title: A Boolean gene regulatory model of heterosis and speciation.
abstract: BACKGROUND
  Modelling genetic phenomena affecting biological traits is important for the development of agriculture as it allows breeders to predict the potential of breeding for certain traits. One such phenomenon is heterosis or hybrid vigor: crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance. Heterosis has become a very useful tool in global agriculture, but its genetic basis remains controversial and its effects hard to predict. We have taken a computational approach to studying heterosis, developing a simulation of evolution, independent reassortment of alleles and hybridization of Gene Regulatory Networks (GRNs) in a Boolean framework. These artificial regulatory networks exhibit topological properties that reflect those observed in biology, and fitness is measured as the ability of a network to respond to external inputs in a pre-defined way.
  
  
  RESULTS
  Our model reproduced common experimental observations on heterosis using only biologically justified parameters, such as mutation rates. Hybrid vigor was observed and its extent was seen to increase as parental populations diverged, up until a point of sudden collapse of hybrid fitness. Thus, the model also describes a process akin to speciation due to genetic incompatibility of the separated populations. We also reproduce, for the first time in a model, the fact that hybrid vigor cannot easily be fixed by within a breeding line, currently an important limitation of the use of hybrid crops. The simulation allowed us to study the effects of three standard models for the genetic basis of heterosis: dominance, over-dominance, and epistasis.
  
  
  CONCLUSIONS
  This study describes the most detailed simulation of heterosis using gene regulatory networks to date and reproduces several phenomena associated with heterosis for the first time in a model. The level of detail in our model allows us to suggest possible warning signs of the impending collapse of hybrid vigor in breeding. In addition, the simulation provides a framework that can be extended to study other aspects of heterosis and alternative evolutionary scenarios.
authors.affiliation: Department of Plant Sciences, University of Cambridge, CB2 3EA, Cambridge, UK. peter.emmrich@jic.ac.uk.|Current address: John Innes Centre, Norwich Research Park, Norwich, NR4 7UH, UK. peter.emmrich@jic.ac.uk.
authors.forename: Peter Martin Ferdinand
authors.initials: PM
authors.lastname: Emmrich
authors.affiliation: Department of Plant Sciences, University of Cambridge, CB2 3EA, Cambridge, UK. h.roberts283@gmail.com.|Current address: The Nuffield Department of Clinical Medicine, Oxford University, Peter Medawar Building for Pathogen Research, Oxford, OX1 3SY, UK. h.roberts283@gmail.com.
authors.forename: Hannah Elizabeth
authors.initials: HE
authors.lastname: Roberts
authors.affiliation: Department of Plant Sciences, University of Cambridge, CB2 3EA, Cambridge, UK. vpancaldi@cnio.es.|Current address: Structural Biology and BioComputing Programme, Spanish National Cancer Research Centre (CNIO), Calle Melchor Fernández Almagro, 3, Madrid, E-28029, Spain. vpancaldi@cnio.es.
authors.forename: Vera
authors.initials: V
authors.lastname: Pancaldi
mesh_terms: D001947:Breeding; D003198:Computer Simulation; D018556:Crops, Agricultural / Q000145:classification / Q000235:genetics*; D004843:Epistasis, Genetic; D053263:Gene Regulatory Networks; D056084:Genetic Fitness; D049810:Genetic Speciation; D006579:Heterozygote; D006823:Hybrid Vigor; D006824:Hybridization, Genetic; D008957:Models, Genetic