def michaelis_menten_fit(counts,
num_repeats=1,
params_guess=None,
return_b=False):
"""Michaelis-Menten fit to rarefaction curve of observed species
Note: there is some controversy about how to do the fitting. The ML model
givem by Raaijmakers 1987 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.
S = Smax*n/(B + n) . n: number of individuals, S: # of species
returns Smax
inputs:
num_repeats: will perform rarefaction (subsampling without replacement)
this many times at each value of n
params_guess: intial guess of Smax, B (None => default)
return_b: if True will return the estimate for Smax, B. Default is just Smax
the fit is made to datapoints where n = 1,2,...counts.sum(),
S = species represented in random sample of n individuals
"""
counts = asarray(counts)
if params_guess is None:
params_guess = array([100, 500])
# observed # of species vs # of individuals sampled, S vs n
xvals = arange(1, counts.sum() + 1)
ymtx = []
for i in range(num_repeats):
ymtx.append(
array([
observed_species(rarefaction.subsample(counts, n))
for n in xvals
]))
ymtx = asarray(ymtx)
yvals = ymtx.mean(0)
# fit to obs_sp = max_sp * num_idiv / (num_indiv + B)
# return max_sp
def fitfn(p, n): # works with vectors of n, returns vector of S
return p[0] * n / (p[1] + n)
def errfn(p, n, y): # vectors of actual vals y and number of individuals n
return ((fitfn(p, n) - y)**2).sum()
p1 = fmin_powell(errfn, params_guess, args=(xvals, yvals), disp=0)
if return_b:
return p1
else:
return p1[0] # return only S_max, not the K_m (B) param
def michaelis_menten_fit(counts, num_repeats=1, params_guess=None,
return_b=False):
"""Michaelis-Menten fit to rarefaction curve of observed species
Note: there is some controversy about how to do the fitting. The ML model
givem by Raaijmakers 1987 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.
S = Smax*n/(B + n) . n: number of individuals, S: # of species
returns Smax
inputs:
num_repeats: will perform rarefaction (subsampling without replacement)
this many times at each value of n
params_guess: intial guess of Smax, B (None => default)
return_b: if True will return the estimate for Smax, B. Default is just Smax
the fit is made to datapoints where n = 1,2,...counts.sum(),
S = species represented in random sample of n individuals
"""
counts = asarray(counts)
if params_guess is None:
params_guess = array([100,500])
# observed # of species vs # of individuals sampled, S vs n
xvals = arange(1,counts.sum()+1)
ymtx = []
for i in range(num_repeats):
ymtx.append( array([observed_species(rarefaction.subsample(counts,n)) \
for n in xvals]))
ymtx = asarray(ymtx)
yvals = ymtx.mean(0)
# fit to obs_sp = max_sp * num_idiv / (num_indiv + B)
# return max_sp
def fitfn(p,n): # works with vectors of n, returns vector of S
return p[0]*n/(p[1] + n)
def errfn(p,n,y): # vectors of actual vals y and number of individuals n
return ((fitfn(p,n) - y)**2).sum()
p1 = fmin_powell(errfn, params_guess, args=(xvals,yvals), disp=0)
if return_b:
return p1
else:
return p1[0] # return only S_max, not the K_m (B) param
def _minimise(self, f, x, **kw):
result = fmin_powell(f, x, linesearch=bound_brent, **kw)
# same length full-results tuple as simplex:
(xopt, fval, directions, iterations, func_calls, warnflag) = result
return (xopt, fval, iterations, func_calls, warnflag)
def _minimise(self, f, x, **kw):
result = fmin_powell(f, x, linesearch=bound_brent, **kw)
# same length full-results tuple as simplex:
(xopt, fval, directions, iterations, func_calls, warnflag) = result
return (xopt, fval, iterations, func_calls, warnflag)
