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Diploid male dynamics under different numbers of sexual alleles and male dispersal abilities

Abstract

Insects in the order Hymenoptera (bees, wasps and ants) present an haplodiploid system of sexual determination in which fertilized eggs become females and unfertilized eggs males. Under single locus complementary sex-determination (sl-CSD) system, the sex of a specimen depends on the alleles at a single locus: when diploid, an individual will be a female if heterozygous and male if homozygous. Significant diploid male (DM) production may drive a population to an extinction scenario called “diploid male vortex”. We aimed at studying the dynamics of populations of a sl-CSD organism under several combinations of two parameters: male flight abilities and number of sexual alleles. In these simulations, we evaluated the frequency of DM and a genetic diversity measure over 10,000 generations. The number of sexual alleles varied from 10 to 100 and, at each generation, a male offspring might fly to another random site within a varying radius R. Two main results emerge from our simulations: (i) the number of DM depends more on male flight radius than on the number of alleles; (ii) in large geographic regions, the effect of males flight radius on the allelic diversity turns out much less pronounced than in small regions. In other words, small regions where inbreeding normally appears recover genetic diversity due to large flight radii. These results may be particularly relevant when considering the population dynamics of species with increasingly limited dispersal ability (e.g., forest-dependent species of euglossine bees in fragmented landscapes)

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Notes

  1. This procedure becomes popular after Zipf (1949), although it was adopted before by Jean-Baptiste Estoup (1912), see Petruszewycz (1973), and also by Felix Auerbach (1913).

  2. This vortex could occur in our model only when the fraction of haploid males reaches the limit \(h^* = 0\), a situation that never occurred in our many simulations, even under minimal number of alleles \(A=2\) and minimal male flight radius \(R = 2\).

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Acknowledgments

We are grateful to Suzana Moss de Oliveira for a critical reading of the manuscript

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Correspondence to Paulo Murilo Castro de Oliveira.

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This article forms part of a special issue of Theory in Biosciences in commemoration of Olaf Breidbach.

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Faria, L.R.R., Soares, E.D.G., Carmo, E.d. et al. Diploid male dynamics under different numbers of sexual alleles and male dispersal abilities. Theory Biosci. 135, 111–119 (2016). https://doi.org/10.1007/s12064-016-0226-x

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  • DOI: https://doi.org/10.1007/s12064-016-0226-x

Keywords

  • Diploid male vortex
  • Haplodiploidy
  • Inbreeding
  • Hymenoptera
  • Population dynamics
  • Sl-CSD