How to Read Cumulative Probability Plots and Tables

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Current Version: 23 Jan. 2002

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

Reading Cumulative Probability Plots

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.

Reading Cumulative Probability Tables

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.

95% Confidence Interval

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.