# Approaching Rosalind Problems

I’ve been working through the Rosalind problems over the last week. They are an interesting set of problems exploring the space between Biology and Computation. I decided to take notes while doing one problem. This blog post is a basic outline of my process for problem solving.

### Step 1 - Read The Problem And Background

Always read the problem. I’ve gotten a number of problems wrong in programming challenges because I didn’t read the instructions thoroughly. Rosalind provides some background info which I’ve found helpful as well. It is especially good for learning the relevant biology vocabulary. For this blog post I did the problem Mendel’s First Law.

### Step 2 - Verify That You Can Read The Data

All of the Rosalind problems supply a data file and I’ve fallen into a pattern of starting out by reading in the file to ensure I know what’s going on. For this problem the provided file is `2 2 2`

. Since all the entries are the same it would be hard to verify I was reading and interpreting the file correctly. Because of this I used `1 2 3`

as my example file. Then I wrote the code to put each of these values in a well named variable.

1 2 3 4 5 |
dominant, hetero, recessive = File.read("iprb.txt").chomp.split(' ').map(&:to_i) puts "Dominant #{dominant}" puts "Heterozygous #{hetero}" puts "Recessive #{recessive} |

### Step 3 - Ponder And Devise A Strategy

My first strategy was to calculate how many ways there were to have the at least one dominant allele. Here’s some basic thoughts on that: From the background given I know that if one parent has the dominant allele the the resulting organism must have the dominant allele. Probability of one parent have the dominant allele is

```
dominant not-dominant dominant
-------- + ------------- * ----------
total total total - 1
```

Then I remembered that since there are fewer ways get two recessive alleles I should calculate that instead and then subtract the result from one. (Basic law of probability).

#### Math:

Probability of two recessive parents mating:

```
recessive recessive - 1
--------- * -------------
total total - 1
```

Probability of two heterozygous parents mating:

```
heterozygous heterozygous - 1
------------ * ------------------
total total - 1
```

Punnet square for heterozygous mating

```
| | Y | y |
|---+----+----|
| Y | YY | Yy |
| y | Yy | yy |
```

Only 1/4 of those will be recessive so we take the probability of two heterozygous mating and multiply it by 1/4.

```
heterozygous heterozygous - 1 1
------------ * ------------------ * -----
total total - 1 4
```

Finally the probability of a heterozygous and a recessive organism mating:

```
heterozygous recessive recessive heterozygous
------------ * ------------ + ------------ * --------------
total total - 1 total total - 1
```

Punnet square for heterozygous & recessive mating

```
| | Y | y |
|---+----+----|
| y | Yy | yy |
| y | Yy | yy |
```

In this case half the offspring have two recessive alleles so multiply the probability by 1/2.

### Step 4 - Write The Code

First thing I realized was that we need floats so I had to change the import code slightly. I changed the to_i to a to_f.

```
dominant, hetero, recessive = File.read("iprb.txt").chomp.split(' ').map(&:to_f)
```

All my calculations require the total so I do that once:

```
total = dominant + hetero + recessive
```

Now calculate the probability of two recessive organisms mating:

```
r_r = (recessive / total) * ((recessive - 1) / (total - 1))
```

Now heterozygous organisms mating:

```
h_h = (hetero / total) * ((hetero - 1) / (total - 1))
```

Now the hetero + recessive matings:

```
h_r = (hetero / total) * (recessive / (total - 1)) + (recessive / total) * (hetero / (total - 1))
```

Now I incorporate the fractions from the punnet squares:

```
recessive_total = r_r + h_h * 1/4 + h_r * 1/2
```

This is the probability of a recessive organism. The problem asked for the probability of a dominant organism so I take 1 - recessive_total

```
puts 1 - recessive_total
```

All together:

1 2 3 4 5 6 7 8 9 |
dominant, hetero, recessive = File.read("iprb.txt").chomp.split(' ').map(&:to_f) total = dominant + hetero + recessive r_r = (recessive / total) * ((recessive - 1) / (total - 1)) h_h = (hetero / total) * ((hetero - 1) / (total - 1)) h_r = (hetero / total) * (recessive / (total - 1)) + (recessive / total) * (hetero / (total - 1)) recessive_total = r_r + h_h * 1/4 + h_r * 1/2 puts 1 - recessive_total 1 - recessive_total |

When all this code runs it gives `0.78333`

which is the expected result.

### Step 5 - Download The Real Data Set

Now I downloaded the real dataset, ran it through my code, and pasted the result into the text box.

### Step 6 - Celebrate

I recommend celebrating with cookies.

### Post-script

This problem can also be solved by simulating all possible matings and then calculating the percentage that have the dominant allele.

1 2 3 4 5 6 7 8 9 |
dominant, hetero, recessive = File.read("iprb.txt").chomp.split(' ').map(&:to_f) def is_dominant? organism organism.include? "Y" end d_ary = Array.new(dominant) { ["Y", "Y"] } h_ary = Array.new(hetero) { ["Y", "y"] } r_ary = Array.new(recessive) { ["y", "y"] } ary = d_ary + h_ary + r_ary children = [] (0...ary.length).each do |i| (0...ary.length).each do |j| next if i == j p1 = ary[i] p2 = ary[j] children << [p1[0], p2[0]] children << [p1[0], p2[1]] children << [p1[1], p2[0]] children << [p1[1], p2[1]] end end d_children, r_children = children.partition { |o| is_dominant?(o) } puts d_children.count.to_f / children.count |