Unravelling the evolutionary history of organisms – one of the main goals of phylogenetic research – remains a challenging prospect due to a number of theoretical and analytical aspects. Particularly, trying to reconstruct evolutionary patterns based on current genetic data (the most common way phylogenetic trees are estimated) is prone to the erroneous influence of some secondary factors. One of these is referred to as ‘incomplete lineage sorting’, which can have a major effect on how phylogenetic relationships are estimated and the statistical confidence we may have around these patterns. Today, we’re going to take a look at incomplete lineage sorting (shortened to ILS for brevity herein) using a game-based analogy – a Pachinko machine. Or, if you’d rather, the same general analogy also works for those creepy clown carnival games, but I prefer the less frightening alternative.
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.