The Normal Distribution

September 30, 2006

Evolution is all about populations. And genetics. And selection pressure and genetic drift and speciation.

But it’s mostly about the normal distribution.

So what is the normal distribution?

Ok, imagine you measured the height of 10,000 people. You can easily get the average height by adding all the heights together and dividing by 10,000. Say this came out as 5’8″.

What proportion of the group were exactly 5’8″ tall? How many were 5’7″ or 6’2″?

So, you divide all the heights into groups. Say from 0″ to 1″, from 1″ to 2″, etc, all the way up to 12’6″ to 12’7″

Then you counted the number pf people who fell into each group, and plotted it onto a chart. The chart would look something like this:

… but probably not as nice and smooth because reality is never as neat as theory.

The shape of that chart is a normal distribution. It also gets called ‘The Bell Curve’ because it looks like the cross-section of a bell.

One thing to notice is that it’s easy to get the average from a normal distribution. It’s the value under the highest point of the distribution.

Most naturally occurring measurements (like height, IQ, length of tongue, etc) follow a normal distribution. There are lots of statistical measurements that you can use to check whether measurements are normally distributed (like ‘skewness’ and ‘kurtosis’) but we won’t bother with them just now, they just complicate things.

The Oxford English Dictionary defines evolution as ‘any net change in the genetics of a population’.

To all intents and purposes we can take this as ‘any change to the normal distribution of a characteristic within a population’.

That’s why evolution is all about the normal distribution. Except when it isn’t, but I’m not going to worry about that.


If you’re interested in writing software, check out my other blog: Coding at The Coal Face

Written while listening to:

Butterflies and Hurricanes by Muse from the album Absolution


Plug In Baby by Muse from the album Origin Of Symmetry


Stay Loose by Belle & Sebastian from the album Dear Catastrophe Waitress


9 Responses to “The Normal Distribution”

  1. Sreenathan Says:

    If evolution is all about normal distribution, then how genetic distance will be assessed?

  2. drherbie Says:

    Well, at least someone’s reading this …

    First I should start with some caveats/excuses:
    1. It’s been a long time since I actively studied evolution (not since 1999).
    2. I’m writing this for people who don’t understand evolution or population genetics, so I’m glossing over a lot of the pesky details.
    3. Just becuase I have a PhD doesn’t mean I know what I’m talking about.

    The normal distribution I’m describing is a measurement of phenotype (the actual physical aspects of the population) while genetic distance is a measure of genotype (it actually uses ‘junk’ DNA which is *not* under selective pressure).

    I’m using the normal distribution as a visualisation of a phenotype under selection to show the effects that selection pressure will have. I want readers to understand the mechanisms of evolution, if not all the icky genetics stuff. I’ll be adding some simulation software code as I go along to help with demonstrations.

    Genetic distance is a measure of the mutations that have arisen within the DNA and is not liked to phenotype.

    I have to hold my hand up at this point and say that I never really understood how genetic distance was actually measured (apart from knowing that they use test-tubes and wear white coats). I’m from the hand-waving, theoretical part of evolutionary biology.

    I would *assume* that if genetic distance is being measured between populations then an average value is used for comparison, rather that just measuring one individual in each population. With the normal distribution of the phenotype we would be comparing the means too, but using parametric statistics to discriminate the difference.

    To be honest I’ve never really seen the point of genetic distance due to the assumptions that are made — it pretty much assumes a constant rate of mutation — and it only serves to compartmentalise people’s views of evolution.
    We need cladograms and taxonomy to enable communication about species, but we can’t even decide on a good definition of what a species is.

    My personal view of evolution is much more holistic, with ‘species’ being simply variations on a theme within a wide ocean of genetic possabilities.

    Well, I don’t know if you gained an answer for all that, but if you read this far you deserve a medal. Or at least a firm handshake and a hearty ‘congratulations’.


  3. […] Models are often build on the principles of the Normal Distribution and will deal with changes in mean and standard deviation over time, or in regard to some other variable. […]

  4. […] random element to the genetic makeup of the population.  And as you should know if you read my first post, changes to the genetic makeup of a population is called […]

  5. […] are often build on the principles of the Normal Distribution and will deal with changes in mean and standard deviation over time, or in regard to some other […]

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