Journal of Applied Phycology

, Volume 2, Issue 3, pp 249–257 | Cite as

Macrocystis pyrifera in New Zealand: testing two mathematical models for whole plant growth

  • Melvin A. Nyman
  • Murray T. Brown
  • Michael Neushul
  • Jonathan A. Keogh


A Leslie-Lewis matrix projection model and a Markov chain model for whole plant growth in the giant Kelp,Macrocystis pyrifera, are developed and compared. Parameters of the models are estimated from field data gathered from several plants in New Zealand over a four-month period. Interpretations of the results are discussed.

Key words

Macrocystis discrete models kelp whole plant projection matrix New Zealand 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson N (1974) A mathematical model for the growth of giant kelp. Simulation (April): 97–106.Google Scholar
  2. Bosch CA (1971) Redwoods: A population model. Science 172: 345–349.Google Scholar
  3. Clendenning KA (1964) Photosynthesis and growth inMacrocystis pyrifera. Proc. 4th International Seaweed Symposium: 55–65.Google Scholar
  4. Coon D (1981) Studies of whole plant growth inMacrocystis angustifolia. Bot. mar. 24: 19–27.Google Scholar
  5. Enright N, Ogden J. (1979) Applications of transition matrix models in forest dynamics:Araucaria in Papua New Guinea andNothofagus in New Zealand. Australian J. Ecol. 4: 3–23.Google Scholar
  6. Gerard VA, Kirkman H (1984) Ecological observations on a branched, loose-lying form ofMacrocystis pyrifera (L. ) C. Agardh in New Zealand. Bot. mar. 27: 105–109.Google Scholar
  7. Jackson GA (1987) Modeling the growth and harvest yield of the giant kelpMacrocystis pyrifera. Mar. Biol. 95: 611–624.Google Scholar
  8. Kain (Jones) JM (1982) Morphology and growth of the giant kelpMacrocystis pyrifera in New Zealand and California. Mar. Biol. 67: 143–157.Google Scholar
  9. Lefkovitch LP (1965) The study of population growth in organisms grouped by stages. Biometrics 21: 1–18.Google Scholar
  10. Leslie PH (1945) On the use of matrices in certain population mathematics. Biometrica 33: 183–212.Google Scholar
  11. Leslie PH (1948) Some further notes on the use of matrices in population mathematics. Biometrica 35: 213–245.Google Scholar
  12. Lewis EG (1942). On the generation and growth of a population. Sankya 6: 93–96.Google Scholar
  13. Lobban CS (1978a) Translocation of14C inMacrocystis pyrifera (Giant Kelp). Pl. Physiol. 61: 583–589.Google Scholar
  14. Moore LB (1943) Observations on the growth ofMacrocystis in New Zealand. Trans. r. Soc. N. Z. 72: 333–340.Google Scholar
  15. North WJ (1971) Growth of the mature giant kelp. In North W (ed.). The Biology of Giant Kelp Beds (Macrocystis) in California. Nova Hedwigia 32: 123–168.Google Scholar
  16. North WJ (1961) Life-span of the fronds of the giant kelp,Macrocystis pyrifera. Nature 190: 1214–1215.Google Scholar
  17. Pennycuick CJ, Compton RM, Beckingham L (1968). A computer model for simulating the growth of a population, or of two interacting populations. J. theor. Biol. 18: 316–329.Google Scholar
  18. Roberts FS (1976) Discrete mathematical models with applications to Social, Biological, and Environmental Problems. Prentice-Hall, Englewood Cliffs.Google Scholar
  19. Skellam JG (1966). Seasonal periodicity in theoretical population ecology. Proc Fifth Berkeley Symposium on Mathematics, Statistics and Probability 4: 179–205.Google Scholar
  20. Skellam JG (1972). Some philosophical aspects of mathematical modeling in empirical science with special reference to ecology. Symposium Br. ecol. Soc. 2: 13–28.Google Scholar
  21. Strang G (1988) Linear Algebra and its Applications (3rd edn.). Harcourt, Brace, Jovanovich. San Diego.Google Scholar
  22. Usher MB (1966) A matrix approach to the management of renewable resources, with special reference to selection forests. J. appl. Ecol. 3: 355–367.Google Scholar
  23. Usher MB (1969) A matrix model for forest management. Biometrics 25: 309–315.Google Scholar
  24. Usher MB (1972) Developments in the Leslie Matrix Model. In: Jeffers JNR (ed.), Mathematical Models in Ecology: Twelfth Symp. British Ecological Society. Blackwell, Oxford, 29–60.Google Scholar
  25. Usher MB (1976) Extensions to models used in renewable resource management, which incorporate an arbitrary structure. J. environ. Management. 4: 123–140.Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Melvin A. Nyman
    • 1
  • Murray T. Brown
    • 2
  • Michael Neushul
    • 3
  • Jonathan A. Keogh
    • 4
  1. 1.Department of Mathematics & Computer ScienceAlma CollegeAlmaUSA
  2. 2.Department of BotanyUniversity of Otago DunedinNew Zealand
  3. 3.Department of Biological SciencesUniversity of California — Santa BarbaraSanta BarbaraUSA
  4. 4.Department of BotanyUniversity of OtagoDunedinNew Zealand

Personalised recommendations