Development and evolution are two fundamental biological processes. While development is the process of construction of the phenotype over life, evolution is the process of change in the genetic and phenotypic composition of the population over generations. However, a longstanding challenge is to mathematically describe simultaneously development and evolution. For instance, quantitative genetics is a prevalent mathematical theory used to describe evolution but considers development as the regression of phenotype on genotype without characterizing how such regression evolves. Consequently, quantitative genetics is said to apply only for short evolutionary timescales, over which such regression coefficients describing development would remain relatively unchanged. Quantitative genetics becomes less suitable in long evolutionary timescales as these regression coefficients evolve. Therefore, to describe long-term evolution, it is necessary to develop mathematical theories that integrate development and evolution, in the sense that they describe how the coefficients describing development evolve.

I have formulated a mathematical integration of development and evolution, which I call evo-devo dynamics. Previous quantitative genetics theory implied that development affects evolution by generating genetic covariation between traits, which diverts evolution on the fitness landscape from the direction of steepest fitness increase. At most, this effect can only shift evolution from one fitness peak to another, but the ultimate evolutionary outcome is a local fitness peak that is solely defined by selection, that is, the fitness landscape. In this sense, this classical theory entails that development plays a minor evolutionary role as the outcome is defined only by selection. My evo-devo dynamics formulation finds that the situation is different when the evolution of development is considered. Evo-devo dynamics finds that the long-term evolution of the phenotype requires tracking the evolution of the underlying genotype, which is not done in quantitative genetics. Doing so entails that evolution can only proceed along a path on the fitness landscape where the relationship between the genotype and phenotype holds. Consequently, evolution converges to path peaks rather than landscape peaks as traditionally assumed. Since path peaks are defined both by selection and development, evo-devo dynamics finds that development plays a major evolutionary role in the sense that development and evolution co-define the evolutionary outcomes.

However, evo-devo dynamics remains of limited scope as it assumes simplified genetics (particularly, continuous rather than discrete genotypic traits), deterministic development, and a single sex.

In this fellowship, I will develop further the mathematical theory of evo-devo dynamics. I will extend the theory to allow for more realistic genetics (discrete genotypic traits), stochastic development (due to both developmental and environmental noise), and two sexes. These extensions aim to answer how development affects evolution under discrete genotypes and stochastic and sex-specific development. These extensions have applications to understand extra-genetic-genetic co-evolution, to bring the theory to genetic data, and to model sex-specific complex phenotype evolution.