Concatenate pairs of columns for entire dataframe

We can create a loop to subset the columns along with the adjacent column, paste it together withdo.call` and assign it as new columns to the new dataset

out <- df[1]
out[paste0("var", 1:3)] <- lapply(seq(2, ncol(df), 2), 
               function(i) do.call(paste0, df[i:(i+1)]))

Using tidyverse, you can compose the modifying expressions ahead of time, then pass them all to transmute in bulk. This solution uses column names and is therefore robust to the column ordering: if you shuffle your allele columns, this should still give you the same answer.

library( tidyverse )

# Create expressions of the form allele1 = str_c(allele1a, allele1b)
v <- str_c("allele",1:3) %>% set_names %>%
    map( ~glue::glue("str_c({.}a, {.}b)") ) %>% map( rlang::parse_expr )

df %>% transmute( id = id, !!!v )
# # A tibble: 20 x 4
#       id allele1 allele2 allele3
#    <int> <chr>   <chr>   <chr>  
#  1     1 AT      CC      AA     
#  2     2 AT      CC      AA     
#  3     3 AT      CC      AA     
#  4     4 AT      CC      AA     
# ...

I modified your data to closer match your description:

df <- data_frame(id = seq(1,20),
             allele1a = rep("A", 20),
             allele1b = c(rep("T", 10), rep("A", 10)),
             allele2a = rep("C", 20),
             allele2b = c(rep("C", 10), rep("G", 10)),
             allele3a = rep("A", 20),
             allele3b = c(rep("A", 10), rep("G", 10)))

Here's a tidyverse way designed to scale fairly well. Instead of hard-coding that you want to pair columns 1 & 2, 3 & 4, and 5 & 6, I'm reshaping to long data to get a variable number, grouping those into pairs by dividing the variable number by 2, collapsing the letters in each pair, and reshaping back to wide. This way, you can do the same procedure on any even number of columns.

library(tidyverse)
...

Filtering for ID 1 to show a glimpse of this:

df %>%
  gather(key = var, value = value, -id) %>%
  mutate(var = str_extract(var, "\\d+") %>% as.numeric()) %>%
  group_by(id) %>%
  mutate(pair = ceiling(var / 2)) %>%
  filter(id == 1)
#> # A tibble: 6 x 4
#> # Groups:   id [1]
#>      id   var value  pair
#>   <int> <dbl> <chr> <dbl>
#> 1     1     1 A         1
#> 2     1     2 T         1
#> 3     1     3 C         2
#> 4     1     4 C         2
#> 5     1     5 A         3
#> 6     1     6 A         3

Then collapsing strings as a summarizing value for each combination of ID and pair:

df %>%
  gather(key = var, value = value, -id) %>%
  mutate(var = str_extract(var, "\\d+") %>% as.numeric()) %>%
  group_by(id) %>%
  mutate(pair = ceiling(var / 2)) %>% 
  group_by(id, pair) %>%
  summarise(combined = paste(value, collapse = ""))
#> # A tibble: 60 x 3
#> # Groups:   id [?]
#>       id  pair combined
#>    <int> <dbl> <chr>   
#>  1     1     1 AT      
#>  2     1     2 CC      
#>  3     1     3 AA      
#>  4     2     1 AT      
#>  5     2     2 CC      
#>  6     2     3 AA      
#>  7     3     1 AT      
#>  8     3     2 CC      
#>  9     3     3 AA      
#> 10     4     1 AT      
#> # ... with 50 more rows

And using spread to get back into a wide format.

df %>%
  gather(key = var, value = value, -id) %>%
  mutate(var = str_extract(var, "\\d+") %>% as.numeric()) %>%
  group_by(id) %>%
  mutate(pair = ceiling(var / 2)) %>% 
  group_by(id, pair) %>%
  summarise(combined = paste(value, collapse = "")) %>%
  mutate(var_combo = paste0("var", pair)) %>%
  select(-pair) %>%
  spread(key = var_combo, value = combined) %>%
  head()
#> # A tibble: 6 x 4
#> # Groups:   id [6]
#>      id var1  var2  var3 
#>   <int> <chr> <chr> <chr>
#> 1     1 AT    CC    AA   
#> 2     2 AT    CC    AA   
#> 3     3 AT    CC    AA   
#> 4     4 AT    CC    AA   
#> 5     5 AT    CC    AA   
#> 6     6 AT    CC    AA

^{Created on 2018-11-07 by the reprex package (v0.2.1)}

using base r you could do:

 a <- seq(2,ncol(df),2)
 b <- paste0(unlist(df[a]),unlist(df[a+1]))
 d <- data.frame(matrix(b,nrow(df)))
 result <- cbind(df[1],d)

This can also be written in a one line:

(dat =  data.frame(matrix(paste0(unlist(df[a<-seq(2,ncol(df),2)]),unlist(df[a+1])),nrow(df))))
   X1 X2 X3
1  AT CC AA
2  AT CC AA
3  AT CC AA
4  AT CC AA
5  AT CC AA
6  AT CC AA
7  AT CC AA
8  AT CC AA
9  AT CC AA
10 AT CC AA
11 AA CG AG
12 AA CG AG
13 AA CG AG
14 AA CG AG
15 AA CG AG
16 AA CG AG
17 AA CG AG
18 AA CG AG
19 AA CG AG
20 AA CG AG

Then cbind it with the id column:

cbind(df[1],dat)

df <- data.frame(id = seq(1,20),
                 var1 = rep("A", 20),
                 var2 = c(rep("T", 10), rep("A", 10)),
                 var3 = rep("C", 20),
                 var4 = c(rep("C", 10), rep("G", 10)),
                 var5 = rep("A", 20),
                 var6 = c(rep("A", 10), rep("G", 10)),
                 stringsAsFactors = FALSE)

df2 <- data.frame(id = df[,1], var1 = paste(df[,2], df[,3], sep = ""), 
                  var2 = paste(df[,4], df[,5], sep = ""), 
                  var3 = paste(df[,6], df[,7], sep = ""))