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=== Heritability and reproductive advantage === There is evidence to support that antler size influences mate selection in the red deer, and has a heritable component. Despite this, a 30-year study showed no shift in the median size of antlers in a population of red deer.<ref name="Kruuk">{{cite journal|last1=Kruuk|first1=Loeske E. B.|author-link=Loeske Kruuk|last2=Slate|first2=Jon|last3=Pemberton|first3=Josephine M.|last4=Brotherstone|first4=Sue|last5=Guinness|first5=Fiona|last6=Clutton-Brock|first6=Tim|year=2002|title=Antler Size in Red Deer: Heritability and Selection but No Evolution|url=https://www.researchgate.net/publication/11103156|url-status=live|journal=Evolution|volume=56|issue=8|pages=1683β95|doi=10.1111/j.0014-3820.2002.tb01480.x|pmid=12353761|archive-url=https://web.archive.org/web/20160916134423/https://www.researchgate.net/profile/Loeske_Kruuk/publication/11103156_Antler_size_in_red_deer_heritability_and_selection_but_no_evolution/links/54478d6b0cf22b3c14e0ea12.pdf|archive-date=September 16, 2016|via=|s2cid=33699313}}</ref> The lack of response could be explained by environmental covariance, meaning that lifetime breeding success is determined by an unmeasured trait which is phenotypically correlated with antler size but for which there is no [[genetic correlation]] of antler growth.<ref name="Kruuk"/> Alternatively, the lack of response could be explained by the relationship between heterozygosity and antler size, which states that males heterozygous at multiple loci, including MHC loci, have larger antlers.<ref name="Gonzalez">{{cite journal |doi=10.1093/jhered/esq049 |pmid=20478822 |title=Low Heterozygosity at Microsatellite Markers in Iberian Red Deer with Small Antlers |journal=Journal of Heredity |volume=101 |issue=5 |pages=553β61 |year=2010 |last1=Perez-Gonzalez |first1=J. |last2=Carranza |first2=J. |last3=Torres-Porras |first3=J. |last4=Fernandez-Garcia |first4=J. L. |doi-access=free }}</ref> The evolutionary response of traits that depend on heterozygosity is slower than traits that are dependent on additive genetic components and thus the evolutionary change is slower than expected.<ref name="Gonzalez"/> A third possibility is that the costs of having larger antlers (resource use, and mobility detriments, for instance) exert enough selective pressure to offset the benefit of attracting mates; thereby stabilizing antler size in the population.
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