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since 23 Jan 2002 |

Current Version: **23 Jan. 2002**

Reading: Plots ---- Tables --- 95% Confidence Intervals

The time to most recent common ancestor (TMRCA) calculations are given in terms of **cumulative probability** plots. These curves plot the probability that times are equal to or less than a given number of generations, i.e. the value on the vertical axis for a point T is the Probability(TMRCA < T), the cumulative probability

Consider the curve below, which is a function of the marker data and assumed mutation rates. Suppose you wish to assume a stepwise mutation model (the green curve). What is the probability that the time to the MRCA is 400 generations or less?

Reading from the curve, the value is 44%.

Hence, for any given T (number of generations), we can easily read off the probability that the actual TMRCA is that value or less.

One can also read these curves in reverse, setting a probability value and then asking how mnay generations correspond to that value.

For example, how many generations are required so that the probability of TRMCA is 80%? Reading from the curve (in this case for the infinite alleles model), this is 48 generations.

The cumulative probability tables simply list the number of generations corresponding to the 50%, 90% and 95% values. Consider the following table:

Method | 50% | 90% | 95% | 95% Confidence Interval |

Infinite Alleles |
20 | 40 | 80 | 15-85 |

Stepwise correction |
40 | 65 | 97 | 20-102 |

This table tells us that if we assume the Infinite Alleles model, there is a 50% probability that the most recent common ancestor is 20 generations or less, a 90% probability that TMRCA is 40 generations or less, and a 95% probability that TRMCA is 80 generations or less.

This table also reports the 95% Confidence Interval, the upper and lower range of values that encompass 95% of the probability for the TRMCA. For the Stepwise mutational model, 95% of the possible TRMCA values (given the molecular data and mutational assumptions) fall between 20 and 102 generations.