Donald R. Burleson, Ph.D.
Copyright (c) 2012 by Donald R. Burleson.
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original authorship is explicitly acknowledged.
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Around 1930 an anomalous skull, together with a diminutive skeleton
(subsequently lost), was unearthed in an abandoned mine shaft in northern Mexico.
Dubbed the StarChild, this relic eventually came to be exhaustively researched by
author Lloyd Pye, who in time engaged a professional geneticist. The skull exhibits
numerous physical abnormalities, including an uncommonly large cranial volume
and an exeedingly tough organic fiber "mesh" embedded in the osseous tissue;
but the real story is to be found in the skull's DNA.

In particular, the most revealing recent discovery has to do with what is called the
FOXP2 gene, which in the human genome occurs on Chromosome 7, where it has a great
deal to do with speech and language development, and probably with modulating the plasticity
of neural circuits in the brain, among its known functions. It is an exceedingly important
gene, and indeed an organism is at risk of suffering grave disorders if anything at all
is wrong with the coding sequence in this gene.

The geneticist working on the StarChild project has released a detailed brief in which he
describes recovering a DNA sequence consisting of 211 consecutive nucleotide base-pairs
from the StarChild's FOXP2 gene. Most complex life forms have some version of this
gene, a type of gene with a "cascading" character as it helps regulate the protein-synthesis
expression of over 300 other "downstream" genes. Thus FOXP2 must function correctly, and
cannot afford to be mutated at all in an organism that is to remain properly functional.
There is a case well known to geneticists in which a family somehow inherited a
FOXP2 gene that was altered such that it contained one incorrectly mutated
base-pair out of the 2,594 base-pairs that comprise the gene, and the result was
that several family members suffered from severe speech development disorders, and an inability
to control the muscles in the lower part of the face.

The geneticist for the StarChild project also made the astonishing discovery that in the
recovered 211 base-pair fragment from the skull's FOXP2 gene, a whopping 62 base-pairs were
different from the corresponding DNA sequence in humans! (By comparison, if one compares
this human gene fragment to the corresponding 211-nucleotide string in the FOXP2 gene of mice,
one finds only 20 different-from-human base-pairs, compared to the 62 that are different
in StarChild FOXP2 DNA coding.)

If one were to suppose that the whole StarChild gene was proportionally as different from human
FOXP2 as the fragment is, the implication would be that the whole gene would have
about 762 bases-pairs different from the human FOXP2 gene. Of course there is no reason
to assume outright that the StarChild's whole gene is proportionally as different-from-human
as the fragment is.

But what I want to point out here is that we may make good use of this information
by enlisting the theory of probability to draw some likely conclusions-- likely but of course
not certain, as statistical inferences about whole data-sources or populations are never
entirely certain, being based on samples taken from the larger body of information. As always,
while we may never have 100% certainty, we can have high probability that our tentative
conclusions are correct, by simply applying some straightforward computations.

To begin with, since 62 of the 211 recovered base-pairs were different from what the
corresponding DNA sequence in humans would show, the sample proportion is simply
p = 62/211 = 0.29384 rounded off. This sample statistic can tell us a number of things.
If samples of size n = 211 were taken repeatedly from the same population (i.e. from the
DNA present in the StarChild skull), the extent to which the sample proportions from those
samples would be varied, or dispersed, may be well approximated by the mathematical
expression for the standard deviation of sample proportions, namely

σp = √[p(1-p)/n] = √[0.29384(1-0.29384)/211]

= √(0.000983403) = 0.03136

approximately. One may employ this standard deviation for any number of purposes, e.g.
for computing a confidence-interval estimate of the overall proportion, i.e. the proportion
in the entire population of DNA present in the Starchild skull, that differs from human.
We may do this by noting that at the sample size n = 211, if samples were taken repeatedly
and if their sample proportions were computed, those sample proportions would roughly follow
a normal curve ("bell curve" or Gaussian distribution), so that about 99% of the sample
proportions would lie within 2.575 standard deviations of the center. This gives a 99%-confidence
interval estimate of the population proportion P:

0.29384 - 2.575(0.03136) < P < 0.29384 + 2.575(0.03136)

or, after rounding the endpoints off,

0.2131 < P < 0.3746.

That is to say, the probability model we are using would suggest a 99% probability that
anywhere from about 21.3% to about 37.5% of the nucleotide-pairs would differ from human.
This analysis is subject to the limitation that the sample of 211 originally recovered does not
actually comprise a wholly random sample (the 211 base-pairs are consecutive, after all)--
but if one regards these probabilistic results as even roughly approximate approaches to the
actual state of the DNA, the implications are that in the FOXP2 gene for the StarChild, well upwards
of 500 base-pairs out of 2,594 are likely to be different from human.

This means that we can dismiss any notion that the StarChild itself is human. If it were, so that
its developmental health would depend upon having a normally structured human FOXP2 cascader gene,
then a discrepancy of more than 500 base-pairs mutated to incorrect forms would have meant that
the organism not only could never have grown to adulthood (Lloyd Pye determined that the StarChild was
an adult when it died, based on the "crazing" in the tissues of its teeth), but in fact it would very
probably have died at conception, or soon after conception.

Under the normal distribution with the parameters specified, one also finds that the probability
that the proportion of different-from-human nucleotide base-pairs exceeds 20% is about 0.9986.
Again, one must entertain these statistical results with an awareness that there is an unavoidable
amount of uncertainty, but even when we regard the results as a rough approximation of the exact
state of things, we are left with the reflection that we have a good probability that
the StarChild is more different from us genetically than we are different from mice.

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