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   . 1991 Dec;40(3):308-21.
   doi: 10.1016/0040-5809(91)90058-n.

Models on butterfly protandry: virgin females are at risk to die

   [36]C Zonneveld^ [37] 1 , [38]J A Metz
   Affiliations (BUTTON) Expand

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     * ^1 Department of Biology, Vrije Universiteit, Amsterdam, The Netherlands.

     * PMID: 1808754
     * DOI: [39]10.1016/0040-5809(91)90058-n

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Models on butterfly protandry: virgin females are at risk to die

   C Zonneveld et al. Theor Popul Biol. 1991 Dec.
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   . 1991 Dec;40(3):308-21.
   doi: 10.1016/0040-5809(91)90058-n.

Authors

   [43]C Zonneveld^ [44] 1 , [45]J A Metz

Affiliation

     * ^1 Department of Biology, Vrije Universiteit, Amsterdam, The Netherlands.

     * PMID: 1808754
     * DOI: [46]10.1016/0040-5809(91)90058-n

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Abstract

   Current models on protandry in butterflies assume that females are mated
   instantaneously upon eclosion. However, for most butterfly species this
   assumption is not realistic. In this paper a model is formulated in which the
   mating rate depends on both male and female density. Given the female presence
   curve, protandry is an evolutionarily stable strategy (ESS) for males. The
   evolutionarily stable amount of protandry decreases with increasing death rate
   and decreasing encounter rate. Given the male presence curve, protandry also is
   an ESS for females. However, male and female ESS are not identical; moreover, in
   the present model a simultaneous ESS does not exist. Protandry critically depends
   on the assumption that females mate only once, whereas males are capable of
   multiple mating. If females too are capable of multiple mating, absence of
   protandry is the ESS for males as well as females. The model predicts that
   protandry depends on population density: protandry should be more pronounced in
   populations with high density than in populations with low density. Protandry
   also depends on sex ratio. It becomes more pronounced when the proportion of
   males among emerging adults increases.

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