Ratios

A ratio is a very clear and useful way to show comparisons between numerical data. A ratio like "1 Brown:1 Blue" tells you that, whatever experiment or activity you just completed, the brown results are about equal in number to the blue results. A ratio like "7 Purple:1 White" tells you that your outcome included about seven times as many purple results as white results.

Suppose you performed the following fruit fly mating experiment:

  1. Parental generation: Wild Type Female mated to Sepia Eyed Male
  2. All offspring (the F1) Wild Type Eyes.
  3. Create an F2 by mating F1 females to F1 males.

Results:

  Males Females
Wild Type Eyes 3755 3777
Sepia Eyes 1261 1202

So what is the phenotypic ratio demonstrated by these results?

First, since we evidently don't have any difference between the male and the female results, let's add them together.

Wild Type eyes: 3755 (males) + 3777 (females) = 7532
Sepia eyes: 1261 (males) + 1202 (females) = 2463

We get an idea of what our ratio is by taking the smallest number among our offspring classes (2463, in this case) and dividing all of the other numbers by that one.

7532/2463 = 3.06 (rounded off to second decimal place)
2463/2463 = 1.00 (of course ;^)

So we have:

  Total Ratio
Wild Type Eyes 7532 3.06
Sepia Eyes 2463 1.00

And this is about as close to a 3:1 ratio as anyone could ask :^) You would reduce the terms to round numbers, and state this ratio as "3 Wild Type:1 Sepia." Note that a ratio can never be correct if it is composed of only numbers. The descriptions (in this case, "Wild Type" and "Sepia") must be included.

If the males and the females have obviously different results, then you need to include gender as part of the ratio. For these data (though there's no obvious reason to do this for this problem), you'd do that by using the 1202 (females with sepia eyes) as your lowest number and dividing the other numbers by that one.

You'd get:

  Total Ratio
Wild Type Males 3755 3.12
Wild Type Females 3777 3.14
Sepia Males 1261 1.05
Sepia Females 1202 1.00

 

You'd describe this ratio as "3 Wild Type Females:3 Wild Type Males:1 Sepia Female:1 Sepia Male." Recall, however, that there's no reason to split the males and females unless their ratios are different. Different ratios for males vs. females often indicate the existence of a sex-linked gene, and should always be noted in figuring phenotypic ratios.

Some final notes and reminders about ratios:

  1. Most of the time, you reduce raw numbers to ratios by dividing all of the numbers by the smallest one. Note that there are exceptions to this. If you get a result that looks like, say, "1.5 Round:1 Flat," then your actual ratio is probably "3 Round:2 Flat." How do you know when that's appropriate? Use your judgment ;^)
  2. If you tabulate your results, and one or more categories turn out to have zero entries, those categories simply do not figure into the ratio. Obviously, you can't divide by zero. Simply ignore those empty categories and figure your ratio based on the categories that actually have results in them.
  3. Sometimes you may find that all of your results are essentially identical. For example, you may have only red eyed offspring. In this case, you simply report your "ratio" as "100% red" or "all red."
  4. Remember that a ratio composed of only numbers is automically incorrect. Your ratio must also include the descriptions which go with the numbers.