Simulating a Map

As an exercise in learning to use the programs, you can simulate a genetic linkage map. The main parameters that you will need to specify are the haploid number of chromosomes, average number of markers per chromosome, and average intermarker distance between consecutive markers. You can also simulate linkage maps in which the telomeres don't have marker information.

Figure 2.3 shows how Rmap simulates a genetic linkage map where $M_{i,j}$ is marker

on chromosome

. We denote the number of chromosomes by

, the average number of markers per chromosome by

and the average intermarker distance by

in centimorgans. Furthermore, the average amount of ``tail'' DNA (DNA outside the most telomeric markers) will be specified by

, again in centimorgans. The standard deviations of

and

will by $\sigma_m$ and $\sigma_d$ , respectively. All of these variables can be specified by command line options, the resource file or by the interactive menu. The standard deviation of

will be $\sigma_t = (\frac{t}{d}) \sigma_d$ . For the

th chromosome, Rmap decides how many markers are on that chromosome

by picking a random number from a normal distribution with mean

and standard deviation $\sigma_m$ . Once this is done, the amount of DNA between consecutive markers $(d_{i,j})$ is simulated as a normal random variable with mean

and standard deviation $\sigma_d$ . Finally, the amount of telomeric or tail DNA $(d_{i,0}, d_{i,m_i})$ is simulated as a normal random variable with mean

and standard deviation $\sigma_t$ . Setting a standard deviation equal to zero means that the quantity in question is not a random variable, but set equal to its mean value.

The parameters $c, m, d, t, \sigma_m$ and $\sigma_d$ can be set using the command line options of Table 2.1 or in the interactive menu. Note that if an input file is specified, all these parameters are ignored and Rmap attempts to translate the input file.

**Figure 2.3:** Chromosome simulated under mode 0
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An alternate method of simulating the genetic linkage map can be invoked by changing the simulation mode parameter from 0 to 1 using the -M command line option. Figure 2.4 presents the method graphically. The length of chromosome

(

) will be normally distributed with mean

and standard deviation $\sigma_d$ . The number of markers on chromosome

(

) will still be normally distributed with mean

and standard deviation $\sigma_m$ , but will be placed on the chromosome following a uniform distribution on the interval

. You should set the values of

and $\sigma_d$ to appropriate levels, as they are for chromosome length rather than intermarker distance in this mode. For example, if you want roughly the same results from this mode as that in the original, then set $d = 16 \times 10 = 160$ in this mode.

**Figure 2.4:** Chromosome simulated under mode 1
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