Mailund on the Internet

I’ve been wanting to write about our paper on the orangutan genome for a while, but I’ve just been too busy so far, so a little late I finally get to it.

Besides the Nature paper, where we contributed to the analysis of the two sub-species of orangutans, we have two companion papers. One is already out in “early access” at Genome Research and the other will be out later in PLoS Genetics. Since the latter paper is not out yet, this post will be about the Genome Research paper.

Coalescent in an isolation model

Since all our work is based on coalescent theory and in particular CoalHMMs, I’ll start there.

Imagine we have two species, and we sample a gene in each. We can then ask, what is the divergence between the two genes? This divergence will be determined by 1) the divergence of the two species, let’s call that T, and 2) the coalescence time between the two genes within the ancestral species, let’s call that C.

The species divergence we assume is fixed for all genes, so while it is unknown it is not a stochastic variable. The coalescence time, however, is stochastic, and from coalescence theory we expect it to be exponentially distributed with a rate determined by the effective population size in the ancestral species.

We call this setup an isolation model, and we will use the distribution of divergence times to make inference about the speciation time and the effective population size in the ancestral species.

The figure below illustrates the setup.

If C is exponentially distributed, and the divergence is given by D=C+T, then we can make inference about both parameters as follows: We sample a number of independent genes and get their divergence time. For the exponential distribution, the mean is equal to the standard deviation, so looking at the standard deviation of the divergences we can get the parameter for the exponential distribution. That gives us the mean value of C, and if we then look at D-E[C] we get an estimate for T.

Below is an example of this, where I’ve estimated the coalescence rate and divergence time from 50 divergence samples.

Complications

This is all very simple, but there are a few problems.

First, you don’t really get independent samples of the divergence time between two species. If you sample n individuals from the first species and m from the second, the n in the first species will all have found a common ancestor before that lineage reach the ancestral species, and the same goes for the m samples in the other species. So no matter how many individuals you look at, you end up with a sample of two in the ancestral species. I’ve written about this before here.

It is not a show-stopper, though, since genes in different parts of the genome are close enough to independent. So if you sample different loci instead of different individuals, you get your independent samples. So while adding more individuals won’t help, having an entire genome to look at gives you plenty of samples.

The second problem is that we cannot actually get samples of the divergence time. You cannot look at two pieces of DNA and from that get their divergence. You need to estimate it. It isn’t really that hard, since you can get a good estimate from the number of differences between the two sequences. That is, if the entire alignment of sequences have the same divergence time.

If there is a recombination somewhere in the sequences, they do not have the same divergence time, and you cannot estimate the divergence.

You can get around this by looking at short DNA segments, where you expect few if any recombinations. You won’t get a good estimate of the divergence then, but you can maybe alleviate this by having a lot of genes (but estimating the coalescence rate based on a standard deviation that have contributions from both the coalescence process and the estimation problems is, well, problematic).

You’d also have to throw most of your data away if you are looking at short segments scattered along the genome (and you cannot have them too close to each other, because then they will no longer be independent).

The CoalHMM approach

The models we develop to deal with this are based on hidden Markov models.

Using these models, we can estimate the divergence time for single nucleotides. Normally you cannot, since they are either equal or difference, and that doesn’t tell you much about their divergence (is it zero for equal and infinity for different?). We can do this, because the flanking DNA contains information about this, whether recombinations have occurred or not, and we can capture this information through the Markov model.

It is a rough approximation to the coalescence process, but as far as we can tell, it works reasonably well.

We are getting pretty close to being able to estimate the distribution of divergence times using hidden Markov models, but the model we use is the one that will be published in PLoS Genetics soon and not the model we used in the Genome Research paper, so I’ll wait a bit with describing how that works.

The model we used in the Genome Research paper is the one described in this paper.

In this model, we do not attempt to estimate the actual divergence times, but instead use something called incomplete lineage sorting. The idea here is, that if we have a third species closely related to the other two, then sometimes the two sister species have such deep divergence times, that one of them can end up being closer related to the third species than its sister species.

This leaves a stronger signal in the DNA and is thus easier to model and make inference about.

The model based on this needs only four states: one state where the two sister species coalesce early, and three states with deep divergence. If the divergence is deep, the topology of relationships between the species should be uniform — each topology is seen with one third probability — and how often we see deep divergences is given by the two speciation times together with the effective population size of the ancestor of the sister species.

As we scan along a genome alignment, we can infer how often we see recent divergences and how often we see deep divergences, and how the deep divergences are distributed along the three topologies.

Below is a figure that Julien made for illustrating this.

With this model, you don’t extract as much information from the genomes as you would if you could estimate the divergence times, but with full genomes to work with, you have plenty of information to get good estimates.

You need three closely related species to work with, though.

Incomplete lineage sorting patterns among human, chimpanzee and orangutan suggest recent orangutan speciation and widespread selection

And now, finally, we get to the paper.

Incomplete lineage sorting patterns among human, chimpanzee and orangutan suggest recent orangutan speciation and widespread selection
Asger Hobolth, Julien Y. Dutheil, John Hawks, Mikkel H. Schierup and Thomas Mailund

Abstract

We search the complete orangutan genome for regions where humans are more closely related to orangutans than to chimpanzees due to incomplete lineage sorting (ILS) in the ancestor of human and chimpanzees. The search uses our recently developed coalescent HMM framework. We find ILS present in ~1% of the genome, and that the ancestral species of human and chimpanzees never experienced a severe population bottleneck. The existence of ILS is validated with simulations, site pattern analysis, and analysis of rare genomic events. The existence of ILS allows us to disentangle the time of isolation of humans and orangutans (the speciation time) from the genetic divergence time, and we find speciation to be as recent as 9-13 mya (contingent on the calibration point). The analyses provide further support for a recent speciation of human and chimpanzee at ~4 mya and a diverse ancestor of human and chimpanzee with an effective population size of ~50,000 individuals. Posterior decoding infers ILS for each nucleotide in the genome and we use this to deduce patterns of selection in the ancestral species. We demonstrate the effect of background selection in the common ancestor of humans and chimpanzees. In agreement with predictions from population genetics, ILS found to be reduced in exons and gene dense regions when we control for confounding factors such as GC content and recombination rate. Finally, we find the broad scale recombination rate to be conserved through the complete ape phylogeny.

In this paper we used humans, chimpanzees and orangutans.

The first question to ask is then, are these three species close enough that we see incomplete lineage sorting?

Without it, we don’t have the signal in the data that we need for the model.

Based on previous estimates of the species divergence times and ancestral effective population size of humans and chimpanzees we could work out that some was expected. So that is a good start. To make sure, though, we used some simpler approaches. We looked at indels to check if there would be signals in these supporting clustering of human and orangutan or chimp and orangutan and found that. We also looked at the distribution of alignment columns and again found some signals for alternative topologies of the three species. So with that checked, we applied the model.

From the model we estimate three things: 1) The speciation times for humans and chimps, and from the African apes and orangutan, 2) the effective population size of the ancestral species, and 3) in which regions of the genome humans and chimps, humans and orangutan, and chimp and orangutan are closest related.

I won’t say much about number two. The effective population size is a weird parameter that can be affected by so many things, that it is really hard to interpret, and right now we just don’t know what really is important, so I’d rather not make any claims (but I’ll say a few things about local effective population sizes towards the end of the post).

Number one is interesting because it tells us something about when humans diverged from the other two apes. Our estimates are measured in the number of substitutions since the divergence, but assuming a molecular clock and assuming we have a good estimate of the rate we can get an estimate in years.

Assuming a rate of around 1 substitution per nucleotide per billion years — an estimate based on several earlier papers that get this number from calibrations with the fossil record — we get a human/chimp speciation around 4-4.5 million years ago, and a human/orangutan speciation around 11-13 million years ago.

I really don’t know how reasonable this is, in relation to the fossil record, so this is when we got John Hawks involved. I have my fingers crossed that he will blog about this at some point.

There are good reasons to be a bit skeptical, though. From recent studies, we know that the substitution rate is lower in humans today, and if that is also true in the past, the estimates should be moved further back in time. We cannot get too far back, though, without running into inconsistencies in the deeper past, but how this will all play out once we do more analysis I cannot say yet. It is something we look into for the gorilla genome (and I’ll just leave that as a cliff hanger for now, I’ll get back to it when we have published that genome).

For number three, I don’t really know. You might be surprised that we are sometimes closer related to the orangutan than the chimpanzee, or you might not. It depends on your prior assumptions, I guess.

We didn’t really find anything cool correlated to the patterns of relatedness, so we don’t have much of a story to tell about this.

Ancestral selection

The final thing we looked at in the paper was correlations between incomplete lineage sorting and gene density.

Why this is interesting gets a bit technical but has to do with the effective population size.  As I mentioned above, it is a bit of a weird parameter, but one that is affected by selection. If you have a selective sweep the genetic diversity is reduced, and you see this as a reduction in the effective population size. The same effect is seen with purifying selection, where again the genetic diversity is reduced and so is the effective population size.

Incomplete lineage sorting is positively correlated with the effective population size, so if you observe a correlation between incomplete lineage sorting and gene density, it is a signal for selection.

We observe this, and take it as a signal that selection rather than just drift has been a major player in the evolution of our genome.

How much of a surprise this is depends on your prior assumptions again, I guess, but it does indicate that neutrality may not always be the obvious null model for genome analysis.

It is a pretty weak signal for this, though, in this analysis. We see so little incomplete lineage sorting for these three species that it is really hard to analyse it in detail.

When we get human, chimp and gorilla, there is a lot more incomplete lineage sorting, and we can do a lot more. We are seeing some cool signals there, but I’ll let that be the second cliff hanger for the gorilla genome paper.

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Hobolth, A., Dutheil, J., Hawks, J., Schierup, M., & Mailund, T. (2011). Incomplete lineage sorting patterns among human, chimpanzee and orangutan suggest recent orangutan speciation and widespread selection Genome Research DOI: 10.1101/gr.114751.110

There’s a paper that came out yesterday in PLoS ONE on visualising LD structure:

The Textile Plot: A New Linkage Disequilibrium Display of Multiple-Single Nucleotide Polymorphism Genotype Data

Kumasaka, Nakamure and Kamatani

Linkage disequilibrium (LD) is a major concern in many genetic studies because of the markedly increased density of SNP (Single Nucleotide Polymorphism) genotype markers. This dramatic increase in the number of SNPs may cause problems in statistical analyses, such as by introducing multiple comparisons in hypothesis testing and colinearity in logistic regression models, because of the presence of complex LD structures. Inferences must be made about the underlying genetic variation through the LD structure before applying statistical models to the data. Therefore, we introduced the textile plot to provide a visualization of LD to improve the analysis of the genetic variation present in multiple-SNP genotype data. The plot can accentuate LD by displaying specific geometrical shapes, and allowing for the underlying haplotype structure to be inferred without any haplotype-phasing algorithms. Application of this technique to simulated and real data sets illustrated the potential usefulness of the textile plot as an aid to the interpretation of LD in multiple-SNP genotype data. The initial results of LD mapping and haplotype analyses of disease genes are encouraging, indicating that the textile plot may be useful in disease association studies.

An example of this new kind of plots looks like this:

At a quick glance it looks like it is displaying haplotype blocks, like you can get in HaploView (although in a nicer graphics).

It isn’t quite that, though.

The textile plot is showing LD between genotypes and not haplotype blocks, so you always have three “blocks” per column, and so you don’t know the phase of the genotypes you are looking at.

The plot simply visualises the genotype LD structure, and I am sure that with a bit of practice they can be used to explore that.

I don’t have that practice, though, so I find them a bit hard to interpret.  They are beautiful, though.

If you are interested in phylogenomics and primate evolution — including human evolution — this new review in Genome Research is a must read.

Phylogenomics of primates and their ancestral populations

Adam Siepel

Genome assemblies are now available for nine primate species, and large-scale sequencing projects are underway or approved for six others. An explicitly evolutionary and phylogenetic approach to comparative genomics, called phylogenomics, will be essential in unlocking the valuable information about evolutionary history and genomic function that is contained within these genomes. However, most phylogenomic analyses so far have ignored the effects of variation in ancestral populations on patterns of sequence divergence. These effects can be pronounced in the primates, owing to large ancestral effective population sizes relative to the intervals between speciation events. In particular, local genealogies can vary considerably across loci, which can produce biases and diminished power in many phylogenomic analyses of interest, including phylogeny reconstruction, the identification of functional elements, and the detection of natural selection. At the same time, this variation in genealogies can be exploited to gain insight into the nature of ancestral populations. In this Perspective, I explore this area of intersection between phylogenetics and population genetics, and its implications for primate phylogenomics. I begin by “lifting the hood” on the conventional tree-like representation of the phylogenetic relationships between species, to expose the population-genetic processes that operate along its branches. Next, I briefly review an emerging literature that makes use of the complex relationships among coalescence, recombination, and speciation to produce inferences about evolutionary histories, ancestral populations, and natural selection. Finally, I discuss remaining challenges and future prospects at this nexus of phylogenetics, population genetics, and genomics.

…and if you are wondering why my blog is so quiet these days, it is because I am swamped with four of the genome projects mentioned in the paper: orangutan, bonobo, gorilla and macaque…

Any summary of this paper that I write will not really do justice to it — you really should read it yourself and you will be happy you did — so I’ll just briefly summarize the topics that Adam covers.

First he covers basic phylogenetics, that is figuring out species relationships.  This is, by now, a well known field and essentially boils down to modeling sequence evolution as Markov chains so you can estimate divergence times and tree relationships from the substitutions between sequences.

For closely related species, though, that is only a small part of the picture, and the more interesting part of the paper involves introducing population genetics to phylogenetics.  You have to remember that speciation somehow involves populations; two species do not just split up, rather groups of individuals diverge and their genomes start diverging as groups rather than individuals.  That leads to varying sequence divergence as you scan along the genomes, and under certain conditions to incomplete lineage sorting, where gene trees are different from species trees.

This doesn’t just cause complications in genomic inference, though.  It provides valuable information about ancestral species and about speciation processes, which is the next topic Adam covers.  For primates, this is especially important.  The time intervals between speciations are short, and the ancestral effective population sizes are large *, so 1) if you ignore this your results will be way off, but 2) if you embrace it you have a lot of information to learn about the ancestry of the primates.

This then leads us to speciation models.  There are plenty of those, where the simplest (allopatric speciation) just assumes that some barrier appears between two populations after which they evolve independently to the point where they can no longer reproduce as hybrids.  That is probably a good model for the chimp/bonobo split, where the Congo River got in the way (chimps can’t swim), but it is a bit simple so more complex scenarios are worth considering for most speciation events.  The point here just is that different scenarios will leave different signals in the genomes, and we should be able to work this out by looking at the extant genomes.

There’s a nice review of the work done so far in the paper, but honestly we are still only at the starting phase of modeling this, and a lot of work remains before we can say anything conclusively about any of the primate speciations.

Next we get to selection.  With the whole neutral theory we have turned to believe that we can explain most of genome evolution with neutral mutations — well I have anyway, but that might just be me.  Recent results, though, hints at selection being a major force in genome evolution anyway. My older colleagues tells me that selection was much more important in theory years back, but my background gave me the intuition that it could pretty much be ignored when comparing genomes; maybe I was wrong on that.

Perhaps the null model when we look at entire genomes shouldn’t be neutrality after all, I don’t know… We are seeing signals to that effect in our own work, anyway, but I’ll tell you all about that later when those papers are out, for now let’s just read Adam’s paper that is much more interesting anyway!

The last part of the paper is on Future Prospects.  Well, most papers are, so no surprise there, but if you are getting into the field there are some interesting areas to start thinking about in this review.

How do we incorporate the ancestral recombination graph (ARG) into phylogenetic analysis?  How do we model it without the combinatorial state space explosion?  How do we infer anything usable from the weak signals that is in the data for this? How do we combine model sophistication with computational efficiency to alleviate the state space explosion? Which model assumptions are essential and which can we get away with approximating?

Let me add a few of my own: How do we model this complex system without too much complex math so that when we have results we can actually interpret the results?  How do we check if deviations from our model actually shows evidence for some model over another, and are not just showing that we have the wrong model?

Go read the paper!  Seriously, it is a great read!

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* Yeah, about ancestral population sizes… there are consistent estimates of very large ancestral effective population sizes, using very different methods, but generally it seems like the ancestral species were more diverge than the extant species are.  The consistent results, with different methods, indicates that this might be true, but it still is somewhat suspicious, but I guess we will learn more over the coming years as we get more data and more sophisticated methods.

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Siepel, A. (2009). Phylogenomics of primates and their ancestral populations Genome Research, 19 (11), 1929-1941 DOI: 10.1101/gr.084228.108

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Two of my main interests are hidden Markov models and selection.  A paper from this spring, in Genetics, combines the two:

Detecting Selective Sweeps: A New Approach Based on Hidden Markov Models

Boitard, Schlötterer and Futschik

Detecting and localizing selective sweeps on the basis of SNP data has recently received considerable attention. Here we introduce the use of hidden Markov models (HMMs) for the detection of selective sweeps in DNA sequences. Like previously published methods, our HMMs use the site frequency spectrum, and the spatial pattern of diversity along the sequence, to identify selection. In contrast to earlier approaches, our HMMs explicitly model the correlation structure between linked sites. The detection power of our methods, and their accuracy for estimating the selected site location, is similar to that of competing methods for constant size populations. In the case of population bottlenecks, however, our methods frequently showed fewer false positives.

Selective sweeps

Under a simple Wright-Fisher model, a neutral mutation that is just introduced into a population  can slowly increase and decrease in frequency until it is eventually either fixed in the population, which happens with probability , or until it is lost from the population againg, which happens with probability of course.

The expected time from such a mutation is introduced into the population and until it is fixed, if it is lucky to be fixed, is generations.  During this time, the descendant chromosomes of the original mutant chromosome will be subjected to new mutations and to recombinations.

Once this mutation is fixed, everyone in the population will of course share that particular mutation (ignoring back-mutations and such here), but because of recombination nearby sites will not necessarily all be derived from the original mutation chromosome.  Close to the mutation site — where few recombinations will have broken up the sequence — most chromosomes will be derived from the mutation chromosome and as we move away from the mutation site fewer chromosomes will be derived from that original chromosome.

Now, if the mutation introduced has a selective advantage, essentially the same process will play out.  In each generation there is a slightly higher chance that this mutation will have off-springs, but that is essentially the only difference.

What this means is that initially there is still a very good chance that the mutation will be lost — even with slightly better odds accidents do happen — but once the mutation has reached a reasonable frequency it is almost guaranteed to reach fixation — unless a lot of accidents happen.

Once the frequency of the site under selection is high enough it will very quickly reach fixation.  The expected time it takes depends on the selection strength but unless the selective advantage is very small it will reach fixation a lot faster than if it was neutral.  Think logarithmic time in the size of the population compared to linear time.

Since it reaches fixation much faster than a neutral mutation, fewer mutations and fewer recombinations will have time to occur, so a much wider region around the mutation site will be shared by all descendant chromosomes.  Combined, this means that for a selected site you expect a wide region with a more recent shared ancestor than you would expect at a neutral site, a phenomena called a selective sweep.

Site frequency spectra

Now, from the population genetics model you can work out — putting your thinking hat on or just simulate — the expected distribution of derived and ancestral alleles: the site frequency spectrum.  This will be different from neutral alleles and selected alleles because of the shorter time back to the common ancestor for the selected sites.  The shorter site means that there is a general reduction in polymorphism near a selected site, and derived alleles that appeared on chromosomes with the beneficial mutation will be at a higher frequency than they would be if they weren’t “hitchhiking” on the selection of the beneficial mutation.

The pattern is a bit complicated by recombination, since you need to take into account that the further away from the selected site you look, the weaker the hitchhiking effect will be; a new mutation can only hitchhike as long as it is linked to the selected site, and recombinations break that link.

Anyway, the different spectra of derived and ancestral alleles can be used to detect selective sweeps.  Two methods that exploit this, that is relevant for this post, are Kim and Stephan (2002) and Nielsen et al. (2005).

Of course, selection is not the only thing that can mess up the site frequency spectrum and make it different from the expected neutral distribution.  Demographic effects like expending populations and bottlenecks can look very similar to selection effects, so we cannot absolutely rule out neutrality if we see a deviation from the expected spectrum.  Still, the site frequency spectra of neutrality versus selection can be used for scanning for selection.

Detecting sweeps in a hidden Markov model

The new result in the Genetics paper is a hidden Markov model that uses site frequency spectra to scan for selective sweeps.

Using an HMM means that the model can capture spatial patterns along a genome and capture transitions from “neutral” regions — where no sweep has occurred or is occurring — from “selected” regions — where a sweep occurred or is occurring.  So you don’t have to assume that a locus you are looking at is either a neutral region or a selected region and you don’t have to fiddle around with sliding windows to scan a genome, you explicitly capture the changing patters.

One of the nice properties of HMMs for genomic scans and the reason I love them so much.

The model Boitard et al. develop is quite simple.  They have three states: a neutral state, a selected state, and an intermediate used to capture sites that are slightly caught up in the hitchhiking but not close enough to a selected site to get the full effect.

The transition matrix has a single parameter, , that is the probability that a neutral or selected site switches to the intermediate state (and the intermediate state switches to those two with equal probability set to ).

This of course has the unfortunate effect that the prior distribution (stationary distribution) of the chain will give you 25% chance of a site being neutral, 25% chance of it being selected and 50% chance of being intermediate, which doesn’t really match my expectation of the amount of selection in, say, a human genome. Also, the (prior) expected length of a sweeped region is the same as a neutral region which also does not match my intuition.  With enough data, though, the likelihood should overrule the prior so perhaps it is not too much of a worry…

The emissions of the model are frequencies of derived alleles, so for each site it will emit a frequency that depends on the state.  This is where they capture the different expected frequencies depending on whether a site is neutral or selected.

They use the Kim and Stephan’s and Nielsen et al. methods for this, to develop three variations of HMMs: HMMA, using Kim and Stephan, HMMB using Nielsen et al. and HMMB-SEQ, that also uses Nielsen et al. but only considers segregating sites.  The latter is only for comparison purposes and of course ignores a lot of the information in the data, since the amount of non-segregating sites reflects the general level of polymorphism in a region which again is dependent on the depth of the local genealogy and will be affected by selection.

They use simulations under neutrality to fix the parameter so they get a 5% false positive rate, and then use the models to scan for sweeps.

They get an okay power for detecting sweeps, but compared to the previous methods they don’t get that much since they did pretty good as well:

Where they refer to this table in the paper they say they have a higher power, but compared to the CLsw column, the Kim and Stephan’s method, they do not.  After all, it is difficult to beat a power of 1.

They do, however, appear to be more robust to bottlenecks where the two other methods have very high false positive rates:

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Boitard, S., Schlotterer, C., & Futschik, A. (2009). Detecting Selective Sweeps: A New Approach Based on Hidden Markov Models Genetics, 181 (4), 1567-1578 DOI: 10.1534/genetics.108.100032
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From my own experience I know that it can be hard to get access to data that you would really love to analyse, but I didn’t expect it to be quite this bad, even for data that is required to be available by the journals where the papers describing the data are published:

Empirical study of data sharing by authors publishing in PLoS journals

Savage and Vickers, PLoS ONE 2009

Background

Many journals now require authors share their data with other investigators, either by depositing the data in a public repository or making it freely available upon request. These policies are explicit, but remain largely untested. We sought to determine how well authors comply with such policies by requesting data from authors who had published in one of two journals with clear data sharing policies.

Methods and Findings

We requested data from ten investigators who had published in either PLoS Medicine or PLoS Clinical Trials. All responses were carefully documented. In the event that we were refused data, we reminded authors of the journal’s data sharing guidelines. If we did not receive a response to our initial request, a second request was made. Following the ten requests for raw data, three investigators did not respond, four authors responded and refused to share their data, two email addresses were no longer valid, and one author requested further details. A reminder of PLoS’s explicit requirement that authors share data did not change the reply from the four authors who initially refused. Only one author sent an original data set.

Conclusions

We received only one of ten raw data sets requested. This suggests that journal policies requiring data sharing do not lead to authors making their data sets available to independent investigators.

Getting a 10% success rate, when it should be 100% is pretty bad…
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