Last updated: 2020-04-24

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Knit directory: Comparative_APA/analysis/

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Rmd 93d00f3 brimittleman 2020-04-24 add info content 
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Packages/functions for this:

vegan: diversity, can calculate shannon or simpson

I will probably do this in python because I can go gene by gene easier:

scipy stats example

This is good because I will be able to change the base and see how it effects the measurements

https://kite.com/python/docs/scipy.stats.entropy

default base is e

from scipy.stats import entropy
import numpy as np
from math import log, e
entropy([1/2, 1/2], base=2)
  
#shannon 
Shannon2 = -np.sum(pA*np.log2(pA))

I most likely want to use a uniform prior. for this. I could get more complicated in the future by weighting differences by utr and intron. this would help find “more surpising” results.

simpson- squares the probability

from ecopy import diversity 

diversity(x, medod="simpson")


#x- side x species matrix, sites are rows, columns are species - ie column counts, row == pas
library(vegan)
Loading required package: permute
Loading required package: lattice
This is vegan 2.5-3
data(BCI)
dim(BCI)
[1]  50 225
H <- diversity(BCI)
length(H)
[1] 50
diversity(c(.5,.5,.5))
[1] 1.098612
diversity(c(.25,.75,.25))
[1] 0.9502705
#more peak= lower 


diversity(c(.5,.5,.5), "simpson")
[1] 0.6666667
diversity(c(.25,.75,.25),"simpson")
[1] 0.56
#more peak= lower


diversity(c(.5,.5,.5), "inv")
[1] 3
diversity(c(.25,.75,.25),"inv")
[1] 2.272727

Seem like it is most simple to use the mean usages for this.

First test:

use entropy in python with different bases. -base 2 is the classic shannon and it uses the - when probabilities are given (ie uniform prior)

the python code will work with my meta file for now and take species as an input.

mkdir ../data/InfoContent

python InfoContentShannon.py Human
python InfoContentShannon.py Chimp

Results:

HumanResInfo= read.table("../data/InfoContent/Human_InfoContent.txt", header = T,stringsAsFactors = F) %>% rename(Human_Base2=base2, Human_basee= basee)
ChimpResInfo= read.table("../data/InfoContent/Chimp_InfoContent.txt", header = T,stringsAsFactors = F) %>% rename(Chimp_Base2=base2, Chimp_basee= basee)

BothResInfo= HumanResInfo %>% inner_join(ChimpResInfo, by=c("gene", "numPAS")) %>% filter(numPAS > 1)

First plot the distributions:

BothResInfo_2= BothResInfo %>% select(gene, contains("Base2")) %>% gather("species", "base2", -gene)

ggplot(BothResInfo_2, aes(x=base2, fill=species)) + geom_density(alpha=.3)
Warning: Removed 1 rows containing non-finite values (stat_density).

Human shift higher, ie less density:

BothResInfo_e= BothResInfo %>% select(gene, contains("basee")) %>% gather("species", "basee", -gene)

ggplot(BothResInfo_e, aes(x=basee, fill=species)) + geom_density(alpha=.3)
Warning: Removed 1 rows containing non-finite values (stat_density).

I want to look at this by dominance:

ggplot(BothResInfo_2,aes(x=base2, fill=species)) + geom_histogram() + facet_grid(~species)
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Warning: Removed 1 rows containing non-finite values (stat_bin).

Plot human vs chimp:

ggplot(BothResInfo,aes(x=Human_Base2,y= Chimp_Base2 )) + geom_point() + geom_abline(slope=1, intercept = 0) + stat_cor() + geom_density_2d(col="blue")
Warning: Removed 1 rows containing non-finite values (stat_cor).
Warning: Removed 1 rows containing non-finite values (stat_density2d).
Warning: Removed 1 rows containing missing values (geom_point).

ggplot(BothResInfo,aes(x=Human_Base2,y= Chimp_Base2 ,col=numPAS)) + geom_point(alpha=.4) + geom_abline(slope=1, intercept = 0)
Warning: Removed 1 rows containing missing values (geom_point).

Does number explain:

summary(lm(BothResInfo$Human_Base2 ~BothResInfo$numPAS))

Call:
lm(formula = BothResInfo$Human_Base2 ~ BothResInfo$numPAS)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.88694 -0.20022  0.06073  0.23527  0.53990 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.209838   0.008559   24.52   <2e-16 ***
BothResInfo$numPAS 0.314404   0.001527  205.93   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3166 on 8448 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.8339,    Adjusted R-squared:  0.8339 
F-statistic: 4.241e+04 on 1 and 8448 DF,  p-value: < 2.2e-16
summary(lm(BothResInfo$Chimp_Base2 ~BothResInfo$numPAS ))

Call:
lm(formula = BothResInfo$Chimp_Base2 ~ BothResInfo$numPAS)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.76846 -0.25131  0.06184  0.27657  0.67339 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.108685   0.010226   10.63   <2e-16 ***
BothResInfo$numPAS 0.307373   0.001824  168.49   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3784 on 8449 degrees of freedom
Multiple R-squared:  0.7706,    Adjusted R-squared:  0.7706 
F-statistic: 2.839e+04 on 1 and 8449 DF,  p-value: < 2.2e-16

So this is working but the number of PAS explains most of the variation. Maybe I can normalize this out and look at residuals:

BothResInfoRes= BothResInfo %>% mutate(HumanNorm=residuals(BothResInfo$Human_Base2~BothResInfo$numPAS),ChimpNorm=residuals(BothResInfo$Chimp_Base2~BothResInfo$numPAS))

pull in dominance:

HumanRes=read.table("../data/DomDefGreaterX/Human_AllGenes_DiffTop.txt", col.names = c("Human_PAS", "gene","Human_DiffDom"),stringsAsFactors = F)

ChimpRes=read.table("../data/DomDefGreaterX/Chimp_AllGenes_DiffTop.txt", col.names = c("Chimp_PAS", "gene","Chimp_DiffDom"),stringsAsFactors = F)

BothRes=HumanRes %>% inner_join(ChimpRes,by="gene")

BothRes_10=BothRes %>% filter(Chimp_DiffDom >=0.1 | Human_DiffDom>=0.1) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=10) 
BothRes_20=BothRes %>% filter(Chimp_DiffDom >=0.2 | Human_DiffDom>=0.2) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=20)
BothRes_30=BothRes %>% filter(Chimp_DiffDom >=0.3 | Human_DiffDom>=0.3) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=30)
BothRes_40=BothRes %>% filter(Chimp_DiffDom >=0.4 | Human_DiffDom>=0.4) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=40)
BothRes_50=BothRes %>% filter(Chimp_DiffDom >=0.5 | Human_DiffDom>=0.5) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=50)
BothRes_60=BothRes %>% filter(Chimp_DiffDom >=0.6 | Human_DiffDom>=0.6) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=60)
BothRes_70=BothRes %>% filter(Chimp_DiffDom >=0.7 | Human_DiffDom>=0.7) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=70)
BothRes_80=BothRes %>% filter(Chimp_DiffDom >=0.8 | Human_DiffDom>=0.8) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=80)
BothRes_90=BothRes %>% filter(Chimp_DiffDom >=0.9 | Human_DiffDom>=0.9) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=90)

BothResAll=BothRes_10 %>% bind_rows(BothRes_20) %>% bind_rows(BothRes_30) %>% bind_rows(BothRes_40) %>% bind_rows(BothRes_50) %>% bind_rows(BothRes_60) %>% bind_rows(BothRes_70) %>% bind_rows(BothRes_80) %>% bind_rows(BothRes_90)

I want dominance in 1 or both at .4.

BothRes_40_each= BothRes_40 %>% mutate(Dom=ifelse(Human_DiffDom>=.4, ifelse(Chimp_DiffDom >=.4, "Both", "Human"), "Chimp"))

BothRes_40_each %>% group_by(Dom) %>% summarise(n())
# A tibble: 3 x 2
  Dom   `n()`
  <chr> <int>
1 Both   1565
2 Chimp   906
3 Human   257
BothRes_40_each %>% group_by(Set,Dom) %>% summarise(n())
# A tibble: 6 x 3
# Groups:   Set [2]
  Set       Dom   `n()`
  <chr>     <chr> <int>
1 Different Both     22
2 Different Chimp   114
3 Different Human    46
4 Same      Both   1543
5 Same      Chimp   792
6 Same      Human   211
BothRes_40_eachsm= BothRes_40_each %>% select(gene, Set, Dom)


BothResInfoDom= BothResInfo %>% full_join(BothRes_40_eachsm, by="gene", fill="None") %>%  mutate(Set= replace_na(Set, "None"),Dom= replace_na(Dom, "None"))


ggplot(BothResInfoDom,aes(x=Human_Base2,y= Chimp_Base2, col=Dom )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + scale_color_brewer(palette = "Set2") + labs(x="Human Information", y="Chimp Information", title="Shannon Information Index colored by whether gene has a dominanat PAS")
Warning: Removed 1 rows containing missing values (geom_point).

ggplot(BothResInfoDom,aes(x=Human_Base2,y= Chimp_Base2, col=Set )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + scale_color_brewer(palette = "Set2") +geom_density2d()+ labs(x="Human Information", y="Chimp Information", title="Shannon Information Index colored by Dominance Structure ")
Warning: Removed 1 rows containing non-finite values (stat_density2d).

Warning: Removed 1 rows containing missing values (geom_point).

BothResInfoDom$numPAS=as.factor(BothResInfoDom$numPAS)
ggplot(BothResInfoDom,aes(x=Human_Base2,y= Chimp_Base2, col=numPAS )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + labs(x="Human Information", y="Chimp Information", title="Shannon Information Index colored by Dominance Structure ") + facet_grid(~Dom) + scale_color_brewer(palette = "Spectral")
Warning in RColorBrewer::brewer.pal(n, pal): n too large, allowed maximum for palette Spectral is 11
Returning the palette you asked for with that many colors
Warning: Removed 10 rows containing missing values (geom_point).

Dominance and number of PAS:

BothResInfoDom$numPAS=as.numeric(as.character(BothResInfoDom$numPAS))
ggplot(BothResInfoDom,aes(x=Dom, y=numPAS)) +geom_boxplot() +stat_compare_means()

Ratio problem!!!!

but the confounder is biological- number of PAS.


sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] vegan_2.5-3     lattice_0.20-38 permute_0.9-4   workflowr_1.6.0
 [5] ggpubr_0.2      magrittr_1.5    forcats_0.3.0   stringr_1.3.1  
 [9] dplyr_0.8.0.1   purrr_0.3.2     readr_1.3.1     tidyr_0.8.3    
[13] tibble_2.1.1    ggplot2_3.1.1   tidyverse_1.2.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2         lubridate_1.7.4    assertthat_0.2.0  
 [4] rprojroot_1.3-2    digest_0.6.18      utf8_1.1.4        
 [7] R6_2.3.0           cellranger_1.1.0   plyr_1.8.4        
[10] backports_1.1.2    evaluate_0.12      httr_1.3.1        
[13] pillar_1.3.1       rlang_0.4.0        lazyeval_0.2.1    
[16] readxl_1.1.0       rstudioapi_0.10    whisker_0.3-2     
[19] Matrix_1.2-15      reticulate_1.10    rmarkdown_1.10    
[22] labeling_0.3       munsell_0.5.0      broom_0.5.1       
[25] compiler_3.5.1     httpuv_1.4.5       modelr_0.1.2      
[28] pkgconfig_2.0.2    mgcv_1.8-25        htmltools_0.3.6   
[31] tidyselect_0.2.5   fansi_0.4.0        crayon_1.3.4      
[34] withr_2.1.2        later_0.7.5        MASS_7.3-51.1     
[37] grid_3.5.1         nlme_3.1-137       jsonlite_1.6      
[40] gtable_0.2.0       git2r_0.26.1       scales_1.0.0      
[43] cli_1.1.0          stringi_1.2.4      reshape2_1.4.3    
[46] fs_1.3.1           promises_1.0.1     xml2_1.2.0        
[49] generics_0.0.2     RColorBrewer_1.1-2 tools_3.5.1       
[52] glue_1.3.0         hms_0.4.2          parallel_3.5.1    
[55] yaml_2.2.0         colorspace_1.3-2   cluster_2.0.7-1   
[58] rvest_0.3.2        knitr_1.20         haven_1.1.2