Medelian inheritence

Mendelian inheritence.ipynb

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    "Mendelian inheritance\n",
    "=======================\n",
    "\n",
    "- Given three integers $k$, $m$ and $n$, representing a population of $k + m + n$ individuals in which:\n",
    "    - $k$ are homozygous dominant (A,A)\n",
    "    - $m$ are heterozygous (A, a)\n",
    "    - $n$ are homozygous recessive (a, a)\n",
    "- Return the probability that any two individual will produce an offspring containing a dominant allele\n",
    "\n",
    "\n",
    "**Percent  offspring containing dominant allele:**\n",
    "\n",
    "\\begin{align}\n",
    "k + k &= 100\\% \\\\\n",
    "k + m &= 100\\% \\\\\n",
    "k + n &= 100\\% \\\\\n",
    "m + m &= 75\\% \\\\\n",
    "m + n &= 50\\% \\\\\n",
    "n + n &= 0\\% \\\\\n",
    "\\end{align}\n",
    "\n",
    "**Probability of selecting a pair at random:**  \n",
    "\\begin{align}\n",
    "\\text{pop} &= k + m + n \\\\\n",
    "P(k,m) &= \\frac{k}{\\text{pop}} \\times \\frac{m}{\\text{pop} -1} \\\\\n",
    "P(m,m) &= \\frac{m}{\\text{pop}} \\times \\frac{m-1}{\\text{pop} -1} \\\\\n",
    "\\end{align}\n",
    "\n",
    "If we multiply each of these by the probability of producing an offspring with a dominant allele, i.e:\n",
    "\n",
    "\\begin{align}\n",
    "P  &= \\frac{m}{\\text{pop}} \\times \\frac{n}{\\text{pop} -1} \\times 0.5\n",
    "\\end{align}\n",
    "\n",
    "Then sum the probability of all outcomes"
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    "mendel <- function(k, m, n){\n",
    "    \n",
    "    pop <- k + m + n\n",
    "    \n",
    "    p1 <- k / pop\n",
    "    p2 <- (m / pop) * (k / (pop - 1))\n",
    "    p3 <- (m / pop) * ((m - 1)/ (pop - 1)) * 0.75\n",
    "    p4 <- (m / pop) * (n / (pop - 1)) * 0.5\n",
    "    p5 <- (n / pop) * (m / (pop - 1)) * 0.5\n",
    "    p6 <- (n / pop) * (k / (pop - 1))\n",
    "    # n + n will be zero, don't need to calculate\n",
    "\n",
    "    out <- p1 + p2 + p3 + p4 + p5 + p6\n",
    "    return(out)\n",
    "}"
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   "source": [
    "mendel(2,2,2)"
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    "mendel(6, 8, 4)"
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