Supplementary material 1
One potential consequence of unreplicated artificial selection experiments is the excess of
false positive results. This problem has been addressed in papers by N. D. Henderson [1] [2]
and Konarzewski et al. [3] where it is suggested that effect size can be used to identify false
positive associations between the selected trait and the secondary correlated trait, where the
inbreeding coefficient (F) and the heritability (h2) of the secondary traits were accounted for.
Thus, in order to have an indication of whether the observed differentiation in telomere
length was caused by genetic drift or could be ascribed to genetic correlations with the trait
under selection (tarsus length) we parameterized the models by Henderson [1] in alignment
with Konarzewski et al. [3]. This involved estimating the magnitude of the separation in
telomere length between 2002 and 2005 as the standard phenotypic deviation (d) according to
eqn. 14 in Konarzewski et al. [3] as well as estimating the 95% confidence interval (95% CI)
in telomere length resulting from differentiation due to genetic drift and sampling error
between 2002 and 2005 (i.e. assuming the genetic correlation between tarsus length and
telomere length to be zero) according to eqn. 17 in Konarzewski et al. [3] .
In order to obtain a measure of F we used the inbreeding coefficient previously
estimated among 5 islands (from our main house sparrow study area at Helgeland ca 170 km
further north from Leka) where the level reported from all islands pooled was found to be F =
0.05 [4].
Obtaining a measure of the heritability in telomere length was trickier, as no such
estimates have been reported in house sparrow populations, and estimates on narrow sense
heritability (h2) in birds are so far few. Some studies has found that telomere length is more
related to mothers than fathers using parent – offspring regression, however, such studies
does not properly account for environmental effects and the relatedness of individuals.
However, Asgahar et al. 2014 [5] applied the ‘animal model’ and found heritability for
telomere length to be h2 = 0.35 in great reed warblers (Acrocephalus arundinaceus) in
Sweden after accounting for maternal effects. We applied their estimate of heritability to
parameterize eqn. 17 in Konarzewski et al. [3], as this estimate (to our knowledge) is the only
heritability estimate from which the relatedness among individuals (i.e. pedigree) and the
environmental effects are thoroughly accounted for by applying the animal model. Thus we
implicitly assumed that the heritability estimate for telomere length in reed warblers may be
similar also for other passerines, such as house sparrows.
Accordingly, we estimated the magnitude of the separation in telomere length
between 2002 and 2005 as the standard phenotypic deviation (d) according to eqn. (14) in
Konarzewski et al. [3] and found this to be d = 1.15. We then estimated the 95% confidence
interval (95% CI) in telomere length resulting from differentiation due to genetic drift and
sampling error between 2002 and 2005 (i.e. assuming the genetic correlation between tarsus
length and telomere length to be zero) according to eqn. 17 in Konarzewski et al. [3] and
found this to be 95% CI = 0.83. Thus, the magnitude of differentiation (d) is outside the 95 %
confidence interval which indicates that the observed differentiation in telomere length is
larger then what can be expected by drift alone. Accordingly, this supported the hypothesis
that a negative genetic correlation between the trait under selection (tarsus size) caused the
observed reduction in telomere length at Leka 2005 compared to 2002. The estimates of d
and 95% CI lie typically within the magnitude of other comparable studies, where genetic
correlations explain the change in a secondary character in artificial selection experiments
(see table 3 in Konarzewski et al. [3] ). Our result is of course only indicative as it is based on
the best available estimates of F and h2 and the 95% CI is sensible to variation in h2, which
may deviate from the ones in the house sparrow population at Leka. For further discussions
see Henderson [1] and Konarzewski et al. [3].
References
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