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In many pine species (Family Pinaceae), ovulate cones structurally resemble a turbine, which has been widely interpreted as an adaptation for improving pollination by producing complex aerodynamic effects. We tested the turbine interpretation by quantifying patterns of pollen accumulation on ovulate cones in a wind tunnel and by using simulation models based on computational fluid dynamics. We used computer-aided design and computed tomography to create computational fluid dynamics model cones. We studied three species: Pinus radiata, Pinus sylvestris, and Cedrus libani. Irrespective of the approach or species studied, we found no evidence that turbine-like aerodynamics made a significant contribution to pollen accumulation, which instead occurred primarily by simple impaction. Consequently, we suggest alternative adaptive interpretations for the structure of ovulate cones. aerodynamics | computational fluid dynamics | computed tomography | wind pollination

Pollination commonly limits seed production, as addition of pollen to stigmas often increases fecundity. This response is usually interpreted as evidence that plants' stigmas receive too few pollen grains to maximize ovule fertilization (quantity limitation); however, many genetic studies demonstrate that poor-quality pollen can also reduce seed production (quality limitation). We explore both aspects of pollen limitation theoretically with a dose-response model that incorporates a saturating negative-exponential relation of seed production to pollen receipt. This relation depends on aspects of ovule production, pollen import, pollen-pistil interactions and seed development, all of which can contribute to pollen limitation. Our model reveals that quantity limitation is restricted to the lowest range of pollen receipt, for which siring success per pollen grain is high, whereas quality limitation acts throughout the range of pollen receipt if plants do not import the highest-quality pollen. In addition to pollinator availability and efficiency, quantity limitation is governed by all post-pollination aspects of seed production. In contrast, quality limitation depends on the difference in survival of embryos sired by naturally delivered pollen vs. by pollen of maximal quality. We briefly illustrate the distinction between these two components of pollen limitation with results from the mistletoe Tristerix corymbosus. Our model also shows that the standard pollen-supplementation technique neither estimates the total intensity of pollen limitation nor distinguishes between its quantity and quality components. As an alternative, we propose a methodological protocol that requires both measurement of seed production following excess pollination with only outcross pollen and quantification of the dose-response relation of seed output to pollen receipt. This method estimates both the total extent of pollen limitation and its two components. Finally, we consider the influences on quantity and quality limitation, which reveals that quantity limitation probably occurs much less often than has been inferred from pollen-supplementation experiments. These interpretations suggest that an expanded perspective that recognizes the fecundity consequences of pollination with poor-quality pollen would promote ecological understanding of pollen limitation. Key words: plant reproduction; pollen limitation; pollen quality; pollination; seed production; supplemental pollination; Tristerix corymbosus.

A model is presented that describes gene flow levels influenced by animal pollinators between source and sink populations, using bumblebees and oilseed rape (Brassica napus) as an illustration. A likelihood analysis of the model's practical application reveals discrepancies in gene flow levels predicted by the model; it is posited that other factors such as wind pollination may account for these discrepancies.

Recent reviews of plant--pollinator mutualistic networks showed that generalization is a common pattern in this type of interaction. Here we examine the ecological correlates of generalization patterns in plant--pollinator networks, especially how interaction patterns covary with latitude, elevation, and insularity. We review the few published analyses of whole networks and include unpublished material, analyzing 29 complete plant--pollinator networks that encompass arctic, alpine, temperate, Mediterranean, and subtropical--tropical areas. The number of interactions observed (I) was a linear function of network size (M) the maximum number of interactions: 1n I = 0.575 + 0.61 1nM; [R.sup.2] = 0.946. The connectance (C), the fraction of observed interactions relative to the total possible, decreased exponentially with species richness, the sum of animal and plant species in each community (A + P): C = 13.83 exp[-0.003(A + P)]. After controlling for species richness, the residual connectance was significantly lower in highland (>1500 m elevation) than in lowland networks and differed marginally among biogeographic regions, with both alpine and tropical networks showing a trend for lower residual connectance. The two Mediterranean networks showed the highest residual connectance. After correcting for variation in network size, plant species were shown to be more generalized at higher latitude and lowland habitats, but showed increased specialization on islands. Oceanic island networks showed an impoverishment of potential animal pollinators (lower ratio of animal to plant species, A : P, compared to mainland networks) associated with this trend of increased specialization. Plants, but not their flower-visiting animals, supported the often-repeated statements about higher specificity in the tropics than at higher latitudes. The pattern of interaction build-up as diversity increases in pollination networks does not differ appreciably from other mutualisms, such as plant--seed disperser networks or more complex food webs. Key words: food web; geographic variation; insects; interaction-web connectance; mutualism; networks; plant--animal interaction; pollination; specialization.

Use of the mass-action model of pollen transfer for the flowering plant Erythronium Grandiflorum shows that only 0.4% of the pollen taken from the anthers is used in self-pollination, indicating that the equilibrium rate of self-pollen deposition should be 50% instead of the observed 0.5%. This difference between the actual and estimated figures may be due to inbreeding depression and also because the functional relationship between self-pollination and discounting assumed in the mass-action model may not apply to this flowering plant. Hence pollen discounting does not explain the continuance of outcross pollination in Erythronium Grandiflorum.

A set of mathematical models is developed to describe the relationship between the sizes of pollen grains and female receptors which result in maximum anemophilous pollen transfer. The models predict anemophilous plants should have Stokes numbers in the range of 1.0 to 2.72. The Stokes number is a function of both pollen size and effective receptive surface size. The models were tested with data gathered for 28 assumed anemophilous species and 20 known zoophilous species. The models identify anemophily with an accuracy of approximately 75%. If pollen size alone is used to determine anemophily, then accuracy drops to only 50%. The Stokes number criterion reported here could help in the determination of anemophily of extant and fossil plant taxa.