Evolving notes, images and sounds by Luis Apiolaza

# Author: Luis(Page 1 of 71)

A few posts ago I was talking about heritabilities (like here) and it’s time to say something about genetic correlations. This is how I explain correlations to myself or in meetings with colleagues. Nothing formal, mostly an analogy.

Say we have to draw a distribution of breeding values for one trait (X) and, rather than looking from the side, we look at it from the top. It looks like a straight line, where the length gives an idea of variability and the cross marks the mean. We can have another distribution (Y), perhaps not as long (so not so variable) or maybe longer.

Often variables will vary together (co-vary, vary at the same time) and we can show that by drawing the lines at an angle, where they cross at their means. If you look at the formula for the covariance (co-variance, because traits co-vary, get it?), we grab the deviation from the mean for the two traits for each of the observations, multiply them, add them all up and get their average. We get positive values for the product when both traits are above or below the mean; we get negative values when one trait is below the mean and the other above it. Covariances are a pain, as they can take any value. Instead we can use “standardised” covariances, that vary between -1 and 1: we call these things *correlations*.

If the angle between the distributions is less than 90 degrees, increasing the values of one of the traits is (on average) accompanied by an increase on the other trait. then we have a positive covariance and, therefore, a positive correlation. The smaller the angle, the closer to a correlation of 1.

If the angle is 0 degrees (or close to it), changing the value of one trait has no (or very little) effect on the other trait. Zero correlation.

If the angle is greater than 90 degrees, changing the value of one trait tends to reduce the values of the other trait. The closer the angle to 180 degrees (so the positive values of one distribution are closer to the negative values of the other distribution), the closer to a -1 correlation.

Why do we care about these correlations? We use them all over the place in breeding. Sometimes as a measure of trade-off, as in “if I increase X, what will happen with Y?” or correlated response to selection. We also use them to understand how much information in one trait is contained in another trait, as in “can I use X as a selection criteria for Y?”. And a bunch of other uses, as well. But that’s another post.

I like food. I mean well beyond eating to survive: I do enjoy flavours. Thai is my favourite cuisine but I have a rule: I will try any food that I’m offered at least once. Sometimes the surprise is positive, sometimes it’s horrible; but that’s my rule.

I don’t know how I ended up in this Our World in Data page, but it is a good comparison. There will be quite a bit of variability depending on the specifics of the production system (beef in country X vs country Y, grass fed vs grain fed, etc), but I am interested in the rough scale. And the difference is huge.

Of course greenhouse gasses are only one of the environmental considerations when comparing different types of food. Water use, fertiliser use, soil conservation, pollution runoffs, etc come to mind. This is even before considering animal welfare; I like animals walking around and I pay more for that type of product.

I like the taste of beef but I have to say that I am eating it much less frequently than I used to five years ago. I am not asking you to be vegetarian or vegan—I am neither. In fact I am not asking you to do anything, but I just keep on looking at the graph thinking what I can do better while still enjoying food as much as I do.

I was reading a LinkedIn post that said “heritability is the extent to which differences in observed phenotypes can be attributed to genetic differences”.

There is this idea floating around assuming that if a trait is highly heritable, therefore genetics explains most differences we observe. I have seen it many times, both when people discuss breeding and even in political discussions. I vividly remember a think tank commentator stating that given IQ was highly heritable it is likely that millionaires make more money because their parents were more intelligent, or something along those lines.

I created the figure below using a dataset with wood basic density measurements (how much solid “stuff” you have in a set volume of wood) for trees growing in 17 different environments. The heritability of wood density is around 0.6; however, the differences between some environments are larger than the differences within environments.

We have to remember that heritabilities apply to specific populations and specific environments. Moreover, if we think of the mixed model analysis, we are fitting both fixed and random effects, so we are “correcting/controlling/putting individuals on the same footing” with our fixed effects, before having a look at the variation that is left over. We are then saying that out of that left over genetics explains a proportion of the variation (this is much smaller than the variation before accounting for other sources of variability).

In the case of wood density of radiata pine, the environment (particularly temperature explained by latitude and elevation and soil nutrients like boron) has a larger effect than genetics when looking across multiple trials. The trials with higher density are farther North in New Zealand, which is warmer. Once we are inside one of the trials, genetics explains 60% of the variability. In the same way, once we account for all other social differences, we are left with a much smaller level of variability to try explaining income differences with genetics.

I was chatting with a colleague (Salvador Gezan) in April about teaching, learning and books, and he suggested “have a look at Rex Bernardo’s book”. I searched for it in my university library, no luck. I thought “well, just ask for it as an interlibrary loan. Surely we can borrow a copy from another university in the country and get it in a few days”.

I forgot all about the interloan for three months (!), when I received an email from my university library, saying something like “Hey, we couldn’t find the book you were looking for in NZ. However, we ordered a copy for you”. Then another email today, “Hey, please come and pick up your book from the central library”.

And here I am, at the library with THE copy of the book. We are that small in NZ.

P.S. Salvador and I both did our undergrad at the Universidad de Chile, just with a few years difference.

After “professional Twitter’s” demise I joined LinkedIn (less than a year ago) to keep in touch with colleagues. Overall, I like the posts from people I chose to follow and dislike most of the “suggested by the algorithm” motivational, HR, marketing, leadership, etc. posts.

However, the best part, at least for me, is to see updates by our Forestry students. Looking at their new jobs, either in New Zealand or very far away. Pictures in the office, dealing with tree establishment, forest fires, forest management, processing, etc. It makes me happy to feel even tangentially connected to their new experiences outside the university. Cheers to all of them.