Non-particulate inheritance revisited: Evolution in systems with Parental Variability-Dependent Inheritance

Abstract

In non-genetic systems, such as culture, inheritance is often non-particulate. Owing to blending and consequent loss of variability, however, selection in such systems has been considered ineffective. The issue of loss of variability was solved by the Galton-Pearson model, which assumes a constant offspring variability and predicts gradual adaptation regardless of model parameters. The supposition of constant offspring variability is, however, arbitrary, and it is rather unrealistic in the context of social learning, because variability of inputs may affect the resulting trait acquisition. We present an alternative non-particulate inheritance model, 'Parental Variability-Dependent Inheritance', in which offspring variability is proportional to parental variability. Results of computer simulations show that despite its simplicity, this model can, even from the same initial conditions, result in one of two stable states: successful adaptation or loss of variability. Successful adaptation is more probable in larger populations with a larger relative offspring variability and an intermediate level of selection. A third possible outcome is an unstable, chaotic increase in variability, which takes place when relative offspring variability is too large to be trimmed by selection. Without any additional assumptions, this inheritance system results in punctuated evolution.