Fig 2 - WHERE TO FIND LINKED MICROSATELLITES Fig 1 - STAR-LIKE GENEALOGIES Demographic expansions produce characteristic genealogies where most coalescent events occurred at the time just before the expansion, when population size was small. The mismatch distribution expanded to linked microsatellites Miguel Navascués* & Olivier Hardy Laboratoire Eco-Ethologie Évolutive, Faculté des Sciences, Université Libre de Bruxelles, Avenue F.D. Roosevelt 50, Campus du Solbosch, 1050 Brussels, Belgium * Current address: Laboratoire d'Ecologie, École Normale Supérieure, 46 rue d'Ulm 75230 Paris Cedex 05, France. E-mail: m.navascues@gmail.com Pi ;0 ,1 ,=∑ j=i ∞ Pj ;0 ,1 ,×Pi ; j The use of genetic data to make inferences on demographic dynamics is one of the common applications of population genetics. Many statistical methods employed on this task are based on coalescent theory which describes the genealogical relationships among a group of genes as a function of population demography (fig 1). The theoretical background provided by the coalescent describes the distribution of mutations among the sample of genes under different demographic scenarios. However, the applicability of these predictions to empirical genetic data will be hampered by the mutational mechanisms that can erase or distort some of the useful information with back or parallel mutations. The inclusion of mutation models in theoretical predictions can improve the performance of statistical methods. Li (1977) described the probability distribution for the number of mutations (j) between a pair of haplotyes evolving under a demographic expansion. Schneider & Excoffier (1999) introduced a correction on that equation that allowed describing the distribution of the number of genetic differences (i) for mutation model for DNA sequence polymorphisms (see equation). Polymorpshim on linked microsatellites (repetitive DNA sequences of short repeat motif, fig 2) is sensitive to demographic expansions (Navascués et al. 2006). However large number of homoplasious mutations are expected on these markers which affects the estimation of demographic parameters. In order to improve the accuracy on these estimates we have developed a correction similar to that of Schneider & Excoffier (1999) but using the stepwise mutation model to describe microsatellite evolution. REFERENCES ● Li (1977) Genetics 85:331–337 ● Navascués et al. (2006) Molecular Ecology 15:2691–2698 ● Schneider & Excoffier (1999) Genetics 152:1079–1089 ACKNOWLEDGMENTS I am grateful to Brent Emerson & Concetta Burgarella for their support and discussion. This study was partially funded by the European Science Foundation ConGen Exchange Grant 1142 0 2000 4000 6000 8000 10000 12000 1 6 11 16 21 26 31 36 41 46 generations population size -0.216 2.725 6.784 -2.639 7.328 4.361 Sim τ = 7 -0.100 0.872 4.900 -1.498 2.398 3.502 Sim τ = 5 -0.144 0.493 2.856 -0.654 0.564 2.346 Sim τ = 3 0.025 0.154 1.024 -0.115 0.083 0.885 Sim τ = 1 bias mean squared error mean among estimates bias mean squared error mean among estimates Maximum likelihood estimator, model with homoplasy Maximum likelihood estimator, model without homoplasy Table 1 θ0=2N0μ θ1=2N1μ τ=2tμ Data was simulated for a set of linked loci evolving under a stepwise mutation model in a population going through a demographic expansion. Four different ages (τ) for the expansion were simulated and maximum likelihood estimates were obtained for the time of expansion using a model without homoplasy [using only Li's P(j;θ0,θ1,τ)] and a model accounting for homoplasy [using P(i;θ0,θ1,τ) with the correction based on the stepwise mutation model]. Table 1 shows how bias and error decrease when using the model corrected for homoplasy, specially for older expansions. probability distribution of the number genetic differences (i) given a demographic model (θ0,θ1,τ) probability distribution of the number of mutations (j) given a demographic model (θ0,θ1,τ) probability distribution of