Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Paper
  • Published:
Theory in Biosciences Aims and scope Submit manuscript

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)

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

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 \(R = 2\).

References

  • Aguiar WM, Sofia SH, Melo GAR, Gaglianone MC (2015) Changes in orchid bee communities across forest-agroecosystem boundaries in Brazilian Atlantic Forest landscapes. Environ Entomol 44:1465–1471. doi:10.1093/ee/nvv130

    Article  PubMed  Google Scholar 

  • Antolin MF, Strand MR (1992) Mating system of Bracon hebetor (Hymenoptera, Braconidae). Ecol Entomol 17:1–7

    Article  Google Scholar 

  • Auerbach F (1913) Das Gesetz der Bevlkerungskonzentration. Petermanns Geogr Mitt 59:73–76

    Google Scholar 

  • Beye M, Hasselmann M, Fondrk MK, Page RE Jr, Omholt SW (2003) The gene csd is the primary signal for sexual development in the honeybee and encodes an SR-type protein. Cell 114:419–429

    Article  CAS  PubMed  Google Scholar 

  • Butcher RDJ, Whitfield WGF, Hubbard SF (2000) Complementary sex determination in the genus Diadegma (Hymenoptera: Ichneumonidae). J Evolution Biol 13:593–606

    Article  Google Scholar 

  • Conwan DP, Stahlhut JK (2004) Functionally reproductive diploid and haploid males in an inbreeding hymenopteran with complementary sex determination. PNAS 101:10374–10379

    Article  Google Scholar 

  • Cook JM (1993) Sex determination in the Hymenoptera: a review of models and evidence. Heredity 71:421–436

    Article  Google Scholar 

  • Cook JM, Crozier RH (1995) Sex determination and population biology in the Hymenoptera. Trends Ecol Evol 10:281–286

    Article  CAS  PubMed  Google Scholar 

  • Darrouzet E, Gévar JM, Guignard Q, Aron S (2015) Production of early diploid males by European colonies of the invasive hornet Vespa velutina nigrithorax. PLOS One 10:e0136680

    Article  PubMed  PubMed Central  Google Scholar 

  • de Oliveira PMC, de Oliveira SM (2010) Física em Computadores, Livraria da Física Editora, São Paulo (in Portuguese, but with routines presented in C computer language)

  • Dick CW, Roubik DW, Gruber KF, Bermingham E (2004) Long-distance gene flow and cross-Andean dispersal of lowland rainforest bees (Apidae: Euglossini) revealed by comparative mitochondrial DNA phylogeography. Mol Ecol 13:3775–3785

    Article  CAS  PubMed  Google Scholar 

  • Duchateau MJ, Hoshiba H, Velthuis HHW (1994) Diploid males in the bumble bee Bombus terrestris: sex determination, sex alleles and viability. Entomol Exp Appl 71:263–269. doi:10.1111/j.1570-7458.1994.tb01793.x

    Article  Google Scholar 

  • Dudley R (1995) Extraordinary flight performance of orchid bees (Apidae: Euglossini) hovering in heliox (80 % He // 20 % O\(_2\)). J Exp Biol 198:1065–1070

    PubMed  Google Scholar 

  • Elias J, Mazzi D, Dorn S (2009) No need to discriminate? Reproductive diploid males in a parasitoid with complementary sex determination. PLoS One 4:e6024

    Article  PubMed  PubMed Central  Google Scholar 

  • Estoup JB (1912) Gammes sténographiques. In: Recueil de textes choisis pour l’acquisition méthodique de la vitesse, précédé d’une introduction par, 3e édition. Institut Stenographique, Paris, pp 140

  • Giangarelli DC, Freiria GA, Ferreira DG, Aguiar WM, Penha RES, Alves AN, Gaglianone MC, Sofia SH (2015) Orchid bees: a new assessment on the rarity of diploid males in populations of this group of Neotropical pollinators. Apidologie 46:606–617

    Article  Google Scholar 

  • Gu HN, Dorn S (2003) Mating system and sex allocation in the gregarious parasitoid Cotesia glomerata. Anim Behav 66:259–64

    Article  Google Scholar 

  • Harpur BA, Sobhani M, Zayed A (2012) A review of the consequences of complementary sex determination and diploid male production on mating failures in the Hymenoptera. Entomol Exp Appl 146:156–164. doi:10.1111/j.1570-7458.2012.01306.x

    Article  Google Scholar 

  • Heimpel GE, de Boer JG (2008) Sex determination in the Hymenoptera. Ann Rev Entomol 53:209–230

    Article  CAS  Google Scholar 

  • Hein S, Poethke HJ, Dorn S (2009) What stops the ’diploid male vortex’? A simulation study for species with single locus complementary sex determination. Ecol Model 220:1663–1669

    Article  Google Scholar 

  • Kukuk PF, May B (1990) Diploid males in a primitively eusocial bee, Lasioglossum ( Dialictus) zephyrum (Hymenoptera: Halictidae). Evolution 44:1552–1558

    Article  Google Scholar 

  • López-Uribe MM, Almanza MT, Ordoñez M (2007) Diploid male frequencies in Colombian populations of euglossine bees. Biotropica 39:660–662

    Article  Google Scholar 

  • López-Uribe MM, Morreale SJ, Santiago CK, Danforth BN (2015) Nest suitability, fine-scale population structure and male-mediated dispersal of a solitary ground nesting bee in an urban landscape. PLoS One 10:e0125719. doi:10.1371/journal.pone.0125719

    Article  PubMed  PubMed Central  Google Scholar 

  • Ma W-J, Kuijper B, de Boer JG, van de Zande L, Beukeboom LW, Wertheim B, Pannebakker BA (2013) Absence of complementary sex determination in the parasitoid wasp genus Asobara (Hymenoptera: Braconidae). PLoS One 8:e60459. doi:10.1371/journal.pone.0060459

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Metzger M, Bernstein C, Hoffmeister TS, Desouhant E (2010) Does kin recognition and sib-mating avoidance limit the risk of genetic incompatibility in a parasitic wasp? PLoS One 5:e13505

    Article  PubMed  PubMed Central  Google Scholar 

  • Milet-Pinheiro P, Schlindwein C (2005) Do euglossine males (Apidae, Euglossini) leave tropical rainforest to collect fragrances in sugarcane monocultures? Rev Bras Zool 22:853–858

    Article  Google Scholar 

  • Morato EF, Martins RP (2006) An overview of proximate factors affecting the nesting behavior of solitary wasps and bees (Hymenoptera: Aculeata) in preexisting cavities in wood. Neotrop Entomol 35:285–298

    Article  PubMed  Google Scholar 

  • Nowak MA, Tarnita CE, Wilson EO (2010) The evolution of eusociality. Nature 466:1057–1062

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ode PJ, Antolin MF, Strand MR (1995) Brood-mate avoidance in the parasitic wasp Bracon hebetor Say. Anim Behav 49:1239–1248

    Article  Google Scholar 

  • Owen RE, Packer L (1994) Estimation of the proportion of diploid males in populations of Hymenoptera. Heredity 72:219–227

    Article  Google Scholar 

  • Petruszewycz M (1973) L’histoire de la loi d’Estoup-Zipf: documents. Math Sci Hum 44:41–56

    Google Scholar 

  • Rosa JF, Ramalho M, Monteiro D, Silva MD (2015) Permeability of matrices of agricultural crops to Euglossina bees (Hymenoptera, Apidae) in the Atlantic Rain Forest. Apidologie 46:691–702

    Article  Google Scholar 

  • Ross KG, Vargo EL, Keller L, Trager JC (1993) Effect of founder event on variation in the genetic sex-determining system of the fire ant Solenopsis invicta. Genetics 135:843–854

    CAS  PubMed  PubMed Central  Google Scholar 

  • Roubik DW, Weight LA, Bonilla MA (1996) Population genetics, diploid males, and limits to social evolution of euglossine bees. Evolution 50:931–935

    Article  Google Scholar 

  • Ruf D, Dorn S, Mazzi D (2011) Females leave home for sex: natal dispersal in a parasitoid with complementary sex determination. Anim Behav 81:1083–1089

    Article  Google Scholar 

  • Sá Martins JS, de Oliveira PMC (2004) Computer simulations of statistical models and dynamic complex systems. Braz J Phys 34:1077

    Article  Google Scholar 

  • Stouthamer R, Luck RF, Werren JH (1992) Genetics of sex determination and the improvemen of biological control using parasitoids. Environ Entomol 21:427–435

    Article  Google Scholar 

  • Takahashi NC, Peruquetti RC, Del Lama MA, Campos LAO (2001) A reanalysis of diploid male frequencies in euglossine bees (Hymenoptera: Apidae). Evolution 55:1897–1899

    Article  CAS  PubMed  Google Scholar 

  • Tonhasca A, Albuquerque GS, Blackmer JL (2002) Dispersal of euglossine bees between fragments of the Brazilian Atlantic Forest. J Trop Ecol 19:99–102

    Article  Google Scholar 

  • van Wilgenburg E, Driessen G, Beukeboom LW (2006) Single locus complementary sex determination in Hymenoptera: an ’unintelligent’ design? Front Zool 3:1–15

    Article  PubMed  PubMed Central  Google Scholar 

  • Whiting PW (1943) Multiple alleles complementary sex determination of Habrobracon. Genetics 28:365–382

    CAS  PubMed  PubMed Central  Google Scholar 

  • Wikelski M, Moxley J, Eaton-Mordas A, Lpez-Uribe MM, Holland R, Moskowitz D, Roubik DW, Kays R (2010) Large-range movements of Neotropical orchid bees observed via radio telemetry. PLoS One 5:e10738

    Article  PubMed  PubMed Central  Google Scholar 

  • Wu Z, Hopper KR, Ode PJ, Fuester RW, Tuda M, Heimpel GE (2005) Single-locus complementary sex determination absent in Heterospilus prosopidis (Hymenoptera: Braconidae). Heredity 95:228–234

    Article  CAS  PubMed  Google Scholar 

  • Yokoyama S, Nei M (1979) Population dynamics of sex-determining alleles in honey bees and self-incompatibility alleles in plants. Genetics 91:609–626

    CAS  PubMed  PubMed Central  Google Scholar 

  • Zayed A, Constantin SA, Packer L (2007) Successful biological invasion despite a severe genetic load. PLoS One 2:e868

    Article  PubMed  PubMed Central  Google Scholar 

  • Zayed A, Packer L (2001) High levels of diploid male production in a primitively eusocial bee (Hymenoptera: Halictidae). Heredity 87:631–636

    Article  CAS  PubMed  Google Scholar 

  • Zayed A, Packer L (2005) Complementary sex determination substantially increases extinction proneness of haplodiploid populations. PLOS One 102:10742–10746

    CAS  Google Scholar 

  • Zayed A, Roubik DW, Packer L (2004) Use of diploid male frequency data as an indicator of pollinator decline. Proc R Soc Lond B Biol Sci 271:S9–S12

    Article  Google Scholar 

  • Zipf GK (1949) Human behavior and the principle of least effort. Addison-Wesley, Oxford

    Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. Instituto Latino-Americano de Ciências da Vida e da Natureza, Universidade Federal da Integração Latino-Americana, Av. Tancredo Neves 6731, Foz do Iguaçu, PR, 85.867-970, Brazil

    Luiz R. R. Faria, Elaine Della Giustina Soares & Eduardo do Carmo

  2. Instituto Mercosul de Estudos Avançados, Universidade Federal da Integração Latino-Americana, Av. Tancredo Neves 6731, Foz do Iguaçu, PR, 85.867-970, Brazil

    Paulo Murilo Castro de Oliveira

  3. Instituto de Física, Universidade Federal Fluminense, Av. Litorânea s/n, Niterói, RJ, 24210-340, Brazil

    Paulo Murilo Castro de Oliveira

Authors
  1. Luiz R. R. Faria
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elaine Della Giustina Soares
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eduardo do Carmo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Paulo Murilo Castro de Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paulo Murilo Castro de Oliveira.

Additional information

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

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

Keywords

Search

Navigation