Category: genetic variation

Race, Genes, and Breast Cancer

An explanation for “health disparities” – it’s all in the genes.

So, the System “take” is that “race is a social construct with no biological validity” and that “racial (presumably ‘social race?’) differences in health outcomes are all due to ‘White racism.”  What then to make of this, emphasis added:

PURPOSE:
Triple-negative breast cancer (TNBC) is most prevalent in young women of African ancestry (WAA) compared to women of other ethnicities. Recent studies found a correlation between high expression of the transcription factor Kaiso, TNBC aggressiveness, and ethnicity. However, little is known about Kaiso expression and localization patterns in TNBC tissues of WAA. Herein, we analyze Kaiso expression patterns in TNBC tissues of African (Nigerian), Caribbean (Barbados), African American (AA), and Caucasian American (CA) women.
METHODS:
Formalin-fixed and paraffin embedded (FFPE) TNBC tissue blocks from Nigeria and Barbados were utilized to construct a Nigerian/Barbadian tissue microarray (NB-TMA). This NB-TMA and a commercially available TMA comprising AA and CA TNBC tissues (AA-CA-YTMA) were subjected to immunohistochemistry to assess Kaiso expression and subcellular localization patterns, and correlate Kaiso expression with TNBC clinical features.
RESULTS:
Nigerian and Barbadian women in our study were diagnosed with TNBC at a younger age than AA and CA women. Nuclear and cytoplasmic Kaiso expression was observed in all tissues analyzed. Analysis of Kaiso expression in the NB-TMA and AA-CA-YTMA revealed that nuclear Kaiso H scores were significantly higher in Nigerian, Barbadian, and AA women compared with CA women. However, there was no statistically significant difference in nuclear Kaiso expression between Nigerian versus Barbadian women, or Barbadian versus AA women.
CONCLUSIONS:
High levels of nuclear Kaiso expression were detected in patients with a higher degree of African heritage compared to their Caucasian counterparts, suggesting a role for Kaiso in TNBC racial disparity.

Reality: Race is real, biologically relevant, and is reflected in important genetic differences that affect health outcomes.  The thing about reality is that it doesn’t change just because of hysterical SJW screeching. It is what it is.

Footnote: One wonders if the age differences in TNBC diagnoses comparing Nigerian and Barbadian females to “African American” females is due to the degree of European admixture in the latter.  Note that a more harsh outcome is with the former group, despite that the latter group is, according to the SJWs, more subject to “racism.”  Also note that nuclear Kaiso expression is obviously not the whole story as there was no difference between the different Negro groups for that metric, while age of diagnoses did differ. One possibility is that Kaiso does contribute to greater Negro propensity to TNBC, but that the AA group is partially protected (as I suggest above) by  a degree of White genetic admixture.

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Tales of Fst: Sallis vs. Lewontin

A small scale yet informative analysis of genetic variation.

We are all aware of the “more variation within groups than between groups” argument against the biological validity of race.

Now, I believe – or at least hope – that honest population geneticists (albeit very few if any exist) know better not to make absurd claims about Lewontin’s “finding” – that it “makes race meaningless” or that “people are more closely related to members of other races than members of their own race.”  At least they won’t say that among themselves, in their publications, or among other types of academics, but maybe they’ll still try to fool the rubes; after all, from my personal experience most population geneticists are anti-White SJW leftists.

The problem is more with your rank-and-file leftist, your Tim Wise types, your opinion writers, “anthropologists,” openly political population geneticists (the majority who are apparently dishonest), writers of “popular science,” politicians, bloggers, anti-White activists, etc. who make absurd comments about “more genetic variation within than between.”  Not only do they foolishly proclaim that it invalidates the race concept by making distinctive grouping impossible – that is absurd as Edwards so cogently pointed out – but they are even in error on a more fundamental level.

You hear these people make the most bizarre claims – that “more variation within than between” means that “Whites are genetically more similar to Blacks than they are to other Whites”- comments that reflect a complete misunderstanding of the concept (to be fair, those “academics” who have for decades championed Lewontinism to the rubes have, in my opinion, intentionally attempted to promote such a misunderstanding for political reasons).

You see, the basic problem is that these people think there is something special – in the negative sense – about classifying people by race (or ethnicity) that creates the Lewontin finding.  Because there is more genetic variation within “races” – for example, more variation within Whites than between Whites and Blacks – they think that means that if you were to compare one random group of Whites to another similar group of Whites then there would be more genetic variation between those groups of Whites than within those same groups (ignore the gaps of logic in this implicit, or sometimes overt, leftist “argument).  In other words, they say or imply, something like this:

Race is such a bad way to divide people, it is so wrong and meaningless, that WHEN you divide people by race THEN you get the result that there is more genetic variation within groups than between them.  [Implication: this difference in the apportionment of variation occurs as a result of binning people by race].  If we were to bin people randomly, arbitrarily, or by how “closely related they are independent of race” (whatever that means), then there would be more variation between than within groups, but when we use this stupid artificial racial boundary we see more variation within.  Indeed, the fact that binning people by race creates a situation that genetic variation is greater within the group proves that race is an invalid concept – how can a grouping that creates “more genetic variation within groups” be better than random groupings or aracial groupings that do not (we assume) do so?

You see, this is the implied message.  Race (and ethnicity) are negatively “privileged” groupings that create the Lewontin “finding” – after all, that’s how he reported it, and after all, that’s how it’s been discussed for decades, through the lens of racial classification.

My argument has been that this is a complete misunderstanding.  See this.  Excerpts, emphasis added:

With respect to Lewontin’s well known “there is more genetic variation within groups than between groups” we need to clarify whether the 85:15 split has any meaning other than the fact that the bulk of human genetic variation is randomly distributed. 

Comparing Danes vs. Nigerians: 85% variation within each group and 15% between.  The same would be observed with Japanese vs. Iranians. 

What if you considered a mixed group of Danes + Nigerians as a single population, and the same for Japanese + Iranians?  If you then apportioned genetic variation between D+N vs. J+I you would still get more variation within than between. 

If you went in the opposite direction, and considered Japanese from Tokyo as one population and Japanese from Kyoto as another population, the same within/between distinction would hold.  If you compared one Japanese family to another, you would also see more genetic variation within the group (family) than between families. 

As has been pointed out previously by others, a significant amount of genetic variation is found within single individuals; thus, if you were to compare one Japanese individual to another,~ half the genetic variation would be found within the single individual. 

For any set of human groups, one would expect to find more genetic variation within the group than between groups.  

Hence, the “within group” component of genetic variation is found within any defined set of individuals, and is randomly distributed among individuals.  It cannot be used to assert that members of an ethny are more dissimilar than to other ethnies, nor can it be used as a legitimate argument against the reality of genetically distinct population groups. 

And this doesn’t even touch upon the fact that with respect to many phenotypically relevant traits under selective pressure, racial differences in allele frequency is so great that there is actually greater genetic variation between compared to within groups.

Thus, most genetic variation is randomly distributed among individuals irrespective of classification. It has nothing to do with race (or ethnicity).  Racial classifications are not – as the leftists slyly imply – in any way special in exhibiting more variation within than between.  ALL and ANY human groups – even random, arbitrary groupings of people from within the same race or ethnic group, will show the same pattern of more variation within than between.  You can mix up groups of different races and get the same result.  You can create any arbitrary groups of individuals, in endless combination, and no matter how you do it, you will always get more variation within then between.

I doubt Lewontin and all the other academics who have foisted his “finding” on the masses were/are so stupid as to not realize this. They must understand that any and all human groupings, no matter how random or absurd, will show the same pattern.  Then, I suspect, knowing this, they decided to specifically choose racial classification as an example in order to trick people to believe that race is invalid, and do so for political reasons.

In actuality, the reality is the opposite, the genetic variation argument actually supports race, since the portion of genetic variation that is between groups is greatest when you bin people based on this concrete biological concept, and the between group variation portion is smaller (or in some cases virtually non-existent) when you bin people by random, or other arbitrary, methods.  Dividing Whites from Blacks is when you get the greatest amount of variation between, NOT dividing Whites from other Whites.  There was never reason to expect that human genetic differentiation was so extreme that the differences in genetic variation between groups would be greater than the unstructured variation found within groups.  If that was so, we would be totally different species, rather than variations (no pun intended) of one species.  

Let’s look at some data, but first, some comments on methods.  I have criticized Fst (and is variants) before – it is a lousy metric for measuring genetic distance, kinship, etc.  What it is – a measure of relative genetic variation

The fixation index is a measure of how populations differ genetically. One derivation of the fixation index is FST = (HT – HS)/HT, in which HT and HS represent heterozygosity of the total population and of the subpopulation, respectively. This derivation measures the extent of genetic differentiation among subpopulations. The value of FST can theoretically range from 0.0 (no differentiation) to 1.0 (complete differentiation, in which subpopulations are fixed for different alleles).  

A simple visualization of this idea is that of two squirrel subpopulations that are physically separated by a canyon and therefore cannot interbreed. Each subpopulation is homozygous for one allele of a SNP (in other words, each individual of one subpopulation might have a C at that position, while individuals from the other subpopulation have a T). The heterozygosity of the total population (HT) would therefore be 0.5. The heterozygosity of each subpopulation (HS) would be 0.0 (because every member of the subpopulation is homozygous). The calculation of FST in this oversimplified case would be (0.5 – 0.0)/0.5 = 1.0. In other words, 100% of the genetic variation of this population is between subpopulations, with zero variation within subpopulations.  

While a value of 1.0 for the fixation index is theoretically possible, such value in reality is usually much smaller. In general, high FST values reflect a low level of shared alleles between individuals in the sampled population and the total population. Conversely, low FST values indicate that members of the subpopulation share alleles with the total population. The proportion of individuals in a population that carry a certain allele varies over time and is influenced by the forces of migration, genetic drift, and natural selection.

But this is exactly the point – when discussing Lewontin a measure of relative genetic variation is exactly what we need, the weakness of Fst for kinship is a strength when tackling Lewontin.  In other words, we can use Fst to measure that portion of genetic variation that is between groups, with the balance being than within the groups.  For getting a precise measure of kinship, genetic similarity and difference – Fst is suboptimal.  For measuring within/between genetic variation, Fst is exactly what you need (and can give a crude estimation of distance).

After all, consider what Lewontin did – from the Wikipedia article linked above:

In the 1972 study “The Apportionment of Human Diversity”, Richard Lewontin performed a fixation index (FST) statistical analysis using 17 markers, including blood group proteins, from individuals across classically defined “races” (Caucasian, African, Mongoloid, South Asian Aborigines, Amerinds, Oceanians, and Australian Aborigines). He found that the majority of the total genetic variation between humans (i.e., of the 0.1% of DNA that varies between individuals), 85.4%, is found within populations, 8.3% of the variation is found between populations within a “race”, and only 6.3% was found to account for the racial classification. Numerous later studies have confirmed his findings.[5] Based on this analysis, Lewontin concluded, “Since such racial classification is now seen to be of virtually no genetic or taxonomic significance either, no justification can be offered for its continuance.

Let’s consider “1000 Genomes” data for 99 Nigerians and 99 CEU Whites (Northwestern Europeans from Utah – in other words, folks like Mitt Romney).  Let’s consider three SNPs and calculate Fst for different examples of groupings. 

First, a direct comparison of these two racial groups (Nigerians vs. CEU Whites), as it is usually done – calculating Fst of different distinct population groups compared to each other.

(UPDATE: I have changed the data format after getting criticism from some correspondents that the original version was not optimally clear to the layman. Hopefully the new version is better).  The first data:

Nigerians vs. CEU Whites

Fst = 0.1718

We observe the usual result.  The Fst between these two groups is 0.1718.  So, essentially, 17% of the total genetic variation inherent in the total of 198 individuals is that between the two racial groups of 99 each, and 83% is found within each group of 99.  The calculations from the Left always end there, with heavy breathing and triumphant cries of “more variation within than between” when we classify by “race.”  Let us continue the analysis.

Let us now arbitrarily break up each of the two populations into three subgroups of equal numbers (three groups 33 Nigerians and three groups of 33 CEU Whites) and measure Fst comparing now the intra-racial groups (Nigerians s. Nigerians and Whites vs. Whites).

Nigerians broken up into three “populations” of 33 individuals each:

Three arbitrary groups of Nigerians

1 vs. 2  Fst =   0.0024

1 vs. 3  Fst = – 0.0150

2 vs. 3  Fst =  -0.0027

Negative Fst (in red) is essentially the same as zero.  Thus, there is very little to no fraction of the total variation between these groups, virtually all within.  So – hey! – “more variation within than between” even in randomly picked individuals from single ethnic groups, exactly as I predicted (and which is consistent with simple common sense – something leftists lack).  Of course, this is not surprising (or shouldn’t be), comparing Nigerians to Nigerians there should not be a significant difference in variation between the groups, as the individuals are derived from the same population. BUT THIS IS EXACTLY THE POINT. When comparing races, we DO see a significant fraction of between group variation, because races are distinct and valid biological entities.  The fact that the between group variation in the inter-racial case is smaller than within group variation does not invalidate race – why would one imagine that human races would be so differentiated that you would have most of the variation between groups?  Most of that variation is random. One sees any significant Fst only when comparing different population groups, because they are distinct. The same pattern holds with dog breeds – more variation within than between (see below). In the Nigerian example presented here, there may be a lot of variation within groups, but that’s on an individual-to-individual level; the group in general is similar to itself as shown when arbitrarily broken up into sub-groups.

And of course, this individual-to-individual variation exists not only within groups but between groups, in fact between all individuals, and it does NOT in any way mean that members of a group are genetically more similar to members of other groups than they are to their own. The fact that group members are virtually ALWAYS more similar to same-group members has been shown (many times in fact and can be observed via private genetic testing – remember when Decode was giving ethnic similarity matches, even with 23andMe data?) – see here.

When looking at many markers at the same time, groups and the individuals within can be easily distinguished racially – see Edwards’ article for the logic there, and why Lewontin’s finding is a “fallacy” with respect to racial classification.

I would also like to point out that genetic variation is not the same as genetic difference.  Indeed, on a fundamental level, these concepts are not the same.  Degrees of variation is not the same as difference (or distance). If one were to catalog the types of ethnic populations extant in, say, New York City and San Diego, there would be differences.  One could clearly distinguish between the two – more Jews and Puerto Ricans and Dominicans and Caribbean Blacks in New York, and more Mexicans in San Diego, among other differences.  The populations of these two cities are distinct, and “distant” in their differences.  But the internal differences are even greater: consider the myriad ethnic types in NYC.  So, the ethnic variation within these cities is greater than that between, even though the two cities have highly distinct, easily classifiable populations, and these differences are not “trivial” but affect every aspect of life in those areas.

Back to the main point: if we apply the same SJW racial comments to the intra-group data, we’ll have to say that because Nigerians exhibit more variation within the group than between groups then there are no such thing as Nigerians, and yet at the same time the groups of Nigerians have low to Fst in comparison with each other, but significant Fst when compared to Whites and Asians.  So, at the same time, Nigerians do and no not exist as a group, a logical impossibility.  

And if, as the Left claims, Whites are more genetically different from each other than from Blacks, then White-White Fst should be greater than that of White-Black Fst, and one should see a considerable portion of the genetic variation in a White-White comparison to be between groups of Whites as opposed to within. 

[Note: In a logical sense, the leftist argument is absurd – they would clam that between group variation of the three White sub-groups would be great precisely because the amount of within group variation of the original White group is so large, and measure this with Fst, which compares the two.  But this is, again, the point: the claims of the Left are inherently and logically absurd, and when followed through to their conclusion leads one to a logical paradox – the greater the portion of within group variation then the greater the portion of between group variation when looking solely at that group.  On the other hand, Fst is a relative measure, and one can argue that the White-White comparison is qualitatively different from the logical perspective from the White-Black one. In either case, my approach achieves its goal – either the Left’s arguments are inherently illogical, OR, if you want to claim that their arguments are logical, I show in this post that the arguments are factually wrong, as the data yield the opposite results from leftist predictions].

The data for CEU Utah Whites:

Three arbitrary groups of CEU Whites

1 vs. 2  Fst =  -0.0094

1 vs. 3  Fst =   0.0072

2 vs. 3  Fst =  -0.0041

Again, minuscule to zero Fst (negative [red font] = zero). Once again, we observe the same “more within than between” pattern with arbitrary divisions of a group of humans.  Note that Fst is greatest with the inter-racial comparison (0.1718), precisely because races are valid biological entities with the greatest genetic distance between them (while Fst is not the best measure for distance, it does reflect differences in genetic distance, so is valid for such relative comparisons).

None of this should come as a surprise, since population genetics studies looking at Fst of different parts of a single country (indigenous natives) – such as, say, Germany or Italy, show relatively low Fst.  Nevertheless, it is useful to demonstrate that an arbitrary intra-population division not only mimics the racial finding (more variation within than between), but does so in a more extreme manner.

The preceding has been an appetizer; now we get to the main course.  The twin tenets of the radical Left view of Lewontin’s “finding” are:

1. Race (or even ethnicity) is an especially wrong classification scheme that (implied: specifically) results in “more genetic variation within than between” groups, because it artificially separates all the people of different “races” (leftist scare quotes) who are actually genetically similar.

2. Thus, the “more within than between” means that groups like Nigerians and Northwest European Utah Whites are more genetically similar to members of the other group than they are to members of their own group.

By now, we should know that this is nonsense, as is the claim that races don’t exist, but let’s continue to take this leftist farce at face value.  If these twin tenets are true, then arbitrarily creating multi-“racial” groups – say, random mixed groups each consisting of Nigerians and Utah Whites together in the same groups – would result in a larger Fst comparing these mixed groups, with relatively more variation between and relatively less within.  Or – let us be more charitable with all the leftist delusions and logical impossibilities.  Let us merely state that if the Left is correct, and that conceptions of race and ethnicity are meaningless due to the apportionment of genetic variation, then, at minimum, Fst comparisons of the mixed groups should be no less than that of between the racially defined groups.  That’s the most conservative interpretation of the Left, and the one that makes them seem less stupid and illogical.  What’s the data then?  Here it is (negative Fst again in red font):

Three arbitrary groups of mixed Nigerians and CEU Whites together

1 vs. 2  Fst =   0.0029

1 vs. 3  Fst =   0.0105

2 vs. 3  Fst =  -0.0047

This is crucially important. Mixing the two groups together has greatly reduced or eliminated Fst – it has essentially eliminated the between group genetic variation.  Here, virtually all the variation is within group.  This is a complete and perfect refutation of the extreme leftist (mis)interpretation of Lewontin’s “findings.”  The results from comparing variation between and within mixed race groups, contrasted to that obtained from monoracial groups, is exactly the opposite of what would obtain if leftist fantasies were correct.

One could continue playing around with genetic data in this manner, with larger data sets, random number generators to form groups, etc., but the point has already been established.  Thus, you can pick names randomly out of any diverse big city phonebook – New York for example – and use these random people to form groups, and if you would analyze the genetic variation of these random and arbitrary aracial groupings you will find more variation within than between AND a smaller Fst compared to real inter-racial comparisons.

Now, it can be – and should be – argued that the arguments and findings in this blog post are simple, common-sense, intuitive, even trivial.  OF COURSE random groups would have even more genetic variation within and OF COURSE racial groups will have a larger Fst, indicative of a larger share of variation between.  Of course races are real biological groups and of course the Left is wrong.  But given leftist hysteria and mendacity over race and genetics, the issue had to be formally demonstrated, which it was here.  It is unfortunate one must waste time “proving” things so obvious it is the equivalent of “the sky is blue” but so it goes in the modern world.

A comparison with the situation with dog breeds is also instructive.  There is much about dog breed genetics online, from both the Right and Left, and much of that is misleading; instead let’s read what an expert on the subject has to say, concentrating on the implications for Lewontinism:

The phenotypic diversity of the world’s 350 to 400 dog breeds is mirrored in their genetic diversity. Although most breeds have existed for less than two centuries, the level of diversity (FST) in dogs is about twice that found in humans (FST averages 0.28 among dog breeds).

So, we see that due to intense artificial selection, Fst between dog breeds is about twice of that between human races, despite the fact that many dog breeds are recent developments in evolutionary time.  Very well.  The most important fact that we observe here is that despite all of this intense artificial selection and the vast phenotypic differences between breeds, Fst for dog breeds is 0.28, meaning that the vast majority of the genetic variation – 72% in fact – is found within breeds; only 28% is between.  Consider the huge – existential in fact, defining the identities and utility of different dog types – marked heritable differences between dog breeds in physical appearance, physical capabilities, size, intelligence, and behavior and note that despite all these enormous differences there is still “more genetic variation within than between.”  More genetic variation within dog breeds than between!  What would the Left say?  Is the difference between a vicious Pit Bull and a placid Pug merely the figment of your imagination?  Does “more variation within than between” mean that the differences between a Chihuahua and a Mastiff are merely a “social construct?”  Do we claim that “dog breeds do not exist?”  Now consider again the vast differences between dog breeds and ponder the implications of the fact that human inter-racial between-group genetic variation reaches a full 50% of that between dog breeds.  Once again: the differences between humans is a full 50% of the enormity of difference between dog breeds that was derived from a regimen of constant intense and directed artificial selection. Racial differences are not only real, they are staggeringly large.

Let’s finish up by going back to the Wikipedia article on the Lewontin fallacy.

….biological anthropologist Jonathan Marks agrees with Edwards that correlations between geographical areas and genetics obviously exist in human populations, but goes on to note that “What is unclear is what this has to do with ‘race’ as that term has been used through much in the twentieth century—the mere fact that we can find groups to be different and can reliably allot people to them is trivial. Again, the point of the theory of race was to discover large clusters of people that are principally homogeneous within and heterogeneous between, contrasting groups. Lewontin’s analysis shows that such groups do not exist in the human species, and Edwards’ critique does not contradict that interpretation.

Typical Jewish flim-flam. Marks proposes an unachievable, unrealistic strawman definition of “race” so as to declare that it does not exist. Given the reality of unstructured (“random”) genetic variation that exists between any and all groupings of humans, it stands to reason that grouping by race will also show the same intra-group variation.  BUT THE GROUPS ARE STILL DIFFERENT AND MEMBERS OF THE SAME GROUP WILL ALWAYS BE MORE SIMILAR MEMBERS OF THEIR SAME GROUP COMPARED TO OTHER GROUPS.  That is what race is, no one says that a race has to consist of genetically homogeneous individuals.  Are families – apart from identical twins – genetically homogeneous?  Only in comparison to other families.  Each family will have considerable internal variation.  But they are different. Marks states “the mere fact that we can find groups to be different and can reliably allot people to them is trivial.”  So, he declares that the fact that humans can reliably be allotted to different groups – the essence of race – is trivial, before postulating his strawman version.  Well, Marks, the “trivial” differences lead to differences of phenotype that are acted upon by various forms of selection, thus affecting the underlying gene frequencies, and, hence, the adaptive fitness of the individuals in question. The underlying essence of life is natural selection and adaptive fitness based on genetic differences and kinship.  Thus, according to Marks, the fundamental basis of life on Earth – the genetic distinctiveness of organisms and their representation in subsequent generations – is “trivial.”  Genetic differences, no matter how ‘trivial,” can increase or decrease in frequency and thus constitute adaptive interests for evolved organisms, like humans.  To deny the fundamental meaning of this with misleading verbiage, to consider representation in the next generation is “trivial” is anti-science and anti-reality.  Note to leftists: the variation equivalent of halfway from a Chihuahua and a Mastiff is not a “trivial” amount of genetic variation.

The real translation from the likes of Marks: racial preservation of Whites is “trivial.”  That’s what it is all about, of course.  Nonsense about races having to be hermetically sealed clones completely variant from other clonal races is just Jewish meme wars against White ethnic genetic interests.

The view that, while geographic clustering of biological traits does exist, this does not lend biological validity to racial groups, was proposed by several evolutionary anthropologists and geneticists prior to the publication of Edwards critique of Lewontin.

Err…” geographic clustering of biological traits” (including gene frequencies) is precisely what race is, so if such clustering exists, race exists.  I suppose one can, like Marks or any other mendacious Jew (a redundancy) redefine “race” using unrealistic criteria so you can proclaim “race does not exist” but that is meaningless.  One can define human” in like manner.  Thus, a “human” is any nine foot tall hominid with naturally blue hair who has an IQ of 10,000.  Such individuals do not exist, hence there are no such thing as humans. QED.

In summary:

1. There is nothing special, defining, or “privileged” about race (or ethnicity with respect to “more genetic variation within than between.”  Any and all human groups or mixtures of groups, no matter how arbitrarily or randomly chosen will always exhibit the same pattern, because the pattern is due to individual human variation and that variation is present no matter how groups of humans are arraigned. Making a big deal of this “finding” when it comes to race derives from leftist sociopolitical motivations.

2. The “more variation within than between” in no way invalidates the race concept, as Edwards (and I) pointed out.  Even Marks concedes classification is possible; he just labels it “trivial” – and this subjective assertion is also motivated by leftist social and political beliefs.  The apportionment of genetic variation certainly does not invalidate genetic differences and similarities between groups, and the greater genetic distances between the major racial groups.

3. Strawman definitions of race implying that races have to be genetically homogeneous are ludicrous and also motivated by leftist concerns.  Given that genetic variation is randomly distributed among all people, such will as a matter of course be found within groups, including races.  However, Fst increases as we consider ever more distinct racial groups, as an increasing portion of the total genetic variation derives from between group differences.  Given the large totality of such differences, a consistent distinctive genome is sufficient to define biological races, along with the background of random variation.  And that’s not trivial.  An analogy would be an extremely important radio message, of life-dependent importance, that you are listening to among a larger degree of random noise, of static.  The static may be louder, but it is the message that is important, and by proper adjustments to your methodology, you can cancel out the static and listen to the message.  For humans, the message is nothing less than our adaptive fitness, the over-riding importance of genetic continuity, of genetic interests – the ultimate interests.

A Bit of Racial Reality

It’s sad that one must continuously reinforce the obvious and proven fact of the biological basis of race.

This is one of Strom’s better efforts, emphasis added:

An article at the Harvard University Web site (and Harvard is heavily-Jewish in both student population and administration) argues that since “almost half” of alleles in the human genome are found in all seven major regions of the globe, there can’t be human races. Now, that’s really a bizarre argument. It means that by their own admission most human alleles (genetic variants) are not found in all regions, yet they persist in their claims. The article even admits (after invoking Donald Trump as one cause for all this terrible belief in human races — give me a break) that “7.4% of over 4000 alleles [studied] were specific to one geographical region” — that’s almost 300 alleles, and 7.4 per cent. — as we shall see in a moment — is a huge degree of difference, more than enough to account for human racial variation, even human-animal species variations. As one commenter pointed out, in 2012 the National Library of Medicine published a study of bears showing that having just half of the alleles shared among two populations was enough to prove that the populations were not only different races but entirely different species! In the scientists’ exact words, this degree of genetic difference was consistent with the two populations being “different species with little or no gene flow among extant populations.” So, if two groups share about half of their alleles, it proves they’re different species — if they’re bears. But if they’re humans, it proves the exact opposite — not only are they all the same species, but there’s not even any racial variation among them. It’s pretty obvious that someone is lying here, and I don’t think it’s the guys and gals studying the bears.

By the way, I call “BS” on the idea that Watson and Venter are more similar genetically to a Korean than they are to each other. If you sample sufficient number of alleles, that is NOT going to be the case.  See this.

As the authors used more and more markers to compare the three major racial groups (Europeans, East Asians, and sub-Saharan Africans), the less stringent clustering measurements rapidly fell to a 0% overlap, as expected from previous studies.  What about the more stringent measurement “w”, which looks at comparisons between individuals, and does not consider group data?  Once the authors reached 1,000 (or more) markers, the genetic overlap between these groups essentially reached zero. It is useful at this point to quote the authors about this fundamentally important finding: 
This implies that, when enough loci are considered, individuals from these population groups will always be genetically more similar to members of their own group.
With respect to the question of whether individual members of one group may be genetically more similar to members of another group, they write:
However, if genetic similarity is measured over many thousands of loci, the answer becomes ‘never’ when individuals are sampled from geographically separated populations.
Thus, the naive “anti-racist” view, actually stated at times (e.g., the NOVA program on race), that it is possible for individual Europeans and Africans to be more genetically similar to each other than to members of their own race, is simply false.  Any such “finding” is simply due to insufficient numbers of DNA markers being used.
With an adequate methodology, individual members of the major racial groups will always be more similar to members of their own group than to members of other groups.  Some may not like this and deem it “racist”, but these are the scientific facts, nonetheless.

Read this, which, by the way, is from a Jewish researcher, emphasis added:

What makes the current study, published in the February issue of the American Journal of Human Genetics, more conclusive is its size. The study is by far the largest, consisting of 3,636 people who all identified themselves as either white, African-American, East Asian or Hispanic. Of these, only five individuals had DNA that matched an ethnic group different than the box they checked at the beginning of the study. That’s an error rate of 0.14 percent. 
Neil Risch, PhD, a UC-San Francisco professor who led the study while he was professor of genetics at Stanford, said that the findings are particularly surprising given that people in both African-American and Hispanic ethnic groups often have a mixed background. “We might expect these individuals to cross several different genetic clusters,” he noted. That’s not what the study found. Instead, each self-identified racial/ethnic group clumped into the same genetic cluster.
The people in this research were from 15 locations within the United States and in Taiwan. This broad distribution means that the results are representative of racial/ethnic groups throughout the United States rather than a small region that might not reflect the population nationwide.
For each person in the study, the researchers examined 326 DNA regions that tend to vary between people. These regions are not necessarily within genes but are genetic signposts on chromosomes that come in a variety of forms at the same location.
Without knowing how the participants had identified themselves, Risch’s team ran the results through a computer program that grouped individuals according to patterns of the 326 signposts. This analysis could have resulted in any number of different clusters, but only four clear groups turned up. And in each case the individuals within those clusters all fell within the same self-identified racial group.
“This shows that people’s self-identified race/ethnicity is a nearly perfect indicator of their genetic background,” Risch said.

And here is one of my old articles on the subject at Amren.

Also see this.

However, racial reality is not the same thing as “racial purity.”

An Empirical Racial Soul?

A brief materialist look at “spiritual race” mechanisms.

Readers of this blog are probably aware that I – a scientific materialist and empiricist – am critical of “spiritual race” theories, including ideas about a “racial soul” or “race soul,”  whether these are derived from Spengler, Yockey, Evola, or German Nazism.

However, is there perhaps an area of overlap between biological and spiritual race theory, one in which ideas of a “racial soul” and “spiritual race” – an innate sense of self, instinctive behaviors and preferences, and metaphysical beliefs and aspirations connected to particular ethnies – have some sort of discoverable, knowable, physical basis, a materialist foundation?  In other words, spiritual race exists but is not something independent of matter and of the physical body but is a derivation of it; the race soul being an emergent property of biological racial characteristics, influenced by culture and a people’s history, their “genetic memory” as a ethnocultural-historical entity.

One could speculate that characteristics of a “racial soul” are influenced by:

1. Genetics; complex epistasis of many gene variants and their expression that influence behavior in a manner beyond the current level of understanding of definitive “genes that affect behavior.”

2. Epigenetic influences that are stable over time because they are constantly reinforced by cultural/historical/environmental factors, some of which are themselves influenced by epigenetics (self-reinforcing) or underlying genetic differences (gene-culture effects and canalisation).  

While I believe that epigenetic influences are grossly overestimated by ideologues of both the Left and Right, who have political reasons for de-emphasizing genetic determinism, it is wrong to lurch in the opposite direction and completely disregard potential epigenetic mechanisms.

3. Learned behaviors, passed down through the generations, which appear instinctive and unlearned because they are long-term, subtle and complex, and hence invisible to casual and immediate observation.

4. The combination of 1,2, and 3 so as to produce reproducible ethnic and racial traits that are seemingly unconnected to strict biological race, and seemingly so because the level of analysis is superficial and only looking at direct and immediate relationships between “one gene and one phenotype.”

Please note that if complex “cross-talk” exists between culture/environment on the one hand, and genetics/epigenetics on the other, manifested as a “racial soul” – or “spiritual race” – then by altering a group’s culture and environment, one can change the underlying physical basis of their racial soul.  Is one reason for the degeneration of Whites in recent history – their complete spiritual and moral collapse – due to the poisoning of their culture and the decay of their environment due to Leftist/Jewish influences?

Also note that given variability within a race as regards genes and epigenetics, and different life experiences of individuals, outliers of the racial soul can exist (as noted, e.g., by Yockey and Evola) – a member of one “biological race” belongs to a different “spiritual race” – mechanistically explained by unusual combinations of influences 1-4 listed above.  But for an entire group, and most of its members, the racial soul should be consistent (and also, unfortunately, consistently susceptible to degeneration).

At this point, it is imperative to further consider “cross-talk” between genes and culture, and between epigenetic influences, genes, and culture, and the process of “canalisation.”

Canalisation is a measure of the ability of a population to produce the same phenotype regardless of variability of its environment or genotype. It is a form of evolutionary robustness. The term was coined in 1942 by C. H. Waddington to capture the fact that “developmental reactions, as they occur in organisms submitted to natural selection…are adjusted so as to bring about one definite end-result regardless of minor variations in conditions during the course of the reaction”. He used this word rather than robustness to take into account that biological systems are not robust in quite the same way as, for example, engineered systems. 

Biological robustness or canalisation comes about when developmental pathways are shaped by evolution. Waddington introduced the concept of the epigenetic landscape, in which the state of an organism rolls “downhill” during development. In this metaphor, a canalised trait is illustrated as a valley (which he called a creode) enclosed by high ridges, safely guiding the phenotype to its “fate”. Waddington claimed that canals form in the epigenetic landscape during evolution, and that this heuristic is useful for understanding the unique qualities of biological robustness.

Thus, it is part of the racial soul to reproduce the same phenotype regardless of variation in the environment, or even regardless of fluctuating variation (e.g., from genetic drift, bottlenecks, etc.) in the genotype – as long as certain core components of the genotype remain intact.

Also consider the related hypothesis of “evolutionary capacitance.”

Evolutionary capacitance is the storage and release of variation, just as electric capacitors store and release charge. Living systems are robust to mutations. This means that living systems accumulate genetic variation without the variation having a phenotypic effect. But when the system is disturbed (perhaps by stress), robustness breaks down, and the variation has phenotypic effects and is subject to the full force of natural selection. An evolutionary capacitor is a molecular switch mechanism that can “toggle” genetic variation between hidden and revealed states. If some subset of newly revealed variation is adaptive, it becomes fixed by genetic assimilation. After that, the rest of variation, most of which is presumably deleterious, can be switched off, leaving the population with a newly evolved advantageous trait, but no long-term handicap. For evolutionary capacitance to increase evolvability in this way, the switching rate should not be faster than the timescale of genetic assimilation.

This mechanism would allow for rapid adaptation to new environmental conditions. Switching rates may be a function of stress, making genetic variation more likely to affect the phenotype at times when it is most likely to be useful for adaptation.

Different ethnies contain different types of, and levels, of such genetic variation; hence, human groups differ, qualitatively and quantitatively, in their evolutionary capacitance.  What this means in terms of a “racial soul” is that different groups may not reflect a type of phenotypic difference in one environment, but once exposed to a different, stressful environment, robustness breaks down and the inherent genetic variation is expressed in phenotypes previously masked.  This expression of masked phenotypes is one manifestation of the “racial soul.”

Note that canalization and evolutionary capacitance reflect the concept of a racial soul in opposite manners.  The former describes the robustness, the consistent replication, of racial behavior and racial expression in various environments (with perturbations within limits) – thus, different ethnies will consistently reproduce aspects of their racial souls even when transplanted to new living spaces, such as groups migrating to the same common territory (e.g., America).  The latter concept describes situations in which differential expression of a racial soul is masked, hidden, because canalization stabilizes phenotypic expression within a particular environment, but this expression of the racial soul is unleashed upon transition to a more radically different environment.  Thus, different groups, which appear similar in behavior on the surface, will reveal radically different behaviors – seemingly instinctive behaviors – for example in times of war, upheaval, or even radical changes in cultural paradigms.  

Both poles of racial expression – the robustness of canalisation in which the revealed states are stable within a certain degree of environmental variation and the unleashing of hidden states of racial expression built up through evolutionary capacitance – should have materialist, physical explanations.  Canalisation is due to gene-culture co-evolution (with perhaps epigenetics playing a role), while evolutionary capacitance is due to inherent genetic (and possibly epigenetic) variation of ethnies that creates the potential for behaviors that, hidden at one time, become revealed and expressed at another time.

Both of these poles of expression – the uncanny consistency of group expression and the hidden abilities of groups that become revealed in times of stress – can be considered aspects of race typically labeled as “spiritual race” and the “racial soul.”

On related notes, see “genetic memory” (mentioned above) – also discussed here – as well as Jung’s “collective unconscious.”  If we are to seriously consider these ideas from the standpoint of materialist biological science, then the same mechanisms discussed above likely apply.

With sufficient understanding and technical advances, it may be possible at some point in the future to evaluate these ideas, and determine whether there is an underlying material basis – actual physical mechanisms – for these postulated phenomena, and, more fundamentally, determine the validity of the actual existence of these phenomena for the human condition.  In other words, does a “racial soul” really exist and, if so, what is its physical, mechanistic basis?

Genetic Structure and Altruistic Self-Sacrifice

A more precise accounting is required.

We are all aware of Haldane’s oft-quoted assertion that he would lay down his life for two brothers or eight cousins, the genetic payoff of such altruistic self-sacrifice being the equivalence – as measured by ”bean-bag” genetics – of the numbers of gene copies between these sets of relatives.

In general, I am in broad agreement with the sentiment, although as we shall see, it requires modification.  Even more broadly, those on the Far Right invoke this paradigm to support the idea of altruistic self-sacrifice in favor of larger numbers of an ethny, in defense if ethnic genetic interests.  Likewise, I support that as well, with the proper modifications as with the smaller-scale examples of familial relatives.

Even though at first glance, Haldane’s reasoning seems sound, likely most people would be hesitant to follow that advice.  In large part, this is the natural impulse of self-preservation, but there are other reasonable objections that can be made.

One could argue, all else being equal, that judging between two sets of equivalent genetics, it’s better to preserve yourself for reasons of control.  A person concerned enough with genetic continuity that they would consider such altruistic self-sacrifice is someone likely to start a family, care for children, and properly actualize the continuity. Can you be sure your two brothers would do the same?  Why are they in the position that they need your sacrifice to begin with?  Are they stupid?  Reckless? Are you sure they’ll act in support of your (in this case indirect) genetic continuity with the same vigor you would do for yourself?  So, to be safe, maybe you need to raise the bar for self-sacrifice to three brothers or ten cousins?

A more important reason, and one that may be intuitively sensed by most people even though they wouldn’t be able to explain it, or likely even articulate their feeling about it, is that there is more about kinship than mere numbers of gene copies.  Genetic structure is important – what genes are coinherited and, to the layman’s eye, what phenotypic traits (derived from those genes) are inherited together.  Of course, family is going to be more similar here than (co-ethnic) strangers, but similarity is not identity.  Even with siblings (apart from identical twins, which are a special case), recombination and independent assortment will ensure that your brothers will have a distinct genetic stricture from you.  Now, granted, these same processed, even with a co-ethnic mate, will ensure that your children will also have a different genetic structure than you, but, all else being equal, your brothers’ children will be more unlike you, with respect to genetic structure, than your own children, as the “starting point” (you vs. your brothers) is already different. So, when genetic structure is taken into account, two brothers are not really your genetic equivalent.  Apart from an identical twin, you have no genetic equivalent, just degrees of relative similarity and difference, even after numbers of gene copies are accounted for.  Then how many brothers are sufficient for self-sacrifice?  This requires a more rigorous analysis, which will be dependent upon accurate measures of genetic structure, and that’s not something we can expect SJW population geneticists are likely to do. However, while the overall Haldane argument – and its Salterian extension – makes sense the numbers given based on “bean bag” genetics is going to be an underestimation of where you need to draw the line in sacrificing yourself for others.  On the other hand, the reverse is true – if you have to choose between your brothers and strangers, or between co-ethnics and non-ethnics, taking genetic structure into account means that helping your brothers and your co-ethnics is even more important than before, because in comparison to more genetically alien peoples, genetic structure amplifies how much more close you are to your brothers and your co-ethnics.  It’s a double-edged sword: it makes your own preservation a bit more important, but it also makes the preservation of those more similar to you more important than those more distant.

Now, one can argue that after several generations of recombination and independent assortment – even assuming endogamous mating within the ethny – genetic structures derived from your posterity and those of your brothers will be more or less the same, converging on the common pool of ethny-specific genetic structures.  So, while in the first generation, your offspring and that of your brothers may be distinct with respect to genetic structure, that difference would be attenuated over time and, as long as endogamous mating is maintained, your posterity and theirs would reflect similar genetic structures.  But there are problems here.  First, a rigorous analysis is required; perhaps some differences would continue over at least several generations; even if these differences are small, they nevertheless would need to be accounted for.  Second, if it is true that familial genetic strictures would tend, over time, to converge on more generalized ethny-specific structures, then why bother favoring two brothers over two random co-ethnics?  The brothers would share more of your genes, yes, and be more similar as far as genetic structure, but if one invokes “long term intergenerational effects” with respect to questioning the need to account for structure in modifying Haldane’s argument, then one can use the same “intergenerational effect” to directly question Haldane’s original premise.  The answer I believe is that one must do the best they can at a given time in maximizing their genetic payoff, and hope that subsequent generations do the same. In the absence of the required analysis, one can simply argue that looking to the next generation, differences in genetic structure are important and, hence, two brothers are not quite the genetic equivalence of yourself.  Your structure is different from theirs and the genetic payoff of your reproduction is greater for your than both of theirs combined.  So, maybe you need to hold out and sacrifice for three (or more) brothers instead, including for the other reason outlined above. Note that these fine points deal with very close genetic similarity.  When we are talking about racially alien peoples, the genetic distance becomes even more amplified with genetic structure, and in the absence of panmixia, ethny-specific patterns of genetic structure are broadly stable over evolutionary time (we can see that the Iceman is genetically more similar to Europeans than to, say, Asians  of Africans, as one example).

In the absence of the sort of careful quantitative analysis that population geneticists won’t do, from a qualitative standpoint, it would be prudent to require more of a genetic payoff before engaging in Haldane-style altruistic self-sacrifice.  On the other hand, when considering a choice in investing between two genetic entities, picking the group genetically closer to you is even more important when considering genetic structure.  So, when the choice is between self vs. family or family vs. ethny, genetic structure will require a larger genetic payoff before agreeing to sacrifice the interests of the former for the latter. However, when considering a relative choice between ethny one vs. ethny two, genetic structure means that choosing the more similar-to-you ethny is even more important than with “bean-bag” genetics.  

The overall Salterian imperative remains the same as before, once these adjustments are made.

Yet Even More DifferInt

More DifferInt model results.

Note that genepool is exactly the same between both populations, but rearranging genotype combinations gives some differentiation at single and multiple locus measurements even when including elementary genic differences, and there is complete differentiation at the level of multiple locus genotypes neglecting elementary genic differences, even though the genepools are identical and there is not a very large number of genotype rearrangements between the populations. This shows how rapidly complete differentiation is achieved when considering discrete genotype combinations.

(A = 1, T = 2, C = 3, G = 4, first number = number of individuals per genotype)

 #Population1

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  4 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  4 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 1  3 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  3 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

#Population2

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  3 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  3 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1 2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  4 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  4 4

Genepool: 0.0000

Single locus including elementary genic differences: 0.0167

Single locus neglecting elementary genic differences: 0.0333

Multiple locus including elementary genic differences: 0.0410

Multiple locus neglecting genic differences: 1.0000

Yet More DifferInt

More on genetic integration.

Some interesting quotes from this paper; emphasis added:

The elementary genic difference does not distinguish homologous from non-homologous genes. Hence, the homologous and non-homologous gene arrangements within the objects affect the elementary genic differences between them only through their sum. For example, in the case of diploid individuals scored at two gene loci A and B, say, the genotypes A1A1/B1B2 and A1A2/B1B3 represent three (A1, B1, B2) and four (A1, A2, B1, B3), respectively, of the total of five gene-types. A1 is represented by two copies in the first genotype and by one copy in the second, and the remaining four gene-types are represented by at most one copy in each of the two genotypes. The sum of copy number differences between the two genotypes thus equals four. After division by twice the number of individual genes in a genotype (i.e. 2·4), this yields 0.5

as the elementary genic difference. The same result is obtained for the two genotypes A1A2/B1B2 and A1A2/B3B3, even though all genic differences are now due to the alleles at a single locus (B).

Proceeding from lower to higher levels of integration, one expects an increase in differentiation among populations simply because of the larger varietal potential inherent in more complex structures. Since differentiation is based on distances, the distance between two populations should therefore also increase, or at least not decrease, with integration level.

…it appears that differentiation among populations with respect to their forms of gene association may be a normal occurrence. This insight questions the common practice of restricting the measurement of population differentiation to the allelic level (e.g. FST), thereby ignoring the considerable effects of gene association on population differentiation.

One major finding of the paper is that model data routinely give no increase in differentiation (measured including elementary genic differences) with increasing genetic integration, but real data does show increases.  One wonders if large scale human SNP data would demonstrate such differences, as opposed to the limited SNP data or model systems I have used, which demonstrate increased differentiation only when elementary genic differences are neglected.  On the other hand, as I’ve previously written, neglecting elementary genic differences is, I believe, more compatible with my idea of genetic structure.

That said, one can, if they choose allele structure carefully, produce models that do the exact opposite, have equality at the lower levels of genetic integration, but differentiation at the highest level.

Here is an interesting population model I devised and tested with DifferInt; the differences between the two populations are highlighted.  Note that total numbers of each allele are the same, and the total numbers of single locus genotypes are the same as well.  Thus, genepool differentiation is zero (0.000), as is single locus genotype differentiation, also zero (0.000).  The arrangement of the first and ninth single locus genotypes, together, were changed in six of ten individuals between the two populations, thus producing differentiation specifically at the level of multilocus genotypes. 

(A = 1, T = 2, C= 3, G = 4; first number = number of individuals) 

MLG with EGD: 0.0246

MLG w/o EGD: 0.6000 (6/10 individuals per population altered)

#Population1

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

 1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

#Population2

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  3 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 2  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1 2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4

1  1 1  2 2  2 3  3 3  1 1  1 4 1 1  2 2  2 3  3 3  1 1  1 4