Marine Biology

, Volume 95, Issue 2, pp 209–215 | Cite as

Evaluation of variance approximation techniques for non-linear photosynthesis—irradiance models

  • R. C. Zimmerman
  • J. Beeler SooHoo
  • J. N. Kremer
  • D. Z. D'Argenio


Parameters derived from photosynthesis-irradiance (P-I) models, although often empirical in nature, are useful indicators of the photoadaptive state of phytoplankton in culture and in situ. However objective criteria for determining significant changes in P-I curves are rarely provided, because confidence intervals for parameters of non-linear models are not estimated easily. Examination of least-squares residuals in parameter space and Monte Carlo approaches have been used to estimate confidence regions around parameter values, but the computationally intensive nature of these methods has prevented their routine application. We present an alternative method of estimating confidence intervals for parameters of P-I curves that runs quickly on a microcomputer and is easily combined with common parameter-estimation routines. This algorithm was tested using a 3-parameter P-I model and curves describing a wide range of photoadaptive states, with different numbers of observations and different amounts of inherent variability. The method produced results comparable to the Monte Carlo technique. This analysis makes it possible to specify the sample size required to define parameters with acceptable confidence as a function of data variance and photoadaptive state. In most reasonable situations, 25 observations are sufficient.


Phytoplankton Photosynthesis Variance Approximation Approximation Technique Data Variance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • R. C. Zimmerman
    • 1
  • J. Beeler SooHoo
    • 1
  • J. N. Kremer
    • 2
  • D. Z. D'Argenio
    • 3
  1. 1.Allan Hancock FoundationUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Biological SciencesUniversity of Southern CaliforniaLos AngelesUSA
  3. 3.Department of Biomedical Engineering, School of EngineeringUniversity of Southern CaliforniaLos AngelesUSA

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