MBT/Genetics 541 Homework Assignment 5

Due Friday May 11

• Do a computer simulation of a coalescent with (say) 10 copies of a gene. For this you need a source of random numbers. If you have a function (such as in Unix the rand/srand pair of functions or the random/srandom pair) that gives you a uniform random fraction U between 0 and 1, if you take -ln(U) that will be an exponentially distributed quantity with expectation 1. To make an exponentially distributed quantity with expectation M, just multiply that by M.

  Start with the 10 copies, numbered in some order. Choose a random time (we are going backwards in time) when two will coalesce, and choose which two (using random fractions) coalesce. Then you have 9 lineages. Do the same for the 9, changing the expected time to coalescence appropriately. Contine till there is 1.

  Print out a summary of who coalesced and when.

  Run your program a number of times. Are the coalescences quicker when there are more lineages (i.e. earlier in the process)? Is there much random variation in how many generations it takes for the whole set of lineages to coalesce?