Abstract
As with all living things, annual plants have different ways of adapting to the environment. Adaptation may occur via: (1) physiological versatility, (2) developmental flexibility and (3) genetic evolution. Adaptation (1) is associated with a rapid response to short term changes in the environment, such as the opening or closing of the stomata in the leaves of plants with a change in the ambient temperature or humidity. Adaptation (2) is associated with response due to a more long term conditioning by the environment, such as limited flowering of a plant due to a dry season. Adaptation (3) is the genetic adaptation in response to particular semi-permanent conditions in the environment. If these conditions should change, then it may take several seasons to produce a new genetic adaptation.
Adaptations (2) and (3) are examined here in the context of two different habitats, that of growth under limited nutrient and growth under limited sunlight. The viewpoint is taken that survival is a direct consequence of maximizing seed production.
In the limited nutrient habitat, it is assumed that a nutrient conversion efficiency represents a control parameter subject to genetic selection. In the limited sunlight habitat, it is assumed that the percent allocation of total growth into seeds is a control variable subject to developmental flexibility. In each case, controls which result in maximum seed production are determined. Results are compared between a monoculture and a mixture of two different species.
Preview
Unable to display preview. Download preview PDF.
References
Cohen, D., "Maximizing Final Yield when Growth is Limited by Time or by Limiting Resources", J. Theor. Biol. 33, 299–307, 1971.
Cohen, D., Communication to the author June 1976.
DeAngelis, D.L., Goldstein, R.A., O'Neill, R.V., "A Model for Trophic Interaction", Ecology, Vol. 56, No. 4, pp 881–892, 1975.
Leitmann, G., An Introduction to Optimal Control, McGraw-Hill, New York, 1966.
Leitman, G., Cooperative and Non-cooperative Many Players Differential Games, Springer-Verlag, New York, 1974.
May, R.M., Stability and Complexity in Model Ecosystems, Princeton, New Jersey, 1974.
Nash, J., "Non-Cooperative Games", Annals of Mathematics, Vol. 54, No. 2, 1951.
Pianka, E.R., Evolutionary Ecology, Harper and Row, New York, 1974.
Pimentel, D., "Population Regulation and Genetic Feedback", Science, 159, 1432–7, 1968.
Smith, J.M., The Theory of Evolution, Penguin, Middlesex, 1975.
Trenbath, B.R., "Biomass Productivity of Mixtures", Advances in Agronomy Vol. 26, pp. 177–210, 1974.
Trenbath, B.R., Communication to the author, Dec. 1976.
Vincent, T.L. and Mason, J.D., "Disconnected optimal Trajectories", Journal of Optimization Theory and Applications, Vol. 3, No. 4, pp 263–281, 1969.
Vincent, T.L. and Pulliam, R.H., "A Controls Approach to Two Problems in Theoretical Biology", to be submitted for publication, 1977.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1977 Springer-Verlag
About this paper
Cite this paper
Vincent, T.L. (1977). Environmental adaptation by annual plants (an optimal control/games viewpoint). In: Hagedorn, P., Knobloch, H.W., Olsder, G.J. (eds) Differential Games and Applications. Lecture Notes in Control and Information Sciences, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009073
Download citation
DOI: https://doi.org/10.1007/BFb0009073
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08407-5
Online ISBN: 978-3-540-37179-3
eBook Packages: Springer Book Archive