Tree height and crown shape, as results of competitive games

Yoh Iwasa, Dan Cohen, Jesus Alberto Leon

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

Games between trees are studied to explain the height and the crown shape in a community. It is assumed that each tree maximizes the net productivity under the light environment, which is determined by surrounding trees. In both models, the asymmetry of competition is important, because higher leaves shade lower leaves but the lower don't shade the higher. In the tree-height game, each tree is assumed to choose a height given its crown shape. The height at a monomorphic equilibrium, in which all the trees of a community have the same height, increases with the tree density and the amount of leaves per tree, but decreases with the cost coefficient and the crown thickness. When the crown is thin enough, a polymorphic equilibrium appears, in which a community includes trees of different heights but with the same fitness. In the crown-shape game, each tree is assumed to choose the distribution of foliage along the height axis. A lone tree should have a hemispherical crown as the optimum. The monomorphic equilibrium in which all the trees in a community have the same crown shape is calculated. As the tree density increases, the average height of a crown of each tree increases and the height on the tree with the maximum foliage increases, but each tree should have some foliage all the way down to the ground. Several reasons for foliage cutoff at the lowest layer are discussed.

Original languageEnglish
Pages (from-to)279-297
Number of pages19
JournalJournal of Theoretical Biology
Volume112
Issue number2
DOIs
Publication statusPublished - Jan 21 1985
Externally publishedYes

Fingerprint

Crowns
tree crown
Game
leaves
Productivity
Leaves
shade
Costs
Choose
Fitness
Asymmetry
Lowest

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Tree height and crown shape, as results of competitive games. / Iwasa, Yoh; Cohen, Dan; Leon, Jesus Alberto.

In: Journal of Theoretical Biology, Vol. 112, No. 2, 21.01.1985, p. 279-297.

Research output: Contribution to journalArticle

Iwasa, Yoh ; Cohen, Dan ; Leon, Jesus Alberto. / Tree height and crown shape, as results of competitive games. In: Journal of Theoretical Biology. 1985 ; Vol. 112, No. 2. pp. 279-297.
@article{677419a63ea347fbb72b4fa313f1cd7c,
title = "Tree height and crown shape, as results of competitive games",
abstract = "Games between trees are studied to explain the height and the crown shape in a community. It is assumed that each tree maximizes the net productivity under the light environment, which is determined by surrounding trees. In both models, the asymmetry of competition is important, because higher leaves shade lower leaves but the lower don't shade the higher. In the tree-height game, each tree is assumed to choose a height given its crown shape. The height at a monomorphic equilibrium, in which all the trees of a community have the same height, increases with the tree density and the amount of leaves per tree, but decreases with the cost coefficient and the crown thickness. When the crown is thin enough, a polymorphic equilibrium appears, in which a community includes trees of different heights but with the same fitness. In the crown-shape game, each tree is assumed to choose the distribution of foliage along the height axis. A lone tree should have a hemispherical crown as the optimum. The monomorphic equilibrium in which all the trees in a community have the same crown shape is calculated. As the tree density increases, the average height of a crown of each tree increases and the height on the tree with the maximum foliage increases, but each tree should have some foliage all the way down to the ground. Several reasons for foliage cutoff at the lowest layer are discussed.",
author = "Yoh Iwasa and Dan Cohen and Leon, {Jesus Alberto}",
year = "1985",
month = "1",
day = "21",
doi = "10.1016/S0022-5193(85)80288-5",
language = "English",
volume = "112",
pages = "279--297",
journal = "Journal of Theoretical Biology",
issn = "0022-5193",
publisher = "Academic Press Inc.",
number = "2",

}

TY - JOUR

T1 - Tree height and crown shape, as results of competitive games

AU - Iwasa, Yoh

AU - Cohen, Dan

AU - Leon, Jesus Alberto

PY - 1985/1/21

Y1 - 1985/1/21

N2 - Games between trees are studied to explain the height and the crown shape in a community. It is assumed that each tree maximizes the net productivity under the light environment, which is determined by surrounding trees. In both models, the asymmetry of competition is important, because higher leaves shade lower leaves but the lower don't shade the higher. In the tree-height game, each tree is assumed to choose a height given its crown shape. The height at a monomorphic equilibrium, in which all the trees of a community have the same height, increases with the tree density and the amount of leaves per tree, but decreases with the cost coefficient and the crown thickness. When the crown is thin enough, a polymorphic equilibrium appears, in which a community includes trees of different heights but with the same fitness. In the crown-shape game, each tree is assumed to choose the distribution of foliage along the height axis. A lone tree should have a hemispherical crown as the optimum. The monomorphic equilibrium in which all the trees in a community have the same crown shape is calculated. As the tree density increases, the average height of a crown of each tree increases and the height on the tree with the maximum foliage increases, but each tree should have some foliage all the way down to the ground. Several reasons for foliage cutoff at the lowest layer are discussed.

AB - Games between trees are studied to explain the height and the crown shape in a community. It is assumed that each tree maximizes the net productivity under the light environment, which is determined by surrounding trees. In both models, the asymmetry of competition is important, because higher leaves shade lower leaves but the lower don't shade the higher. In the tree-height game, each tree is assumed to choose a height given its crown shape. The height at a monomorphic equilibrium, in which all the trees of a community have the same height, increases with the tree density and the amount of leaves per tree, but decreases with the cost coefficient and the crown thickness. When the crown is thin enough, a polymorphic equilibrium appears, in which a community includes trees of different heights but with the same fitness. In the crown-shape game, each tree is assumed to choose the distribution of foliage along the height axis. A lone tree should have a hemispherical crown as the optimum. The monomorphic equilibrium in which all the trees in a community have the same crown shape is calculated. As the tree density increases, the average height of a crown of each tree increases and the height on the tree with the maximum foliage increases, but each tree should have some foliage all the way down to the ground. Several reasons for foliage cutoff at the lowest layer are discussed.

UR - http://www.scopus.com/inward/record.url?scp=0000526654&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000526654&partnerID=8YFLogxK

U2 - 10.1016/S0022-5193(85)80288-5

DO - 10.1016/S0022-5193(85)80288-5

M3 - Article

VL - 112

SP - 279

EP - 297

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 2

ER -