def get_pfix_transformed(p0, x4Ns, h):
"""
Try to get the same result as the function in the kimura module.
Change of variables according to eqn 3 of Chen et al.
When I type
(integral from 0 to p of exp(b*s*(x-a)**2) ) /
(integral from 0 to 1 of exp(b*s*(x-a)**2) )
I get
( erfi(sqrt(b)*sqrt(s)*a) - erfi(sqrt(b)*sqrt(s)*(a-p)) ) /
( erfi(sqrt(b)*sqrt(s)*a) - erfi(sqrt(b)*sqrt(s)*(a-1)) )
@param p0: proportion of mutant alleles in the population
@param x4Ns: 4Ns
@return: fixation probability
"""
if not x4Ns:
# This is the neutral case.
return p0
if h == 0.5:
# This is the genic case.
# Checking for exact equality of 0.5 is OK.
return math.expm1(-x4Ns * p0) / math.expm1(-x4Ns)
b = 2.0 * h - 1.0
a = h / (2.0 * h - 1.0)
q = cmath.sqrt(b) * cmath.sqrt(x4Ns)
#
top = kimura.erfi(q * a) - kimura.erfi(q * (a - p0))
bot = kimura.erfi(q * a) - kimura.erfi(q * (a - 1))
return top / bot
def get_pfix_transformed(p0, x4Ns, h):
"""
Try to get the same result as the function in the kimura module.
Change of variables according to eqn 3 of Chen et al.
When I type
(integral from 0 to p of exp(b*s*(x-a)**2) ) /
(integral from 0 to 1 of exp(b*s*(x-a)**2) )
I get
( erfi(sqrt(b)*sqrt(s)*a) - erfi(sqrt(b)*sqrt(s)*(a-p)) ) /
( erfi(sqrt(b)*sqrt(s)*a) - erfi(sqrt(b)*sqrt(s)*(a-1)) )
@param p0: proportion of mutant alleles in the population
@param x4Ns: 4Ns
@return: fixation probability
"""
if not x4Ns:
# This is the neutral case.
return p0
if h == 0.5:
# This is the genic case.
# Checking for exact equality of 0.5 is OK.
return math.expm1(-x4Ns*p0) / math.expm1(-x4Ns)
b = 2.0 * h - 1.0
a = h / (2.0 * h - 1.0)
q = cmath.sqrt(b) * cmath.sqrt(x4Ns)
#
top = kimura.erfi(q*a) - kimura.erfi(q*(a-p0))
bot = kimura.erfi(q*a) - kimura.erfi(q*(a-1))
return top / bot
def get_pfix_transformed(p0, s_in, h):
"""
Try to get the same result as the function in the kimura module.
Change of variables according to eqn 3 of Chen et al.
When I type
(integral from 0 to p of exp(b*s*(x-a)**2) ) /
(integral from 0 to 1 of exp(b*s*(x-a)**2) )
I get
( erfi(sqrt(b)*sqrt(s)*a) - erfi(sqrt(b)*sqrt(s)*(a-p)) ) /
( erfi(sqrt(b)*sqrt(s)*a) - erfi(sqrt(b)*sqrt(s)*(a-1)) )
"""
s = s_in * 2
b = 2.0 * h - 1.0
#XXX
if not b:
return float('nan')
# transform h to alpha and beta, represented here by a and b
a = h / (2.0 * h - 1.0)
# intermediate parameter
q = cmath.sqrt(b) * cmath.sqrt(s)
#
"""
top = 2*q*cmath.exp(a*a*b*s)
bot_a = kimura.erfi(q*(1-a))
bot_b = kimura.erfi(q*a)
"""
top = kimura.erfi(q*a) - kimura.erfi(q*(a-p0))
bot = kimura.erfi(q*a) - kimura.erfi(q*(a-1))
return top / bot
def get_pfix_transformed_limit(x4Ns, h):
"""
This is an approximation analogous to an approximation by Kimura.
@param x4Ns: 4Ns
@param h: dominance parameter
@return: 2N times fixation probability
"""
if not x4Ns:
# This is the neutral case.
return 1.0
if h == 0.5:
# This is the genic case.
# Checking for exact equality of 0.5 is OK.
return -x4Ns / math.expm1(-x4Ns)
a = h / (2.0 * h - 1.0)
b = 2.0 * h - 1.0
q = cmath.sqrt(b) * cmath.sqrt(x4Ns)
#
top = 2 * q * cmath.exp((q * a)**2)
bot_a = kimura.erfi(q * a)
bot_b = kimura.erfi(q * (1 - a))
return top / (cmath.sqrt(math.pi) * (bot_a + bot_b))
def get_pfix_transformed_limit(x4Ns, h):
"""
This is an approximation analogous to an approximation by Kimura.
@param x4Ns: 4Ns
@param h: dominance parameter
@return: 2N times fixation probability
"""
if not x4Ns:
# This is the neutral case.
return 1.0
if h == 0.5:
# This is the genic case.
# Checking for exact equality of 0.5 is OK.
return - x4Ns / math.expm1(-x4Ns)
a = h / (2.0 * h - 1.0)
b = 2.0 * h - 1.0
q = cmath.sqrt(b) * cmath.sqrt(x4Ns)
#
top = 2*q*cmath.exp((q*a)**2)
bot_a = kimura.erfi(q*a)
bot_b = kimura.erfi(q*(1-a))
return top / ( cmath.sqrt(math.pi) * (bot_a + bot_b) )
def get_pfix_transformed_limit(s_in, h):
s = s_in * 2
b = 2.0 * h - 1.0
#
if not s:
#XXX is this right
# limit s->0 of
# (1/sqrt(pi)) * ( 2*sqrt(b)*sqrt(s)*exp(a*a*b*s) ) /
# ( erfi(sqrt(b)*sqrt(s)*(1-a)) + erfi(sqrt(b)*sqrt(s)*a) )
return 1.0
if not b:
#XXX is this right
# limit as p->0 of (1/p) * ( expm1(-s*p) / expm1(-s) )
return s*math.exp(s) / math.expm1(s)
# transform h to alpha and beta, represented here by a and b
a = h / (2.0 * h - 1.0)
# intermediate parameter
q = cmath.sqrt(b) * cmath.sqrt(s)
#
top = 2*q*cmath.exp((q*a)**2)
bot_a = kimura.erfi(q*a)
bot_b = kimura.erfi(q*(1-a))
return top / ( cmath.sqrt(math.pi) * (bot_a + bot_b) )
