Calculate MichaelisMenten fit to rarefaction curve of observed OTUs.
The MichaelisMenten 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:  counts : 1D array_like, int
num_repeats : int, optional
params_guess : tuple, optional


Returns:  S_max : double

See also
Notes
There is some controversy about how to do the fitting. The ML model given in [R51] 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 leastsquares.
References
[R51]  (1, 2) Raaijmakers, J. G. W. 1987 Statistical analysis of the MichaelisMenten equation. Biometrics 43, 793803. 