Confounded, augmented and constrained replicator dynamics: Complex selection processes and their measurement

The quantitative methodology derived from replicator dynamics for empirical studies of economic evolution is becoming increasingly well developed in theory but is rarely applied in practice. One reason is the relatively naïve nature of current methods, which focus on the evolution of a single characteristic in a single environment. This assumption constrains the analysis of real selection processes in which firms operate in several markets and their products have several characteristics that interact to determine fitness. This entails that measurement of economic selection becomes confounded: characteristics that are associated with firm growth are not becoming more frequent in the population. The reason for confounded selection is that characteristics interact to augment or constrain the rate and direction of evolution and one-dimensional, single trait replicator dynamics cannot cope with confounded selection. The contribution of this paper is to develop an approach that serves to explicitly analyse confounded selection. The primary elements of the method are the selection gradients of the characteristics and the covariance matrix of the characteristics. Based on these, the method motivates a taxonomy of selection based on the interaction of characteristics. Applying the method to a population of firms will shed light on potentially confounded selection. It will reveal the indirect effects of characteristics on selection and the augmentation and constraints created thereby.