ducey MJ (2012) Models relating stem growth to crown length dynamics: application to loblolly pine and Norway spruce. Trees 26:469–478

    Article  Google Scholar 

  • Valentine HT, Ludlow AR, Furnival GM (1994b) Modeling crown rise in even-aged stands of Sitka spruce or loblolly pine. For Ecol Manage 69:189–197

    Article  Google Scholar 

  • Waring RH, Schlesinger WH (1985) Forest ecosystems. Concepts and management. Academic Press, Orlando

    Google Scholar 

  • White HL (1935) The interaction of factors in the growth of Lemna. XII. The interaction of nitrogen and light intensity in relation to root length. Ann Bot 1:649–654

    Article  Google Scholar 

  • Zeide B (1998) Fractal analysis of foliage distribution in loblolly pine crowns. Can J For Res 28:106–114

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

7.1 Electronic supplementary material

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mäkelä, A., Valentine, H.T. (2020). Tree Structure Revisited: Eco-Evolutionary Models. In: Models of Tree and Stand Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-35761-0_7

Download citation

Publish with us

Policies and ethics