/*-------------------------------------------------------------

Copyright (C) 2000 Peter Clote, Sebastian Will
All Rights Reserved.

written by Peter Clote
modified by Sebastian Will

Permission to use, copy, modify, and distribute this
software and its documentation for NON-COMMERCIAL purposes
and without fee is hereby granted provided that this
copyright notice appears in all copies.


THE AUTHOR AND PUBLISHER MAKE NO REPRESENTATIONS OR
WARRANTIES ABOUT THE SUITABILITY OF THE SOFTWARE, EITHER
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
PARTICULAR PURPOSE, OR NON-INFRINGEMENT. THE AUTHORS
AND PUBLISHER SHALL NOT BE LIABLE FOR ANY DAMAGES SUFFERED
BY LICENSEE AS A RESULT OF USING, MODIFYING OR DISTRIBUTING
THIS SOFTWARE OR ITS DERIVATIVES.

-------------------------------------------------------------*/


/* histoneMutation.c

   Solution to exercise 1 in chapter 2

   Exercise:
   It is estimated that the nucleotide substitution rate lambda per
   site per year for nuclear DNA of higher primates is 1.3 x
   10^{-9}. Histone H4 consists of 105 amino acids, hence 315
   nucleotides. Assuming that nucleotide substitutions occur uniformly
   across the 315 sites of histone H4, what is the least number of
   nucleotide substitutions, where with probability at least 0.5 a
   substitution has occurred at the same site? Using lambda, estimate
   the amount of time which has elapsed for this to occur.

 */

#include <stdio.h>

main() {
  int n=0;
  double x=1.0;
  double years;
  
  while (x >= 0.5) {
    x *= (double) (315-n)/315;
    n++;
    
    printf("x:%f ",x);
    printf("n:%d ",n);
    printf("years:%e\n",(n/1.3)*1e9);
    
  }
  /* for n is the probability less than 0.5, hence take n-1 */
  n--;
  years = (n/1.3)*1e9; /* years = n/lambda, where lambda=1.3*10^-9 */
  // note the use of exponential notation 1e9 instead of
  // 1000000000 to denote one billion

  printf("n:%d\n",n);
  printf("years:%e\n",years);

}

/*-------------------------------------
Answer
n:21
years:1.615385e+10
Since this is about 15 billion years, and it is
believed that the earth has existed for 5 billion years,
and life, beginning with cyanobacteria (blue-green algae)
only for about 2 or 3 billion years, it is unlikely that
there has been a mutation twice in the same position
of histone.
--------------------------------------*/