The University of Chicago Explaining Variation in the Effect of Floral Density on Pollinator Visitation. Author(s): Carla J. Essenberg Reviewed work(s): Source: The American Naturalist, Vol. 180, No. 2 (August 2012), pp. 153-166 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/10.1086/666610 . Accessed: 15/07/2012 13:27 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press, The American Society of Naturalists, The University of Chicago are collaborating with JSTOR to digitize, preserve and extend access to The American Naturalist. http://www.jstor.org vol. 180, no. 2 the american naturalist august 2012 Explaining Variation in the Effect of Floral Density on Pollinator Visitation Carla J. Essenberg* Department of Biology, University of California, Riverside, California 92521 Submitted March 24, 2011; Accepted April 2, 2012; Electronically published June 14, 2012 Online enhancements: appendix, PDF file. Dryad data: http://dx.doi.org/10.5061/dryad.mf172sf0. cke 1983). Many studies have reported effects of plant abstract: Pollinator responses to floral density have important density on plant reproductive success, usually positive implications for plant biology. In particular, a decline in pollinator visitation at low density can cause an Allee effect (a positive relation (e.g., Kunin 1997a; Ghazoul 2005; Dauber et al. 2010). of fitness to density) in the plant population, which heightens that Although other mechanisms, such as changes in inbreed- population’s vulnerability to extinction. Empiricists have reported a ing rates (Karron et al. 1995) or the frequency of inter- variety of relations between flower or plant density and pollinator specific pollen transfer (Kunin 1993; Morales and Traveset visitation rates. Here I develop and test a model that provides ex- 2008), can contribute, changes in pollinator visitation rates planations for this diversity. The model assumes that pollinators with increasing floral density are among the main causes distribute themselves between a focal patch of flowers and the sur- rounding environment so as to maximize foraging success. The re- of these effects (Kunin 1997a; Ghazoul 2005). sulting relation of per-flower visitation rate to focal-patch floral den- The relation of pollinator visitation to floral density is sity is nonlinear, with positive effects at low floral densities and complex. Although many studies have documented in- weaker or negative effects at higher densities. The relation is influ- creases in visitation rates with increasing plant or floral enced by floral density in the surrounding environment and traits densities, others have found no effects or negative effects of both the plants and their pollinators. In a field experiment, floral (e.g., Campbell and Motten 1985; Kunin 1993, 1997b; Tot- density of Holocarpha virgata ssp. virgata had a nonlinear effect on per-flower visitation that was largely consistent with the model’s land and Matthews 1998; Feldman 2006; Bernhardt et al. predictions. By producing testable hypotheses based on biologically 2008; Feldman 2008; Elliott and Irwin 2009; Jakobsson et reasonable assumptions, this model serves as a starting point for al. 2009; Dauber et al. 2010). Some explanations offered explaining an important facet of plant-pollinator mutualisms. for this variation are that density effects depend on the presence or absence of other flowering species (Kunin Keywords: pollination, mutualism, Allee effects, density, ideal free distribution. 1993; Feldman 2008), the spatial scale over which the re- lation is observed (Dauber et al. 2010), or the range of densities considered (Rathcke 1983). In this article, I ex- Introduction plore the last of these possibilities and suggest several new ones. My goal is to identify specific, testable hypotheses Responses of foragers to resource densities can have sig- that provide consistent explanations for the seemingly con- nificant effects on the ecology of lower trophic levels (e.g., tradictory results of previous empirical studies. Holt and Kotler 1987; Abrams 1993; Rohani et al. 1994; In contrast to the large empirical literature, little the- Krˇivan 1997, 2003; Bernstein et al. 1999). In plant-polli- nator interactions, increases in pollinator foraging activity oretical attention has been devoted to the effects of plant with increasing floral density can generate facilitation be- density on pollination success. Several models predict that tween plant species (Feldman et al. 2004) and declines in pollinator visitation to one plant species in a mixture plant fitness at low densities (Allee effects; Kunin 1997a; should vary positively with that species’ relative frequency Ghazoul 2005). On the other hand, decreases in pollinator (Bobisud and Neuhaus 1975; Goulson 1994; Kunin and visitation with increasing floral density could strengthen Iwasa 1996). However, the effect of the absolute density intra- and interspecific competition among plants (Rath- of flowers on pollinator visitation has received less atten- tion. Rathcke (1983) hypothesized that at low densities, * E-mail: [email protected]. adding flowers increases per-flower visitation by making a patch more attractive, whereas at high densities the pool Am. Nat. 2012. Vol. 180, pp. 153–166. ᭧ 2012 by The University of Chicago. 0003-0147/2012/18002-52930$15.00. All rights reserved. of pollinators becomes saturated and flowers compete for DOI: 10.1086/666610 pollinators. Rathcke provided only a brief verbal justifi- 154 The American Naturalist Table 1: Symbols used in the model Symbol Parameter or variable A Area (m2) c Energetic cost per unit of traveling time (J/s) f Floral density (flowers/m2) h Handling time per flower (s/flower visit/pollinator) k Ratio of the energetic cost per unit of handling time to the energetic cost per unit of travel time n Energy, in the form of nectar or other floral rewards, produced by each flower per unit of time (J/flower/s) p Pollinator density in a particular area; i.e., the focal patch or background area (pollinators/m2) P Total number of actively foraging pollinators in the system r Average energy gained per flower visit (J/flower visit, J/flower visit/pollinator) s “Search speed,” a constant that is proportional to the pollinators’ speed when traveling between flowers and also increases as flowers become more clumped (m/s)a t Average travel time per flower (s/flower visit/pollinator) v Visits per flower (flower visits/flower/s) Note: Symbols with subscript “f” refer to the focal patch, whereas those with subscript “b” refer to the area with which it competes (i.e., the background). Possible units are listed in parentheses in the second column. a See “Derivation of the Equation for Travel Time per Flower,” available online. cation for this hypothesis. A more rigorous approach is flower visitors defend food resources (Johnson and Hub- needed to clarify the circumstances and spatial scale(s) to bell 1974; Ewald and Carpenter 1978; Kodric-Brown and which her hypothesis applies and to identify other variables Brown 1978), competition is primarily exploitative in that influence the relation of visitation to floral density. many temperate insect pollinators (Waddington 1976; In this article, I model the effect of local floral density Pyke 1978; Zorn-Arnold and Howe 2007). Although on per-flower pollinator visitation, assuming optimally flower-visiting behavior can be influenced by motivations foraging, nonterritorial pollinators. I focus on situations other than maximizing foraging efficiency (e.g., Sapir et in which flowers are all similar and are treated indiscrim- al. 2005; Ings and Chittka 2008), I do not address these inately by pollinators, so that patch choice rather than issues in my model. Optimal-foraging models often suc- flower choice drives the effect. My aim is to generate ex- cessfully predict behavior of pollinators, particularly bees planations for variation in the effects of local floral density. (Pyke 1978, 1984; Schmid-Hempel et al. 1985; Goulson I begin by outlining the assumptions of the model and 2003). analytically deriving predictions for a simplified version in Within this context, the model is constructed as follows: which the rate of pollinator energy expenditure is constant. flowers in a focal patch compete with those in the sur- I then relax this assumption and explore numerical model rounding area for a set number of pollinators. I assume results using parameter values obtained from bee-polli- that all flowers produce identical rewards, that all polli- nated systems, which allow me to identify more specifically nators are identical, and that floral density outside of the how each parameter will influence density effects. I also focal patch is constant and uniform. Pollinators forage for show how choice of foraging currency (net rate of energy nectar and distribute themselves so that foraging success gain vs. efficiency) influences model predictions. Finally, is equal inside and outside of the focal patch. I first use I present a field experiment in which I measured the shape the net rate of energy gain as the measure of foraging of the relation of visitation to floral density and compare success because it is the most commonly used metric and its results to model predictions. is supported by many studies (reviewed in Pyke et al. 1977; Stephens and Krebs 1986): p A Model of the Effect of Floral Density on net rate of energy gain Pollinator Visitation energy gain per f lower Ϫ energy used per f lower . Pollinators commonly distribute themselves so that for- foraging time per f lower aging success is the same across available resource patches (1) (Dreisig 1995; Ohashi and Yahara 2002; Abraham 2005; Lefebvre and Pierre 2006).