#!/usr/bin/env python
# coding: utf-8

# In[1]:


# to go from 10% to 90% of the population
# is a log difference of 4.5

import numpy as np
import pandas as pd

logdiff990 = np.log(9/.1)

logdiff990


# In[2]:


# at a 1% survival advantage per generation with 100%
# assortative mating and a 25-year generation takes...

time990_1percent = logdiff990/.01 * 25

time990_1percent


# In[10]:


Reproductive_Advantage = [.0005, .001, .002, .005, .01, .02, .05, .10, .20]
Time_990 = []

for i in range(9):
    Time_990 = Time_990 + [25 * logdiff990/Reproductive_Advantage[i]]
    
Scratch = (Reproductive_Advantage, Time_990)

Rep_Adv_array = np.array(Scratch)


# In[11]:


Scratch = pd.DataFrame(Rep_Adv_array)

Rep_Adv_df = Scratch.transpose()

Rep_Adv_df.columns=['Reproductive Advantage', 'Time to Go from 9 to 90 Percent']

Rep_Adv_df


# In[13]:


# Suppose we start out with a 7.4-fold difference—exp(2), that is, 
# between population X and Y...
# for how long a duration of time will the frequency for X be greater
# than 50% and the frequency for Y be less than 50%?
#
# the answer, where r is the generational reproductive advantage
# and g is the length of a generation, is: g * ln(2)/r

Reproductive_Advantage = [.0005, .001, .002, .005, .01, .02, .05, .10, .20]
Duration = []

for i in range(9):
    Duration = Duration + [25 * np.log(2)/Reproductive_Advantage[i]]
    
Scratch = (Reproductive_Advantage, Duration)

Duration_array = np.array(Scratch)

Scratch = pd.DataFrame(Duration_array)

Duration_df = Scratch.transpose()

Duration_df.columns=['Reproductive Advantage', 'Duration']

Duration_df


# In[15]:


# Time to grow from 1% to 50%

Reproductive_Advantage = [.0005, .001, .002, .005, .01, .02, .05, .10, .20]
Time_to_Grow_from_1_Percent = []

for i in range(9):
    Time_to_Grow_from_1_Percent = Time_to_Grow_from_1_Percent + [25 * np.log(50)/Reproductive_Advantage[i]]
    
Scratch = (Reproductive_Advantage, Time_to_Grow_from_1_Percent)

Time_to_Grow_from_1_Percent_array = np.array(Scratch)

Scratch = pd.DataFrame(Time_to_Grow_from_1_Percent_array)

Time_to_Grow_from_1_Percent_df = Scratch.transpose()

Time_to_Grow_from_1_Percent_df.columns=['Reproductive Advantage', 'Time to Grow from 1 Percent']

Time_to_Grow_from_1_Percent_df