EVOLUTION AND THE HISTORY OF LIFE: TEMPO, MODE, AND TIME SCALE

Evolution is a generic description of ‘change’ or ‘formation’ or ‘growth’ that is usually conceived as constructive, gradual, peaceful, and progressive in some sense. Evolution is a descriptive interpretation that we give to the long history of life as we view it in hindsight, grateful to be alive, even though we know that life’s history wasn’t always constructive, peaceful, and progressive. Evolution is more history than it is a single simple process, but it has a central mechanism at its core: natural selection. This is a gradual, step-by-step, non-random process by which variable traits change as a result of functional advantage and differential reproduction. What are the steps, what is the variation, what is the change, and what is non-random about it? Change-scaled-to-variation and step-size define evolutionary ‘tempo.’ The nature of the non-randomness defines evolutionary ‘mode.’ Tempo and mode are not only separable but also independent: as independent as the slope and intercept parameters of a line.

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).