Abstracts of Posters 8-th European Conference on Mathematical ...

<strong>European</strong> <strong>Conference</strong> on Ma<strong>th</strong>ematical and Theoretical Biology 2011
Evolutionary Ecology; Wednesday, June 29, 14:30
Atsushi Yamauchi
Center for Ecological Research, Kyoto University
e-mail: a-yama@ecology.kyoto-u.ac.jp
Yutaka Kobayashi
Department <strong>of</strong> Biological Science, University <strong>of</strong> Tokyo
Joint evolution <strong>of</strong> sex ratio and reproductive group size
under local mate competition wi<strong>th</strong> inbreeding depression
Local mate competition (LMC) may involve some amount <strong>of</strong> inbreeding between
siblings. Because sib-mating is generally accompanied by inbreeding depression,
natural selection may favor a reduced rate <strong>of</strong> sib-mating, possibly affecting <strong>th</strong>e evolution
<strong>of</strong> sex ratio and reproductive group size. The present study <strong>th</strong>eoretically
investigated <strong>th</strong>e evolution <strong>of</strong> <strong>th</strong>ese traits under LMC in <strong>th</strong>e presence <strong>of</strong> inbreeding
depression. When <strong>th</strong>e reproductive group size evolves, <strong>th</strong>e determination mechanism
<strong>of</strong> sex ratio is important because <strong>th</strong>e time scale <strong>of</strong> <strong>th</strong>e sex ratio response to
reproductive group size can affect <strong>th</strong>e evolutionary process. We consider a spectrum
<strong>of</strong> sex ratio determination mechanisms from purely unconditional to purely
conditional, including intermediate modes wi<strong>th</strong> various relative streng<strong>th</strong>s <strong>of</strong> unconditional
and conditional effects. This analysis revealed <strong>th</strong>at bo<strong>th</strong> <strong>th</strong>e evolutionarily
stable reproductive group size and ratio <strong>of</strong> males increase wi<strong>th</strong> higher inbreeding
depression and wi<strong>th</strong> a larger relative streng<strong>th</strong> <strong>of</strong> an unconditional effect in sex ratio
determination. Unexpectedly, when <strong>th</strong>e sex ratio is controlled purely conditionally,
<strong>th</strong>e reproductive group size cannot exceed <strong>th</strong>ree even under <strong>th</strong>e severest level <strong>of</strong>
inbreeding depression (i.e., le<strong>th</strong>al effect). The present study reveals <strong>th</strong>e conditions
for LMC to evolve <strong>th</strong>rough <strong>th</strong>e analysis <strong>of</strong> <strong>th</strong>e joint evolution <strong>of</strong> reproductive group
size and sex ratio.
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