Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Ronald Fisher needed to develop elaborate models of genetic effects in order to set the foundations of Quantitative Genetics in his 1918 paper “The correlation between relatives on the supposition of Mendelian inheritance”. Since then, many significant implementations have been made to model genetic effects. However, at the verge of one century after Fisher’s kick-off, models of genetic effects keep on being discussed and implemented. Indeed, the relatively recent advent of QTL analyses challenged the state of the art of this field by providing researchers the opportunity to obtain and analyze estimates of genetic effects from real data. In this context, the development of this field was not exempt of some polemics, like the debate about the convenience of the functional and the statistical epistasis approaches. This research topic is meant to provide recent developments in models and estimation of genetic effects and to enrich the discussion about how and why models of genetic effects must be further developed and applied.The articles in this Research Topic shall thus extend, refine and/or provide a refresh look at Fisher’s original models of genetic effects and their application to genetic effects estimation and to improve our understanding of evolutionary processes and breeding programs.

Genetic Effects --- mathematical modelling --- statistical estimation --- Genetic architecture --- gene mapping --- simulation studies --- Epistasis --- gene-by-environment interactions --- Host-Pathogen Interactions --- imprinting

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Legendre wavelets --- collocation method --- three-step Taylor method --- asymptotic stability --- time-dependent partial differential equations --- non-instantaneous impulses --- Caputo fractional derivative --- differential equations --- state dependent delays --- lipschitz stability --- limit-periodic solutions --- difference equations --- exponential dichotomy --- strong nonlinearities --- effective existence criteria --- population dynamics --- discrete Lyapunov equation --- difference equations --- Hilbert space --- dichotomy --- exponential stability --- ?-Laplacian operator --- mean curvature operator --- heteroclinic solutions --- problems in the real line --- lower and upper solutions --- Nagumo condition on the real line --- fixed point theory --- coupled nonlinear systems --- functional boundary conditions --- Schauder’s fixed point theory --- Arzèla Ascoli theorem --- lower and upper solutions --- first order periodic systems --- SIRS epidemic model --- mathematical modelling --- Navier–Stokes equations --- global solutions --- regular solutions --- a priori estimates --- weak solutions --- kinetic energy --- dissipation --- Bäcklund transformation --- Clairin’s method --- generalized Liouville equation --- Miura transformation --- Korteweg-de Vries equation --- second-order differential/difference/q-difference equation of hypergeometric type --- non-uniform lattices --- divided-difference equations --- polynomial solution --- integro-differentials --- Sumudu decomposition method --- dynamical system