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Guide to Patagonia's Monsters & Mysterious beings

I have written a book on this intriguing subject which has just been published.
In this blog I will post excerpts and other interesting texts on this fascinating subject.

Austin Whittall


Thursday, September 29, 2016

Heterozygosity for dummies


Heterozygosity is lower in all non-Africans when compared to Africans.


What does this mean?


First of all what is Hetrerozygosity?


Heterozygosity

We all have two copies of each gene. That is because we got half of our chromosomes (with their respective genes) from each of our parents), making one copy from each of them.


Genes come in different variants, known as alleles.


So if there are two possible alleles: "b" and "B" (one per gene) you may have any of the following combinations arising from the mixing of your parent's genes

  • bb
  • bB
  • Bb
  • BB

That is four options, two in which each gene has the same allele (bb, BB) and therefore you are Homozygous and two in which you have different alleles (bB, Bb) which makes you Heterozygous.


It is evident that homozygosity implies less genetic variability (being BB you lack the "b" allele or if you are bb, you will lack the "B" allele). And this may have consequences regarding your health and surviveability.


Populations.

We must also take into account that the proportion of "b" and "B" in can be different, in other words they are present at different frequencies: "p" and "q" respectively which are not necessarily the same.


In other words the frequency of each genotype (bb, Bb, or BB) in a given population (known as "allele frequency") will depend on the frequencies of each allele:


In a very large (infinte) population where individuals mate at random, we can calculate the allele frequency using the Hardy-Weinberg Theorem using this formula to calculate the frequencies (f) of each of the three genotypes (bb, BB, Bb):

  • f(bb) = p2
  • f(bB) = 2pq
  • f(BB) = q2

And since they are "all" the genotypes, their sum must add up to 100% of the populaton:


100% = p2 + 2(pq) +q2


Say b is present at p = 30% and B has a frequency of q= 70% (both frequencies must aldo add up to 100%), then:


100% = (30%)2 + 2(30% x 70%) + 70%2


100% = 9% + 42% + 49%


So the frequency of bb alleles is only 9% meaning that 9% of the population is homozygous for b. 42% is heterozygous and 49% is homozygous for B.


But in a real world, humans don't mate randomly: they choose partners for different reasons, or, due to cultural rules may marry within their group (endogamy).


Also some homozygous alleles may cause genetic diseases such as cystic fibrosis, Tay-Sachs or phenylketonuria which may kill individuals before they become adults and reproduce, here selection is actively working to modify zygosity.


As populations are not infinte but finite, there is not an endless genetic pool, but a discrete one so in smaller or isolated populations, heterozygosity will fall due to random events (imagine adults that have no offspring, eliminating their alleles from the genetic pool).


The opposite effect is when two isolated populations admix, adding new alleles to the gene pool, increasing heterozygosity.


So, the factors that provoke homozygosity are:

  • Inbreeding
  • Geographic isolation
  • Genetic Drift
  • Cultural practices -i.e. consanguineous marriage or endogamy
  • Positive evolutionary selection

It can fall, on the other hand if there is an isolation-breaking event such as the mixing of two previously isolated populations.


Let's take a look at each of these factors:


1. Interbreeding

The taboos that forbid marrying your next of kin have a genetic basis: those closely related to you will carry many genes identical to yours. Since relatives share alleles, inbreeding will bring together identical copies of an allele more frequently than breeding between unrelated mates, and this increases homozygosity:


"F", the Inbreeding coefficient is the probability that two alleles are identical copies of an allele from a common ancestor. It is also, the proportion of the population that is inbred (having two alleles identical by descent).

We can take the expression used above and adapt it to calculate the frequencies of alleles in an inbred population:


  • f(bb) = p2+2Fpq
  • f(bB) = 2pq (1-F)
  • f(BB) = q2+Fpq

All must add up to 100% of the population.


So if inbreeding coefficient is 20%, the relative frequencies of bb, BB and Bb would be (we will use the same frequencies as in the original example: b is present at p = 30% and B has a frequency of q= 70%):


100% = (30%)2 +2 x 20% x 30% x 70% + 2(30% x 70%)(1-20%) + 70%2 +2 x 20% x 30% x 70%


100% = 13,2% + 33,6% + 53,3%


So the comparison is:


  • bb increases from 9% to 13.2% of the population
  • BB increases from 49% to 53.3% of the population
  • Bb falls from 42% to 33.6% of the individuals

Heterozygosity drops due to inbreeding even though the same alleles are present.


Since some genetic traits are recessive, and manifest themselves only when the two alleles are present, that is, homozygosity for those alleles is present, inbreeding increases the frequency of these recessive traits, which could be as benign as blue vs. dark eyes or nasty as congenital diseases.


Genetic drift

Imagine a population which starts off with p = q = 50%. In other words, the proportion of B and b is identical. Applying Hardy-Weinberg Theorem we can calculate the genotype frequencies:


100% = (50%)2 + 2(50% x 50%) + 50%2


100% = 25% + 50% + 25%


So50% are heterozygous (Bb) while the other half is equally homozygous: 25% are BB and 25% are bb.


But this is in an infinte population and also, the frequencies p and q are probabilities.


Real life may reflect these probabilities in a different way. Look at it this way: when you flip a fair coin there is an equal chance (p=50%) of getting heads and or tails (q=50%). But in practice we all know that you could throw 3 heads in a row and get only 2 tails in a series of five tosses. Which is not a 50 ⁄ 50 proportion. it is 66% ⁄ 40%. You may even get 3 heads in a row in a series of 3 tosses (100 ⁄ 0).


So in small series it is unlikely that the actual real frequency is close to the theoretical probability (p or q).


However, when you use larger series, for instance if you tossed the coin 1,000 times, the ratio would be closer to 50 ⁄ 50 (say 494 tails and 506 heads).


This same effect applies to the probability frequencies in small populations: two heterozygous parents (bB) could have all four offspring that are homozygous (bb) just by chance.


So, in small populations this phenomenon known as "Genetic drift" just by random forces -not by natural selection or deliberate interbreeding- can change the frequency of some alleles in very short time, making them extremely common ("Fixing them") or making them disappear.


Founder Effect

Founder events take place when a small sub-population of a larger one migrates and establishes a new settlement (hence "founder" population). It is obvious that not all the alleles present in the original population will be present in this smaller group. Those left behind will not appear in the new one, this reduces the total quantity or "allele richness" of the new subpopulation.

Liken it to randomly taking 4 M&M's from a bag holding 500 candies, it is probable that you will not pick all the available colors. So if the M&Ms in the bag are red, yellow, green, blue and brown in equal proportions, you could very well have picked: 2 yellow, 1 green, 1 red and no brown or blue candies. So this does in effect reduce the "diversity" or "richness" in the subpopulation but, it may not impact on heterozygosity:


Imagine the population we mentioned befor where 9% were homozygous for b (bb), 42% were heterozygous (Bb) and 49% were homozygous for B (BB). Now lets imagine that a small group from this original one forms a colony elsewhere, and just by chance, 60% of the individuals carry the Bb heterozygosity, while the remaining 40% are BB homozygous.


This new subpopulation will therefore have a higher heterozygosity than the original population (60% vs. 49%), but it will surely be less rich or diverse due to the alleles left behind (M&M analogy).


Founder effect impacts on the "allelic richness" by reducing it but it may no have much effect on hetrerozygosity. This is because the richness is based on the presence of the alleles and not on the internal diversity within them. A rare allele lost during a founder effect reduces the diversity but will probably have little impact on heterozygosity.


Bottleneck

This is a drastic reduction in a population. It could be caused by disease or a natural catastrophe (drought, volcanic eruption, fire, Ice Age, global warming).


Those that survive will carry only part of the genetic diversity of the original population, as those lineages that perished, are gone forever. But this does not mean that heterozygosity drops. Actually, allelic richness falls faster than heterozygosity because bottlenecks usually wipe out ,any low-frequency alleles and this causes an excess of heterozygosity in selectively neutral loci compared to normal populations subjected to genetic drift.


Leberg (1992) investigated loss of heterozygosity and allelic variation experimenting with mosquitofish and found that a decrease in heterozygosity only happens when the bottleneck is extreme and prolonged.


Selection

After the population reduction in founder effects or Bottlenecks & Geographic Isolation (which may also lead to inbreeding due to the smaller population), diversity will increase again due to chance mutations.


Another factor that may modify the genetic patterns is Natural Selection: the bottleneck may have caused the fittest to survive -imagine a disease that those equipped with some genetic advantage manage to survive while the others perish- and therefore selection increases the frequency of certain genes in the new population, when compared to the pre-bottleneck one.


Geographic Isolation

Similar to Bottlenecks, it is the separation of one group from the main population, as when there is a founder event.


Heterozygosity and Human Evolution

So when defenders of the "Out of Africa" theory use heterozygosity to support an African origin for Mankind, they point out that Africans have the highest heterozygosity of all human populations: the others (non-Africans) have lost it as they migrated out of Africa in small bands (founder effect), separated widely (geographic isolation), were more prone to fall prey to natural catastrophe (bottle necks), inbred more frequently as they were smaller populations and in doing so lost heterozygosity which the original basal population in Africa retained.


An example of this is shown in the image below which charts "heterozygosity vs. distance from Africa (Addis Ababa)" (from [1]):



This chart from [5] show more or less the same information:



Allelic Diversity

Having said this, we must point out that "Genetic Diversity" is not only measured by heterozygosity but also by the "number of alleles" present in a given population, that is "allele richness" or "allelic diversity" which is calculated as the average number of alleles per locus.


In other words a population may have a high heterozygosity compared to another and supposedly be "more diverse" but, overall have a lower number of alleles which makes it definitively "less diverse".


An example of this paradox is shown in this paper (Begoña Martínez-Cruz et al., In the heartland of Eurasia: the multilocus genetic landscape of Central Asian populations [1]) which has interesting data in its Table 2 which shows the "Average AR" - allelic richness- and "expected heterozygosity He" for each of the 26 Central Asian populations and other nearby regions:


AR He   Population
12.66 0.819 Central/South Asia
 8.60 0.820 Central Asia - TJK
 8.50 0.812 Central Asia - TJT
 8.50 0.774 Central Asia - UZB


The first two have the same He (heterozygosity) of around 0.82 but notably different allelic diversity (12.66 vs 8.60). The last two have the same allelic diversity (8.5) but different He (0.812 vs. 0.774).


Populations can have a richer genome despite having a lower heterozygosity, of course they could have mutated faster than another population and therefore increased the diversity in their genome adding new variants.


Does this mean higher heterozygosity in Africa mean that it is the cradle of humanity?


It means that heterozygosity is higher there. Just look at the archaic hominins, Neanderthals and Denisovans. Their heterozygosity is far lower than that of any extant human group, but we know that they predate Homo sapiens by several hundreds of thousands of years. They are less heterozygous but older and ancestral:


Prüfer et al. paper on Neanderthals [3] confirms this (highlighted in bold):


"The Neanderthal autosomal genome carries 1.7–1.8 heterozygous sites per 10,000?bp (Supplementary Information section 9). This is 84% of the number of heterozygous sites in the Denisovan genome, 22–30% of that in present-day non-African genomes, and 16–18% of that in present-day African genomes (Extended Data Fig. 1). When regions of homozygosity longer than 2.5?cM stemming from recent as well as long-term inbreeding in the Neanderthal are removed, 2.1–2.2 sites per 10,000 are heterozygous, similar to what is observed in the Denisovan genome. Thus, heterozygosity in Neanderthals as well as Denisovans appears to have been lower than in present-day humans and is among the lowest measured for any organism" [3]


Another paper by Meyer et al. on Denisovans [4] found the same diminshed heterozygosity:

"Denisovan genetic diversity. The high quality of the Denisovan genome allowed us to measure its heterozygosity, i.e., the fraction of nucleotide sites that are different between a person's maternal and paternal genomes (Fig. 5A). Several methods indicate that the Denisovan heterozygosity is about 0.022%. This is ~20% of the heterozygosity seen in the Africans, ~26 to 33% of that in the Eurasians, and 36% of that in the Karitiana, a South American population with extremely low heterozygosity. Because we find no evidence for unusually long stretches of homozygosity in the Denisovan genome, this is not due to inbreeding among the immediate ancestors of the Denisovan individual. We thus conclude that the genetic diversity of the population to which the Denisovan individual belonged was very low compared with that of present-day humans." [4]


This leads me to ask, what if African heterozygosity was enriched by recent admixture with other hominins in Africa? an inflow of different relic alleles elevated African diversity above that of non-Africans. Could current lower Amerindian heterozygosity reflect an ancient population just like that of Denisovans or Neanderthals?


We will look into these questions in my next post when we go over some recent papers on the possibility of an ancient Out of Africa event whose genes ended up in contemporary Papuans and Australians.


Sources


[1] Begoña Martínez-Cruz, Renaud Vitalis, Laure Ségurel, Frédéric Austerlitz, Myriam Georges, Sylvain Théry, Lluis Quintana-Murci, Tatyana Hegay, Almaz Aldashev, Firuza Nasyrova and Evelyne Heyer, In the heartland of Eurasia: the multilocus genetic landscape of Central Asian populations, European Journal of Human Genetics (2011) 19, 216–223; doi:10.1038/ejhg.2010.153; published online 8 September 2010.
[2] Paul Verdu, Trevor J. Pemberton, Romain Laurent, Brian M. Kemp, Angelica Gonzalez-Oliver, Clara Gorodezky, Cris E. Hughes, Milena R. Shattuck, Barbara Petzelt, Joycelynn Mitchell, Harold Harry, Theresa William, Rosita Worl, Ripan S. Malhi Patterns of Admixture and Population Structure in Native Populations of Northwest North America, PLOS Published: August 14, 2014 http://dx.doi.org/10.1371/journal.pgen.1004530
[3] Kay Prüfer, Fernando Racimo, Nick Patterson, Flora Jay, Sriram Sankararaman, Susanna Sawyer, Anja Heinze, Gabriel Renaud, Peter H. Sudmant, Cesare de Filippo, Heng Li, Swapan Mallick, Michael Dannemann, Qiaomei Fu, Martin Kircher, Martin Kuhlwilm, Michael Lachmann, Matthias Meyer, Matthias Ongyerth, Michael Siebauer, Christoph Theunert, Arti Tandon, Priya Moorjani, Joseph Pickrell, James C. Mullikin et al., The complete genome sequence of a Neanderthal from the Altai Mountains, Nature 505, 43–49 (02 January 2014) doi:10.1038/nature12886
[4] Matthias Meyer et al. A High-Coverage Genome Sequence from an Archaic Denisovan Individual, www.sciencemag.org SCIENCE VOL 338 12 Oct 2012
[5] Keith Hunley, Claire Bowern, Meghan Healy, Rejection of a serial founder effects model of genetic and linguistic coevolution, Published 1 February 2012.DOI: 10.1098/rspb.2011.2296


Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia Copyright 2009-2014 by Austin Whittall © 

4 comments:

  1. Hello Austin
    In this essay you explain, among many other things, that the genetic diversity is a function of 2 factors, heterozigosity and number of alleles,…and that a rich one has a positive role in the surviveability of a specie.
    Your approach to the subject is, as usual, very lucid and particularly clarifier…but my knowledge in the matter is limited, so mine are not comments… just questions to try to better understand.
    Given the fact that Neanderthal populations had the lowest heterozigosity, ¿How can be explained that they managed to survive along 150/200 Kya or so, in Eurasia, sometimes in very adverse environments?...
    Could the other factor involved, the allele richness (if known), have been, in contrast, somewhat high, in order to maintain a reasonably rich genetic diversity?....
    My modest and schematic reasoning is the following, ¿Didn´t they need this last, to became into the dominant specie, during most of this period?...
    If not, ¿Up to what degree can we correlate genetic diversity with, what seems to me, an apparently “successful “ population?
    Sorry for too many questions… I may be wrong in more than one concept… but I know of no other site than can put light into this subject.
    Thank in advance for your reply
    Best regards
    Marcelo

    ReplyDelete
  2. Thanks Marcelo for your comment.
    Don't think that my knowledge on this matter is greater than yours, I am a total rookie in this!.
    I too have wondered how did they survive considering that they were so "inbred" (http://phys.org/news/2016-06-inbred-neanderthals-left-humans-genetic.html), so I will look into this, because it seems there is an incongruence here..

    ReplyDelete
  3. I appreciate your honest reply. Indeed, what you are divulging is very relevant, not easy to gather from other sources/papers and is well documented,…and necessarily implies a certain amount of knowledge in the matter. Some subjects are within the very limits of which is known,… certainly, it is impossible to advance in their study without making speculations...which may lead (via further research and development) to interesting, and up to now, unthinkable implications. So… go on with them.
    Thanks for your attention
    Marcelo

    ReplyDelete
  4. "This leads me to ask, what if African heterozygosity was enriched by recent admixture with other hominins in Africa? an inflow of different relic alleles elevated African diversity above that of non-Africans. Could current lower Amerindian heterozygosity reflect an ancient population just like that of Denisovans or Neanderthals?"

    Agree on everything. I've made exactly the same points in several posts on http://anthropogenesis.kinshipstudies.org/. Notably, while we see ancient, divergent and African-specific uniparental markers (Y-DNA A00 and A, mtDNA L0, L1, L2, L4, L5) in African-Americans (a well-attested slave migration from West Africa in recent times), we don't see them anywhere along the putative out-of-Africa route(s) presumably used by humans 50,000 years ago. They are not found in the Sahul, West Eurasia or East Asia. Provided the phylogenies are correct, they must have introgressed in into modern Africans from archaic hominins in Africa.

    ReplyDelete

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