A quantitative formulation of biology's first law

The zero-force evolutionary law (ZFEL) states that in evolutionary systems, in the absence of forces or constraints, diversity and complexity tend to increase. The reason is that diversity and complexity are both variance measures, and variances tend to increase spontaneously as random events accumulate. Here, we use random-walk models to quantify the ZFEL expectation, producing equations that give the probabilities of diversity or complexity increasing as a function of time, and that give the expected magnitude of the increase. We produce two sets of equations, one for the case in which variation occurs in discrete steps, the other for the case in which variation is continuous. The equations provide a way to decompose actual trajectories of diversity or complexity into two components, the portion due to the ZFEL and a remainder due to selection and constraint. Application of the equations is demonstrated using real and hypothetical data.