# Selected, causal, and relevant

What is ”function”? In discussions about junk DNA people often make the distinction between ”selected effects” and ”causal roles”. Doolittle & Brunet (2017) put it like this:

By the first (selected effect, or SE), the function(s) of trait T is that (those) of its effects E that was (were) selected for in previous generations. They explain why T is there. … [A]ny claim for an SE trait has an etiological justification, invoking a history of selection for its current effect.

/…/

ENCODE assumed that measurable effects of various kinds—being transcribed, having putative transcription factor binding sites, exhibiting (as chromatin) DNase hypersensitivity or histone modifications, being methylated or interacting three-dimensionally with other sites — are functions prima facie, thus embracing the second sort of definition of function, which philosophers call causal role …

In other words, their argument goes: a DNA sequence can be without a selected effect while it has, potentially several, causal roles. Therefore, junk DNA isn’t dead.

First, if we want to know the fraction of the genome that is functional, we’d like to talk about positions in some reference genome, but the selected effect definition really only works for alleles. Positions aren’t adaptive, but alleles can be. They use the word ”trait”, but we can think of an allele as a trait (with really simple genetics — its genetic basis its presence or absence in the genome).

Also, unfortunately for us, selection doesn’t act on alleles in isolation; there is linked selection, where alleles can be affected by selection without causally contributing anything to the adaptive trait. In fact, they may counteract the adaptive trait. It stands to reason that linked variants are not functional in the selected effect sense, but they complicate analysis of recent adaptation.

The authors note that there is a problem with alleles that have not seen positive selection, but only purifying selection (that could happen in constructive neutral evolution, which is when something becomes indispensable through a series of neutral or deleterious substitutions). Imagine a sequence where most mutations are neutral, but deleterious mutations can happen rarely. A realistic example could be the causal mutation for Freidreich’s ataxia: microsatellite repeats in an intron that occasionally expand enough to prevent transcription (Bidichandani et al. 1998, Ohshima et al. 1998; I recently read about it in Nessa Carey’s ”Junk DNA”). In such cases, selection does not preserve any function of the microsatellite. That a thing can break in a dangerous way is not enough to know that it was useful when whole.

Second, these distinctions may be relevant to the junk DNA debate, but for any research into the genetic basis of traits currently or in the future, such as medical genetics or breeding, neither of these perspectives is what we need. The question is not what parts of the genome come from adaptive alleles, nor what parts of the genome have causal roles. The question is what parts of the genome have causal roles that are relevant to the traits we care about.

The same example is relevant. It seems like the Friedriech’s ataxia-associated microsatellite does not fulfill the selected effect criterion. It does, however, have a causal role, and a causal role relevant to human disease, at that.

I do not dare to guess whether the set of sequences with causal roles relevant to human health is bigger or smaller than the set of sequences with selected effects. But they are not identical. And I will dare to guess that the relevant set, like the selected effect set, is a small fraction of the genome.

Literature

Doolittle, W. Ford, and Tyler DP Brunet. ”On causal roles and selected effects: our genome is mostly junk.” BMC biology 15.1 (2017): 116.

Annonser

# Nessa Carey ”Junk DNA”

I read two popular science books over Christmas. The other one was in Swedish, so I’ll do that in Swedish.

Nessa Carey’s ”Junk DNA: A Journey Through the Dark Matter of the Genome” is about noncoding DNA in the human genome. ”Coding” in this context means that it serves as template for proteins. ”Noncoding” is all the rest of the genome, 98% or so.

The book is full of fun molecular genetics: X-inactivation, rather in-depth discussion of telomeres and centromeres, the mechanism of noncoding microsatellite disease mutations, splicing — some of which isn’t often discussed at such length and clarity. It gives the reader a good look at how messy genomics can be. It has wonderful metaphors — two baseball bats with magnetic paint and velcro, for example. It even has an amusing account of the ENCODE debate. I wonder if it’s true that evolutionary biologists are more emotional than other biologists?

But it really suffers from the framing as a story about how noncoding DNA used to be dismissed as pointless, and now, surprisingly, turns out to have regulatory functions. This makes me a bit hesitant to recommend the book; you may come away from reading it with a lot of neat details, but misled about the big picture. In particular, you may believe a false history of all this was thought to be junk; look how wrong they were in the 70s, and the very dubious view that most of the human genome is important for our health.

On the first page of the book, junk DNA is defined like this:

Anything that doesn’t code for protein will be described as junk, as it originally was in the old days (second half of the twentieth century). Purists will scream, and that’s OK.

We should scream, or at least shake our heads, because this definition leads, for example, to describing ribosomes and transfer-RNA as ”junk” (chapter 11), even if both of them have been known to be noncoding and functional since at least the 60s. I guess the term ”junk” sticks, and that is why the book uses it, and why biologists love to argue about it. You couldn’t call the book something unspeakably dry like ”Noncoding DNA”.

So, this is a fun a popular science book about genomics. Read it, but keep in mind that if you want to define ”junk DNA” for any other purpose than to immediately shoot it down, it should be something like this:

For most of the 50 years since Ohno’s article, many of us accepted that most of our genome is ”junk”, by which we would loosely have meant DNA that is neither protein-coding nor involved in regulating the expression of DNA that is. (Doolittle & Brunet 2017)

The point of the term is not to dismiss everything that is not coding for a protein. The point is that the bulk of DNA in the genome is neither protein coding nor regulatory. This is part of why molecular genetics is so tricky: it is hard to find the important parts among all the rest. Researchers have become much better at sifting through the noncoding parts of the genome to find the sequences that are interesting and useful. Think of lots of tricky puzzles being solved, rather than of a paradigm being overthrown by revolution.

Literature

Carey, Nessa. (2015) Junk DNA: A Journey Through the Dark Matter of the Genome. Icon Books, London.

Doolittle, W. Ford, and Tyler DP Brunet. (2017) ”On causal roles and selected effects: our genome is mostly junk.” BMC Biology.

# Griffin & Nesseth ”The science of Orphan Black: the official companion”

I didn’t know that science fiction series Orphan Black actually had a real Cosima: Cosima Herter, science consultant. After reading this interview and finishing season 5, I realised that there is also a new book I needed to read: The science of Orphan Black: The official companion by PhD candidate in development, stem cells and regenerative medicine Casey Griffin and science communicator Nina Nesseth with a foreword by Cosima Hertner.

(Warning: This post contains serious spoilers for Orphan Black, and a conceptual spoiler for GATTACA.)

One thing about science fiction struck me when I was watching the last episodes of Orphan Black: Sometimes it makes a lot more sense if we don’t believe everything the fictional scientists tell us. Like real scientists, they may be wrong, or they may be exaggerating. The genetically segregated future of GATTACA becomes no less chilling when you realise that the silly high predictive accuracies claimed are likely just propaganda from a oppressive society. And as you realise that the dying P.T. Westmorland is an imposter, you can break your suspension of disbelief about LIN28A as a fountain of youth gene … Of course, genetics is a little more complicated than that, and he is just another rich dude who wants science to make him live forever.

However, it wouldn’t be Orphan Black if there weren’t a basis in reality: there are several single gene mutations in model animals (e.g. Kenyon & al 1993) that can make them live a lot longer than normal, and LIN28A is involved in ageing (reviewed by Jun-Hao & al 2016). It’s not out of the question that an engineered single gene disruption that substantially increases longevity in humans could be possible. Not practical, and not necessarily without unpleasant side effects, but not out of the question.

Orphan Black was part slightly scary adventure, part festival of ideas about science and society, part character-driven web of relationships, and part, sadly, bricolage of clichés. I found when watching season five that I’d forgotten most of the plots of seasons two through four, and I will probably never make the effort to sit through them again. The first and last seasons make up for it, though.

The series seems to have been set on squeezing as many different biological concepts as possible in there, so the book has to try to do the same. It has not just clones and transgenes, but also gene therapy, stem cells, prion disease, telomeres, dopamine, ancient DNA, stem cells in cosmetics and so on. Two chapters try valiantly to make sense of the clone disease and the cure. It shows that the authors have encyclopedic knowledge of life science, with a special interest in development and stem cells.

But I think they slightly oversell how accurate the show is. Like when Cosima tells Scott to ”run a PCR on these samples, see if there are any genetic markers” and ”can you sequence for cytochrome c?”, and Scott replies ”the barcode gene? that’s the one we use for species differentiation” … That’s what screen science is like. The right words, but not always in the right order.

Cosima and Scott sciencing at university, before everything went pear-shaped. One of the good thing about Orphan Black was the scientist characters. There was a ton of them! The good ones, geniuses with sparse resources and self experimentation, the evil ones, well funded and deeply unethical, and Delphine. This scene is an exception in that it plays the cringe-inducing nerd angle. Cosima and Scott grew after than this.

There are some scientific oddities. They must be impossible to avoid. For example, the section on epigenetics treats it as a completely new field, sort of missing the history of the subfield. DNA methylation research was going on already in the 1970s (Gitschier 2009). Genomic imprinting, arguably the only solid example of transgenerational epigenetic effects in humans, and X inactivation were both being discovered during 70s and 80s (reviewed by Ferguson-Smith 2011). The book also makes a hash of genome sequencing, which is a shame but understandable. It would have taken a lot of effort to disentangle how sequencing worked when the fictional clone experiment started and how it got to how it works in season five, when Cosima runs Nanopore sequencing.

The idea of human cloning is evocative. Orphan Black flipped it on its head by making the main clone characters strikingly different. It also cleverly acknowledged that human cloning is a somewhat dated 20th century idea, and that the cutting edge of life science has moved on. But I wish the book had been harder on the premise of the clone experiment:

By cloning the human genome and fostering a set of experimental subjects from birth, the scientists behind the project would gain many insights into the inner workings of the human body, from the relay of genetic code into observable traits (called phenotypes), to the viability of manipulated DNA as a potential therapeutic tool, to the effects of environmental factors on genetics. It’s a scientifically beautiful setup to learn myriad things about ourselves as humans, and the doctors at Dyad were quick to jump at that opportunity. (Chapter 1)

This is the very problem. Of course, sometimes ethically atrocious fictional science would, in principle, generate useful knowledge. But when when fictional science is near useless, let’s not pretend that it would produce a lot of valuable knowledge. When it comes to genetics and complex traits like human health, small sample studies of this kind (even if it was using clones) would be utterly useless. Worse than useless, they would likely be biased and misleading.

Researchers still float the idea of a ”baseline”, though, but in the form of a cell line, where it makes more sense. See the the (Human) Genome Project-write (Boeke & al 2016), suggesting the construction of an ideal baseline cell line for understanding human genome function:

Additional pilot projects being considered include … developing a homozygous reference genome bearing the most common pan-human allele (or allele ancestral to a given human population) at each position to develop cells powered by ”baseline” human genomes. Comparison with this baseline will aid in dissecting complex phenotypes, such as disease susceptibility.

In the end, the most important part of science in science fiction isn’t to be a factually correct, nor to be a coherent prediction about the future. If Orphan Black has raised interest in science, and I’m sure it has, that is great. And if it has stimulated discussions about the relationship between biological science, culture and ethics, that is even better.

The timeline of when relevant scientific discoveries happened in the real world and in Orphan Black is great. The book has a partial bibliography. The ”Clone Club Q&A” boxes range from silly fun to great open questions.

Orphan Black was probably the best genetics TV show around, and this book is a wonderful companion piece.

Plaque at the Roslin Institute to the sheep that haunts Orphan Black. ”Baa.”

Literature

Boeke, JD et al (2016) The genome project-write. Science.

Ferguson-Smith, AC (2011) Genomic imprinting: the emergence of an epigenetic paradigm. Nature reviews Genetics.

Gitschier, J. (2009). On the track of DNA methylation: An interview with Adrian Bird. PLOS Genetics.

Jun-Hao, E. T., Gupta, R. R., & Shyh-Chang, N. (2016). Lin28 and let-7 in the Metabolic Physiology of Aging. Trends in Endocrinology & Metabolism.

Kenyon, C., Chang, J., Gensch, E., Rudner, A., & Tabtiang, R. (1993). A C. elegans mutant that lives twice as long as wild type. Nature, 366(6454), 461-464.

# ”These are all fairly obvious” (says Sewall Wright)

I was checking a quote from Sewall Wright, and it turned out that the whole passage was delightful. Here it is, from volume 1 of Genetics and the Evolution of Populations (pages 59-60):

There are a number of broad generalizations that follow from this netlike relationship between genome and complex characters. These are all fairly obvious but it may be well to state them explicitly.

1) The variations of most characters are affected by a great many loci (the multiple factor hypothesis).

2) In general, each gene replacement has effects on many characters (the principle of universal pleiotropy).

3) Each of the innumerable possible alleles at any locus has a unique array of differential effects on taking account of pleiotropy (uniqueness of alleles).

4) The dominance relation of two alleles is not an attribute of them but of the whole genome and of the environment. Dominance may differ for each pleiotropic effect and is in general easily modifiable (relativity of dominance).

5) The effects of multiple loci on a character in general involve much nonadditive interaction (universality of interaction effects).

6) Both ontogenetic and phylogenetic homology depend on calling into play similar chains of gene-controlled reactions under similar developmental conditions (homology).

7) The contributions of measurable characters to overall selective value usually involve interaction effects of the most extreme sort because of the usually intermediate position of the optimum grade, a situation that implies the existence of innumerable different selective peaks (multiple selective peaks).

It seems point one is true. People may argue about whether the variants behind complex traits are many, relatively common, with tiny individual effects or many, relatively rare, and with larger effects that average out to tiny effects when measured in the whole population. In any case, there are many causative variants, alright.

Point two — now also known as the omnigenetic model — hinges on how you read ”in general”, I guess. In some sense, universal pleiotropy follows from genome crowding. If there are enough causative variants and a limited number of genes, eventually every gene will be associated with every trait.

I don’t think that point three is true. I would assume that many loss of function mutations to protein coding genes, for example, would be interchangeable.

I don’t really understand points six and seven, about homology and fitness landscapes, that well. The later section about homology reads to me as if it could be part of a debate going on at the time. Number seven describes Wright’s view of natural selection as a kind of fitness whack-a-mole, where if a genotype is fit in one dimension, it probably loses in some other. The hypothesis and the metaphor have been extremely influential — I think largely because many people thought that it was wrong in many different ways.

Points four and five are related and, I imagine, the most controversial of the list. Why does Wright say that there is universal epistasis? Because of physiological genetics. Or, in modern parlance, maybe because of gene networks and systems biology. On page 71, he puts it like this:

Interaction effects necessarily occur with respect to the ultimate products of chains of metabolic processes in which each step is controlled by a different locus. This carries with it the implication that interaction effects are universal in the more complex characters that trace such processes.

The argument seems to persists to this day, and I think it is true. On the other hand, there is the question how much this matters to the variants that actually segregate in a given population and affect a given trait.

This is often framed as a question of variance. It turns out that even with epistatic gene action, in many cases, most of the genetic variance is still additive (Mäki-Tanila & Hill 2014, Huang & Mackay 2016). But something similar must apply to the effects that you will see from a locus. They also depend on the allele frequencies at other loci. An interaction does nothing when one of the interaction partners are fixed. If they are nearly to fixed, it will do nearly nothing. If they’re all at intermediate frequency, things become more interesting.

Wright’s principle of universal interaction is also grounded in his empirical work. A lot of space in this book is devoted to results from pigmentation genetics in guinea pigs, which includes lots of dominance and interaction. It could be that Wright was too quick to generalise from guinea pig coat colours to other traits. It could be that working in a system consisting of inbred lines draws your attention to nonlinearities that are rare and marginal in the source populations. On the other hand, it’s in these systems we can get a good handle on the dominance and interaction that may be missed elsewhere.

Study of effects in combination indicates a complicated network of interacting processes with numerous pleiotropic effects. There is no reason to suppose that a similar analysis of any character as complicated as melanin pigmentation would reveal a simpler genetic system. The inadequacy of any evolutionary theory that treats genes as if they had constant effects, favourable or unfavourable, irrespective of the rest of the genome, seems clear. (p. 88)

I’m not that well versed in pigmentation genetics, but I hope that someone is working on this. In an era where we can identify the molecular basis of classical genetic variants, I hope that someone keeps track of all these A, C, P, Q etc, and to what extent they’ve been mapped.

Literature

Wright, Sewall. ”Genetics and the Evolution of Populations” Volume 1 (1968).

Mäki-Tanila, Asko, and William G. Hill. ”Influence of gene interaction on complex trait variation with multilocus models.” Genetics 198.1 (2014): 355-367.

Huang, Wen, and Trudy FC Mackay. ”The genetic architecture of quantitative traits cannot be inferred from variance component analysis.” PLoS genetics 12.11 (2016): e1006421.

Yours truly outside the library on Thomas Bayes’ road, incredibly happy with having found the book.

# Summer of data science 1: Genomic prediction machines #SoDS17

Genetics is a data science, right?

One of my Summer of data science learning points was to play with out of the box prediction tools. So let’s try out a few genomic prediction methods. The code is on GitHub, and the simulated data are on Figshare.

Genomic selection is the happy melding of quantitative and molecular genetics. It means using genetic markers en masse to predict traits and and make breeding decisions. It can give you better accuracy in choosing the right plants or animals to pair, and it can allow you to take shortcuts by DNA testing individuals instead of having to test them or their offspring for the trait. There are a bunch of statistical models that can be used for genomic prediction. Now, the choice of prediction algorithm is probably not the most important part of genomic selection, but bear with me.

First, we need some data. For this example, I used AlphaSim (Faux & al 2016), and the AlphaSim graphical user interface, to simulate a toy breeding population. We simulate 10 chromosomes á 100 cM, with 100 additively acting causal variants and 2000 genetic markers per chromosome. The initial genotypes come from neutral simulations. We run one generation of random mating, then three generations of selection on trait values. Each generation has 1000 individuals, with 25 males and 500 females breeding.

So we’re talking a small-ish population with a lot of relatedness and reproductive skew on the male side. We will use the two first two generations of selection (2000 individuals) to train, and try to predict the breeding values of the fourth generation (1000 individuals). Let’s use two of the typical mixed models used for genomic selection, and two tree methods.

We start by splitting the dataset and centring the genotypes by subtracting the mean of each column. Centring will not change predictions, but it may help with fitting the models (Strandén & Christensen 2011).

Let’s begin with the workhorse of genomic prediction: the linear mixed model where all marker coefficients are drawn from a normal distribution. This works out to be the same as GBLUP, the GCTA model, GREML, … a beloved child has many names. We can fit it with the R package BGLR. If we predict values for the held-out testing generation and compare with the real (simulated) values, it looks like this. The first panel shows a comparison with phenotypes, and the second with breeding values.

This gives us correlations of 0.49 between prediction and phenotype, and 0.77 between prediction and breeding value.

This is a plot of the Markov chain Monte Carlo we use to sample from the model. If a chain behaves well, it is supposed to have converged on the target distribution, and there is supposed to be low autocorrelation. Here is a trace plot of four chains for the marker variance (with the coda package). We try to be responsible Bayesian citizens and run the analysis multiple times, and with four chains we get very similar results from each of them, and a potential scale reduction factor of 1.01 (it should be close to 1 when it works). But the autocorrelation is high, so the chains do not explore the posterior distribution very efficiently.

BGLR can also fit a few of the ”Bayesian alphabet” variants of the mixed model. They put different priors on the distribution of marker coefficients allow for large effect variants. BayesB uses a mixture prior, where a lot of effects are assumed to be zero (Meuwissen, Hayes & Goddard 2001). The way we simulated the dataset is actually close to the BayesB model: a lot of variants have no effect. However, mixture models like BayesB are notoriously difficult to fit — and in this case, it clearly doesn’t work that well. The plots below show chains for two BayesB parameters, with potential scale reduction factors of 1.4 and 1.5. So, even if the model gives us the same accuracy as ridge regression (0.77), we can’t know if this reflects what BayesB could do.

On to the trees! Let’s try Random forest and Bayesian additive regression trees (BART). Regression trees make models as bifurcating trees. Something like the regression variant of: ”If the animal has a beak, check if it has a venomous spur. If it does, say that it’s a platypus. If it doesn’t, check whether it quacks like a duck …” The random forest makes a lot of trees on random subsets of the data, and combines the inferences from them. BART makes a sum of trees. Both a random forest (randomForest package) and a BART model on this dataset (fit with bartMachine package), gives a lower accuracy — 0.66 for random forest and 0.72 for BART. This is not so unexpected, because the strength of tree models seems to lie in capturing non-additive effects. And this dataset, by construction, has purely additive inheritance. Both BART and random forest have hyperparameters that one needs to set. I used package defaults for random forest, values that worked well for Waldmann (2016), but one probably should choose them by cross validation.

Finally, we can use classical quantitative genetics to estimate breeding values from the pedigree and relatives’ trait values. Fitting the so called animal model in two ways (pedigree package and MCMCglmm) give accuracies of 0.59 and 0.60.

So, in summary, we recover the common wisdom that the linear mixed model does the job well. It was more accurate than just pedigree, and a bit better than BART. Of course, the point of this post is not to make a fair comparison of methods. Also, the real magic of genomic selection, presumably, happens on every step of the way. How do you get to that neat individual-by-marker matrix in the first place, how do you deal with missing data and data from different sources, what and when do you measure, what do you do with the predictions … But you knew that already.

# Journal club of one: ”An expanded view of complex traits: from polygenic to omnigenic”

An expanded view of complex traits: from polygenic to omnigenic” by Boyle, Yang & Pritchard (2017) came out recently in Cell. It has been all over Twitter, and I’m sure it will influence a lot of people’s thinking — rightfully so. It is a good read, pulls in a lot of threads, and has a nice blend of data analysis and reasoning. It’s good. Go read it!

The paper argues that for a lot of quantitative traits — specifically human diseases and height — almost every gene will be associated with every trait. More than that, almost every gene will be causally involved in every trait, most in indirect ways.

It continues with the kind of analysis used in Pickrell (2014), Finucane & al (2015) among many others, that break genome-wide association down down by genome annotation. How much variability can we attribute to variants in open chromatin regions? How much to genes annotated as ”protein bindning”? And so on.

These analyses point towards gene regulation being important, but not that strongly towards particular annotation terms or pathways. The authors take this to mean that, while genetic mapping, including GWAS, finds causally involved genes, it will not necessarily find ”relevant” genes. That is, not necessarily genes that are the central regulators of the trait. That may be a problem if you want to use genetic mapping to find drug targets, pathways to engineer, or similar.

This observation must speak to anyone who has looked at a list of genes from some mapping effort and thought: ”well, that is mostly genes we know nothing about … and something related to cancer”.

They write:

In summary, for a variety of traits, the largest-effect variants are modestly enriched in specific genes or pathways that may play direct roles in disease. However, the SNPs that contribute the bulk of the heritability tend to be spread across the genome and are not near genes with disease-specific functions. The clearest pattern is that the association signal is broadly enriched in regions that are transcriptionally active or involved in transcriptional regulation in disease-relevant cell types but absent from regions that are transcriptionally inactive in those cell types. For typical traits, huge numbers of variants contribute to heritability, in striking consistency with Fisher’s century-old infinitesimal model.

I summary: it’s universal pleiotropy. I don’t think there is any reason to settle on ”cellular” networks exclusively. After all, cells in a multicellular organism share a common pool of energy and nutrients, and exchange all kinds of signalling molecules. This agrees with classical models and the thinking in evolutionary genetics (see Rockman & Paaby 2013). Or look at this expression QTL and gene network study in aspen (Mähler & al 2017): the genes with eQTL tend to be peripheral, not network hub genes.

It’s a bit like in behaviour genetics, where people are fond of making up these elaborate hypothetical causal stories: if eyesight is heritable, and children with bad eyesight get glasses, and the way you treat a child who wears glasses somehow reinforces certain behaviours, so that children who wear glasses grow up to score a bit better on certain tests — are the eyesight variants also ”intelligence variants”? This is supposed to be a reductio ad absurdum of the idea of calling anything an ”intelligence variant” … But I suspect that this is what genetic causation, when fully laid out, will sometimes look like. It can be messy. It can involve elements that we don’t think of as ”relevant” to the trait.

There are caveats, of course:

One reason that there is a clearer enrichment of variant-level annotation such as open chromatin than in gene-level annotation may be that the resolution is higher. We don’t really know that much about how molecular variation translates to higher level trait variation. And let’s not forget that for most GWAS hits, we don’t know the causative gene.

They suggest defining ”core genes” like this: ”conditional on the genotype and expres-
sion levels of all core genes, the genotypes and expression levels of peripheral genes no longer matter”. Core genes are genes that d-separate the peripheral genes from a trait. That makes sense. Some small number of genes may be necessary molecular intermediates for a trait. But as far as I can tell, it doesn’t follow that useful biological information only comes from studying core genes, nor does it follow that we can easily tell if we’ve hit a core or a peripheral gene.

Also, there are quantitative genetics applications of GWAS data that are agnostic of pathways and genes. If we want to use genetics for prediction, for precision medicine etc, we do not really need to know the functions of the causative genes. We need big cohorts, well defined trait measurements, good coverage of genetic variants, and a good idea of environmental risk factors to feed into prediction models.

It’s pretty entertaining to see the popular articles about this paper, and the juxtaposition of quotes like ”that all those big, expensive genome-wide association studies may wind up being little more than a waste of time” (Gizmodo) with researchers taking the opportunity to bring up up their favourite hypotheses about missing heritability — even if it’s not the same people saying both things. Because if we want to study rare variants, or complex epistatic interactions, or epigenomics, or what have you, the studies will have to be just as big and expensive, probably even more so.

Just please don’t call it ”omnigenetics”.

Literature

Boyle, Evan A., Yang I. Li, and Jonathan K. Pritchard. ”An Expanded View of Complex Traits: From Polygenic to Omnigenic.” Cell 169.7 (2017): 1177-1186.

# Mutation, selection, and drift (with Shiny)

Imagine a gene that comes in two variants, where one of them is deleterious to the carrier. This is not so hard to imagine, and it is often the case. Most mutations don’t matter at all. Of those that matter, most are damaging.

Next, imagine that the mutation happens over and over again with some mutation rate. This is also not so hard. After all, given enough time, every possible DNA sequence should occur, as if by monkeys and typewriters. In this case, since we’re talking about the deleterious mutation rate, we don’t even need exactly the same DNA sequence to occur; rather, what is important is how often a class of mutations with the same consequences happen.

Let’s illustrate this with a Shiny app! I made this little thing that draws graphs like this:

This is supposed to show the trajectory of a deleterious genetic variant, with sliders to decide the population size, mutation rate, selection, dominance, and starting frequency. The lines are ten replicate populations, followed for 200 generations. The red line is the estimated equilibrium frequency — where the population would end up if it was infinitely large and not subject to random chance.

The app runs here: https://mrtnj.shinyapps.io/mutation/
And the code is here: https://github.com/mrtnj/shiny_mutation

(Note: I don’t know how well this will work if every blog reader clicks on that link. Maybe it all crashes or the bandwidth runs out or whatnot. If so, you can always download the code and run in RStudio.)

We assume diploid genetics, random mating, and mutation only in one direction (broken genes never restore themselves). As in typical population genetics texts, we call the working variant ”A” and the working variant ”a”, and their frequencies p and q. The genotypes AA, Aa and aa will have frequencies $p^2$, $2 p q$ and $q^2$ before selection.

Damaging variants tend to be recessive, that is, they hurt only when you have two of them. Imagine an enzyme that makes some crucial biochemical product, that you need some but not a lot of. If you have one working copy of the enzyme, you may be perfectly fine, but if you are left without any working copy, you will have a deficit. We can describe this by a dominance coefficient called h. If the dominance coefficient is one, the variant is completely dominant, so that it damages you even if you only have one copy. If the dominance coefficient is zero, the variant is completely recessive, and having one copy of it does not affect you at all.

The average reproductive success (”fitness”) of each genotype is described in terms of selection coefficients, which tells us how much selection there is against a genotype. Selection coefficients range from 0, which means that you’re winning, to 1 which means that you’ve been completely out-competed. For a recessive damaging variant, the AA homozygotes and Aa heterozygotes are unaffected, but the aa homozygotes suffers selection coefficient s.

In the general case, fitness values for each genotype are 1 for AA, $1 - hs$ for Aa and $1 - s$ for aa. We can think of this as the probability of contributing to the next generation.

What about the red line in the graphs? If natural selection keeps removing a mutation from the gene pool, and mutation keeps adding it back in again there may be some equilibrium frequency where they cancel out, and the frequency of the damaging variant is more or less constant. This is called mutation–selection balance.

Haldane (1937) came up with an expression for the equilibrium variant frequency:

$q_{eq} = \frac {h s + \mu - \sqrt{ (hs - \mu)^2 + 4 s \mu } } {2 h s - 2 s}$

I’ve changed his notation a bit to use h and s for dominance and selection coefficient. $\mu$ is the mutation rate. It’s not easy to see what is going on here, but we can draw it in the graph, and see that it’s usually very small. In these small populations, where drift is a major player, the variants are often completely lost, or drift to higher frequency by chance.

(I don’t know if I can recommend learning by playing with an app, but I definitely learned things while making it. For instance that C++11 won’t work on shinyapps.io unless you send the compiler a flag, and that it’s important to remember that both variants in a diploid organism can mutate. So I guess what I’m saying is: don’t use my app, but make your own. Or something.)

Literature

Haldane, J. B. S. ”The effect of variation of fitness.” The American Naturalist 71.735 (1937): 337-349.