articleInfluence of mutation rate on estimators of genetic differentiation-lessons from Arabidopsis thaliana

Background: The analysis of molecular variation within and between populations is crucial to establish strategies for conservation as well as to detect the footprint of spatially heterogeneous selection. The traditional estimator of genetic differentiation (FST) has been shown to be misleading if genetic diversity is high. Alternative estimators of FST have been proposed, but their robustness to variation in mutation rate is not clearly established. We first investigated the effect of mutation and migration rate using computer simulations and examined their joint influence on QST, a measure of genetic differentiation for quantitative traits. We further used experimental data in natural populations of Arabidopsis thaliana to characterize the effect of mutation rate on various estimates of population differentiation. Since natural species exhibit various degrees of self-fertilisation, we also investigated the effect of mating system on the different estimators. Results: If mutation rate is high and migration rate low, classical measures of genetic differentiation are misleading. Only ΦST, an estimator that takes the mutational distances between alleles into account, is independent of mutation rate, for all migration rates. However, the performance of ΦST depends on the underlying mutation model and departures from this model cause its performance to degrade. We further show that QST has the same bias. We provide evidence that, in A. thaliana, microsatellite variation correlates with mutation rate. We thereby demonstrate that our results on estimators of genetic differentiation have important implications, even for species that are well established models in population genetics and molecular biology. Conclusions: We find that alternative measures of differentiation like F'ST and D are not suitable for estimating effective migration rate and should not be used in studies of local adaptation. Genetic differentiation should instead be measured using an estimator that takes mutation rate into account, such as ΦST. Furthermore, in systems where migration between populations is low, such as A. thaliana, QST < FST cannot be taken as evidence for homogenising selection as has been traditionally thought. Background Characterisation of population structure is a pivotal task in population genetics. It is important for inferring the evolutionary history of a species, assisting in conservation studies [1] and measuring dispersal [2-4]. In association mapping and forensic applications, population structure must be corrected for [see [5]]. The characterisation of population structure is also crucial for studies tracking the signature of local adaptation i. e. when natural selection maintains differences in allele frequencies between populations. Indeed, limited migration or population bottlenecks can also cause allele frequencies to diverge. A proper characterisation of population structure is absolutely required to infer the action of local selection on outlier loci with reasonable confidence [6]. One way to quantify population structure is to use the summary statistic FST, which measures population differentiation. If allele frequencies are similar in a set of populations FST will be low, and conversely, if allele frequencies are different FST will be high. Basically, FST and its hierarchical extensions quantify how genetic diversity is partitioned within and between populations or groups of populations (see [5,7-9] for a review of the large body of * Correspondence: demeaux@mpiz-koeln.mpg.de 1 Department of Plant Breeding and Genetics, Max-Planck Institute for Plant Breeding Research, Carl-von-Linné-Weg 10, 50829 Cologne, Germany Full list of author information is available at the end of the article © 2010 Kronholm et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Kronholm et al. BMC Genetics 2010, 11:33 http://www.biomedcentral. com/1471-2156/11/33 Page 2 of 14 theory on FST). FST can also be defined in terms of the ratio of coalescence times, for pairs of alleles from the same population over pairs of alleles from different populations [7]. If we consider only identity by descent, the topology of the genealogy is independent of the number of mutations. FST can be sometimes related to quantities describing migration [2], although this approach has its caveats [4]. In the context of selection, by using many presumably neutral markers one can build a distribution of expected FST values and then compare these to FST values of genes that are hypothesised to be subject to selection [9]. This can also be done for phenotypes using QST, a measure of genetic differentiation in quantitative traits. It has been shown that under neutrality QST is equivalent to a single locus FST, and this relationship is robust to different demographic scenarios [10-12]. This property can be used to compare the QST of a quantitative trait to the distribution of FST from neutral markers and infer whether the trait is influenced by selection [reviewed in [13]]. Some recent studies have raised concerns about the reliability of FST for characterisation of population structure using markers with high mutation rates, such as microsatellites [14-18]. High levels of within population diversity bias FST estimates downwards, because FST is estimated using heterozygosities or genetic variances. If a locus has multiple alleles, classical FST can be low even if populations share no alleles [15,16,19]. In addition to the classical FST, there are other estimators that have been proposed over the years. An analogous estimator to FST, ΦST, takes into account the distances between alleles thereby correcting for mutation rate [7,20]. Classical FST, estimated in the framework of Weir & Cockerham [21] considers only allele identity while ΦST considers distances between the alleles, be it differences in repeat number (e.g. in the case of microsatellite) or number of pairwise differences between DNA haplotypes. Another measure, F'ST, standardises the observed FST value with the maximum possible value that FST could attain given the amount of observed diversity [15]. Finally, Jost derived recently a new measure of genetic differentiation, D [16] to replace GST (or its equivalent for empirical studies FST). D measures allelic differentiation by partitioning heterozygosity into within and between population components [16]. D is defined as , where HT is total heterozygosity, HS subpopulation heterozygosity and n is the number of subpopulations [16]. These estimators provide improved measures of allelic differentiation between populations, yet their usefulness for estimating genetic differentiation in the context of migration or local adaptation is not clearly established. Most previous studies addressed these concerns using GST instead of FST. When GST is used, the mathematics are less complicated. In practise, however, FST has better statistical properties when empirical studies are concerned [see [5]]. For this reason, FST is the statistic of interest in this study. Moreover, in practise the difference between these two statistics is small. Here, we characterize the relationship between different estimators of genetic differentiation and mutation rate using simulations as well as experimental data collected from natural populations. Our study system is Arabidopsis thaliana (L.) Heyhn. (Brassicaceae). We use simulations to characterize the relationship between mutation rate and population differentiation for both molecular markers and quantitative traits and ask the following questions: i) are all estimators of genetic differentiation dependent on mutation rate, ii) is the estimator of differentiation for quantitative traits dependent on mutation rate, iii) does the mating system influence the relationship between mutation rate and estimators of population differentiation. We provide empirical data from Arabidopsis thaliana, a long-standing model for plant molecular biology that has recently become a model in plant population genetics [22]. We show that in A. thaliana, FST is biased downwards for high mutation rate loci. We discuss these results and their implications for various applications of FST analysis, including the reliable detection of variable selection. Methods Data analysis Computer simulations In order to investigate the behaviour of FST, F'ST, ΦST and D under high mutation rates, computer simulations using EasyPop 1.8 [23] were performed. The simulation scheme was set to 10 populations with 500 individuals each, 20 freely recombining loci and random mating hermaphrodites. All loci were set initially as polymorphic by allowing EasyPop to generate the genotypes in the first generation. Populations followed an island model of migration. Migration rates (probability that a given individual will migrate in each generation), m ranged from 0.1 to 0.00001 and mutation rates (probability that a given allele will mutate in each generation), μ from 0.00001 to 0.01. In order to simulate microsatellite loci we first examined a pure single step mutation model. Then we relaxed this assumption by using a mixed mutation model in which the loci followed a single step mutation model but with the probability of 0.2 to mutate to any state. The number of possible allelic states was set to 30. The effect of self-fertilisation was examined by doing simulations with proportion of self-fertilisation set to 0.9. Simulations were run for 2000 generations. In our simulations this D HT HS HS n n = ( ) ( ) − − − 1 1 Kronholm et al. BMC Genetics 2010, 11:33 http://www.biomedcentral. com/1471-2156/11/33 Page 3 of 14 was enough for FST to reach equilibrium. To simulate a realistic sampling situation, 30 individuals were finally sampled from ea