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The aerodynamics and efficiency of wind pollination in grasses
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James E. Cresswell*1, Julian Krick2 , Michael A. Patrick3 and Mohammed Lahoubi4
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4PS, United Kingdom; 2Department of Fluid Mechanics, University of Duisburg-Essen, Lotharstraße 1
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47057 Duisburg, Germany; 3School of Engineering, Computer Science and Mathematics, Harrison
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Building, University of Exeter, EX4 4QF, United Kingdom; 4Département Energétique, Institut
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Catholique d'Arts et Métiers (ICAM), 6 rue Auber, 59046 Lille Cedex, France.
School of Biosciences, University of Exeter, Hatherly Laboratories, Prince of Wales Road, Exeter EX4
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*Correspondence author. E-mail address: j.e.cresswell@ex.ac.uk
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Running headline of not more than 45 characters: Wind pollination in grasses
Wind pollination in grasses: 2
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Summary
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1. Under natural selection for sexual success, the reproductive organs of plants should
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evolve to become highly effective pollen receptors. Among wind-pollinated plants, larger
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reproductive structures appear counter-adapted to accumulate pollen by impaction on their
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windward surfaces, because airborne particles are less able to penetrate the thicker boundary
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layer of larger targets. Therefore, it has been proposed that wind-pollinated plants with pollen
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receptors on relatively large structures, like some grasses (family Poaceae), are
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architecturally adapted to create downstream vortices in which airborne pollen recirculates
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before accumulating on leeward surfaces. From this basis, the striking diversity among the
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grasses in the architecture of their flowering stems has been attributed in part to the existence
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of these contrasting mechanisms for effecting pollen receipt, namely impact collection and
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recirculatory collection.
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2. We investigated the relative importance of impact and recirculatory collection in grasses by
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analysing a model system in silico using Computational Fluid Dynamics and by conducting in
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vivo experiments, both in a wind tunnel and outdoors, using two grass species with compact
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inflorescences, Alopecurus pratensis and Anthoxanthum odoratum.
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3. Irrespective of the experimental approach, we found that although pollen recirculated in the
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leeward eddies of inflorescences, over 95% of the accumulated pollen was collected by
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windward surfaces.
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4. In A. pratensis, the collection efficiency (proportion of oncoming pollen collected) was
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between 5% and 20%, depending on wind speed in the range 0.5 to 1.9 m s-1 and these
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levels conform to those predicted by a mechanistic model of impact collection.
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5. Our results demonstrate that grass species with larger inflorescences are, like those with
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smaller inflorescences, primarily impact collectors of airborne pollen, which suggests that
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dissimilar reproductive morphology among species cannot be attributed to differentiation in
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the mode of pollen capture and, instead, requires reference to other factors, such as the need
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to produce, protect and disperse seeds of different sizes in different environments.
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Key words: Alopecurus pratensis, Anthoxanthum odoratum, CFD, collection efficiency, computational
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fluid dynamics, cross-pollination, Poaceae, pollination
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(312 words)
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Introduction
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An important goal for evolutionists is to explain the conspicuous diversity among seed plants
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in the architecture of reproductive structures, such as cones (Tomlinson & Takaso, 2002),
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flowers (Harder & Barrett, 2006) and inflorescences (Prusinkiewicz, Erasmus, Lane et al.,
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2007). In seed plants, sexual mating depends on the transfer of pollen between flowers on
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different individuals, or cross-pollination. Therefore, under natural selection for sexual
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success, female reproductive organs should evolve to become highly effective pollen
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receptors. In animal-pollinated plants, variation among species in floral architecture typically
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reflects adaptation towards different kinds of pollen vector (Fenster, Armbruster, Wilson et al.,
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2004), which differ in their fit to plant sexual structures and in their behavioural partialities. In
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wind-pollinated plants, there is also evident variation among structures that bear pollen
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receptors, which is curious, because the uniformity of physics and the impartiality of
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airstreams should focus selection and thereby result in convergent evolution of receptor form.
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In actuality, the flowers of most wind-pollinated species conform to a stereotypic syndrome,
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being minute with protuberant stigmas (Whitehead, 1969), but exceptions exist. For example,
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the ovulate cones (megastrobili) of conifers are robust structures with diameters up to 10 mm
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at the time of pollination (Paw U & Hotton, 1989) and the compact inflorescences of certain
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grasses (family Poaceae) have a similar dimension (Friedman & Harder, 2005). Moreover, it
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is unlikely that this variation is aerodynamically neutral, because fluid dynamics theory
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predicts that the ability to collect airborne particles depends greatly on a receptor’s size
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(Perry, 2004). Specifically, if a receptor accumulates oncoming airborne pollen principally by
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a combination of direct interception and inertial collisions (Rubenstein & Koehl, 1977), or
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‘impact collection’, its effectiveness decreases rapidly as its diameter increases across the
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biologically relevant range (Fig. 1), because airborne particles are less able to penetrate the
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thicker boundary layer of larger targets. In this light, the larger ovulate cones and grass
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inflorescences appear counter-adapted for effective wind-pollination, unless they accumulate
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pollen by an alternative mechanism.
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Previously, it has been proposed that wind-pollinated plants with relatively large receptors
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are architecturally adapted to create complex air vortices that trap airborne pollen as follows
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(Niklas, 1982, Niklas, 1985). A solid body in an airstream creates a leeward eddy. If the
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vortex of a pollen receptor’s leeward eddy draws in passing pollen, the grains may recirculate
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and could accumulate on the leeward surfaces of the receptor in several ways. First, the
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pollen may sediment out from a slow-moving portion of the eddies and settle on the receptor
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(Niklas, 1987). Second, the recirculating pollen may be collected through impaction on a
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leeward-facing stigma. Third, in grasses, the inflorescence may be thrust into the leeward
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suspension of recirculating pollen by wind-induced oscillations of its stem caused by the
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‘Honami effect’, named after the ocean-like waving of grass in the wind (Inoue, 1955, cited in
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Niklas, 1987). The combination of leeward recirculation and the Honami effect captures
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pollen by impaction. These theories refer to mechanisms that we collectively term
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‘recirculatory collection’, which is the basis of elegant adaptive explanations for the
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maintenance of large and otherwise suboptimal pollen receptors in the conifers and grasses
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(Niklas, 1982, Niklas, 1987, Friedman & Harder, 2005). We contrast collectors of this sort
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with ‘impact collectors’, which accumulate pollen on their windward surfaces. Recently, it has
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been demonstrated that the ovulate cones of conifers function principally as impact collectors
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(Cresswell, Henning, Pennel et al., 2007). In consequence, whether any plants utilise the
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complex aerodynamics of recirculatory collection in cross-pollination is called into question,
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and so it is necessary to investigate further cases, such as the grasses.
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It is valuable to evaluate the role of recirculatory collection in pollination for two further
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reasons. First, the prospect that cross-pollination in some species depends on complex
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aerodynamics arguably undermines the utility of general mechanistic models of wind
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pollination (Kuparinen, 2006, Hoyle & Cresswell, 2009). Second, if it emerges that grasses in
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general capture airborne pollen by impact collection, it raises questions about whether
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species with dissimilar sizes of pollen receptor vary in the efficacy of their pollination systems.
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For impact collectors, the detrimental effect of increased receptor size can be mitigated by an
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increased mass of individual pollen grains (Paw U & Hotton, 1989), but this implies that plant
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species with larger receptors will have less dispersible pollen. If so, inflorescence
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architecture could identify species that are more susceptible to spatially limited cross-
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pollination, spatially restricted gene flow (Griffiths, 1950), and thereby to Allee effects (Davis,
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Taylor, Lambrinos et al., 2004). Therefore, resolving whether complex aerodynamics plays a
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role in wind pollination among grasses could provide valuable insights into reproduction and
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gene flow in this important family.
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We therefore investigated the relative importance of impact and recirculatory collection in
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grass inflorescences by analysing a model system in silico using Computational Fluid
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Dynamics (CFD) and by conducting in vivo experiments, both in a wind tunnel and outdoors,
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using two grass species with compact inflorescences, Alopecurus pratensis L. (meadow
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foxtail; mean diameter of inflorescence = 6.7 mm, SE = 0.27, n = 17; Fig. 2a) and
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Anthoxanthum odoratum L. (sweet-scented vernal grass; mean = 6.3 mm, SE = 0.36, n = 16;
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Fig 2b).
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Materials and Methods
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COMPUTATIONAL FLUID DYNAMICS
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Using computer-assisted design (CAD), we modelled a flowering stem in silico to represent
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grass species whose inflorescence is a compact panicle (Fig. 3). We constructed a flower,
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or floret, as an oblate spheroid (the ovary) enclosed in two concave surfaces (the lemma and
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palea; Fig. 3a). To simulate a range of realistic stigma positions, each floret had an array of
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five stigmas radiating from the ovary and extending in a plane perpendicular to the opening
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between the palea and lemma (Fig 3b), but stamens were omitted for simplicity. The stigmas
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captured all pollen grains that contacted them, but did not otherwise influence the air flow,
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which maximized their capture efficiency. Pairs of florets were enclosed in concave surfaces
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to represent the glumes, and this structure collectively represented a spikelet. The flowering
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stem comprised 18 identical spikelets arrayed around a central axis (Fig 3c,d), to produce a
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compact spike with protuberant stigmas (Fig. 3e). To characterise its aerodynamic
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performance, the inflorescence was tested in a CFD-simulated wind tunnel. We conducted
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trials at two wind speeds (0.5 and 1.0 m s-1), which were chosen to favour recirculatory
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collection (Niklas, 1987). To ensure a representative range of orientations at each wind
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speed, trials were conducted on inflorescences placed at three different angular rotations of
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the vertical stem (0°, 45° and 90°). At each wind speed, we determined the importance of
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leeward recirculation in pollen capture by inspecting the trajectories of 50 particles that were
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intercepted by a stigma and finding the proportion whose capture was preceded by leeward
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movement in a direction opposite to the prevailing flow in the wind tunnel, which is indicative
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of recirculatory collection. In addition, to determine the effect on pollen collection of the
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presence of supporting structures, we quantified the number of particles captured by stigmas
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in the presence versus absence of the rest of the flowering stem.
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The flowering stem was constructed in silico in a CAD (computer-aided design)
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environment, GAMBIT (Fluent Inc., Lebanon, New Hampshire, USA). To conduct CFD wind
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tunnel simulations, we employed FLUENT® Flow Modeling Software version 6.2 (Fluent Inc.,
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Lebanon, New Hampshire, USA). The CFD computational domain simulated a grass
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inflorescence placed centrally in a cuboid wind tunnel with the flow inlet opposite the outlet.
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To minimize edge effects from the tunnel walls, these four surfaces were moving with the
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same horizontal velocity as the airflow at the inlet. The domain consisted of 1.7 million
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tetrahedral cells. The simulated fluid was air at a temperature of 288.16 K and an
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atmospheric pressure of 101.32 kPa. Its density and dynamic viscosity were 1.22 kg m-3 and
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1.79 kg m-1 s -1, respectively. We used Lagrangian particle tracking to simulate the
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trajectories of spherical pollen grains of 30 m diameter, which approximates the mean pollen
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size in grasses with compact inflorescences (Friedman & Harder, 2005). The density of grass
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pollen is unknown, so we estimated values by solving Stokes law for spheres with settling
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velocities typically observed among wind-pollinated plants (Paw U and Hotton 1989), i.e. 2
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and 5 cm s-1, which yields densities of 112 and 1278 kg m-³ respectively. Airborne particles
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passed rapidly through the domains occupied by stigmatic surfaces, and so the influence of
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gravity was neglected.
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To determine the Reynolds number, R, we defined the characteristic length of the
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compact inflorescence, lch, by its width (Niklas, 1987). With lch = 10.7 mm, which is
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representative for grasses with compact inflorescences (Friedman & Harder, 2005), we
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obtain: flow = 0.5 m s-1, R = 301; flow = 1.0 m s-1, R = 601. In reality, the airflow around a
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grass inflorescence will be turbulent, but the turbulent eddies probably occur at scales of
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similar size to the inflorescence itself and so we assumed that the local flow around it will be
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approximately laminar and, therefore, a laminar model was used to simulate viscous effects.
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For simplicity, collisions between particles and the non-stigmatic surfaces of the grass were
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assumed to be fully elastic and the flow was assumed to be steady and incompressible. In
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FLUENT, all simulations were initially run using the steady-state SIMPLE algorithm and first
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order upwind differencing was used for the spatial derivatives in single precision mode. The
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pollen particles were released from each of 32,500 evenly spaced points on rectangular grids
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on planes placed across the upwind flow inlet.
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EXPERIMENTS IN VIVO
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All trials were conducted on fresh material collected near the University of Exeter campus
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(50°43'N, 3°31'W) in 2009. Inflorescences were stored in vases of water and used within 24 h
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of collection. Pollen was collected indoors from newly dehiscent anthers, stored at room
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temperature, and used within 24 h. Before being used in a trial, each inflorescence was
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carefully checked under a dissection microscope and, where necessary, an artist's fine
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paintbrush was used to remove natural accumulations of pollen from the stigma and other
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surfaces. Experimental trials were conducted in both the controlled airflows of a wind tunnel
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and in uncontrolled, outdoor airflows as follows.
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Wind tunnel experiments
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The wind tunnel had a cross-section of 120  120 mm over a horizontal run of 600 mm with
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an aerodynamically shaped contraction beginning with an initial cross-section of 250  250
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mm, which was identical in all respects except scale to the tunnel pictured in Cresswell et al.
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(2007). The culm of each flowering stem was trimmed so that its inflorescence was situated
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in the central region of the tunnel, where it was placed individually and held basally by a
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streamlined lump of putty (A. pratensis: mean length of trimmed culm = 26.2 mm, SE = 1.78;
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mean length of inflorescence = 63.2 mm, SE = 3.58, n = 15; A. odoratum: culm = 43.6 mm,
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SE = 2.62; inflorescence = 45.5 mm, SE = 2.99, n = 14). In A. pratensis, each inflorescence
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was exposed to an airborne cloud of either pollen of its own species or a pollen analogue,
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Lycopodium spores (Sigma-Aldrich, Gillingham, UK), the latter trials being used to establish
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the utility of the spores as a pollen analogue. We compared the level of recirculation of pollen
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vs. spores by calculating for each a coefficient, r, which expressed the ratio of the density
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(grains mm-2) of pollen captured by wire probes placed leeward: pollen captured by wire
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probes placed windward (details of probes are given below). Confidence intervals on r ratios
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were calculated using a standard formula for the variance of the quotient of two random
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variables (Kelly, 1947). In A. odoratum, each inflorescence was exposed only to an airborne
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cloud of the pollen analogue, Lycopodium spores (Sigma-Aldrich, Gillingham, UK). For
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brevity, we refer to the spores as pollen hereafter.
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Pollen was loaded into a narrow nozzle formed from a trimmed 200 l pipette tip (Life
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Sciences International, Basingstoke, UK) and injected into the contraction of the wind tunnel
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by a single puff from an attached syringe. To produce a uniform cloud, pollen was dispersed
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during injection with a baffle (8  8 mm mounted 25 mm in front of the nozzle) placed 60 mm
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from the tunnel's contraction (Cresswell et al., 2007). After exposure to airborne pollen, we
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counted under a microscope the number of pollen grains adhering to the windward and
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leeward surfaces and, if necessary, subtracted the small number of pollen grains present
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immediately prior to the trial. For A. pratensis, we were able to quantify the pollen collected
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on stigmatic surfaces. For A. odoratum, the stigmas on the specimens that were obtained did
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not retain spores effectively and so we counted the spores that accumulated on the hairy
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surfaces of the glumes. For each grass species, at least three replicate trials were conducted
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at each of three wind speeds: 0.5; 1.0; and 1.9 m s-1. Wind speeds were measured in situ
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with a thermal anemometer (Testo 425, Testo AG, Lenzkirch, Germany).
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In order to determine whether grass inflorescences generated a leeward cloud of
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recirculating pollen, we conducted additional trials in which a fine wire probe (0.5 mm
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diameter) coated with a thin layer of petroleum jelly was suspended vertically either 10 mm or
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20 mm downwind of the inflorescence’s most leeward surface. The number of pollen grains
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adhering to the probe was counted over the 20 mm length that sampled the central region of
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the wind tunnel. The face of the wire on which the particle was found (windward, leeward)
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was used to infer the impacted particle’s previous direction of movement. For each grass
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species, at least three replicate trials were conducted at each probe distance (10 mm, 20 mm)
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at each wind speed (0.5, 1.0 and 1.9 m s-1). Additionally, similar readings were taken with
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this probe and used as controls to quantify the density and direction of movement of the
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pollen cloud in the absence of inflorescences. To demonstrate the consistency of conditions,
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at least three control trials were conducted at regular intervals throughout each series of trials
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at each wind speed.
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Assuming that stigmas of A. pratensis have a surface area typical of grass species with
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similarly sized compact inflorescences, i.e. 7.2 mm2 (Friedman & Harder, 2005), we estimated
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the collection efficiency of the pollination system, C, as the ratio of the density (grains per
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mm2) of airborne pollen on the stigma to the density on an unaccompanied wire probe.
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Confidence intervals on ratio C were calculated using a standard formula for the variance of
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the quotient of two random variables (Kelly, 1947). We used the formulas of Paw U and
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Hotton (1998) to calculate the efficiency of an impact collector with diameter equivalent to that
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of the A. pratensis inflorescence (i.e. 6.7 mm). Specifically, we calculated the Stokes number
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for the system, S, as S = vsetU/gD, where vset is the terminal settling velocity of a pollen grain
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in still air (m s-1), U is the wind speed (m s-1), g is the gravitational acceleration (m s-1) and D
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is the diameter of the structure. In these calculations, we assumed g = 9.8 m s-2. We then
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estimated impaction efficiency, I, as I = S2/(S2 + 1)  100 (Paw U & Hotton, 1989).
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Outdoor experiments.
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In order to investigate pollen reception under field conditions, we used flowering stems that
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had been severed at the soil surface (A. pratensis: mean length of culm = 687 mm, SE =
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43.4, n = 11; A. odoratum: mean = 187 mm, SE = 11.2, n = 6). Experiments were conducted
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outdoors in dry weather with moderate, gusting wind immediately after the flowering stems
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were collected. Each flowering stem was placed 1 m from a large electric fan, which
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supplemented the natural wind. The fan’s speed settings were varied to produce the
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following three flows during trials: A. pratensis: mean speed = 2 m s-1 (range 1 to 3 m s-1) or
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mean = 4 m s-1 (range 3 to 5 m s-1); A. odoratum: mean speed = 2.5 m s-1 (range 0.5 to 5 m s-
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1).
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required to produce outdoors a sufficiently dense cloud of airborne pollen were logistically
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prohibitive to collect, so we employed Lycopodium spores. Clouds of spores were released
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0.3 m upwind of each inflorescence over a period of approximately one minute in order to
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characterize the effects of a variety of wind conditions. For A. pratensis, we quantified the
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number of spores collected on stigmatic surfaces. For A. odoratum specimens, no untreated
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surfaces accumulated spores at sufficient densities, and so we quantified spores on the
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petroleum jelly-coated surfaces of two single florets, one facing leeward and one windward.
Wind speeds were measured with the thermal anemometer. The quantities of pollen
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At least five replicate trials were conducted for each combination of grass species and mean
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wind speed.
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Results
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CFD EXPERIMENTS
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We observed pollen recirculating in leeward eddies (Fig 4), but subsequent contact with
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stigmas rarely occurred, because recirculating particles typically were rapidly picked up by the
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surrounding airflow and transported further downwind. Over all trials, among the trajectories
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of 200 particles that were intercepted by stigmas, only two (i.e. proportion of recirculatory
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captures, Pr = 1%) had ever travelled in an upwind direction and could have experienced
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post-recirculatory capture. Post-recirculatory captures occurred only among pollen grains
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with low settling velocity (vset = 0.02 m s-1: wind speed = 0.5 m s-1, Pr = 2%; wind speed = 1 m
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s-1, Pr = 2%; vset = 0.05 m s-1: wind speed = 0.5 m s-1, Pr = 0%; wind speed = 1 m s-1, Pr =
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0%).
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Over all trials, the presence of supporting structures reduced the effectiveness of stigmas
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by approximately half, but the detrimental effect was strongest in trials of pollen with lower
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settling velocity. Let Iv denote the proportional reduction in stigmatic collection efficiency
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due to the presence of supporting structures when vset = v m s-1. At wind speed = 0.5 m s-1:
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I0.02 = 62% and I0.05 = 52%; at wind speed = 1 m s-1: I0.02 = 57% and I0.05 = 39%.
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WIND TUNNEL EXPERIMENTS
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In the absence of inflorescences, virtually all particles (pollen and spores) that were captured
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by the wire probe accumulated on its leeward surface (99.7% of 4220 particles, n = 17 trials
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at various wind speeds), which indicates that their movement was almost invariably in the
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direction of the tunnel’s prevailing air flow.
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At both wind speeds tested (0.5 m s-1, 1.0 m s-1), Lycopodium spores were found at
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greater relative densities (at least three time greater) in the leeward wake of A. pratensis than
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were conspecific pollen grains, which indicates that spores had a greater potential for
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recirculation than pollen and are therefore likely to overestimate the contribution of
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recirculatory collection to particle accumulation; ratio of density of pollen (grains mm-2)
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captured by wire probes placed leeward: pollen captured by wire probes placed windward at
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wind speed of 0.5 m s-1, rpollen,0.5 = 1.8% (SE = 0.02, n = 3 windward probes, 5 leeward
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probes); ratio of density of spores captured by wire probes placed leeward: spores captured
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by wire probes placed windward at wind speed of 0.5 m s-1, rspores,0.5 = 6.1% (SE = 0.02, n = 3,
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12); rpollen,1.0 = 0.2% (SE = 0.0003, n = 3, 5); rspores,1.0 = 2.0% (SE = 0.01, n = 3, 12).
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In both grass species and irrespective of wind speed, inflorescences accumulated a
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significantly greater majority of pollen or spores on their windward surfaces. In A. pratensis,
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the mean proportion of accumulated pollen grains found on windward stigmas over all trials
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was 99%, with mean = 18.9 pollen grains per windward stigma (SE = 4.9, n = 10) vs. 0.16
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grains per leeward stigma (SE = 0.1; paired t-test, t = 3.81, df = 9, P < 0.005; Fig 5a). In A.
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odoratum, the mean proportion of accumulated spores found on the surfaces of windward-
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facing florets over all trials was 95%, with mean = 42.9 pollen spores per windward floret (SE
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= 6.4, n = 11) vs. 0.19 spores per leeward floret (SE = 0.5; paired t-test, t = 6.48, df = 10, P <
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0.001; Fig 5b).
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In both grass species, the density of airborne particles (particles mm-2) accumulated by a
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wire probe was substantially lower in the leeward wake of the inflorescence than in the
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oncoming particle cloud, but the differential was greatest in A. pratensis (A. pratensis: ratio of
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leeward:oncoming particle density over all trials = 1%; A. odoratum: 10%; Fig 5 c, d). In both
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grass species, significantly less than half of the particles in the leeward wake were moving
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counter to the prevailing direction flow in the tunnel as indicated by accumulation on the
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leeward face of the wire probe (A. pratensis: mean over all trials = 21%, n = 38 pollen grains,
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chi-squared goodness-of-fit test, df = 1, 2 = 12.7, P < 0.001; A. odoratum: mean over all trials
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= 21%, n = 380 spores, chi-squared goodness-of-fit test, df = 1, 2 = 159.3, P < 0.001).
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Possibly, this result suggests that only a minority of recirculating pollen was drawn towards
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the inflorescence.
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The collection efficiency of the pollination system of A. pratensis exhibited an
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approximately linear increase with wind speed (Fig 6). The observed collection efficiency
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corresponds fairly well with that predicted for a simple impact collector of similar dimensions
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(r-squared = 62%; linear regression analysis, F1,8 = 15.7, P < 0.005).
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OUTDOOR EXPERIMENTS.
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In both grass species, flowering stems exhibited substantial oscillations during the
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experimental trials, which appeared to be caused both by intrinsic responses to the passing
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air flow and also by the gusty wind conditions. In both grass species and irrespective of wind
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speed, inflorescences accumulated a significantly greater majority of spores on their
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windward surfaces. In A. pratensis, the mean proportion of spores accumulated by windward
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stigmas over all trials was 97%, with mean = 41.5 spores per windward stigma (SE = 7.40, n
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= 9) vs. 2.6 spores per leeward stigma (SE = 0.74; paired t-test, t = 5.73, df = 8, P < 0.001).
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In A. odoratum, the mean proportion of spores accumulated by windward florets over all trials
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was 97%, with mean = 370 spores per windward surface (SE = 127.1, n = 6) vs. 5 spores per
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leeward surface (SE = 1.7; paired t-test, t = 2.87, df = 5, P < 0.05).
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Discussion
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In certain grasses, the large diameter of compact inflorescences appears counter-adaptive for
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a structure intended for collecting particles by impaction on its windward surfaces and,
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therefore, it has been proposed that it functions instead as a recirculatory collector (Niklas,
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1987, Friedman & Harder, 2005). Like previous studies that used stroboscopic photography
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(Niklas, 1987, Niklas, 1988) and fluid dynamic models (Niklas, 1988) to investigate the
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leeward eddy of grass inflorescences, our study demonstrates leeward recirculation by pollen;
371
in both of the grass species that we investigated, pollen accumulated on wire probes placed
372
in the leeward eddy of a compact inflorescence exposed to oncoming airborne pollen in a
373
wind tunnel and our CFD analyses visualized this leeward recirculation.
374
375
However, our study suggests that recirculatory collection is unlikely to play a substantial
376
role in pollen receipt. In CFD analyses, 99% of the pollen accumulated by stigmas had not
377
experienced leeward recirculation. Irrespective of the grass species studied, at least 95% of
378
pollen accumulated on the inflorescence’s windward surfaces in wind tunnel trials and 97% of
Wind pollination in grasses: 17
379
pollen accumulated on the inflorescence’s windward surfaces in outdoor trials. Two factors
380
were likely to have caused these low levels of leeward accumulation. First, in wind tunnel
381
trials the airborne density of pollen grains in the leeward eddy was at most 5% of that of the
382
oncoming pollen cloud, and only 1% in A. pratensis. Thus, only a sparse suspension of
383
pollen was available to an inflorescence sampling to leeward. Second, the CFD analysis
384
indicated that pollen grains did not recirculate for long even when they became entrained in
385
the larger leeward vortices, but instead they were rapidly picked up by the surrounding airflow
386
and transported away downwind. Leeward captures resulted only when a pollen grain was
387
swept up by small eddies close to the leeward surfaces, which suggests that only a small
388
proportion of recirculating pollen has the prospect of capture. The correspondence between
389
the observed collection efficiency of A. pratensis and that predicted theoretically for an impact
390
collector of similar size further supports the proposition that recirculatory collection is not an
391
important contributor to pollination in this species. The theoretical prediction is only
392
approximate, however, because it is based on the assumption that the target is a smooth
393
cylinder, whereas this is only a first approximation to the structure of a real grass
394
inflorescence.
395
396
Our conclusions are consistent with the findings of two previous studies. First, in a
397
comparative investigation of 25 grass species, Friedman and Harder (2005) found that the
398
estimated settling velocity of a species’ pollen increased with the diameter of the target
399
inflorescence. This relationship is predicted only if pollen receipt occurs by impact collection
400
(Paw U & Hotton, 1989), because species whose inflorescences present larger targets should
401
evolve more massive pollen grains that better penetrate the deeper boundary layer around
402
larger receptors. Moreover, our CFD analyses indicate that heavier pollen is less likely to
403
entrain in leeward eddies. If species with larger receptors rely on recirculatory capture, they
Wind pollination in grasses: 18
404
should therefore evolve lighter pollen grains, which is contraindicated by the settling velocity-
405
receptor diameter relationship found by Friedman & Harder (2005). Second, Friedman and
406
Harder (2004) found that preventing Honami oscillation by immobilizing the culms of three
407
grass species with compact panicles failed to affect pollen receipt, which suggests that
408
oscillatory sampling of recirculating pollen is unimportant. However, our results differ from
409
those of Niklas (1987), whose study of Setaria geniculata, a grass with a compact
410
inflorescence, found that leeward surfaces collected approximately 35% - 70% of the total
411
pollen accumulated by an inflorescence at wind speeds between 0.5 and 1.0 m s -1, whereas
412
leeward surfaces collected less than 5% of the accumulated pollen at similar wind speeds in
413
the two species that we studied. This disparity may be due to differences in the attributes of
414
the grass species studied. Specifically, S. geniculata apparently has a much more pliable
415
culm than the two species that we studied. Even at low wind speeds (e.g. 0.5 m s-1), the
416
flowering stem of S. geniculata oscillates fairly fast (1 Hz) and the culm deforms up to 50
417
degrees from vertical (Niklas 1987); we did not observe similar behaviour in either A.
418
pratensis or A. odoratum. Reportedly, the oscillations of S. geniculata in an airstream can
419
cause panicle surfaces to be deflected into both upwind and downwind orientations (Niklas,
420
1987), in which case the apparent contribution of leeward recirculation must be interpreted
421
with caution (Niklas 1987). Alternatively, it is possible that the highly oscillatory inflorescence
422
of S. geniculata creates special aerodynamic conditions not found in grasses with more
423
robust culms, which favour recirculatory collection. Even if this is so, however, it is
424
problematic to explain the maintenance of compact inflorescences in species with relatively
425
stiff culms, such as A. pratensis and A. odoratum, by reference to their function as
426
recirculatory collectors.
427
Wind pollination in grasses: 19
428
If pollen receipt in grasses with compact inflorescences occurs principally by impact
429
collection on windward surfaces, what does this suggest about the role of morphological
430
adaptation for cross-pollination among grasses? The grasses are particularly notable for the
431
architectural diversity of their flowering stems, which include four identified morphological
432
classes based on two binary distinctions (Friedman & Harder, 2005): inflorescence type
433
(compact or diffuse) and floret size (large or small). The lack of convergence among grasses
434
on a single ideal form for the flowering stem suggests that various combinations of floral and
435
inflorescence traits confer equivalent pollination success (Friedman & Harder 2005). Our
436
study suggests that compact inflorescences, like diffuse inflorescences (Niklas, 1988,
437
Friedman & Harder, 2005), accumulate pollen by impact collection. Given that the collection
438
efficiency of an object is approximately inversely proportional to its diameter in the size range
439
of grass inflorescences (Paw U & Hotton 1988), how can large and small inflorescences have
440
equivalent performance as pollen receptors? We propose some possible mechanisms by
441
which this equivalence could emerge. First, the detrimental effect of the thicker boundary
442
layer around a larger structure could be avoided by sufficiently protuberant stigmas.
443
However, there is no evidence that stigma length varies systematically between compact and
444
diffuse inflorescences (Friedman & Harder 2005), which suggests that it has not evolved as a
445
mitigating adaptation. Second, the thicker boundary layer around a larger target can be
446
better penetrated by more massive particles. Indeed, there is evidence that pollen size
447
increases with inflorescence size (Friedman & Harder 2005). The consequences of variation
448
in pollen size for its dispersibility are unknown, however, but perhaps the generally gregarious
449
habit of grasses allows species with larger pollen grains to avoid Allee effects due to limited
450
cross-pollination at low population density. Overall, the functional explanation of the diversity
451
of panicle, spikelet and floret constructions among grasses remains incomplete, and
452
doubtless requires the incorporation of various factors besides the aerodynamics of pollen
Wind pollination in grasses: 20
453
receipt, such as the need to produce, protect and disperse seeds of different sizes in different
454
environments. The benefits accrued by plants through architectural adaptations towards
455
these factors presumably also offset the otherwise substantial and detrimental effect of the
456
flowering stem’s supporting structures on pollen receipt by stigmas, which our CFD analyses
457
identified.
458
459
Among plants that achieve cross-pollination via an abiotic vector, those with water-borne
460
pollen are unlikely to rely on recirculatory collection through complex vortices (Ackerman,
461
1997), because, all else being equal, flow in water is less turbulent than that in air (Ackerman,
462
2000). For species whose pollen vector is the wind, our study joins others (Cresswell,
463
Davies, Patrick et al., 2004, Cresswell et al., 2007) to demonstrate that recirculatory collection
464
has a minor role in wind pollination in a disparate range of large receptors (ovulate cone,
465
grass inflorescence, zoophilous flower). Overall, we propose that the functional significance
466
of the attributes of wind-pollinated plants is to be understood primarily by reference to their
467
shared principal mode of pollen receipt, which is impact collection. The differential
468
performance that is likely to arise among plants with dissimilarly sized receptors now
469
becomes a significant focus for future research.
470
471
Wind pollination in grasses: 21
472
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473
Ackerman, J. (1997) Submarine pollination in the marine Angiosperm Zostera marina
474
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Ackerman, J.D. (2000) Abiotic pollen and pollination: ecological, functional, and evolutionary
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Cresswell, J.E., Davies, T.W., Patrick, M.A., Russell, F., Pennel, C., Vicot, M. & Lahoubi, M.
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(2004) The aerodynamics of wind pollination in a zoophilous flower. Functional Ecology
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Cresswell, J.E., Henning, K., Pennel, C., Lahoubi, M., Patrick, M.A., Young, P.G. & Tabor,
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G.R. (2007) Conifer ovulate cones accumulate pollen principally by simple impaction.
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Davis, H.G., Taylor, C.M., Lambrinos, J.G. & Strong, D.R. (2004) Pollen limitation causes an
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Allee effect in a wind-pollinated invasive grass (Spartina alterniflora). Proceedings of the
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National Academy of Sciences of the United States of America 101, 13804-13807.
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Fenster, C.B., Armbruster, W.S., Wilson, P., Dudash, M.R. & Thomson, J.D. (2004)
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Pollination syndromes and floral specialization. Annual Review Of Ecology Evolution And
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Systematics 35, 375-403.
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Friedman, J. & Harder, L.D. (2005) Functional associations of floret and inflorescence traits
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Griffiths, D.J. (1950) The liability of seed crops of perenniel ryegrass (Lolium perenne) to
contamination by wind-borne pollen. Journal Of Agricultural Science 4, 19-38.
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Harder, L. & Barrett, S. (2006) Ecology and evolution of flowers. Oxford University Press,
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Kelly, T. (1947) Fundamentals of statistics. Harvard University Press, Cambridge, MA, USA.
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Kuparinen, A. (2006) Mechanistic models for wind dispersal. Trends in Plant Science 11, 296-
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Niklas, K.J. (1985) The aerodynamics of wind pollination. The Botanical Review 52, 328-386.
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Niklas, K.J. (1987) Pollen capture and wind-induced movement of compact and diffuse grass
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panicles - implications for pollination efficiency. American Journal of Botany 74, 74-89.
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Niklas, K.J. (1988) Equations for the motion of airbourne pollen grains near the ovulate
organs of wind-pollinated plants. American Journal of Botany 75, 433-444.
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Perry (2004) Perry's chemical engineers' handbook sixth ed. 20-7820-7882.
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Prusinkiewicz, P., Erasmus, Y., Lane, B., Harder, L.D. & Coen, E. (2007) Evolution and
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525
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527
528
Fig. 1. Theoretical relationship between the impaction efficiency of a filter, I, and its diameter
529
in mm. We define I as the proportion (%) of particles that impact with the filter, given that
530
they were originally on course to pass through its cross-sectional area. The relationship has
531
been calculated from formulas given in Paw U and Hotton (1998) by assuming that the
532
airborne particles have a settling velocity of 0.05 m s-1, the oncoming wind speed is 2 m s-1,
533
and that gravitational acceleration is 9.8 m s-2.
534
Wind pollination in grasses: 25
535
536
537
538
539
540
541
542
543
a.
544
b.
545
546
547
Fig. 2. Flowering stems of grasses with compact inflorescences. Panel (a) Alopecuris
548
pratensis (photograph: Graham Calow) and (b) Anthoxanthum odoratum (photograph: J. K.
549
Lindsey).
Wind pollination in grasses: 26
550
551
552
Fig. 3. Construction of the model flower in silico for analysis by Computational Fluid
553
Dynamics (CFD). Panel indicate: (a) spikelet comprising two florets; (b) position of the five
554
stigmas; (c) plan view of inflorescence showing radial arrangements of spikelets; (d) side view
555
of flowering stem; (e) inflorescence with protuberant stigmas.
Wind pollination in grasses: 27
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
Fig. 4. CFD simulation showing flowering stem with leeward recirculation of particles. Each
573
curve is the trajectory of an individual particle. Wind direction is left to right with speed 1 m s-
574
1.
575
576
Settling velocity of particles is 0.02 m s-1.
Wind pollination in grasses: 28
577
578
579
Fig. 5. Relationships between wind speed (x-axis) and the numbers of particles accumulated
580
either by grass inflorescences (panels a, b) or wire probes (panels c, d) in wind tunnel trials.
581
Panel (a): y-axis (logarithmic scale) indicates the mean number of pollen grains of A.
582
pratensis accumulated on the stigmatic surfaces of a conspecific floret facing either to
583
windward (filled symbols) or to leeward (open symbols); panel (b) : y-axis (logarithmic scale)
584
indicates the mean number of Lycopodium spores accumulated on the surfaces of a floret of
585
A. odoratum facing either to windward (filled symbols) or to leeward (open symbols); panel
586
(c): y-axis (logarithmic scale) indicates the mean density (grains mm-2) of pollen grains of A.
587
pratensis accumulated by a wire probe positioned either 10 mm leeward of an inflorescence
588
(filled squares), 20 mm leeward (open squares), or alone in the wind tunnel (connected
589
diamonds); panel (d): y-axis (logarithmic scale) indicates the mean density of Lycopodium
590
spores (spores mm-2) accumulated by a wire probe positioned either 10 mm leeward of an
Wind pollination in grasses: 29
591
inflorescence (filled squares), 20 mm leeward (open squares), or alone in the wind tunnel
592
(connected diamonds). Symbols connected for inspection purposes only. Error bars indicate
593
1 SE.
594
595
Wind pollination in grasses: 30
596
25
20
I or C 15
(%) 10
5
0
0.0
0.5
1.0
1.5
2.0
Wind speed
597
598
599
600
Fig. 6. For Alopecuris pratensis, relationship between wind speed (x-axis in m sec-1) and
601
either observed collection efficiency (C %) or theoretically estimated impaction efficiency (I %)
602
of the particle collection system (stigmatic surfaces and conspecific pollen) in wind tunnel
603
trials.