In [49]:
plt.rcdefaults()
# Typeface sizes
from matplotlib import rcParams
rcParams['axes.labelsize'] = 12
rcParams['xtick.labelsize'] = 12
rcParams['ytick.labelsize'] = 12
rcParams['legend.fontsize'] = 12
#rcParams['font.family'] = 'serif'
#rcParams['font.serif'] = ['Computer Modern Roman']
#rcParams['text.usetex'] = True
# Optimal figure size
WIDTH = 350.0 # the number latex spits out
FACTOR = 0.90 # the fraction of the width you'd like the figure to occupy
fig_width_pt = WIDTH * FACTOR
inches_per_pt = 1.0 / 72.27
golden_ratio = (np.sqrt(5) - 1.0) / 2.0 # because it looks good
fig_width_in = fig_width_pt * inches_per_pt # figure width in inches
fig_height_in = fig_width_in * golden_ratio # figure height in inches
fig_dims = [fig_width_in, fig_height_in] # fig dims as a list
rcParams['figure.figsize'] = fig_dims
In [2]:
%matplotlib inline
In [3]:
import pandas as pd
import matplotlib.pyplot as plt
pd.set_option('display.mpl_style', 'default')
import statsmodels.api as sm
import itertools
First, let's load the results from the small model of polled included in the default settings. This involves loading four animal files (live cows, dead cows, live bulls, and dead bulls). We will load them and merge them into a single data frame.
In [4]:
# We have 10 relicates for each simulation
for sim in xrange(1,11):
# Load the individual history files
lc = pd.read_csv('med_high/%s/cows_history_pryce_med_high_20.txt'%sim, sep='\t')
dc = pd.read_csv('med_high/%s/dead_cows_history_pryce_med_high_20.txt'%sim, sep='\t')
lb = pd.read_csv('med_high/%s/bulls_history_pryce_med_high_20.txt'%sim, sep='\t')
db = pd.read_csv('med_high/%s/dead_bulls_history_pryce_med_high_20.txt'%sim, sep='\t')
inbreeding = pd.read_csv('med_high/%s/pedigree_20.txt.solinb'%sim, delim_whitespace=True,
skipinitialspace=True, names=['animal','inbreeding'])
# Stack the individual animal datasets
allan = lc.append(dc.append(lb.append(db)))
# Merge in the coefficients of inbreeding (Pandas defaults to an inner join)
all_animals = pd.merge(allan, inbreeding, on='animal')
all_animals['rep'] = sim
if sim == 1:
all_replicates = all_animals
else:
all_replicates = pd.concat([all_replicates, all_animals])
# Print first few lines of dataframe
#all_animals.head()
In [5]:
# Now load the Pryce+recessives data so that we can compare EBV.
# We have 10 relicates for each simulation
for sim in xrange(1,11):
# Load the individual history files
lc = pd.read_csv('med_high/%s/cows_history_pryce_r_med_high_20.txt'%sim, sep='\t')
dc = pd.read_csv('med_high/%s/dead_cows_history_pryce_r_med_high_20.txt'%sim, sep='\t')
lb = pd.read_csv('med_high/%s/bulls_history_pryce_r_med_high_20.txt'%sim, sep='\t')
db = pd.read_csv('med_high/%s/dead_bulls_history_pryce_r_med_high_20.txt'%sim, sep='\t')
inbreeding = pd.read_csv('med_high/%s/pedigree_20.txt.solinb'%sim, delim_whitespace=True,
skipinitialspace=True, names=['animal','inbreeding'])
# Stack the individual animal datasets
allan_r = lc.append(dc.append(lb.append(db)))
# Merge in the coefficients of inbreeding (Pandas defaults to an inner join)
all_animals_r = pd.merge(allan_r, inbreeding, on='animal')
all_animals_r['rep'] = sim
if sim == 1:
all_replicates_r = all_animals_r
else:
all_replicates_r = pd.concat([all_replicates_r, all_animals_r])
# Print first few lines of dataframe
#all_animals.head()
In [6]:
all_replicates['rep'].value_counts()
Out[6]:
In [7]:
# N = culled to maintain herd size
# A = culled for age
# R = culled because of lethal disorder
all_animals['cause'].value_counts()
Out[7]:
How many males and females are in the dataset?
In [8]:
all_animals['sex'].value_counts()
Out[8]:
If we want to plot the average TBV by sex for each generation we first need to construct a dataframe that has the average (mean) TBV for each group-sex combination.
In [9]:
grouped = all_animals.groupby(['sex','born']).mean()
#grouped
# Bulls and cows don't necessarily have identical sets of
# birth generations for founders since those values are
# randomly generated and bulls live longer than cows. In
# order to get the plots to work correctly, we need to
# reindex the aggregated dataframe.
full_index = []
for x in ['F','M']:
for g in all_animals['born'].unique():
full_index.append((x,g))
grouped = grouped.reindex(full_index).reset_index()
grouped = grouped.add_suffix('').reset_index()
grouped = grouped.sort(['level_0','level_1'])
#grouped
Now group the data for the Pryce+recessives scenario
In [10]:
grouped_r = all_animals_r.groupby(['sex','born']).mean()
full_index = []
for x in ['F','M']:
for g in all_animals['born'].unique():
full_index.append((x,g))
grouped_r = grouped_r.reindex(full_index).reset_index()
grouped_r = grouped_r.add_suffix('').reset_index()
grouped_r = grouped_r.sort(['level_0','level_1'])
In [11]:
print 'Average TBV by generation of birth and animal sex for the Pryce scenario'
all_animals.groupby(['sex','born']).mean()['TBV']
Out[11]:
In [12]:
print 'Average TBV by generation of birth and animal sex for the Pryce+recessives scenario'
all_animals_r.groupby(['sex','born']).mean()['TBV']
Out[12]:
In [13]:
fig = plt.figure(figsize=fig_dims, dpi=300, facecolor='white')
# Set nicer limits
xmin ,xmax = 0, 30
ymin, ymax = 0, 0.25
ax = fig.add_subplot(1, 1, 1)
ax.set_xlabel('Generation')
ax.set_ylabel('True Breeding Value')
ax.plot(all_animals.groupby(['born']).mean()['TBV'], label='Pryce', linewidth=2)
ax.plot(all_animals_r.groupby(['born']).mean()['TBV'], label='Pryce+recessives', linewidth=2)
ax.legend(loc='best')
# Deal with ticks marks and labels
x_tick_locs = [t for t in xrange(0, 31, 5)]
x_tick_labels = [t for t in xrange(-10, 21, 5)]
xticks(x_tick_locs, x_tick_labels)
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
# Plot and save
fig.tight_layout(pad=0.1) # Make the figure use all available whitespace
fig.savefig('/Users/jcole/Documents/AIPL/Genomics/Recessives/med-high-average-tbv-by-gen-pryce-rec.png', dpi=300)
Looking at the plot below, it looks as though I may need to bump the difference between cows and bulls in order to separate the two groups a little more. In these results, it looks as though the TBV for the groups don't differ.
In [14]:
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
#labels = ax.set_xticklabels(grouped['level_1'].unique())
ax.set_title('Mean TBV for Bulls and Cows')
ax.set_xlabel('Generation')
ax.set_ylabel('True Breeding Value')
for key, grp in grouped.groupby(['level_0']):
ax.plot(grp['TBV'], label=key)
ax.legend(loc='best')
Out[14]:
In the plot above it looks as though the bulls are "losing" their genetic base advantage in the first generation in which calves are produced. That's because they're being bred to cows that are not a good as they are, on average. Also, this plot includes all animals, including calves that died and cows and bulls that were culled without producing any offspring. A plot of the TBV of parents would be more informative as far as genetic trend goes. In order to do that, we need to count the number of offspring for each parent and merge them back into the all_animals data frame.
In [15]:
# How many calves did each bull sire?
sire_counts = pd.DataFrame(all_animals['sire'].value_counts(), columns=['offspring'])
# The Series index is the bull ID, which we want to convert to a column in the
# DataFrame.
sire_counts['animal'] = sire_counts.index
# We want to drop animal 0 because that's the unknown base-population sire.
sire_counts = sire_counts[sire_counts['animal'] > 0]
len(sire_counts)
Out[15]:
In [16]:
# How many calves did each cow produce?
dam_counts = pd.DataFrame(all_animals['dam'].value_counts(), columns=['offspring'])
# The Series index is the bull ID, which we want to convert to a column in the
# DataFrame.
dam_counts['animal'] = dam_counts.index
# We want to drop animal 0 because that's the unknown base-population sire.
dam_counts = dam_counts[dam_counts['animal'] > 0]
len(dam_counts)
Out[16]:
In [17]:
# Now we do some merging. We must use LEFT OUTER JOINs in order to retain all animals
# even if they weren't parents.
with_sires = pd.merge(all_animals, sire_counts, on='animal', how='left')
with_dams = pd.merge(with_sires, dam_counts, on='animal', how='left')
all_animals = with_dams
all_animals['sex'].value_counts()
Out[17]:
In [18]:
# These are cows
all_animals['offspring_y'].value_counts()
Out[18]:
In [19]:
# These are bulls
all_animals['offspring_x'].value_counts()
Out[19]:
Is there something screwy going on? I don't expect cows to have thousands of offspring.
The thing is, we now have two different columns for the offspring counts, named "offspring_x" and "offspring_y". Can we just combine them using addition? (There's probably a clever way to do this in the join, but I don't know it.
In [20]:
all_animals['offspring_x'].fillna(0, inplace=True)
all_animals['offspring_y'].fillna(0, inplace=True)
all_animals['offspring'] = all_animals['offspring_x'] + all_animals['offspring_y']
What does the distribution of offspring counts look like?
In [21]:
parents = all_animals[all_animals['offspring'] > 0]
parents.hist(column='offspring', by='sex')
Out[21]:
Now I think that we have everything we need in order to subset and plot genetic trend for parents, not just all animals.
In [22]:
grouped = parents.groupby(['sex','born']).mean()
full_index = []
for x in ['F','M']:
for g in all_animals['born'].unique():
full_index.append((x,g))
grouped = grouped.reindex(full_index).reset_index()
grouped = grouped.add_suffix('').reset_index()
grouped = grouped.sort(['level_0','level_1'])
In [23]:
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.set_title('Mean TBV for Parents')
ax.set_xlabel('Generation')
ax.set_ylabel('True Breeding Value')
for key, grp in grouped.groupby(['level_0']):
ax.plot(grp['TBV'], label=key)
ax.legend(loc='best')
Out[23]:
I also want to see what the inbreeding looks like. Plot by generation.
In [24]:
fig = plt.figure(figsize=fig_dims, dpi=300, facecolor='white')
# Set nicer limits
xmin ,xmax = 0, 30
ymin, ymax = 0, 0.25
ax = fig.add_subplot(1, 1, 1)
ax.set_xlabel('Generation')
ax.set_ylabel('Coefficient of inbreeding')
for key, grp in grouped.groupby(['level_0']):
# This is producing the wrong labels on the x axis.
if key == 'M': marker='s'
else: marker = 'o'
ax.plot(grp['inbreeding'], label=key, linewidth=2)
ax.legend(loc='best')
# Deal with ticks marks and labels
x_tick_locs = [t for t in xrange(0, 31, 5)]
x_tick_labels = [t for t in xrange(-10, 21, 5)]
xticks(x_tick_locs, x_tick_labels)
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
# Plot and save
fig.tight_layout(pad=0.1) # Make the figure use all available whitespace
fig.savefig('/Users/jcole/Documents/AIPL/Genomics/Recessives/med-high-inbreeding.png', dpi=300)
Load the four allele frequency files.
In [25]:
rec_names = ['gen',
'Medium, high']
# We have 10 relicates for each simulation
for sim in xrange(1,11):
# Load the individual history files
freqs_random = pd.read_csv('med_high/%s/minor_allele_frequencies_ran_med_high.txt'%sim, \
sep='\t', header=None, names=rec_names)
freqs_toppct = pd.read_csv('med_high/%s/minor_allele_frequencies_toppct_med_high.txt'%sim, \
sep='\t', header=None, names=rec_names)
freqs_pryce = pd.read_csv('med_high/%s/minor_allele_frequencies_pryce_med_high.txt'%sim, \
sep='\t', header=None, names=rec_names)
freqs_rec = pd.read_csv('med_high/%s/minor_allele_frequencies_pryce_r_med_high.txt'%sim, \
sep='\t', header=None, names=rec_names)
freqs_random['rep'] = sim
freqs_toppct['rep'] = sim
freqs_pryce['rep'] = sim
freqs_rec['rep'] = sim
if sim == 1:
all_random = freqs_random
all_toppct = freqs_toppct
all_pryce = freqs_pryce
all_rec = freqs_rec
else:
all_random = pd.concat([all_random, freqs_random])
all_toppct = pd.concat([all_toppct, freqs_toppct])
all_pryce = pd.concat([all_pryce, freqs_pryce])
all_rec = pd.concat([all_rec, freqs_rec])
Now we have final allele frequencies for each of the 10 replicates. We need to take the mean over the replicates for each recessive and plot those.
In [26]:
grouped_random = all_random.groupby(['gen']).mean()
grouped_toppct = all_toppct.groupby(['gen']).mean()
grouped_pryce = all_pryce.groupby(['gen']).mean()
grouped_rec = all_rec.groupby(['gen']).mean()
Plot the minor allele frequencies.
In [50]:
#fig = plt.figure(figsize=fig_dims, dpi=300, facecolor='white')
fig = plt.figure(figsize=(16, 12), dpi=300, facecolor='white')
# Set nicer limits
xmin ,xmax = 0, 20
ymin, ymax = 0, 0.51
recessives = rec_names[1:]
# Compute the expected frequency for each generation.
expected = {}
for i, r in enumerate(recessives):
expected[r] = []
# Red and horned are NOT lethals
if r in ['Horned', 'Red']:
for g in xrange(0,21):
if g == 0:
expected[r].append(grouped_random[r][g])
else:
q0 = expected[r][g-1]
p0 = 1. - q0
q1 = (p0*q0) + q0**2
expected[r].append(q1)
# The others are
else:
for g in xrange(0,21):
if g == 0:
expected[r].append(grouped_random[r][g])
else:
q0 = expected[r][g-1]
p0 = 1. - q0
q1 = (p0*q0) / (p0**2 + (2*p0*q0))
expected[r].append(q1)
# Now, plot all the things.
colors = itertools.cycle(['r', 'g', 'b','k'])
markers = itertools.cycle(['o', 'v', 's', 'd', '^', '*'])
ax = fig.add_subplot(2, 2, 1)
ax.set_title('Random')
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for i, r in enumerate(recessives):
if r != 'Horned':
ax.plot(grouped_random[r], label=r, marker=markers.next(), c=colors.next(), lw=1.5)
# Deal with ticks marks and labels
x_tick_locs = [t for t in xrange(0, 21, 5)]
x_tick_labels = [t for t in xrange(0, 21, 5)]
xticks(x_tick_locs, x_tick_labels)
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.set_ylim(ymin,ymax)
colors = itertools.cycle(['r', 'g', 'b','k'])
markers = itertools.cycle(['o', 'v', 's', 'd', '^', '*'])
ax = fig.add_subplot(2, 2, 2)
ax.set_title('Truncation')
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for i, r in enumerate(recessives):
if r != 'Horned':
ax.plot(grouped_toppct[r], label=r, marker=markers.next(), c=colors.next(), lw=1.5)
# Deal with ticks marks and labels
x_tick_locs = [t for t in xrange(0, 21, 5)]
x_tick_labels = [t for t in xrange(0, 21, 5)]
xticks(x_tick_locs, x_tick_labels)
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.set_ylim(ymin,ymax)
colors = itertools.cycle(['r', 'g', 'b','k'])
markers = itertools.cycle(['o', 'v', 's', 'd', '^', '*'])
ax = fig.add_subplot(2, 2, 3)
ax.set_title('Pryce')
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for i, r in enumerate(recessives):
if r != 'Horned':
ax.plot(grouped_pryce[r], label=r, marker=markers.next(), c=colors.next(), lw=1.5)
# Deal with ticks marks and labels
x_tick_locs = [t for t in xrange(0, 21, 5)]
x_tick_labels = [t for t in xrange(0, 21, 5)]
xticks(x_tick_locs, x_tick_labels)
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.set_ylim(ymin,ymax)
colors = itertools.cycle(['r', 'g', 'b','k'])
markers = itertools.cycle(['o', 'v', 's', 'd', '^', '*'])
ax = fig.add_subplot(2, 2, 4)
ax.set_title('Pryce + recessives')
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
for i, r in enumerate(recessives):
if r != 'Horned':
ax.plot(grouped_rec[r], label=r, marker=markers.next(), c=colors.next(), lw=1.5)
# Deal with ticks marks and labels
x_tick_locs = [t for t in xrange(0, 21, 5)]
x_tick_labels = [t for t in xrange(0, 21, 5)]
xticks(x_tick_locs, x_tick_labels)
# Despine
ax = gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.set_ylim(ymin,ymax)
h, l = ax.get_legend_handles_labels()
leg = plt.figlegend(h, l, loc=(0.90, 0.8), fancybox=True)
rect = leg.get_frame()
rect.set_facecolor('white')
#suptitle = plt.suptitle('Allele Frequency Change Over Time for Several Mating Schemes', x = 0.5, y = 1.05, fontsize=18)
# Plot and save
#plt.tight_layout(pad=1., w_pad=0.5, h_pad=0.5)
fig.tight_layout(pad=0.1) # Make the figure use all available whitespace
fig.savefig('/Users/jcole/Documents/AIPL/Genomics/Recessives/med-high-observed-allele-frequency-changes.png', dpi=300)
Let's try a small multiples-type of plot to show the actual versus expected frequencies.
In [51]:
fig = plt.figure(figsize=(16, 12), dpi=300, facecolor='white')
# Plot Pryce + recessives
colors = itertools.cycle(['r', 'g', 'b'])
for i, r in enumerate(recessives):
ax = fig.add_subplot(1, 1, i)
ax.set_title(r)
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
ax.plot(grouped_rec[r], label='Observed', marker='o', c='k')
ax.plot(expected[r], label='Expected', c='gray')
ax.set_ylim(0.0, 0.51)
legend(loc='best')
plt.tight_layout(pad=1., w_pad=0.5, h_pad=0.5)
fig.savefig('/Users/jcole/Documents/AIPL/Genomics/Recessives/med-high-act-vs-exp-rec.png', dpi=300)
Let's take a look at just the Pryce inbreeding adjustment, then. See if it's less messy.
In [52]:
fig = plt.figure(figsize=(16, 12), dpi=300, facecolor='white')
# Plot Pryce + recessives
colors = itertools.cycle(['r', 'g', 'b'])
for i, r in enumerate(recessives):
ax = fig.add_subplot(1, 1, i)
ax.set_title(r)
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
ax.plot(grouped_pryce[r], label='Observed', marker='o', c='k')
ax.plot(expected[r], label='Expected', c='gray')
ax.set_ylim(0.0, 0.51)
legend(loc='best')
plt.tight_layout(pad=1., w_pad=0.5, h_pad=0.5)
fig.savefig('/Users/jcole/Documents/AIPL/Genomics/Recessives/med-high-act-vs-exp-pryce.png', dpi=300)
Now we're going to fit a linear regression to each recessive in each scenario. The frequency is the dependent variable, and the generation number is the independent variable.
In [41]:
def fit_line(x, y):
"""Return RegressionResults instance of best-fit line."""
X = sm.add_constant(x)
model = sm.OLS(y, X, missing='drop')
fit = model.fit()
return fit
In [42]:
grouped_random_fits = {}
for i, r in enumerate(recessives):
fit = fit_line(grouped_random.index.values, grouped_random[r])
grouped_random_fits[r] = fit
grouped_toppct_fits = {}
for i, r in enumerate(recessives):
fit = fit_line(grouped_toppct.index.values, grouped_toppct[r])
grouped_toppct_fits[r] = fit
grouped_pryce_fits = {}
for i, r in enumerate(recessives):
fit = fit_line(grouped_pryce.index.values, grouped_pryce[r])
grouped_pryce_fits[r] = fit
grouped_rec_fits = {}
for i, r in enumerate(recessives):
fit = fit_line(grouped_rec.index.values, grouped_rec[r])
grouped_rec_fits[r] = fit
expected_fits = {}
for i, r in enumerate(recessives):
fit = fit_line(grouped_rec.index.values, expected[r])
expected_fits[r] = fit
In [43]:
from scipy.special import stdtr
def test_slopes(fit1, fit2, debug=False):
"""Perform a t-test of regression slopes assuming unequal variances."""
sigma_b1_b2 = math.sqrt( fit1.bse[1]**2 + fit2.bse[1]**2 )
t = (fit1.params[1] - fit2.params[1]) / sigma_b1_b2
df = fit1.nobs + fit2.nobs - 4
pvalue = 2*stdtr(df, -abs(t))
if debug:
print 'sigma_b1_b2: ', sigma_b1_b2
print 'fit1.params[1]', fit1.params[1]
print 'fit2.params[1]', fit2.params[1]
print 'fit1.params[1] - fit2.params[1]', fit1.params[1] - fit2.params[1]
print 't: ', t
print 'df: ', df
print 'pvalue: ', pvalue
return t, pvalue
In [44]:
print 'Random versus Pryce+recessives'
for i, r in enumerate(recessives):
tval, pval = test_slopes(grouped_random_fits[r], grouped_rec_fits[r])
if pval < 0.05/11.: significant = '****'
else: significant = ''
print '\t%s:\tt = \t%s\tp = \t%s\t%s' % ( r, tval, pval, significant )
In [45]:
print 'Pryce versus Pryce+recessives'
print '\tTrait\tb0_pryce\t\tb0_rec\t\t\tFaster\tt-value\t\tp-value\t\t\tsig'
print '\t%s' % ( '-'*110 )
for i, r in enumerate(recessives):
tval, pval = test_slopes(grouped_pryce_fits[r], grouped_rec_fits[r])
if pval < 0.05/11.: significant = '****'
else: significant = ''
if grouped_rec_fits[r].params[1] > grouped_pryce_fits[r].params[1]: bigger = 'P'
else: bigger = 'R'
if r == 'Brachyspina': rprint = 'Brachy'
elif r == 'Mulefoot': rprint = 'Mule'
else: rprint = r
print '\t%s\t%s\t%s\t%s\t%s\t%s\t%s' % ( rprint, grouped_pryce_fits[r].params[1],
grouped_rec_fits[r].params[1], bigger,
tval, pval, significant )
In [46]:
print 'Pryce versus Expected'
print '\tTrait\tb0_rec\t\t\tb0_exp\t\t\tFaster\tt-value\t\tp-value\t\t\tsig'
print '\t%s' % ( '-'*110 )
for i, r in enumerate(recessives):
tval, pval = test_slopes(grouped_pryce_fits[r], expected_fits[r])
if pval < 0.05/11.: significant = '****'
else: significant = ''
if grouped_rec_fits[r].params[1] > expected_fits[r].params[1]: bigger = 'E'
else: bigger = 'O'
if r == 'Brachyspina': rprint = 'Brachy'
elif r == 'Mulefoot': rprint = 'Mule'
else: rprint = r
print '\t%s\t%s\t%s\t%s\t%s\t%s\t%s' % ( rprint, grouped_pryce_fits[r].params[1],
expected_fits[r].params[1], bigger,
tval, pval, significant )
In [47]:
print 'Pryce+recessives versus Expected'
print '\tTrait\tb0_rec\t\t\tb0_exp\t\t\tFaster\tt-value\t\tp-value\t\t\tsig'
print '\t%s' % ( '-'*110 )
for i, r in enumerate(recessives):
tval, pval = test_slopes(grouped_rec_fits[r], expected_fits[r])
if pval < 0.05/11.: significant = '****'
else: significant = ''
if grouped_rec_fits[r].params[1] > expected_fits[r].params[1]: bigger = 'E'
else: bigger = 'O'
if r == 'Brachyspina': rprint = 'Brachy'
elif r == 'Mulefoot': rprint = 'Mule'
else: rprint = r
print '\t%s\t%s\t%s\t%s\t%s\t%s\t%s' % ( rprint, grouped_rec_fits[r].params[1],
expected_fits[r].params[1], bigger,
tval, pval, significant )
Reference figure for expected rate of allele frequency change.
In [48]:
fig = plt.figure(figsize=(16, 12), dpi=300, facecolor='white')
markers = itertools.cycle(['o', 'v', 's', 'd', '^', '*'])
# Compute the expected frequency for each generation.
expected = {}
for r in [0.01, 0.05, 0.10, 0.25, 0.75, 0.99]:
expected[r] = []
for g in xrange(0,21):
if g == 0:
expected[r].append(r)
else:
q0 = expected[r][g-1]
p0 = 1. - q0
q1 = (p0*q0) / (p0**2 + (2*p0*q0))
expected[r].append(q1)
ax = fig.add_subplot(1, 1, 1)
#ax.set_title('Expected Change in Allele Frequencies')
ax.set_xlabel('Generation')
ax.set_ylabel('Allele Frequency')
for r in [0.01, 0.05, 0.10, 0.25, 0.75, 0.99]:
l = 'Expected %s' % ( r )
ax.plot(expected[r], label=l, c='k', lw=1.5, marker=markers.next())
ax.set_ylim(0.0, 1.0)
#legend = ax.legend(loc='upper right', shadow=False)
legend(loc='best')
plt.tight_layout(pad=1., w_pad=0.5, h_pad=0.5)
fig.savefig('/Users/jcole/Documents/AIPL/Genomics/Recessives/low-low-expected-allele-frequency-change.png', dpi=300)
In [48]: