Developmental Phenotypic Landscapes

Polly (2008) points out that some evolutionary biologists believe that the additive genetic covariance matrix G, and the vector of selection coefficients are sufficient to predict the rate and direction of phenotypic evolution, at least in the short term. He also notes that long-term evolution, saltatory evolution, and the origin of novelty can typically not be predicted by current statistical genetic methods. Polly (2008) expresses the hope that information about the developmental-genetic processes that give rise to the phenotype would make it possible to develop an integrated theory for the phenotypic evolution that could predict longterm and discontinuous evolution. An important reason for the inability of quantitative genetics to predict long-term evolution is that the relationship between genetic and phenotypic variation is nonlinear. Understanding the causes and consequences of this nonlinearity is important for understanding how developmental information could be usefully adapted to evolutionary biology. Perhaps the most general reason for non-linearity is that the relationships between cause and effect (e.g. transcriptional activator concentration and transcription rate, signaling ligand concentration and downstream signaling pathway activation, substrate concentration and reaction rate) are always saturating and have a hyperbolic or sigmoid form. Regulatory processes inevitably have nonlinear effects: the effect of an inhibitor is non-linear (it is proportional to 1/inhibitor); negative feedback, like inhibition, is non-linear; positive feedback is a non-linear process (it is proportional to K); cooperativity, like positive feedback, is described by a (non-linear) power function. Any process that depends on diffusion of one or more of its components, and is not at steady state, is a nonlinear function of time and space. Finally, the system properties of interacting causal factors can produce highly non-linear relationships between cause and effect even when the independent effect of each cause is perfectly linear (Kacser and Burns 1981; Gilchrist and Nijhout 2001). What effect do these non-linearities have on the shapes of phenotypic landscapes and evolution on those landscapes? In order to answer this we need to consider what a phenotypic landscape actually depicts. There are basically four different kinds of phenotypic landscapes (admitting that they could be parsed differently than I do here), that represent very different things. In the adaptive landscapes of population genetics, the fitness can be described as a function of gene frequencies, and each point on the surface of such a landscape represents a population mean. In quantitative genetics fitness is described as landscape that is a function of trait values, and the population is represented by a dispersed distribution (hopefully multivariate normal) on the surface. Insofar as selection acts only on phenotypes, a fitness landscape is also a phenotypic landscape where fitness is proportional to phenotypic value. Morphometric landscapes, by contrast, describe the relationship among the measured phenotypes. These are essentially descriptions of how different traits covary in a population. Developmental landscapes describe the relationship between the phenotype and the underlying determinants of the phenotype (e.g. genes, environments, processes, antecedent traits). Each point on the landscape describes an individual of a particular genotype in a particular environment. It is this latter kind of landscape that Rice (1998, 2002) had in mind and that has the potential of H. F. Nijhout (&) Department of Biology, Duke University, Durham, NC 27708, USA e-mail: hfn@duke.edu