3
6
9
Supporting Information
Table SI 1. F st
estimates for all used loci and years (upper right half, in bold), and pairwise P-values based on 3000 permutations (bottom left half, in italics). Indicative adjusted nominal level (5%) for
multiple comparisons is P = 0.0167, calculated in FSTAT 2.93 (Goudet et al. 1996). The population
structure difference between 1999 and both 2008 and 2009, but did not differ between 2008 and
2009.
Year 1999 2008 2009
1999
2008 0.00033
0.0090
2009 0.00267 0.59800
0.0069
-0.0013

12
15
18
Table SI 2. Performance of different relatedness estimators (r) based on Siberian jays included in our analyses. Simulation performed in the Software
Coancestry (Wang 2011a) of the mean and variance of r of N = 1000 offspring and N = 1000 unrelated individuals using our data. Dyad Maximum
Likelihood (DyadML) and Ritland’s estimator (Ritland) were closest to the expected r of 0.5 for parent-offspring dyads, and thus we used these
estimators in our analyses (Taylor 2015). The simulations reveal a small standard deviation around the estimated mean relatedness (variance =
0.006-0.04 for offspring; variance = 0.003-0.015 for unrelated individuals) for DyadML and Ritland, reflecting that we used 24 polymorphic markers.
The larger variance for r calculations of offspring based on the Ritland reflects that this estimator is sensitive to rare alleles (Wang 2011b) and thus,
performs better for unrelated individuals than related individuals. kinship category parent-offspring
1999
2008-2009 breeder-immigrant
1999
2008-2009
Ritland DyadML TrioML LynchRd QuellerGt LynchLi
0.451±0.044 0.451±0.006 0.433±0.006 0.408±0.015 0.426±0.009
0.460±0.010 0.471±0.006 0.452±0.007 0.382±0.022 0.423±0.008
0.416±0.010
0.412±0.009
0.009±0.015 0.0466±0.004 0.034±0.003 0.005±0.009 -0.014±0.016 -0.029±0.019
0.008±0.014 0.0409±0.003 0.029±0.002 0.002±0.006 -0.023±0.015 -0.040±0.017
Wang
0.427±0.008
0.426±0.007
-0.018±0.018
-0.026±0.016

21
24
Table SI 3. Observed mean values and variance of the different estimators for parent-retained offspring and breeder-immigrants dyads (values for both male breeder vs non-breeder and female breeder vs non-breeder and thus the sample size is larger than the number of retained offspring
respectively immigrants). The low r estimates of offspring based on the Ritland reflects that this estimator is sensitive to rare alleles (Wang 2011b)
and thus, performs better for unrelated individuals than related individuals. kinship category Ritland DyadML TrioML LynchRd QuellerGt LynchLi Wang parent-offspring
12 0.336 ± 0.014 0.472 ± 0.004 0.465 ± 0.004 0.423 ± 0.014 0.454 ± 0.009 0.467 ± 0.007 0.46 ± 0.005
42 breeder-immigrant
0.411 ± 0.04 0.496 ± 0.003 0.479 ± 0.003 0.464 ± 0.018 0.465 ± 0.007 0.478 ± 0.005 0.483 ± 0.005
25 -0.073 ± 0.013 0.012 ± 0.001 0.008 ± 0 -0.052 ± 0.008 -0.056 ± 0.016 -0.109 ± 0.029 -0.125 ± 0.022
66 0.001 ± 0.008 0.047 ± 0.004 0.036 ± 0.003 0.002 ± 0.007 0.009 ± 0.017 -0.005 ± 0.017 -0.017 ± 0.017

27
30
33
36
39
42
Table SI 4. Person’s product-moment correlation coefficients (Pearson’s R) between the different relatedness estimates for female breeder – non-breeder dyads (upper right half) and male breeder
– non-breeder dyads included in our analyses (bottom left half). All r values are highly correlated.
r estimator DyadML LynchLi LynchRd QuellerGt Ritland TrioML Wang
DyadML
LynchLi m\f
0.926
0.932 m\f
0.962
0.912
0.939
0.980
0.898
0.859
0.997
0.926
0.944
0.972
LynchRd
QuellerGt
Ritland
TrioML
Wang
0.936 0.905 m\f
0.836 0.825 0.919
0.997 0.917 0.924
0.939 0.985 0.907
0.922 0.954 0.957 0.937
0.935 0.983 0.907 m\f
0.829
0.927
0.971
0.867 m\f
0.825
0.823
0.933
0.891 m\f
0.930
0.959
0.878
0.939 m\f
References
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Taylor HR (2015) The use and abuse of genetic marker‐based estimates of relatedness and inbreeding.
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Wang J (2011a) COANCESTRY: a program for simulating, estimating and analysing relatedness and inbreeding coefficients. Molecular Ecology Resources 11, 141-145.
Wang J (2011b) Unbiased relatedness estimation in structured populations. Genetics 187, 887-901.