1) Simulate for 100 time-steps two independent "discrete" Brownian motion models with the same initial values and step size. You can choose these values yourself. At each time-step, each process either takes a positive step or a negative step. The step direction is chosen at random. The resulting variables (the cumulative sum of all previous steps at each time point) for each of the two processes should be taken as two species that have diverged from the same value after t = 0, and they should be stored in a two-column matrix.
2) Simulate the divergence of each species into two daughter-species at t = 100 under the same model for 100 additional time-steps: the results should be stored in a four-column matrix. You have now simulated trait values for a 4-species tree over a period of t=200. Plot the whole evolution for the 200 time-steps on a single graph.
3) Repeat 1) and 2) but now using a different starting value and step size. You now have 2 traits, each simulated under the same 4-species tree in an (approximate) Brownian process model.
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