[T h t h i 1 Ni142

where i is the number of flowers probed per plant, T is the flight time between plants, t is the time between flowers on the same plant, and h is the handling time per flower. As T is usually longer than t, total movement costs would decrease with increasing i. This advantage is greater if pollinators could walk between flowers on plants or inflorescences, which

Fig. 14.3 Time spent by bumble bees on the last- and non-last-probed heads in each visit to a Cirsiumpurpuratum plant. The five horizontal lines of the plot indicate the 10th, 25 th, 50th, 75th, and 90th percentiles of the data (U = 824.5, p = 0.0056; Mann-Whitney U-test). (Adapted from Ohashi 1998.)

Flight distance (m)

Fig. 14.4. Floral display size of plants visited by bumble bees after flying different distances. Bars indicate the average number of available heads per plant (± SE). The size of floral display visited after the flight differed significantly among distance categories (8 Sept H = 12.04, P = 0.002; 5 Oct H = 13.00, p = 0.002; 9 Oct H = 12.69, P = 0.002; Kruskal-Wallis test). (Adapted from Ohashi & Yahara 1998.)

Flight distance (m)

Fig. 14.4. Floral display size of plants visited by bumble bees after flying different distances. Bars indicate the average number of available heads per plant (± SE). The size of floral display visited after the flight differed significantly among distance categories (8 Sept H = 12.04, P = 0.002; 5 Oct H = 13.00, p = 0.002; 9 Oct H = 12.69, P = 0.002; Kruskal-Wallis test). (Adapted from Ohashi & Yahara 1998.)

requires about 90% less energy expenditure per time than flight (Heinrich 1975). As above, however, if large floral displays are infrequent in the population, this hypothesis also may not hold because pollinators would choose small but closer displays more frequently. In fact, some authors have found that pollinators often choose small displays when they are close (Fig. 14.4) (Pyke 1981&). Moreover, the visitation rate per flower rarely increases with floral display size (Table 14.1), which suggests that the reduced movement costs on large displays are of minor importance in determining pollinators' preferences for large displays. Thus, we have to reconsider our view about "attractiveness" of large floral displays.

Incorporating the ideal free distribution into the model

Robertson & Macnair (1995) have suggested that, when plant density is relatively high, optimally foraging pollinators should visit flowers on all sizes of displays at equal rates, following Fretwell & Lucas's (1970) theorem of the "ideal free distribution." The ideal free distribution (IFD) is an equilibrium state that arises as a consequence of repetitive movements of competitors in search of more profitable local areas. In the case of plants and pollinators, the profitability of a plant (mean nectar crop)

may decrease linearly with the average visitation rate per flower, because nectar crop per flower increases linearly with renewal time, at least at the scale of actual inter-visit times (Kadmon 1992). This situation corresponds to the simplest IFD model, i.e., the "continuous input" model (Parker & Sutherland 1986), which expects the average visitation rate per flower to be directly proportional to its nectar productivity. Since nectar production rate per flower often shows no significant correlation with floral display size (Harder & Cruzan 1990 and references therein), this model expects that the average visitation rate per flower would be equal between large and small displays (Dreisig 1995).

Based on this idea, Ohashi & Yahara (1999) have expanded the former model (Eq. 14.1) for the cases where display size is variable. The visitation rate per plant (Vp) is expressed as:

where Vf is the average visitation rate per flower (constant under an IFD). As shown in Fig. 14.2A, pollinator visitation rate per plant (Vp) is a decelerating function of floral display size (F). This prediction agrees well with previous results (Fig 14.1A) (Iwasa et al. 1995 and references therein; but see Sih & Baltus 1987; Andersson 1988; Ohara & Higashi 1994). Moreover, visitation rate per plant (Vp) increases more rapidly at higher plant density. This is because a reduction in the proportion of flowers probed per plant reduces the competition among pollinators on large floral displays. This prediction agrees with the observation that bumble bees visited large floral displays less preferentially at lower plant density (Klinkhamer et al. 1989; Klinkhamer & de Jong 1990; Dreisig 1995). Note that the prediction of our model is opposite to the intuitive prediction deduced from the previous two hypotheses. If the detectability of floral display is most important, the visitation rate per plant (Vp) would increase less rapidly with display size (F) at higher plant density because pollinators could detect smaller sizes of floral display. The same prediction will result when the flight cost is most important, because both the cost of interplant movement (T in Eq. 14.2) and the proportion of flowers probed per plant (tc/F) would decrease with increasing plant density. Clearly, observation of pollinator behavior alone is not a sufficient proof for the relative importance of competition among pollinators. We emphasize the value of simultaneously exploring pollinator behavior and nectar availability in future studies. Moreover, functional responses of pollinators other than bumble bees (birds, honeybees, solitary bees, flies, butterflies, beetles, etc.) need to be explored more intensively.

The strategies that individual pollinators might use to achieve an IFD are still open to question. As Dreisig (1995) suggested, pollinators' preferences for large floral displays may partly explain the IFD. Furthermore, in the real world, nectar distribution among plants may fluctuate over time. If a pollinator could respond to such spatio-temporal variation, it would achieve an IFD more accurately. For example, pollinators are known to fly longer distances after encountering lower rewards ("area-restricted searching"; reviewed by Motro & Shmida 1995). By adopting this rule while foraging along its own "trapline" (Thomson et al. 1997 and references therein), pollinators may efficiently reduce the spatio-temporal bias in nectar distribution. Also, a trapline forager may occasionally sample new plants to detect and respond to temporal changes in nectar distribution among plants (Thomson et al. 1987). The spatial scale on which pollinators should adopt these strategies will depend on the spatial distribution of flowers, the frequency of revisitation, pollinators' energetic requirements, perceptual and memory constraints, and the number of competitors. Clearly too little is known at present to draw any conclusion about these issues.

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