The PCA method is flawed according to a study

In a recent post I discussed a study that questioned the validity of D-statistics; today I will explore two research papers that look into PCA or Principal Components Analysis, a statistical tool widely used in genetics and anthropology, which, according to two papers, may be biased, subjective, and flawed.

What is PCA?

Principal Components Analysis or PCA is a tool used to analyze data. It can be simplified as a method that concentrates, or reduces this data into two dimensions, where the data can be plotted and patterns, or structure identified. Points closer to one another should be similar and associated, those that are more distant in the plot are assumed to be more weakly (or not at all) linked.

You can obtain different information from samples taken from a population, and if there are, say 15 different variables measured for a given sample, it is very complex to pair up the variables and compare the samples to reach a conclusion.

Suppose you are studying bacteria, both pathogens and benign ones, and have defined fifteen variables, collecting data for each of them (length, width, thickness, rugosity, motility, lifespan, etc.). Your goal is to evaluate the influence of these factors on bacterial virulence. It would be impossible unless you could somehow simplify the data without losing information. Imagine if you could concentrate those 15 variables (or 15 dimensions) into just two, it would be much easier to visualize differences or similarities for your analysis.

PCA does just that. Using statistical formulas and computer power it condenses these variables into two main ones, "Principal Components" PC1 and PC2 without losing information, and plots them in a 2-dimensional chart.

Below is a simplified graph showing how three variables, that form a three dimensional space can be compressed into two Principal Components. The points (one sample is equal to one point), are graphed into a three dimensional space, with the three variables, x, y, and z defining their position.

As you can see, the first line (blue) is drawn along the region with most variability in the samples. A second line is drawn perpendicular to it (red). The First Principal Component is PC-1, the other is the Second Principal Component or PC-2. The data is theb "transformed" into a new, 2-D chart, where each point is one of the original samples from the original dataset.

I won't go into statistic, but the transformation is based on evaluating how the variance of the variables of the dataset (how "far" they are from the mean value of the total set), and how they change together (covariance). An example of covariance could be: alchol intake in oz. and driving ability (the higher the intake, the lower the ability to drive).

This analysis results in one main Component PC-1, which reproduces the highest variance, followed by all other perpendicular components ranked by importance. Of these, the second (PC-2) component is chosen.

We should take into account that since PC-1 is more important than PC-2 the differences along the PC-1 axis are greater than those along the PC-2 axis even if the "distance" between points is the same.

Below is a real example from a paper on human population genetics.

PCA global populations. Adapted from Geleta et al, Deep Variational Autoencoders for Population Genetics September 2023 doi:10.1101/2023.09.27.558320

The Africans seem to be most distant from all other groups and compact (more similar with each other), while West Asians are widely spread out along PC-1 (showing intra-population differences); Oceanians seem to form another compact group.

The method is faulty

Thhhe first article criticizing this PCA method is Principal Components Analysis fails to recover phylogenetic structure in hominins, by Levi Y. Raskin, et al., bioRxiv doi: https://doi.org/10.1101/2025.10.31.685754 🔓 (it has been published now in the American Journal of Biological Anthropology doi: 10.1002/ajpa.70306; Vol 190, no. 3: e70306. https://doi.org/10.1002/ajpa.70306.🔒). The authors analyzed studies using "morphometric data" (lengths, widths, angles, distances, thicknesses of bones, skulls, specimens) and found that "...PCA trees inferred from traditional morphometric data were identical to the sampled tree in 0.11% of datasets when we only considered PC axes 1 and 2, and in 2.9% of datasets when we considered all axes. No PCA tree inferred from any of the 2,400,000 shape datasets was identical to the sampled tree, regardless of the number of axes."

Only 11 out of 1000 trees produced by PCA methods with 2 dimensions were valid! And using more dimensions, the success ratio was less than three percent!

This questions the validity of conclusions reached using PCA methods: "Phylogenetic interpretations of the hominin fossil record based on proximity in PC space are inherently flawed and likely to be erroneous. Arguments in the hominin systematics literature based on PCA should therefore be reevaluated using phylogenetically-informed alternatives."

The authors are terminant. Those were best case scenarios. In real studies, bias and missing data could make matters even worse. The paper concludes that "PCA is fundamentally ill-suited and unreliable for inferring hominin evolutionary relationships from morphological data. Studies of hominin systematics that incorporate, and especially those that rely on, PCA as a means of inferring morphological and phylogenetic affinity should therefore be revisited."

This is relevant because many PCA charts using morphometric data assume that those hominins who are closer to each other in the chart, are related in the family tree and belong to a similar lineage. But it seems that this may not be the case. Below is an example of a morphometric PCA (Fig. 6 in Source); in the caption the text says "... High-scoring test subjects cluster together, suggesting cranial morphological similarity between them...":

Another Critical Voice: PCA and its use in genetic studies

An earlier paper published Aug. 29, 2022 by Elhaik E. Principal Component Analyses (PCA)-based findings in population genetic studies are highly biased and must be reevaluated (Sci Rep. 2022; 12(1):14683. doi: 10.1038/s41598-022-14395-4. PMID: 36038559; PMCID: PMC9424212), questioned the validity of conclusions obtained by using PCA. Elhaik is highly critical about its applicability to genetic studies and suggests that they are unreliable, and lead to false interpretations.

"...We demonstrate that PCA results can be artifacts of the data and can be easily manipulated to generate desired outcomes. PCA adjustment also yielded unfavorable outcomes in association studies. PCA results may not be reliable, robust, or replicable as the field assumes. Our findings raise concerns about the validity of results reported in the population genetics literature and related fields that place a disproportionate reliance upon PCA outcomes and the insights derived from them. We conclude that PCA may have a biasing role in genetic investigations and that 32,000-216,000 genetic studies should be reevaluated."

This work looks into the population PCAs, like the one shown furhter up (Africans, Europeans, Asians, etc). It notes that the PCA charts place the populations along the corners of an imaginary triangle: Africans, Europeans, and East Asians on each vertex of the triangle. And this is assumed to be the result of the migration out of Africa, followed by separate divergence and mutations. A conclusion widely accepted by geneticists. However, Elhaik says it isn't so: "Here we show that the appearance of continental populations at the corners of a triangle is an artifact of the sampling scheme since variable sample sizes can easily create alternative results as well as alternative “clines”."

This study states that "PCA can be used to generate conflicting and absurd scenarios, all mathematically correct but, obviously, biologically incorrect and cherry-pick the most favorable solution. This is an example of how vital a priori knowledge is to PCA. It is thereby misleading to present one or a handful of PC plots without acknowledging the existence of many other solutions, let alone while not disclosing the proportion of explained variance."

The manipulation implied by the author is that the outcome of the PCA chart is controlled by the scholar who already "knows" what the chart should reflect "By manipulating the choice of populations, sample sizes, and markers, experimenters can create multiple conflicting scenarios with real or imaginary historical interpretations, cherry-pick the one they like, and adopt circular reasoning to argue that PCA results support their explanation".

Closing comments

PCA is a valid statistical tool, with ample use in marketing, segmentation of customers, in facial recognition, in finance, climate modelling, medicine, and engineering (predictive maintenance, quality control). But, it seems that it use in the fields of anthropology and genetics is not robust or reliable.

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Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia Copyright 2009-2026 by Austin Whittall © 

Templeton's critique (Admixture, Statistical Tools)

American geneticist and statistician Alan R. Tempeleton (b. 1947), at Washington University in St. Louis, U.S., has been an outspoken and vocal critic of the use of Bayesian statitstics to support the Out Of African theory, and the replacement of ancient humans in Asia by our more recent African ancestors.

He holds a master's degree in statistics, so he is an expert in that field, unlike most geneticists (by the way, he also holds a doctorate in human genetics). This places him in the unique position to understand the genetics underlying the black-box algorithms used by researchers. He knows the statistical tools.

Templeton has criticized the incorrect use of Bayesian calculations and the mathematical and formal errors reproduced in different research publications.

His arguments sound solid, and professional. He disputes the missuse of specific statistical tools, as only an expert can. Below are some excerpts from his work.

One paper published in 2023 (Templeton A. The importance of gene flow in human evolution. Hum Popul Genet Genom 2023; 3(3):0005. https://doi.org/10.47248/hpgg2303030005) states the following:

"By the 1980’s CE, the paleontological record had convinced most scientists that the ancestors of humans had first evolved in Africa and then spread out into Eurasia in the early Pleistocene as Homo erectus. However, there was no consensus on what happened next. Three major models emerged by the latter half of the 20th century: the out-of-Africa replacement (OAR) model [1], the candelabra model of racial isolates [2], and the multiregional model [3,4]. Both the OAR and candelabra models posit that the expansion of Homo erectus into Eurasia results in independently evolving populations with no or extremely little genetic interchange. The OAR model in addition assumes a more modern form of humans, Homo sapiens, first evolved in Africa followed by an expansion into Eurasia, where the more modern humans completely replaced the archaic inhabitants of Eurasia. In both of these models, human evolution is dominated by splits into isolated lineages, followed by mostly independent evolution within the isolates. The OAR model in addition posits that the African isolate evolved into a form that expanded into Eurasia where it drove to extinction all the archaic Eurasians without genetic interchange with them. There is no or little role for gene flow in human evolution under these two models: rather, human evolution is dominated by splits, isolation, and extinction of lineages. Weidenreich’s multiregional model takes an opposite position on the importance of these evolutionary forces. There are no splits or isolates in his model because all human populations are interconnected by gene flow.
...
Despite the extensive evidence for gene flow and the lack of evidence of highly isolated evolutionary lineages, much of the human evolutionary literature is still full of “splits’, “divergence times of populations”, and pictures of human evolutionary trees showing separate branches leading to modern day Europeans, Asians, and Africans. These “splits”, “divergence times”, and “trees” are typically estimated with computer programs that will automatically yield a population tree regardless of whether or not the underlying data has a tree-like structure."

This is a clear description of the OOA hypothesis, and the expansion of hominins from Africa into Eurasia. Then he mentions the artifacts and models created with computer programs (trees, splits and dats for the forks of the branches of those trees). This is a novel point of view. It shows how we frame our ideas in models that then restrict how our thoughts can evolve in the future. A generation of geneticists thinks in terms of trees, splits, divergences, and coalescence dates.

In 1995, Templeton developed a statistical method called Nested Clade Phylogeographic Analysis or (NCPA) which uses genetic and geographic data to study how a population evolved (more about it in this paper). He mentions this method in his 2023 article, which continues below:

"... aDNA studies have confirmed the most controversial conclusion from NCPA that there was limited genetic interchange between the expanding out-of-Africa population with Eurasian populations. Moreover, genomic studies have revealed much genetic interchange and movement of human populations over the last 100,000 years, as reviewed in. One common method for achieving such inferences is to assume an evolutionary tree for the populations being sampled, and then calculate from the sequence data various statistical tests such as ABBA/BABA or several other alternatives... These statistics are tests of the null hypothesis that the underlying data do indeed come from a tree of populations. Rejection of this null hypothesis indicates that genetic interchange occurred that violated the assumed tree-like structure. When these tests reject a tree-like structure, often an admixture event of genetic interchange is assumed to have occurred to explain the rejection of the null hypothesis of a tree. For example, Figure 4... presents a typical visualization of this type of analysis."

Figure 4 is reproduced below.

Regarding the term "null hypothesis" used by Templeton, it is a statistical term used when one analyzes if the difference between two features of a population are due to chance, sampling errors, or some unknown real variable. To do so, one defines a null hypothesis (in this case, the differences between populations are due to a tree-like structure) and then performs rigorous statistical tests to compare the samples to see if chance or a real effect is responsible for any differences (usually a Student's t-test, created by English statistician William Sealy Gosset (1876–1937), aka Student), one also specifies a probability (the significance level or p), usually 5%, which sets the rejection threshold. If the calculated probability value from the t-test is lower than the significance level, one can reject the null hypothesis and accept that the results are not caused by random chance alone. In Templeton's example the null hypothesis was that tree populations explain human populations' genetics. But statistical analysis rejects this hypothesis meaning that some other genetic factors have intervened that are not tree-like. To save the day, geneticists have concocted admixture events into their trees to explain away the null hypothesis rejection.

Fig. 4 in Templeton
Figure 4. A simplified version of Figure 8 from [51] that shows the estimated gene flow between populations of modern humans and various archaic populations. Gene flow from modern humans into archaic hominins was not estimated.
Source

Tempelton rejects these admixture patches and the concept itself:

"There are two serious problems with this analytical approach. First, these test statistics have an identifiability problem as they cannot distinguish between a single, virtually instantaneous admixture event, versus multiple, recurring admixture events, versus continuous gene flow, or versus gene flow with isolation by distance.
Hence, figures such as Figure 4 are visually misleading as they imply a degree of knowledge that is not truly available from the test results. Drawing a trellis between populations with gene flow would have been equally justified for Figure 4. Other workers have used fossils from different time periods and/or analytical techniques that make use of the length of introgressed genomic segments to infer recurrent and frequent genetic interchange between Neanderthals and modern humans in Eurasia from 100,000 ybp to 37,000 ybp, and perhaps as far back as 270,000 ybp.
Hence, Figure 4 is not only visually misleading, it displays a false narrative for Neanderthals and modern humans. The only conclusion that is justifiable from these ABBA/BABA and similar analyses is the falsification of the null hypothesis that these populations are interrelated through an evolutionary tree. The null hypothesis of human population evolutionary trees has been falsified again and again since the mid-Pleistocene (as reviewed in Chapter 7 in [19]), and this is not surprising as NCPA already indicated that since the mid-Pleistocene human population structure has been dominated by population movements and/or individual dispersal coupled with interbreeding, with no significant role for splits and isolation"

Then he attacks the statistical logic behind the analysis that leads to these trees, and points out how researchers use computing tools to suit the outcome they are searching for, and don't quite grasp the meaning of the output of these programs:

"The second and more serious reason why figures such as Figure 4 are misleading is that the analytical method of starting with a tree and then adding connections to reflect gene flow is that this approach is statistically inconsistent when the actual relationship of the populations is a more complicated network than a simple tree.
Statistical inconsistency means that the estimators do not converge to the true answer with increasing amounts of data; indeed, the more data you have, the more likely you will have the wrong answer. Patently, inconsistency, just like incoherence, is a highly undesirable statistical property. This inconsistency is illustrated by the work of Pugach et al. They analyzed genomic data from Siberian populations for which some prior demographic historical information was available. Using the TreeMix program that starts with an evolutionary tree of the populations followed by adding on admixture events as needed, they found that the “TreeMix results were not easy to interpret and seem to contradict well-accepted aspects of human population history.” They then analyzed the same data with SpaceMix, a program that does not assume an underlying evolutionary tree. In contrast to TreeMix, the SpaceMix results fit the genomic data better and without contradictions to well-accepted aspects of the population history. SpaceMix indicated a history that included isolation by distance, long-distance dispersals, and multiple admixture events – all of which violate the assumption of a population evolutionary tree. Because of inconsistency, the credibility of figures such as Figure 4 is highly questionable in human evolutionary studies."

Templeton then attacks the use of trees and the lack statistical knowledge or interpretation by scholars:

"Despite the almost universal rejection of tree-like structures in human evolution since the mid-Pleistocene, some workers in this area still construct population trees using programs that will always generate a tree no matter how bad the fit is to a tree, treating each human population as an isolate on its own branch of the tree without any indication of any genetic interchange between branches... These population trees are typically presented without any statistical assessment of how well the tree fits the underlying genetic data. I tested the tree given in [63], and rejected a tree-like structure with a p-value < 10-200. To say the least, this is an abysmal fit, and the utility of such poor-fitting trees to gain insight into human evolution and population structure is highly questionable."

I agree with Templeton, and in the past posted on these tools (Some thoughts about the tools used in genetic admixture analysis), remarking that a craftsman is only as good as his tools.

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Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia Copyright 2009-2026 by Austin Whittall © 

Did Humans admix with Neanderthals? Paper in Nature says NO

Research published in Nature on Dec. 13, 2024 suggests, as its title says, that some models used by scientsts may lead to assume the existence of false introgressions. The word spurious used in the title means "based on false reasoning or information that is not true, and therefore not to be trusted". The paper can be found online: Tournebize, R., Chikhi, L. Ignoring population structure in hominin evolutionary models can lead to the inference of spurious admixture events. Nat Ecol Evol 9, 225–236 (2025). https://doi.org/10.1038/s41559-024-02591-6🔒

A preprint free version is available on line in Biorxiv 🔓

The paper's Abstract is quoted below:

"Abstract
Genomic and ancient DNA data have revolutionized palaeoanthropology and our vision of human evolution, with indisputable landmarks like the sequencing of Neanderthal and Denisovan genomes. Yet, using genetic data to identify, date and quantify evolutionary events—such as ancient bottlenecks or admixture—is not straightforward, as inferences may depend on model assumptions. In the last two decades, the idea that Neanderthals and members of the Homo sapiens lineage interbred has gained momentum. From the status of unlikely theory, it has reached consensus among human evolutionary biologists. This theory is mainly supported by statistical approaches that depend on demographic models minimizing or ignoring population structure, despite its widespread occurrence and the fact that, when ignored, population structure can lead to the inference of spurious demographic events. We simulated genomic data under a structured and admixture-free model of human evolution, and found that all the tested admixture approaches identified long Neanderthal fragments in our simulated genomes and an admixture event that never took place. We also observed that several published admixture models failed to predict important empirical diversity or admixture statistics, and that we could identify several scenarios from our structured model that better predicted these statistics jointly. Using a simulated time series of ancient DNA, the structured scenarios could also predict the trajectory of the empirical D statistics. Our results suggest that models accounting for population structure are fundamental to improve our understanding of human evolution, and that admixture between Neanderthals and H. sapiens needs to be re-evaluated in the light of structured models. Beyond the Neanderthal case, we argue that ancient hybridization events, which are increasingly documented in many species, including with other hominins, may also benefit from such re-evaluation."

Notice how the authors criticise the models used ("mainly supported by statistical approaches that depend on demographic models minimizing or ignoring population structure [but, ignoring] population structure can lead to the inference of spurious demographic events ").

The authors assumed that there were two population groups. One named metapopulation M_A tht generated a second one, M_B between 9 Million years ago and 500 ky. This created two populations (Bipartite structure) within Africa. Then, some individuals from the M_B group left to colonize Europe and Asia splitting some 650 ky ago from the remaining populations that stayed in Africa. Those who went to Eurasia became the metapopulation M_N, originating the Neanderthals or Hn population. The African metapopulations M_A and M_B evolved into Homo sapiens (Hs). Later Hs left Africa and colonized Eurasia forming an M_C metapopulation there. The paper states that "the new Hs Eurasian metapopulation M_C with the African Hs metapopulation M_B (itself connected to the Hs metapopulation M_A). Note however that none of the Hs metapopulations (M_A, M_B and M_C) ever exchanged gene flow with the Hn metapopulation (M_N). In brief, our model does not allow admixture between Hs and Hn."

Therefore this study suggests that instead of actual mating between Homo sapiens and Neanderthals, as a means by which genetic material was shared by both groups, the common fragments of genetic material may have originated in ancestral populations that split and carried them with them through time with no need for admixtwure.

Below is Fig. 1 from the paper, and the original caption is the following: "Simplifed representation of the 1D structured model considered in this study. Time flows from top (past) to bottom (present), with an initial metapopulation M_A consisting of nA (=10) demes exchanging migrants with their neighbours. At some point in the past, the rightmost deme of M_A founds a new metapopulation M_B of nB (=10) demes, with which it will continue exchanging migrants till the present. Later, the rightmost deme of M_B founds the metapopulation M_N of nN (=10) demes which will become Neanderthals. The MN metapopulation will never exchange migrants with any other deme from the other metapopulations. Closer towards the present, the rightmost deme of M_B founds M_C which corresponds to the expansion of H. sapiens towards Eurasia. White feet represent the sampled populations (not the specific demes) for respective sampling times. The location of the sampled demes (within the corresponding metapopulations) is a random variable... Fifty individuals are sampled in M_A and in M_C to represent modern-day YRI and CEU samples respectively. For the Neanderthals (M_N), one individual is sampled at 50 kya."

Fig. 1 in the Biorxiv preprint. Source

Comments

Interesting indeed! Could these admixture events be mere artifacts of these black-box statistical models used by scholars? I have posted some critical comments on these models in the past (See: Some thoughts about the tools used in genetic admixture analysis, Biases in Genetic Models that are generally overlooked). I favor admixture, yet, I also consider that the software used by scientists may not accurately reflect the real population dynamics of our ancestors.

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Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia Copyright 2009-2026 by Austin Whittall ©