Pim e del aar,* pablo burrac o and ivan gomez-mestre*†

1 and 2, and assuming a population size N of 1000.

0.1
0.0

1990 1995 2000 2005 2010 2015

Year
Fig. 3 The heterozygosity of neutral markers used in Q_ST–F_ST comparisons has increased over time. White dots and dashed regression line are allozymes; black dots and continuous regression line are microsatellites.

differentiate between the effects of mutation rate or popu-

lation size ⁄ migration rate on heterozygosity, we make use of the fact that most studies employed either allozymes or microsatellites as neutral markers, and that microsatellites on average have much higher mutation rates than allo- zymes (Ellegren 2004). If the variation among studies in heterozygosity is at least partly driven by mutation rate, then heterozygosity should be lower in studies using allo- zymes. Instead, if variation in heterozygosity is only because of variation in demography among studies, then studies using either allozymes or microsatellites should not differ in heterozygosity, because we have no reason to sus- pect systematic differences in demography. In all cases we assume that the molecular markers used are neutral (as did the original studies). In principle, selection on molecu- lar markers could also induce a correlation between hetero- zygosity and Q_ST–F_ST, but this would require that selection acted on the molecular markers in the majority of studies, so we refute this possibility a priori.

Methods and results
As a starting point for compiling published studies on the topic, we used the latest review of Q_ST–F_ST comparisons by Leinonen et al. (2008). We then further checked all articles that cited Leinonen et al. (2008) for relevancy and indepen- dently extracted values of F_ST and Q_ST when possible. Whenever we encountered a difference with values pub- lished in Leinonen et al. (2008) and the difference could not be resolved in favour of the values published in Lei- nonen et al. (2008), we retained the values extracted by us. In addition, we recorded the published values of within- population expected heterozygosity (H_WITHIN) when pro- vided. Most studies used either allozymes or microsatel- lites ( = STR or SSR markers). To allow for a meaningful comparison among marker types with known different average mutation rates, and because the calculation of H_WITHIN was sometimes methodologically quite different for certain (dominant) markers, the few studies using other types of markers (AFLP, RAPD, ESTP, RFLP, CAPS) were not further considered here. An overview of the final set of studies and values used in our analyses is presented in Table 1 (n = 44 studies, 40 species).

Figure 4 shows the relationship between the difference between Q_ST and F_ST and within-population heterozygosity (Fig. 4). The average Q_ST–F_ST difference across studies clearly lies above the Q_ST–F_ST = 0 line, supporting the con- clusion of Leinonen et al. (2008) that Q_ST is on average larger than F_ST. However, there is also a clear pattern in that the difference Q_ST–F_ST is positively related to heterozygosity. Dividing the studies into groups with heterozygosities either greater or smaller than 0.5, Q_ST–F_ST is significantly greater for studies with high heterozygosity (least squares means

0.261 ± 0.042 SE vs. 0.087 ± 0.038 SE; ANOVA: F_1,42 = 9.34, P = 0.004, R² = 0.18). Similarly, regression of Q_ST–F_ST on het- erozygosity yielded a positive slope (b = 0.277 ± 0.123 SE,

^{(b = 0.391 ± 0.198 SE, F}_1,26 ^{= 3.90, P = 0.059, R2 = 0.13).}

We calculated a simplified expected relationship between heterozygosity and the Q_ST–F_ST difference, using the data of these studies. For this, we assumed that the degree of quantitative and neutral divergence is constant across stud- ies, but that the actual value of F_ST decreases linearly with increasing heterozygosity. We established that Q_ST is indeed not related to heterozygosity (linear regression: F_1,42 = 0.084, P = 0.77, R² = 0.00) and used the mean of Q_ST as an estimate for quantitative divergence (0.341 ± 0.033

SE). As an estimate of mean neutral divergence, we used the intercept of the regression of F_ST on heterozygosity (0.320 ± 0.056 SE). This predicts the following relationship between heterozygosity and the Q_ST–F_ST difference: Q_ST– F_ST = 0.341 ) 0.320 * (1 ) H_WITHIN). This quantitative pre- diction matched the observed regression slope remarkably well (Fig. 4).

With respect to our first alternative explanation for a relationship between heterozygosity and the Q_ST–F_ST differ- ence, there was only a mild non-significant temporal trend for the difference Q_ST–F_ST (F_1,42 = 1.09, P = 0.30). Moreover, the inclusion of the continuous variable ¢year¢ in the model of the regression of Q_ST–F_ST on heterozygosity explained virtually no variance in Q_ST–F_ST (t₄₁ = )0.044, P = 0.97), whereas heterozygosity remained a very influential explan- atory variable (t₄₁ = 1.95, P = 0.058). With respect to our second alternative explanation, mean heterozygosity dif- fered substantially and significantly among studies using either microsatellites or allozymes (Fig. 3; microsatellites:

0.578 ± 0.035 SE, allozymes: 0.245 ± 0.046 SE, ANOVA:

F_1,42 = 33.4, P < 0.0001, R² = 0.44).

Discussion
Is there a bias?
Our main hypothesis is that much higher mutation rates in the neutral markers than in the quantitative genetic loci are causing a strong upward bias in Q_ST–F_ST.

Indeed, we found the positive correlation between het-

erozygosity and the difference Q_ST–F_ST that is predicted by this hypothesis. Moreover, the predicted quantitative rela- tionship between heterozygosity and Q_ST–F_ST based on this hypothesis shows a very good fit with the observed one (Fig. 4), suggesting that this hypothesis is a sufficient explanation for the observed pattern.

We found no significant temporal trend in Q_ST–F_ST, and time explained virtually no variation in Q_ST–F_ST indepen- dent of the effect of heterozygosity. Thus, the idea that the correlation between heterozygosity and Q_ST–F_ST is acciden- tally due to independent temporal trends (e.g. a shift towards markers with higher heterozygosity coinciding with a shift towards systems with higher Q_ST values) is not supported.

Variation in population size and ⁄ or migration rate among studies could also create a correlation between heterozygos-

_{F1,42 = 5.08, P = 0.03, R}² <sub>= 0.11), and a similar pattern was

ity and Q

–F , independent of variation in mutation rate</sub>

Table 1 Overview of studies and values included in our analyses. We only included studies based on allozymes (¢allo¢) or microsat- ellites (¢micro¢) and that provided estimates of F_ST (or a comparable measure of neutral population divergence), Q_ST and within-pop- ulation heterozygosity (H_WITHIN) based on the same, wild populations. G¢st is the unbiased estimator (G¢¢_ST) of Meirmans & Hedrick

2010; k is the number of study populations or regions. Some studies have multiple entries because they included several independent

comparisons, e.g. among populations within regions, and among regions. We excluded the studies on Tigriopus californicus (Edmands

& Harrison 2003) and Arabidopsis thaliana (Kuittinen et al. 1997) in our statistical analyses because they yielded theoretically impossi- ble values of G¢st and ⁄ or Jost’s D > 1

Species	FST	QST	HWITHIN	Jost’s D	G¢st	k	Year	Marker	References
Apodemus flavicollis	0.045	0.138	0.057	0.003	0.047	10	2006	allo	Wojcik et al. (2006)
Arabidopsis thaliana	1.000	0.885	0.000	1.000	1.000	4	1997	allo	Kuittinen et al. (1997)
Brassica insularis	0.210	0.080	0.367	0.205	0.332	4	2001	allo	Petit et al. (2001)
Carduelis chloris	0.030	0.300	0.025	0.001	0.031	12	1997	allo	Merila¨ (1997)
Centaurea corymbosa	0.360	0.341	0.200	0.187	0.450	4	2001	allo	Petit et al. (2001)
Daphnia obtusa	0.280	0.230	0.121	0.061	0.319	8	1993	allo	Spitze (1993)
Daphnia obtusa	0.290	0.290	0.493	0.455	0.573	8	1994	allo	Lynch & Spitze (1994)
Daphnia pulex	0.310	0.350	0.400	0.318	0.517	17	1999	allo	Lynch et al. (1999)
Daphnia pulicaria	0.270	0.526	0.150	0.070	0.318	14	2001	allo	Morgan et al. (2001)
Hordeum spontaneum	0.230	0.630	0.173	0.066	0.278	4	2005	allo	Volis et al. (2005)
Liatris scariosa	0.210	0.300	0.293	0.120	0.297	12	2005	allo	Gravuer et al. (2005)
Littorina saxatilis	0.095	0.253	0.328	0.077	0.141	3	2006	allo	Conde-Pad´ın et al. (2006)
Picea glauca	0.014	0.098	0.341	0.009	0.021	6	2001	allo	Jaramillo-Correa et al. (2001)
Salix viminalis	0.041	0.070	0.157	0.009	0.049	14	1996	allo	Lascoux et al. (1996)
Scabiosa canescens	0.164	0.096	0.273	0.089	0.226	6	1998	allo	Waldmann & Andersson (1998)
Scabiosa columbaria	0.123	0.453	0.306	0.074	0.177	6	1998	allo	Waldmann & Andersson (1998)
Scathophaga stercoraria	0.009	0.144	0.234	0.003	0.012	5	2008	allo	Demont et al. (2008)
Amphicarpaea edgeworthii	0.578	0.688	0.333	0.722	0.867	19	2009	micro	Liang et al. (2009)
Arabidopsis thaliana	0.600	0.630	0.346	0.866	0.707	12	2005	micro	Le Corre (2005)
Arabidopsis thaliana	0.890	0.820	0.062	0.602	0.949	9	2005	micro	Stenøien et al. (2005)
Arabidopsis thaliana	0.639	0.664	0.315	1.221	0.933	3	1997	micro	Kuittinen et al. (1997)
Brachionus plicatilis	0.482	0.218	0.355	0.615	0.747	6	2009	micro	Campillo et al. (2009)
Bufo calamita	0.030	0.260	0.638	0.068	0.083	5	2004	micro	Gomez-Mestre & Tejedo (2004)
Coregonus lavaretus	0.120	0.250	0.608	0.233	0.306	11	2005	micro	Østbye et al. (2005)
Corynopoma riisei	0.025	0.052	0.688	0.060	0.080	18	2010	micro	Arnqvist & Kolm (2010)
Cynopterus sphinx	0.030	0.030	0.755	0.109	0.122	8	2002	micro	Storz (2002)
Daphnia pulicaria	0.390	0.526	0.400	0.459	0.650	14	2001	micro	Morgan et al. 2001)
Eucalyptus globulus	0.090	0.129	0.750	0.330	0.360	10	2006	micro	Steane et al. (2006)
Ficedula hypoleuca	0.010	0.480	0.809	0.046	0.052	16	2009	micro	Lehtonen et al. (2009)
Gasterosteus aculeatus	0.190	0.540	0.653	0.490	0.548	10	2006	micro	Leinonen et al. (2006)
Gasterosteus aculeatus	0.080	0.140	0.788	0.369	0.377	8	2007	micro	Raeymaekers et al. (2007)
Gasterosteus aculeatus	0.150	0.800	0.710	0.457	0.517	18	2008	micro	Cano et al. (2008)
Hirundo rustica	0.001	0.268	0.920	0.017	0.013	3	2010	micro	Santure et al. (2010)
Osmerus mordax	0.024	0.550	0.640	0.087	0.067	2	2003	micro	Saint-Laurent et al. (2003)
Osmerus mordax	0.013	0.680	0.673	0.054	0.040	2	2003	micro	Saint-Laurent et al. (2003)
Primula sieboldii	0.172	0.227	0.670	0.526	0.521	5	2009	micro	Yoshida et al. (2009)
Rana arvalis	0.340	0.460	0.354	0.565	0.526	2	2007	micro	Knopp et al. (2007)
Rana temporaria	0.235	0.810	0.618	0.596	0.615	6	2003	micro	Palo et al. (2003)
Rana temporaria	0.058	0.265	0.580	0.102	0.138	6	2010	micro	Richter-Boix et al. (2010)
Salmo trutta	0.065	0.465	0.721	0.239	0.233	4	2008	micro	Jensen et al. (2008)
Salvelinus fontinalis	0.153	0.230	0.630	0.615	0.414	2	2005	micro	Perry et al. (2005)
Scatophaga stercoraria	0.010	0.144	0.797	0.050	0.049	5	2008	micro	Demont et al. (2008)
Thlaspi caerulescens	0.150	0.151	0.567	0.277	0.346	6	2007	micro	Jimenez-Ambriz et al. (2007)
Thymallus thymallus	0.100	0.350	0.150	0.029	0.118	3	2002	micro	Koskinen et al. (2002)
Tigriopus californicus	0.327	0.130	0.138	0.117	0.379	3	2003	micro	Edmands & Harrison (2003)
Tigriopus californicus	0.811	0.120	0.221	1.826	1.041	3	2003	micro	Edmands & Harrison (2003)
Tigriopus californicus	0.803	0.300	0.180	1.074	0.979	6	2003	micro	Edmands & Harrison (2003)
Tyto alba	0.011	0.353	0.657	0.023	0.032	18	2010	micro	Antoniazza et al. (2010)
Vitellaria paradoxa	0.047	0.189	0.320	0.026	0.069	11	2005	micro	Sanou et al. (2005)