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Increase in ant density promotes dual effects on bee behaviour and plant reproductive performance

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Abstract

Floral rewards do not only attract pollinators, but also herbivores and their predators. Ants are attracted by extrafloral nectaries (EFNs), situated near flowers, and may interfere with the efficiency and behaviour of pollinators. We tested the hypothesis that the impacts of ant–pollinator interactions in plant–pollinator systems are dependent on (1) the seasonal activity of EFNs, which increase ant abundance closer to flowers; (2) consequently, an ant effect, where ants decrease the temporal niche overlap of bees due to predator avoidance; and (3) ant density, where higher densities may negatively affect plant–pollinator interactions and plant performance. We studied two ant–plant–pollinator systems based on Banisteriopsis campestris and Banisteriopsis malifolia plant species. The periods of high ant abundance coincided with plant species blooming. The presence of ants around flowers reduced the visitation rates of the smaller bees and the temporal niche overlap between bee species was not higher than randomly expected when ants had free access. Additionally, we observed variable ant effects on fruit set and duration of bee visits to both Malpighiaceae species when ant density was experimentally kept constant on branches, especially on B. campestris. Our goal was to show the dual role of ant density effects, especially because the different outcomes are not commonly observed in the same plant species. We believe that reduced temporal niche overlap between floral visitors due to ant presence provides an opportunity for smaller bees to improve compatible pollination behaviour. Additionally, we concluded that ant density had variable effects on floral visitor behaviours and plant reproductive performance.

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References

  • Agostinelli C, Lund U (2013) R package “circular”: Circular Statistics (version 0.4-7)

  • Albrecht M, Gotelli NJJ (2001) Spatial and temporal niche partitioning in grassland ants. Oecologia 126:134–141. doi:10.1007/s004420000494

    Article  CAS  PubMed  Google Scholar 

  • Altmann J (1974) Observational study of behavior: sampling methods. Behaviour 49:227–266. doi:10.1163/156853974X00534

    Article  CAS  PubMed  Google Scholar 

  • Alves-dos-Santos I, Machado IC, Gaglianone MC (2007) História natural de abelhas coletoras de óleo. Oecologia Bras 11:554–557

    Google Scholar 

  • Alves-Silva E (2011) Post fire resprouting of Banisteriopsis malifolia (Malpighiaceae) and the role of extrafloral nectaries on the associated ant fauna in a Brazilian Savanna. Sociobiology 55:327–339

    Google Scholar 

  • Alves-Silva E, Del-Claro K (2013) Effect of post-fire resprouting on leaf fluctuating asymmetry, extrafloral nectar, and ant–plant–herbivore interactions. Naturwissenschaften 100:525–532. doi:10.1007/s00114-013-1048-z

    Article  CAS  PubMed  Google Scholar 

  • Alves-Silva E, Del-Claro K (2016) On the inability of ants to protect their plant partners and the effect of herbivores on different stages of plant reproduction. Austral Ecol 41:263–272. doi:10.1111/aec.12307

    Article  Google Scholar 

  • Alves-Silva E, Bächtold A, Barônio GJ et al (2013a) Influence of Camponotus blandus (Formicinae) and flower buds on the occurrence of Parrhasius polibetes (Lepidoptera: Lycaenidae) in Banisteriopsis malifolia (Malpighiaceae). Sociobiology 60:30–34. doi:10.13102/sociobiology.v60i1.30-34

    Article  Google Scholar 

  • Alves-Silva E, Barônio GJ, Torezan-Silingardi HM, Del-Claro K (2013b) Foraging behavior of Brachygastra lecheguana (Hymenoptera: Vespidae) on Banisteriopsis malifolia (Malpighiaceae): extrafloral nectar consumption and herbivore predation in a tending ant system. Entomol Sci 16:162–169. doi:10.1111/ens.12004

    Article  Google Scholar 

  • Alves-Silva E, Bächtold A, Barônio GJ et al (2015) Ant–herbivore interactions in an extrafloral nectaried plant: are ants good plant guards against curculionid beetles? J Nat Hist 49:841–851. doi:10.1080/00222933.2014.954020

    Article  Google Scholar 

  • Assunção MA, Torezan-Silingardi HM, Del-Claro K (2014) Do ant visitors to extrafloral nectaries of plants repel pollinators and cause an indirect cost of mutualism? Flora Morphol Distrib Funct Ecol Plants 209:244–249. doi:10.1016/j.flora.2014.03.003

    Article  Google Scholar 

  • Baker-Méio B, Marquis RJ (2012) Context-dependent benefits from ant-plant mutualism in three sympatric varieties of Chamaecrista desvauxii. J Ecol 100:242–252. doi:10.1111/j.1365-2745.2011.01892.x

    Article  Google Scholar 

  • Barônio GJ, Torezan-Silingardi HM (2017) Temporal niche overlap and distinct bee ability to collect floral resources on three species of Brazilian Malpighiaceae. Apidologie 48:168–180. doi:10.1007/s13592-016-0462-6

    Article  Google Scholar 

  • Barônio GJ, Haleem MA, Marsaioli AJ, Torezan-Silingardi HM (2017) Characterization of Malpighiaceae flower-visitor interactions in a Brazilian savannah: how do floral resources and visitor abundance change over time. Flora 234:126–134. doi:10.1016/j.flora.2017.07.015

    Article  Google Scholar 

  • Bates D, Mächler M, Bolker B, Walker S (2015) Fitting linear mixed-effects models using lme4. J Stat Softw. doi:10.18637/jss.v067.i01

    Google Scholar 

  • Biesmeijer JC, Richter JAP, Smeets M, Sommeijer MJ (1999) Niche differentiation in nectar-collecting stingless bees: the influence of morphology, oral choice and interference competition. Ecol Entomol 24:380–388. doi:10.1046/j.1365-2311.1999.00220.x

    Article  Google Scholar 

  • Blüthgen N, Stork NE, Fiedler AK et al (2004) Bottom–up control and co-occurrence in complex communities: honeydew and nectar determine a rainforest ant mosaic. Oikos 106:344–358. doi:10.1111/j.0030-1299.2004.12687.x

    Article  Google Scholar 

  • Boas JCV, Fava WS, Laroca S, Sigrist MR (2013) Two sympatric Byrsonima species (Malpighiaceae) differ in phenological and reproductive patterns. Flora 208:360–369. doi:10.1016/j.flora.2013.05.003

    Article  Google Scholar 

  • Brito AF, Presley SJ, Santos GMM (2012) Temporal and trophic niche overlap in a guild of flower-visiting ants in a seasonal semi-arid tropical environment. J Arid Environ 87:161–167. doi:10.1016/j.jaridenv.2012.07.001

    Article  Google Scholar 

  • Bronstein JL (1994) Conditional outcomes in mutualistic interactions. Trends Ecol Evol 9:214–217. doi:10.1016/0169-5347(94)90246-1

    Article  CAS  PubMed  Google Scholar 

  • Byk J, Del Claro K (2010) Nectar- and pollen-gathering Cephalotes ants provide no protection against herbivory: a new manipulative experiment to test ant protective capabilities. Acta Ethol 3:33–38

    Article  Google Scholar 

  • Byk J, Del-Claro K (2011) Ant–plant interaction in the Neotropical savanna: direct beneficial effects of extrafloral nectar on ant colony fitness. Popul Ecol 53:327–332

    Article  Google Scholar 

  • Calixto ES, Lange D, Del-Claro K (2015) Foliar anti-herbivore defenses in Qualea multiflora Mart. (Vochysiaceae): changing strategy according to leaf development. Flora 212:19–23. doi:10.1016/j.flora.2015.02.001

    Article  Google Scholar 

  • Cappellari SC, Melo GAR, Aguiar AJC, Neff JL (2012) Floral oil collection by male Tetrapedia bees (Hymenoptera: Apidae: Tetrapedini). Apidologie 43:39–50. doi:10.1007/s13592-011-0072-2

    Article  Google Scholar 

  • Castro-Arellano I, Lacher TE, Willig MR, Rangel TF (2010) Assessment of assemblage-wide temporal niche segregation using null models. Methods Ecol Evol 1:311–318

    Google Scholar 

  • Cembrowski AR, Tan MG, Thomson JD, Frederickson ME (2014) Ants and ant scent reduce bumblebee pollination of artificial flowers. Am Nat 183:133–139. doi:10.1086/674101

    Article  PubMed  Google Scholar 

  • Cosacov A, Nattero J, Cocucci AA (2008) Variation of pollinator assemblages and pollen limitation in a locally specialized system: the oil-producing Nierembergia linariifolia (Solanaceae). Ann Bot 102:723–734. doi:10.1093/aob/mcn154

    Article  PubMed  PubMed Central  Google Scholar 

  • Crawley MJ (2012) The R book, 2nd edn. Wiley, England

    Book  Google Scholar 

  • Dáttilo W, Aguirre A, Flores-Flores RV et al (2015) Secretory activity of extrafloral nectaries shaping multitrophic ant–plant–herbivore interactions in an arid environment. J Arid Environ 114:104–109. doi:10.1016/j.jaridenv.2014.12.001

    Article  Google Scholar 

  • Dáttilo W, Aguirre A, De la Torre PL et al (2016) Trait-mediated indirect interactions of ant shape on the attack of caterpillars and fruits. Biol Lett 12:20160401. doi:10.1098/rsbl.2016.0401

    Article  PubMed  PubMed Central  Google Scholar 

  • Del-Claro K, Marquis RJ (2015) Ant species identity has a greater effect than fire on the outcome of an ant protection system in Brazilian Cerrado. Biotropica 47:459–467. doi:10.1111/btp.12227

    Article  Google Scholar 

  • Del-Claro K, Oliveira PS (2000) Conditional outcomes in a neotropical treehopper-ant association: temporal and species-specific variation in ant protection and hemipteran fecundity. Oecologia 124:156–165

    Article  CAS  PubMed  Google Scholar 

  • Del-Claro K, Rico-Gray V, Torezan-Silingardi HM et al (2016) Loss and gains in ant–plant interactions mediated by extrafloral nectar: fidelity, cheats, and lies. Insectes Soc 63:207–221. doi:10.1007/s00040-016-0466-2

    Article  Google Scholar 

  • Dworschak K, Blüthgen N (2010) Networks and dominance hierarchies: does interspecific aggression explain flower partitioning among stingless bees? Ecol Entomol 35:216–225. doi:10.1111/j.1365-2311.2010.01174.x

    Article  Google Scholar 

  • Ferreira CA, Torezan-Silingardi HM (2013) Implications of the floral herbivory on Malpighiacea plant fitness: visual aspect of the flower affects the attractiveness to pollinators. Sociobiology 60:323–328. doi:10.13102/sociobiology.v60i3.323-328

    Article  Google Scholar 

  • Fournier LA (1974) Un método cuantitativo para la medición de características fenológicas em árboles. Turrialba 24:422–423

    Google Scholar 

  • Galen C, Geib JC (2007) Density-dependent effects of ant on selection for bumblebee pollination in Polemonium viscosum. Ecology 88:1202–1209. doi:10.1890/06-1455

    Article  PubMed  Google Scholar 

  • Gonzálvez FG, Santamaría L, Corlett RT, Rodríguez-Gironés MA (2013) Flowers attract weaver ants that deter less effective pollinators. J Ecol 101:78–85. doi:10.1111/1365-2745.12006

    Article  Google Scholar 

  • Gottsberger G, Silberbauer-Gottsberger I (2006) Life in the Cerrado: a South American tropical seasonal vegetation. Origin, Structure, Dynamics and Plant Use, vol 1. Germany

  • Harder LD, Barrett SC (2006) Ecology and evolution of flowers. Oxford University Press, New York

    Google Scholar 

  • Holland JN, Chamberlain SA, Miller TEX (2011) Consequences of ants and extrafloral nectar for a pollinating seed-consuming mutualism: ant satiation, floral distraction or plant defense? Oikos 120:381–388

    Article  Google Scholar 

  • Janzen DH (1975) The ecology of plants in the tropics. Edward Arnold, Londres

    Google Scholar 

  • Junker RR, Blüthgen N (2010) Floral scents repel facultative flower visitors, but attract obligate ones. Ann Bot 105:777–782. doi:10.1093/aob/mcq045

    Article  PubMed  PubMed Central  Google Scholar 

  • Junker R, Chung AYC, Blüthgen N (2007) Interaction between flowers, ants and pollinators: additional evidence for floral repellence against ants. Ecol Res 22:665–670. doi:10.1007/s11284-006-0306-3

    Article  Google Scholar 

  • Kaminski LA, Freitas AVL (2010) Natural history and morphology of immature stages of the butterfly Allosmaitia strophius (Godart) (Lepidoptera: Lycaenidae) on flower buds of Malpighiaceae. Stud Neotrop Fauna Environ 45:11–19. doi:10.1080/01650520903495826

    Article  Google Scholar 

  • Karron JD, Holmquist KG, Flanagan RJ, Mitchell RJ (2009) Pollinator visitation patterns strongly influence among-flower variation in selfing rate. Ann Bot 103:1379–1383. doi:10.1093/aob/mcp030

    Article  PubMed  PubMed Central  Google Scholar 

  • Koptur S, Jones IM, Peña JE (2015) The influence of host plant extrafloral nectaries on multitrophic interactions: an experimental investigation. PLoS ONE 10:e0138157. doi:10.1371/journal.pone.0138157

    Article  PubMed  PubMed Central  Google Scholar 

  • Lach L (2007a) A mutualism with a native membracid facilitates pollinator displacement by Argentine ants. Ecology 88:1994–2004. doi:10.1890/06-1767.1

    Article  PubMed  Google Scholar 

  • Lach L (2007b) Argentine ants displace floral arthropods in a biodiversity hotspot. Divers Distrib 14:281–290. doi:10.1111/j.1472-4642.2007.00410.x

    Article  Google Scholar 

  • Lach L (2008) Floral visitation patterns of two invasive ant species and their effects on other hymenopteran visitors. Ecol Entomol 33:155–160. doi:10.1111/j.1365-2311.2007.00969.x

    Article  Google Scholar 

  • Lach L, Hobbs RJ, Majer JD (2009) Herbivory-induced extrafloral nectar increases native and invasive ant worker survival. Popul Ecol 51:237–243. doi:10.1007/s10144-008-0132-2

    Article  Google Scholar 

  • Lanan MC, Bronstein JL (2013) An ant’s-eye view of an ant-plant protection mutualism. Oecologia 172:779–790. doi:10.1007/s00442-012-2528-0

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Lange D, Del-Claro K (2014) Ant–plant interaction in a tropical savanna: may the network structure vary over time and influence on the outcomes of associations? PLoS ONE 9:e105574. doi:10.1371/journal.pone.0105574

    Article  PubMed  PubMed Central  Google Scholar 

  • Lange D, Dáttilo W, Del-Claro K (2013) Influence of extrafloral nectary phenology on ant-plant mutualistic networks in a neotropical savanna. Ecol Entomol 38:463–469. doi:10.1111/een.12036

    Article  Google Scholar 

  • Lange D, Calixto ES, Del-Claro K (2017) Variation in extrafloral nectary productivity influences the ant foraging. PLoS ONE 12:e0169492. doi:10.1371/journal.pone.0169492

    Article  PubMed  PubMed Central  Google Scholar 

  • Li J, Wang Z, Tan K et al (2014) Giant Asian honeybees use olfactory eavesdropping to detect and avoid ant predators. Anim Behav 97:69–76. doi:10.1016/j.anbehav.2014.08.015

    Article  Google Scholar 

  • Lunau K, Unseld K, Wolter F (2009) Visual detection of diminutive floral guides in the bumblebee Bombus terrestris and in the honeybee Apis mellifera. J Comp Physiol A 195:1121–1130. doi:10.1007/s00359-009-0484-x

    Article  Google Scholar 

  • Mamede MCH, Amorim AM, Sebastiani R (2016) Malpighiaceae. In: List. Espécies da Flora do Bras. Accessed 10 Aug 2017

  • Mello MAR, Bezerra ELS, Machado IC (2013) Functional roles of centridini oil bees and Malpighiaceae oil flowers in biome-wide pollination networks. Biotropica 45:45–53. doi:10.1111/j.1744-7429.2012.00899.x

    Article  Google Scholar 

  • Mendes FN, Rêgo MMC, Albuquerque PMC (2011) Fenologia e biologia reprodutiva de duas espécies de Byrsonima Rich. (Malpighiaceae) em área de Cerrado no Nordeste do Brasil. Biota Neotrop 11:103–115. doi:10.1590/S1676-06032011000400011

    Article  Google Scholar 

  • Mitchell RJ, Irwin RE, Flanagan RJ, Karron JD (2009) Ecology and evolution of plant–pollinator interactions. Ann Bot 103:1355–1363. doi:10.1093/aob/mcp122

    Article  PubMed  PubMed Central  Google Scholar 

  • Nakagawa S, Schielzeth H (2013) A general and simple method for obtaining R 2 from generalized linear mixed-effects models. Methods Ecol Evol 4:133–142. doi:10.1111/j.2041-210x.2012.00261.x

    Article  Google Scholar 

  • Ness JH (2006) A mutualism’s indirect costs: the most aggressive plant bodyguards also deter pollinators. Oikos 113:506–514

    Article  Google Scholar 

  • Nogueira A, Rey PJ, Alcántara JM et al (2015) Geographic mosaic of plant evolution: extrafloral nectary variation mediated by ant and herbivore assemblages. PLoS ONE 10:1–24. doi:10.1371/journal.pone.0123806

    Google Scholar 

  • Peter CI, Johnson SD (2008) Mimics and magnets: the importance of color and ecological facilitation in floral deception. Ecology 89:1583–1595. doi:10.1890/07-1098.1

    Article  PubMed  Google Scholar 

  • Pianka ER (1973) The structure of lizard communities. Annu Rev Ecol Syst 4:53–74

    Article  Google Scholar 

  • Polatto LP, Chaud-Netto J, Alves-Junior VV (2014) Influence of abiotic factors and floral resource availability on daily foraging activity of bees. J Insect Behav 27:593–612. doi:10.1007/s10905-014-9452-6

    Article  Google Scholar 

  • Rech AR, Kayna A, Oliveira PE, Machado IC (2014) Biologia da polinização. Ministério do Meio Ambiente, Brasília

    Google Scholar 

  • Renault CK, Buffa LM, Delfino MA (2005) An aphid–ant interaction: effects on different trophic levels. Ecol Res 20:71–74. doi:10.1007/s11284-004-0015-8

    Article  Google Scholar 

  • Réu WF, Del-Claro K, Reu WF (2005) Natural history and biology of Chlamisus minax Lacordaire (Chrysomelidae: Chlamisinae). Neotrop Entomol 34:357–362

    Article  Google Scholar 

  • Santos GMM, Carvalho CAL, Aguiar CML et al (2013) Overlap in trophic and temporal niches in the flower-visiting bee guild (Hymenoptera, Apoidea) of a tropical dry forest. Apidologie 44:64–74. doi:10.1007/s13592-012-0155-8

    Article  Google Scholar 

  • Schäffler I, Dötterl S (2011) A day in the life of an oil bee: phenology, nesting, and foraging behavior. Apidologie 42:409–424. doi:10.1007/s13592-011-0010-3

    Article  Google Scholar 

  • Schoereder J, Sobrinho T, Madureira M et al (2010) The arboreal ant community visiting extrafloral nectaries in the Neotropical cerrado savanna. Terr Arthropod Rev 3:3–27. doi:10.1163/187498310X487785

    Article  Google Scholar 

  • Shenoy M, Radhika V, Satish S, Borges RM (2012) Composition of extrafloral nectar influences interactions between the myrmecophyte Humboldtia brunonis and its ant associates. J Chem Ecol 38:88–99. doi:10.1007/s10886-011-0052-z

    Article  CAS  PubMed  Google Scholar 

  • Sigrist MR, Sazima M (2004) Pollination and reproductive biology of 12 species of neotropical malpighiaceae: stigma morphology and its implications for the breeding system. Ann Bot 94:33–41. doi:10.1093/aob/mch108

    Article  PubMed  PubMed Central  Google Scholar 

  • Stefani V, Pires TL, Torezan-Silingardi HM, Del-Claro K (2015) Beneficial effects of ants and spiders on the reproductive value of Eriotheca gracilipes (Malvaceae) in a tropical savanna. PLoS ONE 10:e0131843. doi:10.1371/journal.pone.0131843

    Article  PubMed  PubMed Central  Google Scholar 

  • TeamCore-R (2016) A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

    Google Scholar 

  • Torezan-Silingardi HM (2012) Flores e animais: uma introdução à história natural da polinização. In: Del Claro K, Torezan-Silingardi HM (eds) Ecologia evolutiva das interações plantas-animais: uma abordagem ecológico-evolutiva. Technical Books Editora, Rio de Janeiro, pp 111–139

    Google Scholar 

  • Velasque M, Del-Claro K (2016) Host plant phenology may determine the abundance of an ecosystem engineering herbivore in a tropical savanna. Ecol Entomol 41:421–430. doi:10.1111/een.12317

    Article  Google Scholar 

  • Vilela AA, Torezan-Silingardi HM, Del Claro K (2014) Conditional outcomes in ant-plant–herbivore interactions influenced by sequential flowering. Flora (Jena) 209:359–366. doi:10.1016/j.flora.2014.04.004

    Article  Google Scholar 

  • Vogel S (1974) Olblumen und olsammelnde Bienen. Trop und Subtrop Pflanzenwelt 7:285–547. doi:10.1002/fedr.19770880110

    Google Scholar 

  • Vogel S (1990) History of the Malpighiaceae in the light of pollination ecology. Mem N Y Bot Gard 55:130–142

    Google Scholar 

  • Wagner D, Kay A (2002) Do extrafloral nectaries distract ants from visiting flowers? An experimental test of an overlooked hypothesis. Evol Ecol Res 4:293–305

    Google Scholar 

  • Wardhaugh CW (2015) How many species of arthropods visit flowers? Arthropod Plant Interact 9:547–565. doi:10.1007/s11829-015-9398-4

    Article  Google Scholar 

  • Zar JH (2010) Biostatistical analysis. Pearson Prentice Hall, New Jersey

    Google Scholar 

  • Zuur AF, Ieno EN, Walker NJ et al (2009) Mixed effects and extensions in ecology with R. Springer, New York

    Book  Google Scholar 

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Acknowledgements

The authors are grateful to Clube de Caça e Pesca Itororó de Uberlândia (CCPIU) for making the ecological reserve available and for the receptivity of the staff. The authors are also grateful to Dr. Helena Maura Torezan-Silingardi and Dr. Vinícius Lourenço Garcia Brito from Universidade Federal de Uberlândia (UFU) and to Dr. Wesley Dáttilo from Instituto de Ecología (INECOL) for useful corrections and suggestions to the manuscript, and to Victor Aguiar de Souza Penha for his corrections and suggestions during the English review. GJB is also grateful to the Brazilian funding agency Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for the PhD scholarship granted from April 2013 to March 2017. KDC is thankful to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Amparo à Pesquisa de Minas Gerais (FAPEMIG) for the financial support.

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    Gudryan J. Barônio & Kleber Del-Claro

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Barônio, G.J., Del-Claro, K. Increase in ant density promotes dual effects on bee behaviour and plant reproductive performance. Arthropod-Plant Interactions 12, 201–213 (2018). https://doi.org/10.1007/s11829-017-9573-x

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