skbio.diversity.alpha.
michaelis_menten_fit
(counts, num_repeats=1, params_guess=None)[source]¶Calculate Michaelis-Menten fit to rarefaction curve of observed OTUs.
State: Experimental as of 0.4.0.
The Michaelis-Menten equation is defined as:
where \(n\) is the number of individuals and \(S\) is the number of OTUs. This function estimates the \(S_{max}\) parameter.
The fit is made to datapoints for \(n=1,2,...,N\), where \(N\) is the total number of individuals (sum of abundances for all OTUs). \(S\) is the number of OTUs represented in a random sample of \(n\) individuals.
Parameters: |
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Returns: | S_max – Estimate of the \(S_{max}\) parameter in the Michaelis-Menten equation. |
Return type: | double |
See also
Notes
There is some controversy about how to do the fitting. The ML model given in [1] is based on the assumption that error is roughly proportional to magnitude of observation, reasonable for enzyme kinetics but not reasonable for rarefaction data. Here we just do a nonlinear curve fit for the parameters using least-squares.
References
[1] | Raaijmakers, J. G. W. 1987 Statistical analysis of the Michaelis-Menten equation. Biometrics 43, 793-803. |