Two alleles are identical-by-double-reduction (IBDR) if they originate from the same (by origin) allele in the parent. We let "a" be the probability of zero IBDR alleles, "b" be the probability of one IBDR pair, "c" be the probability of two IBDR pairs, etc...

gsegmat_symb(ploidy, out = c("str", "exp"))

Arguments

ploidy

The ploidy of the species

out

Should we return a character matrix ("str") or an expression matrix ("exp")?

Value

A character or expression matrix containing the mathematical form for the segregation matrix. Element (i, j) is the probability a parent with dosage i-1 produces a gamete with dosage j-1.

See also

gsegmat() for numerical expressions.

Author

David Gerard

Examples

gsegmat_symb(4)
#>   0               1        2              
#> 0 "a+b"           "0"      "0"            
#> 1 "(1/2)a+(3/4)b" "(1/2)a" "(1/4)b"       
#> 2 "(1/6)a+(1/2)b" "(2/3)a" "(1/6)a+(1/2)b"
#> 3 "(1/4)b"        "(1/2)a" "(1/2)a+(3/4)b"
#> 4 "0"             "0"      "a+b"          
gsegmat_symb(6)
#>   0                1                 2                 3               
#> 0 "a+b"            "0"               "0"               "0"             
#> 1 "(1/2)a+(2/3)b"  "(1/2)a+(1/6)b"   "(1/6)b"          "0"             
#> 2 "(1/5)a+(2/5)b"  "(3/5)a+(4/15)b"  "(1/5)a+(4/15)b"  "(1/15)b"       
#> 3 "(1/20)a+(1/5)b" "(9/20)a+(3/10)b" "(9/20)a+(3/10)b" "(1/20)a+(1/5)b"
#> 4 "(1/15)b"        "(1/5)a+(4/15)b"  "(3/5)a+(4/15)b"  "(1/5)a+(2/5)b" 
#> 5 "0"              "(1/6)b"          "(1/2)a+(1/6)b"   "(1/2)a+(2/3)b" 
#> 6 "0"              "0"               "0"               "a+b"           
gsegmat_symb(8)
#>   0                          1                
#> 0 "a+b+c"                    "0"              
#> 1 "(1/2)a+(5/8)b+(3/4)c"     "(1/2)a+(1/4)b"  
#> 2 "(3/14)a+(5/14)b+(15/28)c" "(4/7)a+(5/14)b" 
#> 3 "(1/14)a+(5/28)b+(5/14)c"  "(3/7)a+(5/14)b" 
#> 4 "(1/70)a+(1/14)b+(3/14)c"  "(8/35)a+(2/7)b" 
#> 5 "(1/56)b+(3/28)c"          "(1/14)a+(5/28)b"
#> 6 "(1/28)c"                  "(1/14)b"        
#> 7 "0"                        "0"              
#> 8 "0"                        "0"              
#>   2                                 3                
#> 0 "0"                               "0"              
#> 1 "(1/8)b+(1/4)c"                   "0"              
#> 2 "(3/14)a+(1/28)b+(5/28)b+(3/7)c"  "(1/14)b"        
#> 3 "(3/7)a+(5/56)b+(5/28)b+(15/28)c" "(1/14)a+(5/28)b"
#> 4 "(18/35)a+(1/7)b+(1/7)b+(4/7)c"   "(8/35)a+(2/7)b" 
#> 5 "(3/7)a+(5/28)b+(5/56)b+(15/28)c" "(3/7)a+(5/14)b" 
#> 6 "(3/14)a+(5/28)b+(1/28)b+(3/7)c"  "(4/7)a+(5/14)b" 
#> 7 "(1/8)b+(1/4)c"                   "(1/2)a+(1/4)b"  
#> 8 "0"                               "0"              
#>   4                         
#> 0 "0"                       
#> 1 "0"                       
#> 2 "(1/28)c"                 
#> 3 "(1/56)b+(3/28)c"         
#> 4 "(1/70)a+(1/14)b+(3/14)c" 
#> 5 "(1/14)a+(5/28)b+(5/14)c" 
#> 6 "(3/14)a+(5/14)b+(15/28)c"
#> 7 "(1/2)a+(5/8)b+(3/4)c"    
#> 8 "a+b+c"