# 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