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r-selection refers to evolutionary competition in the rate of a population's exponential increase. This is contrasted with K-selection, in which populations in steady-state compete in efficiency of resource conversion. Evolution in nature…
Heritability is a central parameter in quantitative genetics, both from an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within and between genotype variability. This approach…
In plant and animal breeding studies a distinction is made between the genetic value (additive + epistatic genetic effects) and the breeding value (additive genetic effects) of an individual since it is expected that some of the epistatic…
Co-heritability is an important concept that characterizes the genetic associations within pairs of quantitative traits. There has been significant recent interest in estimating the co-heritability based on data from the genome-wide…
In many models of genotypic evolution, the vector of genotype populations satisfies a system of linear ordinary differential equations. This system of equations models a competition between differential replication rates (fitness) and…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
Genome-Wide Association Studies (GWAS) explain only a small fraction of heritability for most complex human phenotypes. Genomic heritability estimates the variance explained by the SNPs on the whole genome using mixed models and accounts…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Regression is typically treated as a curve-fitting process where the goal is to fit a prediction function to data. With the help of conditional generative adversarial networks, we propose to solve this age-old problem in a different way; we…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
The development of a complex disease is an intricate interplay of genetic and environmental factors. "Heritability" is defined as the proportion of total trait variance due to genetic factors within a given population. Studies with…
This paper shows that differentiating the lifetimes of two phenotypes independently from their fertility can lead to a qualitative change in the equilibrium of a population: since survival and reproduction are distinct functional aspects of…
Linear mixed models (LMMs) are a powerful and established tool for studying genotype-phenotype relationships. A limiting assumption of LMMs is that the residuals are Gaussian distributed, a requirement that rarely holds in practice.…
Training population selection for genomic selection has captured a great deal of interest in animal and plant breeding. In this article, we derive a computationally efficient statistic to measure the reliability of estimates of genetic…
Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here we discuss probabilistic models of…
The distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution,…
Modelling the evolution of a continuous trait in a biological population is one of the oldest problems in evolutionary biology, which led to the birth of quantitative genetics. With the recent development of GWAS methods, it has become…
We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The…
An equivalence between an integro-differential operator M and an evolution operator Ln is determined. From this equivalence the fundamental solution of Ln is estimated in terms of the fundamental solution related to the third-order operator…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…