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...

Inferences regarding phylogenetic patterns and constraints on the evolution of characters often can be derived only from comparisons of extant species. If the phylogeny of these species is known, then the mean phenotypes of taxa can be partitioned into heritable phylogenetic effects and nonheritable residual components. Methods are presented for the estimation of phylogenywide means of characte...

Life-history theory predicts that resource scarcity constrains individual optimal reproductive strategies and shapes the evolution of life-history traits. In species where the inherited structure of social class may lead to consistent resource differences among family lines, between-class variation in resource availability should select for divergence in optimal reproductive strategies. Evaluat...

Most spatial models of host-parasite interactions either neglect the possibility of pathogen evolution or consider that this process is slow enough for epidemiological dynamics to reach an equilibrium on a fast timescale. Here, we propose a novel approach to jointly model the epidemiological and evolutionary dynamics of spatially structured host and pathogen populations. Starting from a multi-s...

Biodiversity plays a vital role for ecosystem functioning in a changing environment. Yet theoretical approaches that incorporate diversity into classical ecosystem theory do not provide a general dynamic theory based on mechanistic principles. In this paper, we suggest that approaches developed for quantitative genetics can be extended to ecosystem functioning by modeling the means and variance...

Evolutionary biology is a study of life's history on Earth. In researching this history, biologists are often interested in attempting to reconstruct phenotypes for the long extinct ancestors of living species. Various methods have been developed to do this on a phylogeny from the data for extant taxa. In the present article, I introduce a new approach for ancestral character estimation for dis...

Epistasis, the interaction between genes, is a topic of current interest in molecular and quantitative genetics. A large amount of research has been devoted to the detection and investigation of epistatic interactions. However, there has been much confusion in the literature over definitions and interpretations of epistasis. In this review, we provide a historical background to the study of epi...

A model is presented in which alleles at a number of loci combine to influence the value of a quantitative trait that is subject to stabilizing selection. Mutations can occur to alleles at the loci under consideration. Some of these mutations will tend to increase the value of the trait, while others will tend to decrease it. In contrast to most previous models, we allow the mean effect of muta...

During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space. How such multimodal patterns in phenotype space can emerge from a single ancestral species is a fundamental question in biology. Frequency-dependent competition is one potential mechanism for such pattern formation, as has previously been shown i...

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated paramete...