When sexual selection in hosts benefits parasites.

In host-parasite coevolution, the parasite is selected to increase its infectivity while host is selected to resist the parasite infection. It is widely held that parasite-mediated sexual selection can further amplify the selective pressure on the host to overcome parasite infection. In this paper we focus on certain types of parasites, those that can impair the activity of the host immune function to prevent signs of sickness.

Analyzing genomic data using tensor-based orthogonal polynomials with application to synthetic RNAs.

An important goal in molecular biology is to quantify both the patterns across a genomic sequence and the relationship between phenotype and underlying sequence. We propose a multivariate tensor-based orthogonal polynomial approach to characterize nucleotides or amino acids in a given sequence and map corresponding phenotypes onto the sequence space. We have applied this method to a previously published case of small transcription activating RNAs.

Universal rules for the interaction of selection and transmission in evolution.

The Price equation shows that evolutionary change can be written in terms of two fundamental variables: the fitness of parents (or ancestors) and the phenotypes of their offspring (descendants). Its power lies in the fact that it requires no simplifying assumptions other than a closed population, but realizing the full potential of Price's result requires that we flesh out the mathematical representation of both fitness and offspring phenotype. Specifically, both need to be treated as stochastic variables that are themselves functions of parental phenotype.

Stochasticity and non-additivity expose hidden evolutionary pathways to cooperation.

Cooperation is widespread across the tree of life, with examples ranging from vertebrates to lichens to multispecies biofilms. The initial evolution of such cooperation is likely to involve interactions that produce non-additive fitness effects among small groups of individuals in local populations. However, most models for the evolution of cooperation have focused on genealogically related individuals, assume that the factors influencing individual fitness are deterministic, that populations are very large, and that the benefits of cooperation increase linearly with the number of cooperative interactions.

The place of development in mathematical evolutionary theory.

Development plays a critical role in structuring the joint offspring-parent phenotype distribution. It thus must be part of any truly general evolutionary theory. Historically, the offspring-parent distribution has often been treated in such a way as to bury the contribution of development, by distilling from it a single term, either heritability or additive genetic variance, and then working only with this term.

Evolution with stochastic fitness and stochastic migration.

Background: Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size.

A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution.

Background: Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly.

Theoretical approaches to the evolution of development and genetic architecture.

Developmental evolutionary biology has, in the past decade, started to move beyond simply adapting traditional population and quantitative genetics models and has begun to develop mathematical approaches that are designed specifically to study the evolution of complex, nonadditive systems. This article first reviews some of these methods, discussing their strengths and shortcomings. The article then considers some of the principal questions to which these theoretical methods have been applied, including the evolution of canalization, modularity, and developmental associations between traits.

Developmental associations between traits: covariance and beyond.

Statistical associations between phenotypic traits often result from shared developmental processes and include both covariation between the trait values and more complex associations between higher moments of the joint distribution of traits. In this article, an analytical technique for calculating the covariance between traits is presented on the basis of (1). the distribution of underlying genetic and environmental variation that jointly influences the traits and (2).

Perspective: Evolution and detection of genetic robustness.

Robustness is the invariance of phenotypes in the face of perturbation. The robustness of phenotypes appears at various levels of biological organization, including gene expression, protein folding, metabolic flux, physiological homeostasis, development, and even organismal fitness. The mechanisms underlying robustness are diverse, ranging from thermodynamic stability at the RNA and protein level to behavior at the organismal level.

A general population genetic theory for the evolution of developmental interactions.

The development of most phenotypic traits involves complex interactions between many underlying factors, both genetic and environmental. To study the evolution of such processes, a set of mathematical relationships is derived that describe how selection acts to change the distribution of genetic variation given arbitrarily complex developmental interactions and any distribution of genetic and environmental variation. The result is illustrated by using it to derive models for the evolution of dominance and for the evolutionary consequences of asymmetry in the distribution of genetic variation.

THE EVOLUTION OF CANALIZATION AND THE BREAKING OF VON BAER'S LAWS: MODELING THE EVOLUTION OF DEVELOPMENT WITH EPISTASIS.

Evolution can change the developmental processes underlying a character without changing the average expression of the character itself. This sort of change must occur in both the evolution of canalization, in which a character becomes increasingly buffered against genetic or developmental variation, and in the phenomenon of closely related species that show similar adult phenotypes but different underlying developmental patterns. To study such phenomena, I develop a model that follows evolution on a surface representing adult phenotype as a function of underlying developmental characters.