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Next week I’ll be attending a Nescent Academy “master class” on quantitative genetics, led by two teachers who have made major advances in this field. They will be assisted by other teachers who have done important work in the field. I’m really glad to have the opportunity so close to home: it’s always nice when the best students and teachers in a field come to my home town to lead a workshop like this πŸ˜‰

This is a good opportunity to talk about quantitative genetics. What is it? As with many scientific topics, it means different things to different people, depending on your main research question. I do theory, but other researchers are primarily concerned with analyzing data, and conducting experiments. Quantitative genetics is a helpful set of ideas in all three of these areas, so I will try to explain my understanding of all of them.

First of all what is genetics? Genetics is the science of inheritance. The basic question of genetics is how do parents pass their traits to their offspring? We know the basics are that parents pass “particles of inheritance” to their offspring (genes) that the offspring express, thus creating likeness between offspring and parents. This theory works for traits like eye color and hair color, but what about for something like height? Height is a different kind of trait altogether, and people have known for a long time that offspring do not typically display the height of one parent or another, the way they do with eye color.

This disparity was actually the source of a vitriolic debate between “Mendelians” and “biometricians” at the turn of the twentieth century. The biometricians had been studying traits like human height in humans and animals for many decades, and then several botanists rediscovered the work of Mendel and started testing it out on plants and fruit flies. Mendelians caricaturishly believed that mutation was the only necessary evolutionary mechanism, and that Mendelian inheritance was the only mode of inheritance possible. They couldn’t explain the patterns of inheritance in traits like height, however.

The solution was a “fudge” or a “hack” by R.A. Fisher: what if height was controlled not by a single gene, but by many throughout the genome? Offspring will inherit some of these from mom, some from dad and the outcome should be a mix of contributions to the trait from each parent. Height, after all, or any trait, is a human construction, imposed by researchers onto an organism: why should there be just one gene that controls something arbitrarily decided by someone with a measuring tape? The outcome, Fisher showed, of Mendelian inheritance of a huge number of genes contributing small effects would be just the patterns observed by the biometricians. Keep in mind that in the first half of the twentieth century, people did not know what the actual genetic material was, or least of all how it worked.

Quantitative genetics then is a hack that ignores the genetic details of a particular trait and simply looks at the statistical patterns between parents and offspring. For experimenters, the crucial concerns are setting up breeding experiments that can explain how traits are inherited. For example, maternal half-sibs (offspring all born from the same mother) can eliminate the effects of the mother on the offspring. If the offspring all come from the same mother, then the mother’s genes will not explain the variation in the offspring. Only the population of fathers can supply the variation seen in the offspring.

Another approach to quantitative genetics comes straight from animal husbandry: if you want to breed animals that produce more of a certain product (the typical example is milk), then you can use equations to calculate how many cows to breed, and what their milk yields need to be, in order to produce a certain milk yield in the next generation. The difference in milk yield between offspring and parents is the “response to selection,” in this case artificial selection. This is the very idea of selective breeding that Darwin analogized to natural selection, so this same farming idea carries through to those of us studying the evolution of quantitative traits.

This last aspect is mainly my interest in quantitative genetics. We can use the equations I described in the last paragraph, and iterate them to simulate or describe the evolutionary process. The equilibrium solutions to these equations can tell us what traits are likely to evolve, all without going into the genetic details. Quantitative genetics involves a large number of approximations — skipping over the details — and that’s the nice thing about it mathematically. Despite using so many approximations, the equations are usually quite accurate.

The most recent development in quantitative genetics actually involves going beyond those approximations and mapping out actual genetic loci that are involved in the inheritance of quantitative traits. This is called Quantitative Trait Locus (QTL) analysis, and is also being called QTN analysis, for “quantitative trait nucleotide.” The meaning of the “N” should tell you just how specific some of these studies are getting. There is a controversy about this, however, since it appears that many studies from humans and animals show quite conclusively that the “hack” of quantitative genetics may not be so much a hack as a scientific reality. Genome-wide association studies and others that look at the whole genome are starting to show that indeed many loci of small effects are a better explanation than few genes of large effect in many cases, including human height and schizophrenia. This is especially weird, since Fisher’s “infinitesimal hypothesis” was only meant to solve a very specific problem, and probably was not meant as a real scientific hypothesis. What does this say about the operation of science?

I hope to meet some of you there next week. Thanks for reading.

Matthew V. Rockman (2012). THE QTN PROGRAM AND THE ALLELES THAT MATTER FOR EVOLUTION: ALL THAT’S GOLD DOES NOT GLITTER Evolution, 1-17 DOI: 10.1111/j.1558-5646.2011.01486.x