Further to this, we can expand the site-frequency spectrum to compare across populations. Instead of having a simple 1-dimensional frequency distribution, for a pair of populations we can have a grid. This grid specifies how often a particular allele occurs at a certain frequency in Population A and at a different frequency in Population B. This can also be visualised quite easily, albeit as a heatmap instead. We refer to this as the 2-dimensional SFS (2DSFS).
The same concept can be expanded to even more populations, although this gets harder to represent visually. Essentially, we end up with a set of different matrices which describe the frequency of certain alleles across all of our populations, merging them together into the joint SFS. For example, a joint SFS of 4 populations would consist of 6 (4 x 4 total comparisons – 4 self-comparisons, then halved to remove duplicate comparisons) 2D SFSs all combined together. To make sense of this, check out the diagrammatic tables below.
The different forms of the SFS
Which alleles we choose to use within our SFS is particularly important. If we don’t have a lot of information about the genomics or evolutionary history of our study species, we might choose to use the minor allele frequency (MAF). Given that SNPs tend to be biallelic, for any given locus we could have Allele A or Allele B. The MAF chooses the least frequent of these two within the dataset and uses that in the summary SFS: since the other allele’s frequency would just be 2N – the frequency of the other allele, it’s not included in the summary. An SFS made of the MAF is also referred to as the folded SFS.
Alternatively, if we know some things about the genetic history of our study species, we might be able to divide Allele A and Allele B into derived or ancestral alleles. Since SNPs often occur as mutations at a single site in the DNA, one allele at the given site is the new mutation (the derived allele) whilst the other is the ‘original’ (the ancestral allele). Typically, we would use the derived allele frequency to construct the SFS, since under coalescent theory we’re trying to simulate that mutation event. An SFS made of the derived alleles only is also referred to as the unfolded SFS.
Applications of the SFS
How can we use the SFS? Well, it can moreorless be used as a summary of genetic variation for many types of coalescent-based analyses. This means we can make inferences of demographic history (see here for more detailed explanation of that) without simulating large and complex genetic sequences and instead use the SFS. Comparing our observed SFS to a simulated scenario of a bottleneck and comparing the expected SFS allows us to estimate the likelihood of that scenario.
The SFS can even be used to detect alleles under natural selection. For strongly selected parts of the genome, alleles should occur at either high (if positively selected) or low (if negatively selected) frequency, with a deficit of more intermediate frequencies.
Adding to the analytical toolbox
The SFS is just one of many tools we can use to investigate the demographic history of populations and species. Using a combination of genomic technologies, coalescent theory and more robust analytical methods, the SFS appears to be poised to tackle more nuanced and complex questions of the evolutionary history of life on Earth.
A recurring analytical method, both within The G-CAT and the broader ecological genetic literature, is based on coalescent theory. This is based on the mathematical notion that mutations within genes (leading to new alleles) can be traced backwards in time, to the point where the mutation initially occurred. Given that this is a retrospective, instead of describing these mutation moments as ‘divergence’ events (as would be typical for phylogenetics), these appear as moments where mutations come back together i.e. coalesce.
From a mathematical perspective, the coalescent model is actually (relatively) simple. If we sampled a single gene from two different individuals (for simplicity’s sake, we’ll say they are haploid and only have one copy per gene), we can statistically measure the probability of these alleles merging back in time (coalescing) at any given generation. This is the same probability that the two samples share an ancestor (think of a much, much shorter version of sharing an evolutionary ancestor with a chimpanzee).
Normally, if we were trying to pick the parents of our two samples, the number of potential parents would be the size of the ancestral population (since any individual in the previous generation has equal probability of being their parent). But from a genetic perspective, this is based on the genetic (effective) population size (Ne), multiplied by 2 as each individual carries two copies per gene (one paternal and one maternal). Therefore, the number of potential parents is 2Ne.
Although this might seem mathematically complicated, the coalescent model provides us with a scenario of how we would expect different mutations to coalesce back in time if those idealistic scenarios are true. However, biology is rarely convenient and it’s unlikely that our study populations follow these patterns perfectly. By studying how our empirical data varies from the expectations, however, allows us to infer some interesting things about the history of populations and species.
This makes sense from theoretical perspective as well, since strong genetic bottlenecks means that most alleles are lost. Thus, the alleles that we do have are much more likely to coalesce shortly after the bottleneck, with very few alleles that coalesce before the bottleneck event. These alleles are ones that have managed to survive the purge of the bottleneck, and are often few compared to the overarching patterns across the genome.
In a similar vein, the coalescent can also be used to test how long ago the two contemporary populations diverged. Similar to gene flow, this is often included as an additional parameter on top of the coalescent model in terms of the number of generations ago. To convert this to a meaningful time estimate (e.g. in terms of thousands or millions of years ago), we need to include a mutation rate (the number of mutations per base pair of sequence per generation) and a generation time for the study species (how many years apart different generations are: for humans, we would typically say ~20-30 years).
While each of these individual concepts may seem (depending on how well you handle maths!) relatively simple, one critical issue is the interactive nature of the different factors. Gene flow, divergence time and population size changes will all simultaneously impact the distribution and frequency of alleles and thus the coalescent method. Because of this, we often use complex programs to employ the coalescent which tests and balances the relative contributions of each of these factors to some extent. Although the coalescent is a complex beast, improvements in the methodology and the programs that use it will continue to improve our ability to infer evolutionary history with coalescent theory.
One particular distinction we need to make early here is the difference between allele frequency and allele identity. In these analyses, often we are working with the same alleles (i.e. particular variants) across our populations, it’s just that each of these populations may possess these particular alleles in different frequencies. For example, one population may have an allele (let’s call it Allele A) very rarely – maybe only 10% of individuals in that population possess it – but in another population it’s very common and perhaps 80% of individuals have it. This is a different level of differentiation than comparing how different alleles mutate (as in the coalescent) or how these mutations accumulate over time (like in many phylogenetic-based analyses).
Fixed differences are sometimes used as a type of diagnostic trait for species. This means that each ‘species’ has genetic variants that are not shared at all with its closest relative species, and that these variants are so strongly under selection that there is no diversity at those loci. Often, fixed differences are considered a level above populations that differ by allelic frequency only as these alleles are considered ‘diagnostic’ for each species.
To distinguish between the two, we often use the overall frequency of alleles in a population as a basis for determining how likely two individuals share an allele by random chance. If alleles which are relatively rare in the overall population are shared by two individuals, we expect that this similarity is due to family structure rather than population history. By factoring this into our relatedness estimates we can get a more accurate overview of how likely two individuals are to be related using genetic information.
The wild world of allele frequency
Despite appearances, this is just a brief foray into the many applications of allele frequency data in evolution, ecology and conservation studies. There are a plethora of different programs and methods that can utilise this information to address a variety of scientific questions and refine our investigations.
We’ve discussed standing genetic variation before on The G-CAT, but often in a different light (and phrasing). For example, when we’ve talked about founder effect: that is, when a population is formed from only a few different individuals which causes it to be very genetically depauperate. In populations under strong founder effect, there is very little standing genetic variation for natural selection to act upon. This has long been an enigma for many pest species: how have they managed to proliferate so widely when they often originate from so few individuals and lack genetic diversity?
One of the most fundamental aspects of natural selection and evolution is, of course, the underlying genetic traits that shape the physical, selected traits. Most commonly, this involves trying to understand how changes in the distribution and frequencies of particular genetic variants (alleles) occur in nature and what forces of natural election are shaping them. Remember that natural selection acts directly on the physical characteristics of species; if these characteristics are genetically-determined (which many are), then we can observe the flow-on effects on the genetic diversity of the target species.
Although we might expect that natural selection is a fairly predictable force, there are a myriad of ways it can shape, reduce or maintain genetic diversity and identity of populations and species. In the following examples, we’re going to assume that the mentioned traits are coded for by a single gene with two different alleles for simplicity. Thus, one allele = one version of the trait (and can be used interchangeably). With that in mind, let’s take a look at the three main broad types of changes we observe in nature.
Arguably the most traditional perspective of natural selection is referred to as ‘directional selection’. In this example, nature selection causes one allele to be favoured more than another, which causes it to increase dramatically in frequency compared to the alternative allele. The reverse effect (natural selection pushing against a maladaptive allele) is still covered by directional selection, except that it functions in the opposite way (the allele under negative selection has reduced frequency, shifting towards the alternative allele).
Natural selection doesn’t always push allele frequencies into different directions however, and sometimes maintains the diversity of alleles in the population. This is what happens in ‘balancing selection’ (sometimes also referred to as ‘stabilising selection’). In this example, natural selection favours non-extreme allele frequencies, and pushes the distribution of allele frequencies more to the centre. This may happen if deviations from the original gene, regardless of the specific change, can have strongly negative effects on the fitness of an organism, or in genes that are most fit when there is a decent amount of variation within them in the population (such as the MHC region, which contributes to immune response). There are a couple other reasons balancing selection may occur, though.
One example is known as ‘heterozygote advantage’. This is when an organism with two different alleles of a particular gene has greater fitness than an organism with two identical copies of either allele. A seemingly bizarre example of heterozygote advantage is related to sickle cell anaemia in African people. Sickle cell anaemia is a serious genetic disorder which is encoded for by recessive alleles of a haemoglobin gene; thus, a person has to carry two copies of the disease allele to show damaging symptoms. While this trait would ordinarily be strongly selected against in many population, it is maintained in some African populations by the presence of malaria. This seems counterintuitive; why does the presence of one disease maintain another?
Well, it turns out that malaria is not very good at infecting sickle cells; there are a few suggested mechanisms for why but no clear single answer. Naturally, suffering from either sickle cell anaemia or malaria is unlikely to convey fitness benefits. In this circumstance, natural selection actually favours having one sickle cell anaemia allele; while being a carrier isn’t ordinarily as healthy as having no sickle cell alleles, it does actually make the person somewhat resistant to malaria. Thus, in populations where there is a selective pressure from malaria, there is a heterozygote advantage for sickle cell anaemia. For those African populations without likely exposure to malaria, sickle cell anaemia is strongly selected against and less prevalent.
Another form of balancing selection is called ‘frequency-dependent selection’, where the fitness of an allele is inversely proportional to its frequency. Thus, once the allele has become common due to selection, the fitness of that allele is reduced and selection will start to favour the alternative allele (which is at much lower frequency). The constant back-and-forth tipping of the selective scales results in both alleles being maintained at an equilibrium.
This can happen in a number of different ways, but often the rarer trait/allele is fundamentally more fit because of its rarity. For example, if one allele allows an individual to use a new food source, it will be very selectively fit due to the lack of competition with others. However, as that allele accumulates within the population and more individuals start to feed on that food source, the lack of ‘uniqueness’ will mean that it’s not particularly better than the original food source. A balance between the two food sources (and thus alleles) will be maintained over time as shifts towards one will make the other more fit, and natural selection will compensate.
A third category of selection (although not as frequently mentioned) is known as ‘disruptive selection’, which is essentially the direct opposite of balancing selection. In this case, both extremes of allele frequencies are favoured (e.g. 1 for one allele or 1 for the other) but intermediate frequencies are not. This can be difficult to untangle in natural populations since it could technically be attributed to two different cases of directional selection. Each allele of the same gene is directionally selected for, but in opposite populations and directions so that overall pattern shows very little intermediates.
In direct contrast to balancing selection, disruptive selection can often be a case of heterozygote disadvantage (although it’s rarely called that). In these examples, it may be that individuals which are not genetically committed to one end or the other of the frequency spectrum are maladapted since they don’t fit in anywhere. An example would be a species that occupies both the desert and a forested area, with little grassland-type habitat in the middle. For the relevant traits, strongly desert-adapted genes would be selected for in the desert and strongly forest-adapted genes would be selected for in the forest. However, the lack of gradient between the two habitats means that individuals that are half-and-half are less adaptive in both the desert and the forest. A case of jack-of-all-trades, master of none.
Direction of selection
Although it would be convenient if natural selection was entirely predictable, it often catches up by surprise in how it acts and changes species and populations in the wild. Careful analysis and understanding of the different processes and outcomes of adaptation can feed our overall understanding of evolution, and aid in at least pointing in the right direction for our predictions.
Often, we like to think of evolution fairly anthropomorphically; as if natural selection actively decides what is, and what isn’t, best for the evolution of a species (or population). Of course, there’s not some explicit Evolution God who decrees how a species should evolve, and in reality, evolution reflects a more probabilistic system. Traits that give a species a better chance of reproducing or surviving, and can be inherited by the offspring, will over time become more and more dominant within the species; contrastingly, traits that do the opposite will be ‘weeded out’ of the gene pool as maladaptive organisms die off or are outcompeted by more ‘fit’ individuals. The fitness value of a trait can be determined from how much the frequency of that trait varies over time.
So, if natural selection is just probabilistic, does this mean evolution is totally random? Is it just that traits are selected based on what just happens to survive and reproduce in nature, or are there more direct mechanisms involved? Well, it turns out both processes are important to some degree. But to get into it, we have to explain the difference between genetic drift and natural selection (we’re assuming here that our particular trait is genetically determined).
When we consider the genetic variation within a species to be our focal trait, we can tell that different parts of the genome might be more related with natural selection than others. This makes sense; some mutations in the genome will directly change a trait (like fur colour) which might have a selective benefit or detriment, while others might not change anything physically or change traits that are neither here-nor-there under natural selection (like nose shape in people, for example). We can distinguish between these two by talking about adaptive or neutral variation; adaptive variation has a direct link to natural selection whilst neutral variation is predominantly the product of genetic drift. Depending on our research questions, we might focus on one type of variation over the other, but both are important components of evolution as a whole.
Genetic driftis considered the random, selectively ‘neutral’ changes in the frequencies of different traits (alleles) over time, due to completely random effects such as random mutations or random loss of alleles. This results in the neutral variation we can observe in the gene pool of the species. Changes in allele frequencies can happen due to entirely stochastic events. If, by chance, all of the individuals with the blue fur variant of a gene are struck by lightning and die, the blue fur allele would end up with a frequency of 0 i.e. go extinct. That’s not to say the blue fur ‘predisposed’ the individuals to be struck be lightning (we assume here, anyway), so it’s not like it was ‘targeted against’ by natural selection (see the bottom figure for this example).
Contrastingly to genetic drift, natural selectionis when particular traits are directly favoured (or unfavoured) in the environmental context of the population; natural selection is very specific to both the actual trait and how the trait works. A trait is only selected for if it conveys some kind of fitness benefit to the individual; in evolutionary genetics terms, this means it allows the individual to have more offspring or to survive better (usually).
While this might be true for a trait in a certain environment, in another it might be irrelevant or even have the reverse effect. Let’s again consider white fur as our trait under selection. In an arctic environment, white fur might be selected for because it helps the animal to camouflage against the snow to avoid predators or catch prey (and therefore increase survivability). However, in a dense rainforest, white fur would stand out starkly against the shadowy greenery of the foliage and thus make the animal a target, making it more likely to be taken by a predator or avoided by prey (thus decreasing survivability). Thus, fitness is very context-specific.
Who wins? Drift or selection?
So, which is mightier, the pen (drift) or the sword (selection)? Well, it depends on a large number of different factors such as mutation rate, the importance of the trait under selection, and even the size of the population. This last one might seem a little different to the other two, but it’s critically important to which process governs the evolution of the species.
In very small populations, we expect genetic drift to be the stronger process. Natural selection is often comparatively weaker because small populations have less genetic variation for it to act upon; there are less choices for gene variants that might be more beneficial than others. In severe cases, many of the traits are probably very maladaptive, but there’s just no better variant to be selected for; look at the plethora of physiological problems in the cheetah for some examples.
Genetic drift, however, doesn’t really care if there’s “good” or “bad” variation, since it’s totally random. That said, it tends to be stronger in smaller populations because a small, random change in the number or frequency of alleles can have a huge effect on the overall gene pool. Let’s say you have 5 cats in your species; they’re nearly extinct, and probably have very low genetic diversity. If one cat suddenly dies, you’ve lost 20% of your species (and up to that percentage of your genetic variation). However, if you had 500 cats in your species, and one died, you’d lose only <0.2% of your genetic variation and the gene pool would barely even notice. The same applies to random mutations, or if one unlucky cat doesn’t get to breed because it can’t find a mate, or any other random, non-selective reason. One way we can think of this is as ‘random error’ with evolution; even a perfectly adapted organism might not pass on its genes if it is really unlucky. A bigger sample size (i.e. more individuals) means this will have less impact on the total dataset (i.e. the species), though.
Both genetic drift and natural selection are important components of evolution, and together shape the overall patterns of evolution for any given species on the planet. The two processes can even feed into one another; random mutations (drift) might become the genetic basis of new selective traits (natural selection) if the environment changes to suit the new variation. Therefore, to ignore one in favour of the other would fail to capture the full breadth of the processes which ultimately shape and determine the evolution of all species on Earth, and thus the formation of the diversity of life.