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Why I am a Fibonacci Fan

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  • Why I am a Fibonacci Fan

    Note that the number of ancestors who could contribute segments to an individual’s X chromosome within each generation follows the Fibonacci sequence but starts after 0 and depends on the sex of the individual.

    The Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34 etc. Each succeeding number is the sum of the previous two numbers, e.g. 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5 etc.

    Where sequence number n = 3, the Fibonacci number is 2.

    As the number of generations (g) increases (starting with g = 0 for an individual), the expected % of potential ancestors who contribute to the individual’s X chromosome within each ancestral generation in a pedigree fan chart will decrease. For example, in a male, at 3 generations (g = 3), the percentage of X ancestors is 3/8 X 100% or 37.5% . By 7 generations (g = 7), the percentage of X ancestors decreases to 21/128 X 100% or 16.4%, assuming no pedigree collapse (cousins marrying cousins).

    Luke Hutchison was one of the first to point out the importance of the Fibonacci Sequence as it applies to the X chromosome in 2004 when he worked for Sorenson Molecular Genealogy Foundation.

    I found a formula that we as genealogists can use here:
    http://www.maths.surrey.ac.uk/hosted...ibFormula.html . By applying Binet’s Formula for the nth Fibonacci number, we can substitute the corresponding generation (g); n = g + 1 for a male and n = g + 2 for a female. So now you can figure out the number of X ancestors in any given generation. You can also figure out the ratio of X to autosomal ancestors in that generation by dividing the X ancestors by 2 to the (g)th power. The autosomal ancestors increase exponentially but the X contributors increase according to the Fibonacci code.

    Here is a piece of math trivia derived from Binet's formula: did you know that (barring pedigree collapse) for a male, the percentage of X ancestors at 20 generations back is only about 1% of ancestors in that generation? That is far fewer than you might have expected.

    Why is this important? Because as you go back in time on an X chromosome fan chart, the number of ancestors who did NOT give you an X chromosome keeps getting larger and larger until pedigree collapse (cousins marrying cousins) makes the fan chart implode upon itself. See fan chart here: http://www.thegeneticgenealogist.com...-x-chromosome/ and you will see how the white areas of non-X-matching ancestors gets larger and larger. You don't have to understand the math formula to appreciate this phenomenon.

    When you have an X match with a cousin, you can start by eliminating all the ancestors who are not X contributors - that means any two males in a row (father to son) and their predecessors can be crossed off the list of likely recent ancestors in common.

    Kathy

  • #2
    DNA & the Golden Ratio

    The Golden Ratio is a mathematical oddity that is often found in nature; the size of the chambers in the nautilus shell, the number of petals in flowers, the shape of the human ear and many more examples. I recently read where a dentist even suggested that the “perfect smile” is where the central incisor and the lateral incisor are in proportion to the Golden Ratio.

    The Golden Ratio is usually explained as follows: a line segment of length T with segments A and B must equal T/A = A/B = ~1.618.

    The only sequence of numbers that meet these conditions are the Fibonacci series. So it occurs to me that in the 3 billion nucleotides in our genome there must be many cases of where one would find a Fibonacci series.

    Just food for thought.

    Jim Gates

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    • #3
      The only sequence of numbers that meet these conditions are the Fibonacci series. So it occurs to me that in the 3 billion nucleotides in our genome there must be many cases of where one would find a Fibonacci series.

      ____________________
      waleeed

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