title: Inbreeding depression under mixed outcrossing, self-fertilization and sib-mating.
abstract: Biparental inbreeding, mating between two relatives, occurs at a low frequency in many natural plant populations, which also often have substantial rates of self-fertilization. Although biparental inbreeding is likely to influence the dynamics of inbreeding depression and the evolution of selfing rates, it has received limited theoretical attention in comparison to selfing. The only previous model suggested that biparental inbreeding can favour the maintenance of stable intermediate selfing rates, but made unrealistic assumptions about the genetic basis of inbreeding depression. Here we extend a genetic model of inbreeding depression, describing nearly recessive lethal mutations at a very large number of loci, to incorporate sib-mating. We also include a constant component of inbreeding depression modelling the effects of mildly deleterious, nearly additive alleles. We analyze how observed rates of sib-mating influence the mean number of heterozygous lethals alleles and inbreeding depression in a population reproducing by a mixture of self-fertilization, sib-mating and outcrossing. We finally use the ensuing relationship between equilibrium inbreeding depression and population selfing rate to infer the evolutionarily stable selfing rates expected under such a mixed mating system.
  
  
  
  We show that for a given rate of inbreeding, sib-mating is more efficient at purging inbreeding depression than selfing, because homozygosity of lethals increases more gradually through sib-mating than through selfing. Because sib-mating promotes the purging of inbreeding depression and the evolution of selfing, our genetic model of inbreeding depression also predicts that sib-mating is unlikely to maintain stable intermediate selfing rates.
  
  
  
  Our results imply that even low rates of sib-mating affect plant mating system evolution, by facilitating the evolution of selfing via more efficient purging of inbreeding depression. Alternative mechanisms, such as pollination ecology, are necessary to explain stable mixed selfing and outcrossing.
authors.affiliation: Centre d'Ecologie et des Sciences de la Conservation (UMR7204), Sorbonne Universités, MNHN, CNRS, UPMC, 57 rue Cuvier, Paris, 75005, France. porcher@mnhn.fr.
authors.forename: Emmanuelle
authors.initials: E
authors.lastname: Porcher
authors.affiliation: Department of Life Sciences, Imperial College London, Ascot, Berkshire, UK.
authors.forename: Russell
authors.initials: R
authors.lastname: Lande
mesh_terms: D005075:Biological Evolution; D003433:Crosses, Genetic; D056084:Genetic Fitness; D006579:Heterozygote; D006720:Homozygote; D007178:Inbreeding; D000071422:Inbreeding Depression; D008957:Models, Genetic; D010944:Plants / Q000235:genetics*; D057945:Self-Fertilization
keywords: Biparental inbreeding; Inbreeding depression; Mixed mating; Mutation; Nearly recessive lethals; Self-fertilization