Archive for ‘Mathematics’

November 24, 2014

Consanguinity & DNA Probabilities — #Genealogy #DNA #Kinship

by C. Michael Eliasz-Solomon

Stanczyk last wrote a similarly named article, “Genealogy Consanguinity & DNA“, on 25-August-2014. But in the last week, I read two blogs that made me rethink some of the comments that we received to the blog on the probabilities of autosomal DNA (the non Y-DNA and non mt-DNA). I also read a blog once by William Dollarhide that a Family Tree should represent the DNA, the Consanguinity (how much blood shared). Although I respect the tremendous body of work and prolonged expertise of Mr. Dollarhide, my immediate reaction  was, “No, it does NOT”!

So today’s blog is a mash-up of my August 25th blog, two recent blogs I read, and William Dollarhide’s blog article on the Family Tree represents the DNA.

First off, let me state my bias up front, that I believe the Family Tree represents Legally Defined Familial Relationships as held out by the Family Tree’s owner and that copies or derivative versions or edited/annotated versions are NOT valid! There has been a long history from at least the earliest dynasties of the Pharaohs and probably even older than that the “king”, let me gender-neutral the term, the monarch decides who is family and who is erased from family histories and who inherits and who does not inherit. So we see a very early reason why family trees ARE legal based. If the wife of the monarchical family could not produce a LEGAL heir to inherit or continue the dynasty, one was often adopted or perhaps produced with a surrogate spouse. So we also have a new counter argument enter on very early in the history of families … adoptions. The adopted child may or may not possess some consanguineous blood (DNA). It was not unusual for children of siblings to be adopted if they were orphaned. Or perhaps we can view more upheaval from recent times producing ad-hoc adoptions of non-kin. We need not just accept the modern day gay-couples who adopt or couples with fertility issues who perhaps adopt an overseas child , who may or may not share any consanguinity with either parent, but are none-the-less, legal family members of a family and as such should be in the family tree. We can easily recall just the upheaval of World War II where children from Jewish families were often times ad-hoc adopted in order to save the child’s life and perhaps raised to adulthood without the knowledge of their true DNA (until later). There have been many such stories.

DNA was a late 20th century discovery, so before its discovery, there was simply no way of knowing for sure that a baby arriving from its mother’s womb, was the sire of any man in particular. Here, again we find examples of mistakenly assumed child of both parents, has the DNA of the mother, but none of the father. Yet in most cases, the family tree shows the child with the couple who raised the child and were held out to be its parents (legally).

We have also seen people use a last name to pretend or to get others to think they are from a family. I am thinking now of a man who used the Rockerfeller name when he had no consanguinity with the famous family. There have also been people who claim to have been a long-lost member of the executed Romanov family. But these people are not legally related to the more famous families by their covert or overt claims of familial ties. They are not to be represented in any LEGALLY sanctioned family tree of their creation, nor anyone else’s with those famous families. These faux family members could be EXCLUDED on the basis of DNA in all probability.

We come back to the PROBABILITY portion of this article. DNA and what are the probabilities of consanguineous relatives in the autosomal DNA (not in the direct paternal or maternal lines which can be mathematically determined with reasonable accuracy). When I wrote the blog article from August 25th, people began to immediately take issue with the data visualization that I had sourced on the autosomal boxes. For example, should siblings be 50% consanguineous? In most probabilities, yes. Now let me limit probabilities where by the mother and father are both known for certain — otherwise the mathematics goes out the window.

So siblings share 50% correct? What about identical twins? Who may or may not be 100% identical in DNA. What about fraternal twins or any of the other myriad multiples that can be conceived of? Oh, their DNA probabilities are likely much higher than siblings born from separate births, maybe approaching 100% shared DNA. So now the probabilities of consanguinity are skewed for future generations depending on which child you are in direct lineage from.

Autosomal ProbabilitiesWhat is the accepted standard for probabilities? I recently read a blog by Iowa DNA Project. She included a chart from The International Society of Genetic Genealogists. I have included that chart in this article.

The chart answers most of the questions from people on my first blog that I was not able to answer definitively. Notice one caveat to those probabilities !  These are what we can EXPECT as the probabilities for shared consanguinity.

Why are they not guaranteed? Well the first answer occurred to me because of my knowledge of genetic algorithms (and high school science). The first answer is Mutations. Sometimes when the genes copied from one parent or the other, an inexact copy results in the DNA sequence. There are also a few other things that can go wrong in the sequence.

That is perhaps a nice segue to the second blog I read recently, “Why Your DNA Might NOT Match Your Parents“. This article is actually from July 3rd of this year, but which I read last week. What happens when the mother has a rare condition called Chimerism? A short explanation is the mother has two fertilized eggs in her womb, but then one twin fuses to the other and only a single baby develops and is born. In this case, the baby does NOT share DNA with the mother who is in fact the biological mother but technically shares zero consanguinity with the baby. Now Chimerism is rare but since it has happened recently, it is likely it has happened in the past (albeit rarely) of humankind. Well that really screws up the DNA. Now if you were a direct line descendant from a Chimera baby, your DNA does not match the DNA of the rest of the  family. Let that sink in.

Now without even discussing surrogate mothers or other elaborate fertility techniques or even parthenogenesis, I believe I have completely destroyed the William Dollarhide notion of a family tree being a representation of DNA (or consanguinity). I did not even touch upon infidelity, “kings-privilege”, rape/incest/forced insemination or other known or unknown “ad-hoc adoptions” that occur in family trees with/without knowledge of the family members [since DNA and its use is recent and not widely used]. Nor did we discuss legal  dis-owning or disinheritance until this sentence. Those too would impact a family tree.

Perhaps all Family Trees really are Legally Defined Familial Relationships as held out by the family tree owner! Whether we agree or not or whether we know/believe it or not, the long process of DNA replication and historical/legal edicts have irretrievably altered all of our family trees.

The author wishes to include a post-scriptum on his own Legally Defined Familial Relationships (aka my Family Tree). As for my dear wife, Teréza & I, we felt the need to utilize extreme fertility techniques  in our personal life to produce our own biological children. We have also used legal disownments, disinheritance, name changes and an annulment to separate ourselves from others who have sought to make fraudulent claims of familial status … asserted fraudulent relationships in their own utterances:   for purposes of past, present and/or future schemes to possibly gain money from me, my wife, Teréza  or any future estate and/or cause us harm and other damages!

February 16, 2013

Presidents Day — #2013

by C. Michael Eliasz-Solomon

AllUSPresidents

It is President’s Day on Monday. That got me to thinking about Washington and Lincoln. Stanczyk, has had an awful lot of mathematical training – the product of a degree from a School of Engineering. It is funny, the teachings that stick with you your whole life. One of the things that I learned that stuck with me was a little factoid from a Probability & Statistics course. I was taught that in a gathering of just of 19 people that the probability that two of them having the same day of birth (not the same year though) would be 50-50. That in any gathering of 19 people it would be a 50% chance of two people celebrating their birthday on the same day each year!

This being President’s Day weekend, I noted that we have had  44Presidents (only 43 different, since Grover Cleveland was the 22nd and the 24th President). So I asked myself did any two Presidents have the same day of  birth? Now if we ignore the Grover Cleveland issue, and we examine the dates of birth of all US Presidents, we do indeed find that two Presidents had the same day of birth. The day in calendar is November 2nd. The two Presidents who share that day are: Warren G. Harding and James K Polk.

Now you might expect that since we have > 38 Presidents, that there should be two pairs of matches. But the odds are only 50-50. So we have just one matching pair of Presidents. There were a lot of near misses (off by one day). If your birth month is not September or June (each of which only had one President) then the odds are pretty good that you, my dear reader, share a birth day with one of the Presidents. I’d say better than 50-50. So click on the link and see for yourself.

Happy President’s Day!

August 23, 2012

Rapes of Wrath – Tea Party War On Science — #Opinion, #Politics, #Science

by C. Michael Eliasz-Solomon

Stanczyk is a STEM worker. What is STEM? STEM = Science Technology Engineering Mathematics (S.T.E.M.). OK, STEM is an acronym for an area of focus in business and also in education. We need STEM to have a viable growing economy that produces jobs again.

Do not misunderstand me, we also need business people (especially entrepreneurial types), writers of all stripes, lawyers, teachers, etc. The USA (and indeed every country in the world) is not a country of PRODUCERS and NON-PRODUCERS! It is not. We need every worker and we need everyone to be a specialist in something and to do that something to the best of his/her ability because we are all interconnected. A rising tide, raises all boats, not just the yachts. STEM will raise the tide.

So why do Congressmen like Todd Akin [“Legitimate Rape” and “Forcible Rape” dude] (and PAUL RYAN [“Forcible Rape” co-sponsor dude], Steve King (Iowa) [“No Rape If I Didn’t See  It Happen and I have NEVER seen Rape By Incest or Statutory Rape” dude] try to redefine rape? Does anyone not understand the definition of rape? This is NOT an English class exercise — we do not need to rewrite English or Law. They also pretend that Doctors [presumably the medical kind] say there is a “magical” hormone that shuts down rape pregnancy — ignoring 10,000 years of history [Young Earth time frame – or a few million year history for STEM workers].

Now these same kind of People deny the following science:  Biology (“Legitimate Rape”/”Forcible Rape” and magic hormones), Evolution, Climate Change/Global Warming, Economics [defying paying US Bills by a steadfast refusal to raise the debt ceiling which was routine until 2011 Tea Party Caucus], Environmental Science, Geology (except that related to Oil/Gas drilling),   Cutting NASA, Cutting NIH/CDC, etc.

It does NOT stop at STEM subjects. The Tea Party kooks try to rewrite history (“The founders were against slavery” ??? or the Barton faux-history book that said,  “Thomas Jefferson freed his slaves” — this is egregious to Polish Americans as well as African Americans, because it diminishes Taduesz Kosciuszko’s historical will where he left money to buy the freedom of Jefferson’s slaves — something that Jefferson did NOT honor. They have tried to rewrite Christian Holy Tradition by saying that Jesus was a Capitalist (an Ayn Rand Selfish Capitalist at that) and that he did not try to help the poor [ignoring the overturning of temple tables story, sermon on the mount, or camel/eye of the needle parable, prodigal son, etc.]. Most religious people would be deeply offended by them rewriting the Bible and calling it “The Conservative Bible”. [did they not finish the Bible? Read the last chapter of the last book, Revelations for why this is sacrilegious]  This intense rewriting of facts from science, to history, to religion is now flowing into US law, as they try to write laws based upon these “faulty/fake notions”.

There are other consequences too. Did you see BP Oil try to discredit scientists about the rate of oil flow from the blown up Gulf well? This is a consequence of the “anti science” attitude in congress. Blame the worker, the STEM worker, not the corporation-who-is-a-person-and-yet not-an-ethical-person-or-who-cannot-be-imprisoned-person. Science jobs, outside of government or academia are scarce.

If we do not create STEM jobs the economy will continue to falter. Worse yet, if we do not have science researchers/workers then the next pandemic will have far more than economic consequences — real lives will be lost. We are overdue on a pandemic (nearing 100 years since the last pandemic) and we are ensconced in a Great Recession. Perhaps we need more Paul Krugman (New Keynesian) economists or we need to start actually listening to them and creating laws to create jobs, not new definitions of Rape! Isn’t that what the present Congress was elected to do? Then why did they spend time on 40 Rape bills or how many Voter-Id bills the last two years? Wake up America and throw out the Tea Party Caucus who just want to make up their own set of facts nonsense rather than to actually work using REAL knowledge to solve REAL problems.

STEM workers are you listening (or reading) — I am calling you out? This November VOTE and fire Tea Party caucus people. They are easy to find:

  1. They are REDEFINING RAPE
  2. They are PLEDGED to an unelected NH man (Grover Norquist)
  3. They are pushing to EXCLUDE REGISTERED VOTERS — an American Right (not a privilege)

Anyone who made the pledge to NH  or sponsored laws for “Forcible Rape” or passed laws in 2/3 of the US States to exclude REGISTERED voters need to be voted out. Just Fire Them — Mitt Enjoys Firing People, maybe you should turn the tables on Mitt and Paul Ryan and Todd Akin and Steve King and just fire them.

P.S. My apologies for the temperament of my title’s literary allusion to John Steinbeck’s great novel, The Grapes of Wrath. His title came from the song/lyrics …

Mine eyes have seen the glory of the coming of the Lord;
He is trampling out the vintage where the Grapes of
Wrath are stored;

Battle Hymn of the Republic, Julia Ward Howe 1861

May 4, 2012

BIG Genealogy — #Genealogy, #FamilyTree, #GEDCOM

by C. Michael Eliasz-Solomon

When Stanczyk, wrote the title, he was not referring to Ancestry.com or any other endeavor by genealogical companies from the western USA. No, Stanczyk is fascinated with numbers .. of people.

Yesterday, this jester wrote about the Confuscius Family Tree. It is commonly accepted to be the largest genealogy (family tree). But I had to wonder … Why?

It is an old genealogy, dating back to Confucius’ birth in 551 BCE. It is now 2012, so we have a genealogy that is 2,563 years old. My much beloved wife/kids are Jewish. In the Hebrew calendar we are presently in the year 5772. Despite my having been to a Jewish Genealogical Conference and meeting a man who told me his genealogy went back to King David. [This jester resisted the rude/snarky comment that if he researched using both Old & New Testaments he could push his research back to Adam.]

I also did not ask him to show me his documentation, but assuming he could, his genealogy would have been another 500 years earlier (~ 1050BCE) and therefore this tree mathematically speaking (assuming there are other Judeo-Christian couplings before I & my wife) his tree had the potential if you could/would follow all/many branches and not just the direct lineal trunk you have a tree with approximately 100 generations (adding another 17 generations to the 83 for Confucius). This assumes a generation is 30 years. Now if we look at Confucius and see 2560 years = 83 generations, we see an average of 30.84 years per generation — so 30 years per generation is not a bad estimate.

What genealogy could be older still? Well according to the Bible we record the Jewish peoples in Babylonia. So perhaps we can extend King David and/or one of his citizens back to King Hammurabi of Babylonia — that would yield another 650 years (~1700BCE) or about another 22 generations. Let me see if Confucius’ family tree is about 2 Million for 83 generations we get about 24,096 people per generation. So by adding 39 more generations then Hammurabi’s Family Tree should contain approximately another 940,000 people. So come on Iraq produce your family tree of nearly 3 Million people!

What genealogy could be older than that? There is a quote that goes something like, “History knows no time when the Egyptians were not highly developed both physically and intellectually.” True enough, recorded history does go back furthest in the Pharaohnic dynasties. That takes genealogy back to the first dynasty King (Pharoah) Menes, who sure enough had a son who wrote about Astronomy [source: Timechart History Of The World, ISBN 0-7607-6534-0 ]. That takes us to approximately, 3,000 BCE, another 1300 years/44 generations/1.06Million people! Ok, since there is no recorded history earlier than that, we will not have a properly sourced genealogy older than this. So people who are Elizabeth Shown Mills devotees turn your heads away …

What genealogy could possibly be older than that? I read that the indigenous peoples of Australia have an oral history of 48,000 generations! The aboriginal people of Australia date back to about 50,000 BCE, which would be 52,000 years ago/1734 generations/41.8Million people in their family tree. That’s not 48,000 generations, but that is more than twice as much as genealogy researchers test using their FAN24.ged file which has 24 completely full generations with 16.8Million pseudo people.

Now that is what I call BIG Genealogy. But where is that family tree (not FAN24.ged)? Why has no genealogy older than Confucius’ genealogy been found and carried forward to the present day? Is it possible that such a family tree exists?

–Email me!

Related Blog Articles …

Random Musings” (10-March-2010, see musing #2)

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