Journal ArticleDOI
Fitting Nonlinear Models to Biological Data by Marquardt's Algorithm
Reads0
Chats0
TLDR
In this article, a step-by-step derivation of the Marquardt's algorithm is given in terms that require only a knowledge of elementary calculus and matrix algebra, and the method is used to fit the logistic equation to a set of data.Abstract:
Equations describing biological phenomena frequently have parameters entering nonlinearly. A highly efficient method for determining the values of parameters in such equations that will give the best least—squares fit to a set of data is Marquardt's algorithm. A step—by—step derivation of the algorithm is given in terms that require only a knowledge of elementary calculus and matrix algebra. As an example, the method is used to fit the logistic equation to a set of data. See full-text article at JSTORread more
Citations
More filters
Journal ArticleDOI
Mathematical formulation of the relationship between photosynthesis and light for phytoplankton
Alan D. Jassby,Trevor Platt +1 more
TL;DR: Eight different mathematical formulations of the photosynthesis—light curve for phytoplankton were recast in terms of the same two parameters: the initial slope α, and the assimilation number PmB.
Book ChapterDOI
11 – Growth Rates and Models
TL;DR: Length varies with the condition of the fish—for example, whether it is alive, recently killed, after rigor mortis has set in, or at different intervals of time after preservation in formalin or alcohol.
Journal ArticleDOI
A hierarchical set of models for species response analysis
TL;DR: A combination of simple, descriptive models like those pre- sented in this paper and causal models as developed by several others are advocated as a powerful tool towards a fuller under- standing of the dynamics and patterns of vegetational change.
Book
The Population Dynamics of Infectious Diseases: Theory and Applications
TL;DR: This poster discusses the population dynamics and control of hookworm and roundworm infections, as well as the dynamics of bacterial infections, which are related to malaria.
Journal ArticleDOI
An algorithm for temperature-dependent growth rate simulation.
TL;DR: A comparison of various functions which have been used for developmental time estimation and an algorithm for a sigmoid function which can be used in simulations having either a calendar or a physiological time base is presented.
References
More filters
Journal ArticleDOI
Calculation and Miscalculation of the Allometric Equation as a Model in Biological Data
TL;DR: There are several nonlinear regression models in use in biology; what follows is a discussion of one such model, emphasizing the caution which must be exercised in fitting the model by the common approximate method.
Journal ArticleDOI
A Review of Minimization Techniques for Nonlinear Functions
TL;DR: In this article, a review of the existing literature on minimization techniques is presented, focusing on those methods which are primarily useful when a mathematical expression for the function can be obtained, and the practical difficulties associated with the experimental and online use of these methods will not be investigated.
Journal ArticleDOI
Discussion of Calculation of Power Function with Special Reference to Respiratory Metabolism in Fish
TL;DR: If accuracy in predicting oxygen consumption over a wide range of values of body weight is desired, an iterative curve fitting method may be superior to the much used technique of performing a linear regression on logarithmically transformed data.
Related Papers (5)
Feeding, growth, and survival of Engraulis mordax larvae reared in the laboratory
Mathematical formulation of the relationship between photosynthesis and light for phytoplankton
Alan D. Jassby,Trevor Platt +1 more