A few comments on the academic field that this paper lies in. The aim is to use DNA sequences to make inferences about the history of the populations. It's a really vexed area. The core objective is to make statistical inferences about whether giraffes are one "species" or multiple based on observed DNA sequences. The core problem is that we can't easily know or approximate the relevant probability distributions. Compare species-level giraffe taxonomy with a classification problem in which a large training data set is available, like determining whether a speech recording is male or female. For speech we can collect an arbitrarily large training data set. But for giraffes, the equivalent would be to find a large sample of biological lineages which are in all other respects like giraffes but differ in that some of them are one "species" and some multiple, and collect DNA sequences from each of these. It's fantasy -- it doesn't exist.

To go into a bit more detail: to do the inference task we would need at least three things:

1. A definition of "species"

2. The probability distribution of DNA sequences under the null hypothesis

3. (For Bayesian approaches) The probability distribution of DNA sequences under the alternate hypotheses

(1) Is a huge problem because many biologists don't think it's necessary to worry about the definition. Putting that aside temporarily:

(2). If Giraffes are a single species, what is the probability distribution from which our observed DNA sequences were sampled? The answer is that it depends critically on all sorts of other things: social and reproductive biology of giraffes, giraffe demographics, giraffe post-natal dispersal patterns. Maybe the most important is that it depends on the geographic distribution of savanna vegetation types over the past few million years in sub-saharan Africa. We do not know the effects of any of these on the relevant probability distributions. The field of population genetics does allow us to define probability distributions over sampled DNA sequences, but you have to specify the model. And all the above-listed unknowns and more are relevant to the model. From a formal statistical point of view you could place priors on these unknown things and simulate from the marginal distribution of interest, but in practice that is of course fantasy: there's no convincing way to choose priors for such things, and there's no way to test it because giraffe evolution happened once only.

(3). See (2).

The upshot of all this is that while making evolutionary inferences from DNA sequences is a fascinating discipline, it has some serious challenges and limitations: we need to recognize that it is not in as happy a place as other sorts of statistical inferences for which arguments can be made about the relevant probability distributions needed to make the inference. There is a huge disconnect between the statistical and theoretical machinery used in the field, and the ability of practitioners to understand that material. This is absolutely fair enough: people publishing papers on a particular species are likely to be ecologists and conservation biologists; but to understand coalescent theory and the statistical inference techniques used requires graduate-level understanding of stochastic processes, statistical inference theory, computational statistics and other stuff from discrete math etc. But that's not to imply that it would all be fine if people publishing the papers were professional computational statisticians. The real problem is that while we wish that we had the ability to make, and more importantly test, these inferences, the truth is that it's a wildly ambitious inference problem. Throwing fancy math and computational statistics algorithms at it will get some people tenure, and will make graduate students in organismal biology feel intimidated, but it doesn't change that problem.