EVOLUTION AND THE HISTORY OF LIFE: TEMPO, MODE, AND TIME SCALE
To appreciate non-randomness we have to understand randomness. A random-walk time series provides a simple unified model for understanding tempo and time-scale on one hand, and mode and non-randomness on the other. A random walk time series is generated by defining and iterating a time step and a trait change (with or without variance). Time is unidirectional, but trait change has an associated discreet sign, positive or negative, and the randomness of a time series comes from random fluctuation of the sign. What is the step size? Differential reproduction happens on a generation-to-generation time scale, so in an evolutionary model the step size is one generation. What is the trait change for a step in our model? This has to be determined empirically. Randomness is inherent in our model, but this has to be characterized empirically for evolutionary time series in nature. No fluctuation of the sign associated with trait change produces a directional time series. Constant fluctuation of the sign produces a stationary time series. Once we understand this unified model it is straightforward to develop tools to investigate empirical time series, in the history of life or in the laboratory, to determine the relationship of trait change to step size (tempo) and the relative likelihoods of no, random, or constant fluctuation (mode).