Abstract
Plants only interact with neighbors over restricted distances, so local conditions are of great significance for plants. It is therefore important to consider spatial structure and neighborhood effects if we are to understand plants' strategies. We constructed a spatially-explicit, game theory model to explore optimal height growth at the individual-level. In the model, there is no ESS for height growth at the population level, because there is an “instantaneous” optimal height growth strategy for the individual plant that changes depending on the local light environment. The optimal strategy is plasticity in response to local conditions. Game-theoretic models for plant phenotypic traits should move from “mean-field approximations” towards explicit modeling of local interactions.
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References
Ballaré, C.L., Scopel, A.L., Sa´nchez, R.A., 1990. Far-red radiation reflected from adjacent leaves: an early signal of competition in plant canopies. Science 247, 329–332.
Berntson, G.M., Wayne, P.M., 2000. Characterizing the size dependence of resource acquisition within crowded plant populations. Ecology 81, 1072–1085.
Cannell, M.G.R., Rothery, P., Ford, E.D., 1984. Competition within stands of Picea sitchensis and Pinus contorta. Ann. Bot. 53, 349–362.
Crawley, M.J., May, R.M., 1987. Population dynamics and plant community structure: competition between annuals and perennials. J. Theor. Biol. 125, 475–489.
Eriksson, O., 1986. Mobility and space capture in the stoloniferous plant Potentilla anserina. Oikos 46, 82–87.
Gates, D.J., 1978. Bimodality in even-aged plant monocultures. J. Theor. Biol. 71, 525–540.
Geber, M.A., 1989. Interplay of morphology and development on size inequality: a Polygonum greenhouse study. Ecol. Monogr. 59, 267–288.
Falster, D.S., Westoby, M., 2003. Plant height and evolutionary games. Trends. Ecol. Evol. 18, 337–343.
Givnish, T.J., 1982. Adaptive significance of leaf height in forest herbs. Am. Nat. 120, 353–381.
Hauert, C., 2002. Effects of space in 2× 2 games. Int. J. Bifurcat. Chaos. 12, 1531–1548.
Hutchings, M.J., 1986. The structure of plant populations. In: Crawley, M.J. (Ed.), Plant Ecology. Blackwell Scientific, Oxford, pp. 97–136.
Hutchings, M.J., Kroon, H., 1994. Foraging in plants: the role of morphological plasticity in resource acquisition. In: Begon, M., and Fitter, A.H. (Eds.), Advances in Ecological Research, vol. 25. Academic Press, London, pp. 159–238.
Iwasa, Y., and Leon, J.A., 1985. Tree height and crown shape, as results of competitive games. J. Theor. Biol. 112, 279–298.
King, D.A., 1990. The adaptive significance of tree height. Am. Nat. 135, 809–828.
Lindgren, K., Nordahl, M.G., 1994. Evolutionary dynamics of spatial games. Physica D 75, 292–309.
Makela, A., 1985. Differential games in evolutionary theory: height growth strategies of trees. Theor. Popul. Biol. 27, 239–267.
Nagashima, H., Terashima, I., Katoh, K., 1995a. Effects of plant density on frequency distributions of plant height in Chenopodium album stands: analysis based on continuous monitoring of height-growth of individual plants. Ann. Bot. 75, 173–180.
Nagashima, H., Terashima, I., 1995b. Relationships between height, diameter and weight distributions of Chenopodium album plants in stands: effects of dimension and allometry. Ann. Bot. 75, 181–188.
Nagashima, H., 1999. The processes of height-rank determination among individuals and neighborhood effects in Chenopodium album L stands. Ann. Bot. 83, 501–507.
Novoplansky, A., Cohen, D., Sachs, T., 1990. How Portulaca seedlings avoid their neighbors. Oecologia 82, 490–493.
Nowak, M.A., May, R.M., 1992. Evolutionary games and spatial chaos. Nature 359, 826–829.
Nowak, M.A., May, R.M., 1993. The spatial dilemmas of evolution. Int. J. Bifurcat. Chaos. 3, 35–78.
Nowak, M.A., Sigmund, K., 2000. Games on grids. In: Dieckmann, U., Law, R., Metz, J.A.J. (Eds.), The Geometry of Ecological Interactions: simplifying Spatial Complexity, Cambridge University Press, Cambridge, pp. 135–150.
Nowak, M.A., Sigmund, K., 2004. Evolutionary dynamics of biological games. Science 303, 793–799.
Schmitt, J., 1993. Reaction norms of morphological and life-history traits to light availability in Impatiens capensis. Evolution 47, 1654–1668.
Schwinning, S., Weiner, J., 1998. Mechanisms determining the degree of size asymmetry in competition among plants. Oecologia 113, 447–455.
Silvertown, J., Charlesworth, D., 2001. Introduction to Plant Population Biology. 4th edition. Blackwell Science, Oxford.
Stoll, P., Weiner, J., 2000. A neighborhood view of interactions among individual plants. In: Dieckmann, U., Law, R., Metz, J.A.J. (Eds.), The Geometry of Ecological Interactions: simplifying spatial Complexity. Cambridge University Press, Cambridge, pp. 11–27.
Weiner, J., 1984. Neighborhood interference amongst Pinus rigida individuals. J. Ecol. 72, 183–195.
Weiner, J., Thomas, S.C., 1986. Size variability and competition in plant monocultures. Oikos 47, 211–222.
Weiner, J., Berntson, G.M., Thomas, S.C., 1990. Competition and growth form in a woodland annual. J. Ecol. 78, 459–469.
Weiner, J., Thomas, S.C., 1992. Competition and allometry in three species of annual plants. Ecology 73, 648–656.
Weiner, J., Fishman, L., 1994. Competition and allometry in Kochia scoparia. Ann. Bot. 73, 263–271.
Whitelam, G.C., McCormac, A.C., Boylan, M.T. and Quail, P.H. 1992. Photoresponses of Arabidopsis seedlings expressing an introduced oat phyA cDNA: persistence of etiolated plant type responses in light-grown plants. Photochem. Photobiol. 56, 617–621.
Yokozawa, M., Hara, T., 1995. Foliage profile, size structure and stem diameter-plant height relationship in crowded plant populations. Ann. Bot. 76, 271–285.
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Xiao, S., Chen, SY. & Wang, G. An ESS for the Height of a Plant Population, or an Optimal Height for an Individual?—Rethinking Game-Theoretic Models for Plant Height. Bull. Math. Biol. 68, 957–967 (2006). https://doi.org/10.1007/s11538-006-9073-0
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DOI: https://doi.org/10.1007/s11538-006-9073-0