def lik_sp_abd_dbh_agsne(stat_var, pars, n, dbh_list, log = True):
"""Probability of a species having abundance n and its individuals having dbh [d1, d2, ..., d_n] in AGSNE.
Inputs:
stat_var - [G, S, N, E]
pars - [lambda1, beta, lambda3, z] in AGSNE
n - abundance of the species
dbh_list - a list or array of length n with scaled dbh values
"""
G, S, N, E = stat_var
lambda1, beta, lambda3, z = pars
sad = mete_distributions.sad_agsne(stat_var, pars)
#logp = 0
#for d in dbh_list:
#t = np.exp(-(lambda1 + (beta - lambda1) * n + lambda3 * n * d ** 2))
#logp_dn = np.log(G / S / z * 2 * d) + np.log(t) - 2 * np.log(1 - t) + np.log(1 - (S + 1) * t ** S + S * t ** (S + 1))
#logp += logp_dn - np.log(sad.pmf(n))
#logp += np.log(sad.pmf(n)) # Convert conditional distribution to joint distribution
logsum = 0
for d in dbh_list:
logt = -(lambda1 + (beta - lambda3) * n + lambda3 * n * (d ** 2))
t = np.exp(logt)
logsum += logt - 2 * np.log(1 - t) + np.log(1 - (S + 1) * (t ** S) + S * (t ** (S + 1))) + np.log(2 * d)
logp = logsum + n * np.log(G / S / z) - (n - 1) * sad.logpmf(n)
if log == True: return logp
else: return np.exp(logp)
def get_mete_agsne_rad(G, S, N, E, version='precise', pars=None):
"""Compute RAD predicted by the AGSNE.
Arguments:
G, S, N, E - state variables (number of genera, number of species, number of individuals, total metabolic rate)
Keyword arguments:
version - which version is used to calculate the state variables, can take 'precise' or 'approx'
pars - a list of Langrage multipliers [lambda1, beta, lambda3, Z], if these are already available.
If None, Langrage multipliers are calculated from get_agsne_lambdas().
Return a list of expected abundances with length S, ranked from high to low.
"""
if pars is None:
lambda1, beta, lambda3 = get_agsne_lambdas(G, S, N, E, version=version)
lambda3z = agsne_lambda3_z(lambda1, beta, S)
pars = [lambda1, beta, lambda3, lambda3z / lambda3]
sad = medis.sad_agsne([G, S, N, E], pars)
rank = range(1, int(S) + 1)
abundance = list(np.empty([S]))
cdf_obs = [(rank[i] - 0.5) / S for i in range(0, int(S))]
i, j = 1, 0
cdf_cum = 0
while i <= N + 1:
cdf_cum += sad.pmf(i)
while cdf_cum >= cdf_obs[j]:
abundance[j] = i
j += 1
if j == S:
abundance.reverse()
return abundance
i += 1
def lik_sp_abd_dbh_agsne(stat_var, pars, n, dbh_list, log=True):
"""Probability of a species having abundance n and its individuals having dbh [d1, d2, ..., d_n] in AGSNE.
Inputs:
stat_var - [G, S, N, E]
pars - [lambda1, beta, lambda3, z] in AGSNE
n - abundance of the species
dbh_list - a list or array of length n with scaled dbh values
"""
G, S, N, E = stat_var
lambda1, beta, lambda3, z = pars
sad = mete_distributions.sad_agsne(stat_var, pars)
#logp = 0
#for d in dbh_list:
#t = np.exp(-(lambda1 + (beta - lambda1) * n + lambda3 * n * d ** 2))
#logp_dn = np.log(G / S / z * 2 * d) + np.log(t) - 2 * np.log(1 - t) + np.log(1 - (S + 1) * t ** S + S * t ** (S + 1))
#logp += logp_dn - np.log(sad.pmf(n))
#logp += np.log(sad.pmf(n)) # Convert conditional distribution to joint distribution
logsum = 0
for d in dbh_list:
logt = -(lambda1 + (beta - lambda3) * n + lambda3 * n * (d**2))
t = np.exp(logt)
logsum += logt - 2 * np.log(1 - t) + np.log(1 - (S + 1) * (t**S) + S *
(t**(S + 1))) + np.log(
2 * d)
logp = logsum + n * np.log(G / S / z) - (n - 1) * sad.logpmf(n)
if log == True: return logp
else: return np.exp(logp)
def get_mete_agsne_rad(G, S, N, E, version='precise', pars = None):
"""Compute RAD predicted by the AGSNE.
Arguments:
G, S, N, E - state variables (number of genera, number of species, number of individuals, total metabolic rate)
Keyword arguments:
version - which version is used to calculate the state variables, can take 'precise' or 'approx'
pars - a list of Langrage multipliers [lambda1, beta, lambda3, Z], if these are already available.
If None, Langrage multipliers are calculated from get_agsne_lambdas().
Return a list of expected abundances with length S, ranked from high to low.
"""
if pars is None:
lambda1, beta, lambda3 = get_agsne_lambdas(G, S, N, E, version = version)
lambda3z = agsne_lambda3_z(lambda1, beta, S)
pars = [lambda1, beta, lambda3, lambda3z / lambda3]
sad = medis.sad_agsne([G, S, N, E], pars)
rank = range(1, int(S)+1)
abundance = list(np.empty([S]))
cdf_obs = [(rank[i]-0.5) / S for i in range(0, int(S))]
i, j = 1, 0
cdf_cum = 0
while i <= N + 1:
cdf_cum += sad.pmf(i)
while cdf_cum >= cdf_obs[j]:
abundance[j] = i
j += 1
if j == S:
abundance.reverse()
return abundance
i += 1
def bootstrap_SAD(name_site_combo, model, in_dir = './data/', out_dir = './out_files/', Niter = 200):
"""A general function of bootstrapping for SAD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to disk, with one file for R^2 and one for KS statistic.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
beta_ssnt = mete.get_beta(S, N, version = 'untruncated')
beta_asne = mete.get_beta(S, N)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
sad_agsne = mete_distributions.sad_agsne([G, S, N, E], [lambda1, beta, lambda3, agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3])
dist_for_model = {'ssnt_0': stats.logser(np.exp(-beta_ssnt)),
'ssnt_1': stats.logser(np.exp(-beta_ssnt)),
'asne': md.trunc_logser(np.exp(-beta_asne), N),
'agsne': sad_agsne}
dist = dist_for_model[model]
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_rad_' + model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred'][::-1]
obs = pred_obs[pred_obs['site'] == site]['obs'][::-1]
out_list_rsquare = [dat_name, site, str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))]
emp_cdf = mtools.get_emp_cdf(obs)
out_list_ks = [dat_name, site, str(max(abs(emp_cdf - np.array([dist.cdf(x) for x in obs]))))]
for i in range(Niter):
obs_boot = np.array(sorted(dist.rvs(S)))
cdf_boot = np.array([dist.cdf(x) for x in obs_boot])
emp_cdf_boot = mtools.get_emp_cdf(obs_boot)
out_list_rsquare.append(str(mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))))
out_list_ks.append(str(max(abs(emp_cdf_boot - np.array(cdf_boot)))))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_rsquare.txt', ",".join(str(x) for x in out_list_rsquare))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_ks.txt', ",".join(str(x) for x in out_list_ks))
def bootstrap_SAD(name_site_combo,
model,
in_dir='./data/',
out_dir='./out_files/',
Niter=200):
"""A general function of bootstrapping for SAD applying to all four models.
Inputs:
name_site_combo: a list with dat_name and site
model - takes one of four values 'ssnt_0', 'ssnt_1', 'asne', or 'agsne'
in_dir - directory of raw data
out_dir - directory used both in input (obs_pred.csv file) and output
Niter - number of bootstrap samples
Output:
Writes to disk, with one file for R^2 and one for KS statistic.
"""
dat_name, site = name_site_combo
dat = wk.import_raw_data(in_dir + dat_name + '.csv')
dat_site = dat[dat['site'] == site]
dat_clean = clean_data_agsne(dat_site)
G, S, N, E = get_GSNE(dat_clean)
beta_ssnt = mete.get_beta(S, N, version='untruncated')
beta_asne = mete.get_beta(S, N)
lambda1, beta, lambda3 = agsne.get_agsne_lambdas(G, S, N, E)
sad_agsne = mete_distributions.sad_agsne([G, S, N, E], [
lambda1, beta, lambda3,
agsne.agsne_lambda3_z(lambda1, beta, S) / lambda3
])
dist_for_model = {
'ssnt_0': stats.logser(np.exp(-beta_ssnt)),
'ssnt_1': stats.logser(np.exp(-beta_ssnt)),
'asne': md.trunc_logser(np.exp(-beta_asne), N),
'agsne': sad_agsne
}
dist = dist_for_model[model]
pred_obs = wk.import_obs_pred_data(out_dir + dat_name + '_obs_pred_rad_' +
model + '.csv')
pred = pred_obs[pred_obs['site'] == site]['pred'][::-1]
obs = pred_obs[pred_obs['site'] == site]['obs'][::-1]
out_list_rsquare = [
dat_name, site,
str(mtools.obs_pred_rsquare(np.log10(obs), np.log10(pred)))
]
emp_cdf = mtools.get_emp_cdf(obs)
out_list_ks = [
dat_name, site,
str(max(abs(emp_cdf - np.array([dist.cdf(x) for x in obs]))))
]
for i in range(Niter):
obs_boot = np.array(sorted(dist.rvs(S)))
cdf_boot = np.array([dist.cdf(x) for x in obs_boot])
emp_cdf_boot = mtools.get_emp_cdf(obs_boot)
out_list_rsquare.append(
str(mtools.obs_pred_rsquare(np.log10(obs_boot), np.log10(pred))))
out_list_ks.append(str(max(abs(emp_cdf_boot - np.array(cdf_boot)))))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_rsquare.txt',
",".join(str(x) for x in out_list_rsquare))
wk.write_to_file(out_dir + 'SAD_bootstrap_' + model + '_ks.txt',
",".join(str(x) for x in out_list_ks))
