New Preprint: The Facultative Sex Coalescent with Crossing Over Recombination and Multi-Site Gene Conversion

I have submitted a new preprint to bioRxiv, “The Facultative Sex Coalescent with Crossing Over Recombination and Multi-Site Gene Conversion”. Building on previous single-site models, this research investigates how different types of genetic exchange (meiotic recombination, gene conversion) affects linkage disequilibrium (how genetic sites are correlated along a genome) in facultative sexual organisms, which alternate reproduction between biparental sex and asexuality. These results can be used to infer these phenomena from genome sequence data.

You can download the preprint here. I have also published the simulation code used in the analyses, along with documentation. The Facultative Sex Coalescent program is available from GitHub here.

Below is the abstract:

The extent of correlations between loci, as measured by linkage disequilibrium, is commonly used to infer the effect of different types of gene exchange. It can also provide information on rates of sex in facultative sexual organisms, as meiotic crossing over occurs during sexual reproduction. In addition, recent theoretical and empirical work has provided evidence that gene conversion shapes genetic diversity in facultative sexuals. Here we outline computational models of a facultative sexual coalescent process that includes both crossover recombination and multi-site gene conversion, to determine how linkage disequilibrium is affected with facultative sex. We demonstrate that the decay in linkage disequilibrium scales with the rate of sex if it is sufficiently high, indicating that linkage disequilibrium data can be potentially used to deduce rates of sex from genome data. With very low rates of sex, mitotic gene conversion both breaks down associations between alleles and removes within-individual diversity. The two combined effects produce complex linkage disequilibrium patterns. Furthermore, strong population structure and low rates of sex lead to lower average linkage disequilibrium values than those in panmictic populations, due to the influence of low-frequency polymorphisms created by allelic sequence divergence arising in individual subpopulations. These analyses provide information on how to interpret observed linkage disequilibrium patterns in facultative sexuals, and determine what genomic forces are likely to shape them.


New paper: The Evolutionary Interplay between Adaptation and Self-Fertilization


An Arabidopsis thaliana rosette, one of the most extensively studied self-fertilising plants. Picture from Wikimedia Commons.

I’m excited to announce a new review paper, “The Evolutionary Interplay between Adaptation and Self-Fertilization“, recently published in Trends in Genetics.

One of my long-standing research interests is investigating how self-fertilisation (fertilisation of male and female sex cells that are produced by the same individual) affects the fixation of adaptive mutations in a population. To this end, myself, Sylvain Glémin and Thomas Bataillon have reviewed how self-fertilisation and adaptation interact with each other. After providing an introduction of the basic concepts concerning how self-fertilisation affects beneficial genes, the review focuses on three main points:

  1. Self-fertilising species have different adaptation rates. Self-fertilisation can lead to offspring inherting genes from just one parent, as opposed to two under biparental sex. This inheritance mode can create highly uniform genomes, weakening how selection acts on individual mutations, and diminishing the ability for recombination to create new genotypes. (I have previously carried out theoretical investigations on the impact of this reduced effective recombination rate on genetic evolution. For example, self-fertilisation can make it likelier for deleterious mutations to fix with adaptive mutations, or for competing beneficial variants to be lost).
  2. Alterations in how adaptation affects genetic diversity. As adaptive mutations fix, so does any neutral variation lying close to it. This creates a distinctive reduction in genetic diversity around adaptive variants, called a ‘selective sweep’. Self-fertilisation can alter these sweep patterns. Furthermore, changes in a species’ population size can skew signals of genetic adaptation; this effect can be more pronounced under this reproductive mode, so the two outcomes have to be disentangled.
  3. Polygenic adaptation, where traits are affected by multiple interacting genes, is also affected by self-fertilisation. This mating system can rapidly create genotypes exhibiting extremely high (or low) characteristics, such as height or weight. These extremes may respond more quickly to selection in the short-term, but new genetic combinations may not be as easily created in the long-term.

You can read the (open-access!) paper here. Here’s the abstract:

Genome-wide surveys of nucleotide polymorphisms, obtained from next-generation sequencing, have uncovered numerous examples of adaptation in self-fertilizing organisms, especially regarding changes to climate, geography, and reproductive systems. Yet existing models for inferring attributes of adaptive mutations often assume idealized outcrossing populations, which risks mischaracterizing properties of these variants. Recent theoretical work is emphasizing how various aspects of self-fertilization affects adaptation, yet empirical data on these properties are lacking. We review theoretical and empirical studies demonstrating how self-fertilization alters the process of adaptation, illustrated using examples from current sequencing projects. We propose ideas for how future research can more accurately quantify aspects of adaptation in self-fertilizers, including incorporating the effects of standing variation, demographic history, and polygenic adaptation.

The Improbability Principle

In my last blogpost, I touched on how chance and probability are major drivers of evolutionary phenomena. Around the same time I found “The Improbability Principle” by David Hand in the university library, a book that in part discusses the lottery of evolution.

If you’re first thought upon reading that intro was “That’s a strange coincidence!” then this book is for you. Hand, a Professor of Statistics at Imperial College London, uses his life-long expertise of statistical modelling to explain why seemingly improbable events occur with surprising regularity. Lotteries provide a good example of highly unlikely yet frequent events. Evelyn Marie Adams won the jackpot on the New Jersey State lottery twice; once in 1985, and again in 1986. Impossible? Then consider Maurice and Jeanette Garlepy of Alberta who won the jackpot the Canadian Lottery twice; the probability of that outcome is one-in-200 trillion. If dreams are more your cup of Earl Grey, then what explains déja vu, that strange feeling we sometimes get that we’ve lived through something before? Are these flashbacks just freak events, or the inevitable outcomes of each of us doing the same tasks, meeting the same people on a daily basis?

After a series of chapters outlining the basics of statistics and probability calculations, Hand offers five ‘laws’ to explain why seemingly impossible events arise with startling regularity. What could have been a dry book on statistical methods is instead a breezy and frivolous lesson on the roles probabilities play in our day-to-day lives, with each case richly illustrated using fun anecdotes. The five laws are:

  • The law of inevitability: Put simply, something has to happen. Your personal chance of winning the National Lottery is vanishingly small, but someone usually wins every week due to the amount of people who play. Similarly, there’s…
  • The law of truly large numbers: Given enough opportunities for something implausible to happen, it will happen. In 2010 a dog accidentally shot its owner after it stepped on his shotgun. A far-fetched story? Yet As Ben “Bad Science” Goldacre pointed out, two similar cases were reported in 2007, as well as in 2004. The world has plenty of dogs and guns, so puppycide will occur.
  • The law of selection: You can make anything implausible seem inevitable if you state what you’re looking for after the event. Abraham Lincoln apparently dreamed that he was going to be assassinated a week before it happened. Yet how many other people have predicted their own death, but then lived a long life? What about those who foresaw the end of the world, then moped that they had ‘miscalculated’ when we all happily survived?
  • The law of the probability lever: A slight change in circumstances can have huge impacts on predicted outcomes, making improbable events much more likely. Possibly the most infamous example of this law was used in the Sally Clark trial, a solicitor whose two children died young. Clark argued that both children died from natural causes (‘cot death’). The prosecution claimed that the probability of such an event was 1 in 73 million, and Clark was subsequently convicted of murder. However, the prosecutor’s calculation makes the erroneous assumption that each death was an independent event. In reality, if one cot death occurs in a family, subsequent deaths are much more likely so the 1 in 73 million claim is a gross overstatement. Clark was jailed for three years before her wrongful conviction was overturned.
  • The law of ‘near enough’: Did you predict an unlikely event, but it didn’t arise? You can still claim it happened if something similar materialised instead. It’s exceedingly unlikely for someone to win a lottery jackpot twice, but how many compulsive gamblers have won two lesser prizes?
Modified by CombineZP

A bluebottle with compound eyes. Photo from Wikipedia Commons.

One of the fascinating aspects of evolutionary theory is that formation of complex adaptations essentially follows these laws. How did the eye, which started off as light-sensing proteins in unicellular bacteria, evolve into the complex camera-organ that all humans carry? If the rudimentary light-detecting organism were left to mutate by chance then it would be incredibly unlikely to form a complex eye. Natural selection however greatly skews these odds.

Consider a rudimentary bacterium, whose ‘eye’ was a collection of light-sensing proteins. This bacterium will reproduce many times, and eventually some offspring will be produced that will carry more developed ‘eyes’ (a variant of ‘the law of truly large numbers’). These individuals would be more able to survive, so these evolved eyes will persist in nature; rather aptly, this rule is an application of ‘the law of selection’. Repeat this process for millions of years (‘the law of truly large numbers’ in action, again) and eyes will eventually evolve into their complex modern forms. It seems that the Improbability Principle is living and breathing all around us in our natural world.

“On the origin of asexual species by means of hybridisation and drift”

My new commentary piece has just been published in the latest issue of Molecular Ecology. It’s a summary of a paper by Ament-Velásquez et al. on the origin of asexual Lineus ribbon worms.

A prediction for detecting highly asexual organisms is that each gene copy in a diploid species should become extremely divergent from each other over time. This is because with no sexual gene exchange between parents, the two gene copies become essentially isolated from each other, and will hence mutate independently. However, this pattern also arises when a new species is form by hybridisation, due to mixing two distinct sets of genes from parental species. Ament-Velasquez et al. studied gene samples over several species of Lineus worms, and partitioned observed genetic divergence in an asexual species into that arising via hybridisation and asexual genetic isolation.

Click here to read the commentary piece, which gives a further overview of their research as well as reflections on how to dissect the many genetic outcomes of asexual reproduction.

A Chance to Adapt?

On the surface, the logic underlying the theory of natural selection is pretty simple. Individuals exist in an environment, each carrying different genetic variants; one (or more) of these variants are better suited to that environment; and hence this variant is more likely to be passed on to offspring, and spread through the entire population over time. In reality, the means by which adaptations appear and evolve can be wildly complex and counterintuitive. In particular there is a large element of chance that is often overlooked; many adaptive types can easily be lost by bad luck. Far from being of minor evolutionary importance, this effect of chance is fundamental with regards to not only how we think about evolution, but also related issues such as conservation and infectious disease emergence. Furthermore, clarifying the likelihood that new adaptations emerge proved imperative in understanding how powerful natural selection is at driving evolution.

The certainty of chance

Let’s illustrate this point with a hypothetical example. Imagine a dainty field of flowers in tightly packed rows, which you might see if you took a cycling tour of Holland. Now, one of these flowers developed a mutated gene, allowing it to grow taller than the others. This alteration would be beneficial for the flower; it would have premium access to sunlight, water, and pollen with are needed for reproduction. If this flower were particularly lucky, it would be able to leave offspring, each of which would be equally tall. This process repeats over time, until all flowers in the field carry this adaptation and are larger as a result.

For this adaptation to spread though, the first flower has to survive. If you trod on it as you marched your way across this field to visit a historic Dutch windmill, then the adaptation dies with the flower itself. Tough luck, evolution.

In this toy example, the adaptation causing increased height would be likely to spread as it offers a large advantage to reproduction. Yet most beneficial mutations are not so prominent. They’re usually tweaks to the existing body, such as creating refined teeth for eating, or generating muscle protein more efficiently. These types of mutations are much more vulnerable to being killed off by chance. Let’s say that such a mutation appears, which causes the individual carrying it to have a 2% higher chance of leaving offspring, and therefore to pass on this new adaptation, over its lifespan. A classic evolutionary genetics result shows that the probability that it will spread through the population at large is only 4%. (Generally, if the advantage is denoted s, the fixation probability is 2s.)

Why is that? In the example above involving tall flowers, the danger for the new mutant is its rarity. If it is only present in one individual, then the death of its sole carrier will also prevent the adaptation from spreading. When the advantage of the mutant is low, then for the most part the carrier will produce as many offspring as non-mutated individuals. Hence this mutant will be present in only a few individuals for long durations of time; its advantage will only become apparent later. It only takes one population shock during this period to eliminate the adaptive form.

One tall flower appears, then two, over longer period of time…

A role for natural selection

Exploring the role of chance in adaptation was an important question for the first wave of evolutionary genetic theorists, most notably Ronald Fisher and John Haldane. They wanted to resolve whether natural selection could indeed cause the appearance of adaptive forms in nature, and what other forces affected it. At the turn of the twentieth century, Darwin’s idea of evolution was widely accepted, but his explanation for it – natural selection – was hotly debated. The old criticism was that chance selection events could not form the complex biology surrounding us. Some variants of this argument are still used by creationists to argue against the theory of evolution.

Fisher and Haldane’s work on this subject made it clear that while natural selection is not guaranteed, it is still a potent force in driving adaptation. While the chance of any individual adaptation arising is small, it is still much more probable than having these mutations spread without the driving force of natural selection. In the non-selected, or neutral case, the fixation probability is instead one over the population size. Given potentially hundreds of thousands of individuals, this value is much smaller than that expected with selection. Furthermore, mechanisms exists that can increase the emergence probability, such as repeated mutation reintroducing the adaptive type, or evolution proceeding via incremental changes. Indeed, one of Fisher’s favourite quotes was: “Natural selection is a mechanism for generating an exceedingly high degree of improbability”.

A role in infectious disease spread

Considering this chance effect still plays a role in modern studies of adaptation and evolution, and the same logic can be applied to other types of biological phenomena. In 2013, I wrote a paper with Sam Alizon explaining how similar thinking can be used to quantify the danger from emerging infectious diseases. In 1978 a strain of smallpox escaped from a university laboratory, leading to a tragic single fatal case. This lone patient was quickly isolated, preventing a full-scale outbreak in a similar way that removing a rare adaptation above halted its evolution. However, since infectious diseases can rapidly spread from person to person, the role of chance is massively reduced.

“Recombination and Molecular Evolution” in the Encyclopedia of Evolutionary Biology

The Encyclopedia of Evolutionary Biology has just been published, containing plentiful introductory topics on all aspects of the field. I’m pleasantly surprised by how many subject areas are covered, and pleased to see many of my colleagues and peers making contributions.

I was involved with one section, “Recombination and Molecular Evolution“, written with Andrea Betancourt from the University of Veterinary Medicine in Vienna. As the title suggests, we provided a primer on the role that recombination plays in genetic evolution. The piece itself is in two distinct parts. We start by outlining the theoretical reasons as to why recombination is beneficial; broadly, it can unpick genes from bad backgrounds, and create optimal genotypes. The second part places this theory in context, describing how the mixture of recombination and selection affects neutral (i.e. unselected) genetic diversity, which can be inferred from genome scans (see my blogpost on the subject for more information).

Click here to read the article, and to browse the rest of the series.

Bright mice and high risers: Adaptations with a simple genetic basis

What fuels the creation of complex features in life? How does a camera-eye develop, or causes zebras’ stripes to melt into a dazzling camouflage? Natural selection, acting over many generations, ensures that these intricate traits are slowly refined over time to create these, and other, sublime forms.

Such traits are usually the product of many genes acting in concert, the proverbial genetic choir contributing different proteins that build on each other. Hence genomic scans for such traits tend to find a several ‘candidate genes’ underlying them. In some cases, research has uncovered a few key adaptations that are based on the effects of a single, or very few genes. Unearthing these examples is exciting, as they instantly offer elegant case studies and a wealth of information into the process of adaptation. Here, I present a scattering of examples that have found a simple basis for various adaptations. Each is categorised using a ‘just-so story’ style heading, which I found amusing for some reason.

Update 20th March: It’s worth adding that even if the main effect of a trait could be pinpointed to a single gene, then it does not mean that said gene causes that trait. The ultimate outcome is very much dependent on how these genes interact with others in the same genome, as well as the environment they reside in. (I was reminded to add this after seeing Graham Coop of UCDavis post a quote about this issue on Twitter.)

How Tibetans became adapted to their high homelands

Gyantse dzong, Tibet (via Wikipedia Commons)

Gyantse dzong, Tibet (via Wikipedia Commons)

Tibet is one of the most mountainous regions on Earth, with an average elevation of around 4,900 ft. Most people would struggle to live in this environment due to low oxygen levels at these heights. Native Tibetans are able to live freely, having an adapted blood-oxygen regulation system that can cope with the thin air.

In 2010, a study compared the genomes from 50 native Tibetans, and looked for what genes enabled adaptation to this environment. These genomes were compared to those from Han Chinese individuals in order to determine which Tibetan genes might have differed due to adaptation. Comparison of over 20,000 sites revealed several candidates, but a key outlier was the EPAS1 gene, which is known to affect red-blood cell and haemoglobin count. Considering that Tibetans diverged from the Han Chinese 2,750 years ago, the rapid divergence of EPAS1 appears to be one of the quickest adaptations yet discovered.

Reference: “Sequencing of 50 Human Exomes Reveals Adaptation to High Altitude

Why the mice became bright

Aww, it's a brightly coloured deer-mouse (via Wikimedia Commons)

Aww, it’s a brightly coloured deer-mouse (via Wikimedia Commons)

The Sand Hills of Nebraska are home to a type of deer mice with a much brighter coat than their neighbours. This lighter colour, matching the sand under their feet, enables these mice to better blend in with the native soils. Linnen and colleagues found that the Agouti gene was responsible for this different coat colouring. Specifically, the Agouti gene has a chunk of DNA lost from it compared to the variant carried in dark-haired mice. A statistical model that analysed the high degree of similarity between different forms of the Agouti gene (see my previous blog post for details) suggested that it appeared after the formation of the Sand Hills 8,000 years ago. Furthermore, it probably originated as a new mutation before rapidly spreading to descendants, due to the strong selective advantage in evading predation.

Reference: “On the Origin and Spread of an Adaptive Allele in Deer Mice

How sticklebacks lost their armour plates and did so in different ways in different parts of the world
(That’s enough bad titles – Ed.)

Oceanic stickleback fish are known for their striking armour plating. Yet this protection has been partially or fully lost in freshwater sticklebacks as they migrated around the globe. This observation begs the question: was there a common ancestor to these unplated freshwater fish that appeared only once, or did this adaptation repeatedly arise?

High-resolution genetic mapping pinpointed that mutations at the Eda gene were associated with loss of armour plating in freshwater fish. However, different variants of this gene were responsible for the adaptation; while most of the plateless Eda variants were closely related to each other, one population from Nakagawa Creek in Japan exhibited greater similarity to fully plated fishes. Furthermore, even populations of oceanic fishes tended to carry the plateless gene at low frequency. This variant appears to be recessive, in the sense that an offspring needed to inherit the same copy from both parents in order to lose armour plates. If only one copy was inherited, then the ‘dominant’ armour plate gene would be expressed instead.

All this evidence points to the fact that, unlike the previous examples, variants of the Eda gene leading to armour-plate loss arose several times in different locations. The fact that it is generally present at a low frequency means that, when required, sticklebacks entering freshwater habitats will cause this gene to become rapidly selected for.

Reference: “Widespread Parallel Evolution in Sticklebacks by Repeated Fixation of Ectodysplasin Alleles

If you have your own favourite examples of simple adaptation, why not share them in the comments below?