Evolutionary implications

Effects of plant density on the evolution of floral display

Plants growing at low densities are said to experience some reproductive difficulties through alterations in pollinator behavior for at least three reasons. First, they may have trouble attracting pollinators away from competing resources because they are economically inefficient to exploit (Kunin 1997). Second, pollinators are more likely to behave as generalists on sparsely distributed plants and to lose pollen during interspecific flights or clog stigmas with foreign pollen (Kunin 1993). Third, pollinators may probe more flowers per plant at low density, which may increase geitonogamy (Bosch & Waser 1999 and references therein).

In addition to such population-level effects, lowered plant density may cause changes in pollen dispersal among different-sized displays. Ohashi & Yahara's (1999) model predicts that pollinators probe more flowers per plant with decreasing plant density particularly on larger floral displays. Moreover, the model predicts that pollinators would show a weaker preference for visiting large floral displays over small ones at lower plant density. Such an effect could aggravate the relative disadvantage of larger displays growing at low densities; it would reduce xenogamy and increase geitonogamy. To clarify these influences, we describe a model by incorporating pollinators' optimal behavior into the model of pollen transfer. We independently developed this model, but very similar theoretical ideas were developed by Iwasa et al. (1995), who tried to explain the small number of flowers probed by a pollinator per plant as a plant's strategy to maximize pollen dispersal. We assume that: (1) pollen on a pollinator constitutes a single, homogeneous pool; (2) a pollinator deposits and picks up pollen in equal amounts at each flower ("pollination saturation"; de Jong et al. 1993); and (3) this amount is a constant fraction of the amount of pollen held on a pollinator's body. This simple model (the exponential decay model with a constant pollen carryover) is the most commonly used theoretical description of pollen transfer (reviewed by Harder & Barrett 1996). Even when we adopt more realistic models such as the changing carryover model (Morris et al. 1994) or models with pollen loss during transports (Rademaker et al. 1997; Harder & Wilson 1998), the qualitative conclusion of the present analysis remains unchanged. We further assume that: (4) nectar production rate per flower is constant; (5) pollinators are always competing for floral resources; and (6) the plant is self-incompatible and the total number of pollen grains exported from a plant is a measure of its male fitness.

The number of pollen grains exported from a plant per pollinator per visit (E) is expressed as:

E = A + A(1 - d) + A(1 - d)2 +... + A(1 - d)fc-i = A(1 - Ctc) / (1 - C) (14.4)

where A is the amount of pollen held on a pollinator's body, d is the fraction of pollen picked up or deposited at each flower, tc is the number of flowers probed per plant, and C is pollen carryover (C = 1 - d). Then, assuming that pollen dispersal is limited by pollinator visits, the total number of pollen grains exported from a plant with F open flowers (male fitness, W) is found by combining Eqs. 14.3) and 14.4:

W = VpE = VfFA [1 -C(1 - k)F+mk] / {[(1 - k)F + mk] (1 -C)}. (14.5)

Figure 14.5 shows that under the assumption of the IFD (i.e., Vf is constant), male fitness (W) increases with floral display size (F), but the average male fitness gain per flower (W/F) decreases with display size.

Floral display size (F)

Fig. 14.5. Predicted relationship between floral display size (F) and male fitness (W). W is determined by numerical solution of Eq. 14.5, for Vf = 1, m = 1, A = 10, and C = 0.9. The dashed line represents male fitness when k = 1.

Floral display size (F)

Fig. 14.5. Predicted relationship between floral display size (F) and male fitness (W). W is determined by numerical solution of Eq. 14.5, for Vf = 1, m = 1, A = 10, and C = 0.9. The dashed line represents male fitness when k = 1.

Furthermore, male fitness gain per flower diminishes as the relative cost of interplant movement (1 - k) increases, especially when k is larger than 0.5.

Some authors have suggested that the costs associated with geitono-gamy may decrease with increasing display size because the proportion of flowers probed per plant declines on larger plants (Snow et al. 1996). However, our model reveals that the benefits of attracting more pollinators do not counteract the cost of increased geitonogamy, even if pollinator availability and pollen carryover is large (see also de Jong et al. 1993). In addition to this, we found that a small rise in the relative cost of interplant movement dramatically increases the cost of geitonogamy on larger displays. Based on this result, we can suggest that plants that typically grow at low densities (due to competition, predation, colonization to novel habitats, etc.) will be subject to strong natural selection favoring small displays or extended blooming. Both in warm-temperate and cool-temperate forest on Yaku Island, Yumoto (1987) found a suggestive pattern that climbers, epiphytes, and most of the understory shrubs, which typically grow at low density and are visited by specialist pollinators, exhibited extended blooming. At present, however, there are no empirical data on such a tendency in any particular plant-pollinator system.

Note that the optimal floral display size in actual plant-pollinator systems may be often larger than our models would predict because: (1) a plant population consisting of small displays cannot attract sufficient pollinators (Kunin 1997), so that among-population selection for larger displays may be strong enough to oppose individual selection for smaller displays; (2) flowering time can be constrained by biotic and/or abiotic factors such as frost, rainfall, or the availability of seasonal pollinators (Rathcke & Lacey 1985); and (3) the opportunity of geitonogamy can be reduced by spatio-temporal separation of sexes such as dioecy or gynodio-ecy (Thomson & Brunet 1990), synchronized dichogamy (Cruden 1988), and dichogamy coupled with vertical inflorescences (Pyke 1978a).

Can plants manipulate pollinators to their own advantage.' Some possibilities of plant traits that promote movements between plants

If plants can shorten pollinators' visit sequences, they can increase male fitness as a result of decreased geitonogamy. Iwasa et al. (1995) modeled this effect and found that pollinator behavior that maximizes pollen export (male fitness) is qualitatively similar to observed pollinator behavior. Is this agreement fortuitous, or a result of pollinator manipulation by plants in an evolutionary sense? Based on considerations of optimal foraging, we now discuss possible strategies by which plants can manipulate their pollinators to their own advantage.

(1) Low nectar reward. Many authors have reported that lower nectar rewards often cause pollinators to depart earlier from plants and promote interplant movements (e.g., Heinrich 1979b). Lower nectar reward might therefore be advantageous unless pollination is inefficient (Robertson 1992; Iwasa et al. 1995). Moreover, decreased investment in nectar production will allow plants to reallocate resources into ovules, which can improve fitness (Pyke 1991; Sakai 1993).

(2) Gradient of nectar production within a structured inflorescence. On plants with vertical inflorescences, spatial gradient in the nectar productivity (or crop) decreasing from bottom to top may be an important cause of patch depression in place of flower revisitation (see above). In fact, Orth & Waddington (1997) found that carpenter bees foraging on vertical inflorescences with no spatial gradient of nectar rewards probed a larger proportion of flowers than reported in other studies where there was a nectar gradient.

(3) Within-plant variation in nectar productivity per flower. Rathcke (1992) stated that if within-plant variation in nectar per flower increases the likelihood of pollinators' encountering low-reward flowers, it might shorten visit sequences. Observed simple departure rules adopted by pollinators (e.g., Fig. 14.3) seem to support this idea. However, pollinators may alter their departure rules in response to changes in spatial distribution of nectar rewards (Iwasa et al. 1981). Moreover, different pollinator species may adopt different rules of plant departure (Collevatti et al. 1997). Thus, further empirical and theoretical studies are needed before generalizing this argument.

(4) Retention of old flowers coupled with floral color (or scent) change. After they have landed on plants, pollinators often avoid old, less-rewarding flowers by their color or scent, while they have little or no ability to discriminate between different-aged flowers at a distance (Oberrath & Bohning-Gaese 1999 and references therein). Therefore, some authors have suggested that the retention of old flowers -coupled with floral color or scent changes - may enable plants to increase the pollinator visitation rate per plant while simultaneously decreasing the proportion of flowers probed per plant (Gori 1983; Oberrath & Bohning-Gaese 1999). The adaptive value of this strategy may be greatest in plant species bearing small flowers, where the cost of retaining an old flower will be small, pollinators cannot discriminate different-colored flowers at a distance, and clustering of flowers may greatly improve the plant's long-distance attractiveness.

(5) Plant traits increasing the risk of flower revisitation. Spatial memory or directional movement may be affected by some plant traits. For example, Redmond & Plowright (1996) found that bumble bees revisited artificial "flowers" more often in irregular than in uniform configurations. They showed in addition that the presence of landmarks significantly reduced flower revisits when bees had to fly between flowers, but had no effect when bees could walk between flowers. Also, Brown et al. (1997) suggested that spatial working memory capacity of honeybees is limited by their ability to discriminate among locations in close proximity. Therefore, inflorescence architecture (complex or close-packed arrangements of flowers, the absence of bract leaves, etc.) may shorten pollinators' visit sequences, mediated through the increased risk of flower revisitation.

(6) Plant traits reducing the relative cost of interplant movement. If plants can reduce the relative cost of inter-plant movement, they can greatly improve their male fitness (Fig. 14.5). Based on our definition of the mean discounting rate for visiting another plants (k; see above), we suggest two possible strategies. One is asynchronous flowering of adjacent flowers, which would increase the average flight distance within a plant. Another strategy is producing deep flowers - or veiling nectaries behind complex floral structures - which would increase handling time per flower (Harder 1983, 1986). This strategy may be efficient only when autogamy does not increase with handling time per flower (Zimmerman 1988). Deep flowers have been discussed in the context of nectar protection (Corbet 1990), evolutionary race with pollinator tongue (Darwin 1862; Nilsson 1988), the exclusion of generalists (Heinrich 1979b; Laverty 1980), and the promotion of flower constancy (Darwin 1876; Laverty 1994). In addition to these, we indicate a novel functional value of deep flowers, i.e., the promotion of pollen dispersal.

We must note that plants or populations adopting any strategies discussed above may sometimes increase the risk of pollinator deficiency because they could be economically inefficient to exploit (Zimmerman 1988). For example, pollinators often learn to avoid patches with low reward levels (Dreisig 1995) or high reward variation ("risk-aversive foraging"; Perez & Waddington 1996). Despite such possibilities, we feel that the available data indicate that plants can improve their pollen dispersal by altering pollinator behavior. The importance of these characteristics in improving pollen dispersal is totally hypothetical at this time, and again, awaits theoretical and empirical exploration.

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