2L, 10L, 4L, 14L, 4L, 2L, 3L, 1L, 1L, 8L
]])
# Color scheme from Dave Harris in
# https://github.com/weecology/sad-comparison/issues/217
colors = ["#990F0F", "#99700F", "#1F990F", "#710F99"]
plot_labels = ["A", "B", "C"]
fig_example = plt.figure(figsize=(12, 4))
for i in range(3):
ax = plt.subplot(1, 3, i + 1)
ab = ab_array[i]
x_values = np.array(range(max(ab) + 2)[1:])
logser_p = md.logser_solver(ab)
logser_values = md.trunc_logser.pmf(x_values,
logser_p,
upper_bound=float("inf"))
lsll = md.logser_ll(ab, logser_p)
nb_n, nb_p = md.nbinom_lower_trunc_solver(ab)
nb_values = md.nbinom_lower_trunc.pmf(x_values, nb_n, nb_p)
nbll = md.nbinom_lower_trunc_ll(ab, nb_n, nb_p)
pln_mu, pln_sigma = md.pln_solver(ab)
pln_values = md.pln.pmf(x_values, pln_mu, pln_sigma, lower_trunc=True)
plnll = md.pln_ll(ab, pln_mu, pln_sigma)
zipf_par = md.zipf_solver(ab)
zipf_values = zipf.pmf(x_values, zipf_par)
4L, 1L, 1L, 9L, 3L, 8L, 3L, 2L, 10L, 4L, 14L, 4L, 2L, 3L, 1L,
1L, 8L]])
# Color scheme from Dave Harris in
# https://github.com/weecology/sad-comparison/issues/217
colors = ["#990F0F", "#99700F", "#1F990F", "#710F99"]
plot_labels = ["A", "B", "C"]
fig_example = plt.figure(figsize = (12, 4))
for i in range(3):
ax = plt.subplot(1, 3, i + 1)
ab = ab_array[i]
x_values = np.array(range(max(ab) + 2)[1:])
logser_p = md.logser_solver(ab)
logser_values = md.trunc_logser.pmf(x_values, logser_p, upper_bound=float("inf"))
lsll = md.logser_ll(ab, logser_p)
nb_n, nb_p = md.nbinom_lower_trunc_solver(ab)
nb_values = md.nbinom_lower_trunc.pmf(x_values, nb_n, nb_p)
nbll = md.nbinom_lower_trunc_ll(ab, nb_n, nb_p)
pln_mu, pln_sigma = md.pln_solver(ab)
pln_values = md.pln.pmf(x_values, pln_mu, pln_sigma, lower_trunc=True)
plnll = md.pln_ll(ab, pln_mu, pln_sigma)
zipf_par = md.zipf_solver(ab)
zipf_values = zipf.pmf(x_values, zipf_par)
zll = md.zipf_ll(ab, zipf_par)
def model_comparisons(raw_data, dataset_name, data_dir, cutoff=9):
""" Uses raw species abundance data to compare predicted vs. empirical species abundance distributions (SAD) and output results in csv files.
Keyword arguments:
raw_data: numpy structured array with 4 columns: 'site', 'year', 'sp' (species), 'ab' (abundance).
dataset_name: short code to indicate the name of the dataset in the output file names.
data_dir: directory in which to store results output.
cutoff: minimum number of species required to run -1.
SAD models and packages used:
Logseries (macroecotools/macroecodistributions)
Poisson lognormal (macroecotools/macroecodistributions)
Negative binomial (macroecotools/macroecodistributions)
Zipf (macroecotools/macroecodistributions)
Neutral theory: Neutral theory predicts the negative binomial distribution (Connolly et al. 2014. Commonness and rarity in the marine biosphere. PNAS 111: 8524-8529. http://www.pnas.org/content/111/23/8524.abstract
"""
usites = np.sort(np.unique(raw_data["site"]))
# Open output files
f1 = open(data_dir + dataset_name + '_dist_test.csv', 'wb')
output1 = csv.writer(f1)
f2 = open(data_dir + dataset_name + '_likelihoods.csv', 'wb')
output2 = csv.writer(f2)
f3 = open(data_dir + dataset_name + '_relative_L.csv', 'wb')
output3 = csv.writer(f3)
# Insert header
output1.writerow([
'site', 'S', 'N', 'AICc_logseries', 'AICc_pln', 'AICc_negbin',
'AICc_zipf'
])
output2.writerow([
'site', 'S', 'N', 'likelihood_logseries', 'likelihood_pln',
'likelihood_negbin', 'likelihood_zipf'
])
output3.writerow([
'site', 'S', 'N', 'relative_ll_logseries', 'relative_ll_pln',
'relative_ll_negbin', 'relative_ll_zipf'
])
results = []
for site in usites:
subsites = raw_data["site"][raw_data["site"] == site]
subabundance = raw_data["ab"][raw_data["site"] == site]
N = sum(subabundance) # N = total abundance for a site
S = len(subsites) # S = species richness at a site
if (min(subabundance) > 0) and (S > cutoff):
print("%s, Site %s, S=%s, N=%s" % (dataset_name, site, S, N))
# Calculate Akaike weight of species abundance models:
# Parameter k is the number of fitted parameters
k1 = 1
k2 = 2
# Calculate log-likelihoods of species abundance models and calculate AICc values:
# Logseries
p_untruncated = md.logser_solver(subabundance)
L_logser_untruncated = md.logser_ll(
subabundance,
p_untruncated) # Log-likelihood of untruncated logseries
AICc_logser_untruncated = macroecotools.AICc(
k1, L_logser_untruncated, S) # AICc logseries untruncated
relative_ll_logser_untruncated = AICc_logser_untruncated # Relative likelihood untruncated logseries
#Start making AICc list
AICc_list = [AICc_logser_untruncated]
likelihood_list = [L_logser_untruncated]
relative_likelihood_list = [relative_ll_logser_untruncated]
# Poisson lognormal
mu, sigma = md.pln_solver(subabundance)
L_pln = md.pln_ll(subabundance, mu,
sigma) # Log-likelihood of Poisson lognormal
AICc_pln = macroecotools.AICc(k2, L_pln,
S) # AICc Poisson lognormal
relative_ll_pln = macroecotools.AICc(
k1, L_pln, S) #Relative likelihood, Poisson lognormal
# Add to AICc list
AICc_list = AICc_list + [AICc_pln]
likelihood_list = likelihood_list + [L_pln]
relative_likelihood_list = relative_likelihood_list + [
relative_ll_pln
]
# Negative binomial
n0, p0 = md.nbinom_lower_trunc_solver(subabundance)
L_negbin = md.nbinom_lower_trunc_ll(
subabundance, n0, p0) # Log-likelihood of negative binomial
AICc_negbin = macroecotools.AICc(k2, L_negbin,
S) # AICc negative binomial
relative_ll_negbin = macroecotools.AICc(
k1, L_negbin,
S) # Relative log-likelihood of negative binomial
# Add to AICc list
AICc_list = AICc_list + [AICc_negbin]
likelihood_list = likelihood_list + [L_negbin]
relative_likelihood_list = relative_likelihood_list + [
relative_ll_negbin
]
# Zipf distribution
par = md.zipf_solver(subabundance)
L_zipf = md.zipf_ll(subabundance,
par) #Log-likelihood of Zipf distribution
AICc_zipf = macroecotools.AICc(k1, L_zipf, S)
relative_ll_zipf = AICc_zipf
#Add to AICc list
AICc_list = AICc_list + [AICc_zipf]
likelihood_list = likelihood_list + [L_zipf]
relative_likelihood_list = relative_likelihood_list + [
relative_ll_zipf
]
# Calculate AICc weight
weight = macroecotools.aic_weight(AICc_list, S, cutoff=4)
#Calculate relative likelihood
relative_likelihoods = macroecotools.aic_weight(
relative_likelihood_list, S, cutoff=4)
# Convert weight to list
weights_output = weight.tolist()
#Convert relative likelihoods to list
relative_likelihoods_output = relative_likelihoods.tolist()
# Format results for output
for weight in weights_output:
results1 = [[site, S, N] + weights_output]
results2 = [[site, S, N] + likelihood_list]
results3 = [[site, S, N] + relative_likelihoods_output]
results.append([site, S, N] + weights_output + likelihood_list +
relative_likelihoods_output)
# Save results to a csv file:
output1.writerows(results1)
output2.writerows(results2)
output3.writerows(results3)
results = DataFrame(results,
columns=[
'site', 'S', 'N', 'AICc_logseries', 'AICc_pln',
'AICc_negbin', 'AICc_zipf', 'likelihood_logseries',
'likelihood_pln', 'likelihood_negbin',
'likelihood_zipf', 'relative_ll_logseries',
'relative_ll_pln', 'relative_ll_negbin',
'relative_ll_zipf'
])
results.to_csv(os.path.join(data_dir,
dataset_name + '_likelihood_results.csv'),
index=False)
f1.close()
f2.close()
f3.close()