bumble bee

Dreisig (1995)

Low (<0.1 plants m~2) Anchusa officinalis

bumble bee

Dreisig (1995)

Plant density and plant species tJF



High and low Cynoglossum officinale high (in population) low (isolated) Echium vulgare high (in population) low (isolated)


Anchusa officinalis Ar alia hispida Ipomopsis aggregata Ipomopsis aggregata Nepeta cataria

Sagittaria australis Sagittaria latifolia Symphytum officinale

bumble bee bumble bee bumble bee bumble bee hummingbird hummingbird honeybee bumble bee solitary bee bumble bee, solitary bee bumble bee, solitary bee, etc. bumble bee

Klinkhamer et al. (1989)

Klinkhamer & de Jong (1990)

Andersson (1988) Jliomson (1988) Pyke (1978b) Brody & Mitchell (1997) Sih & Baltus (1987)

Muenchow & Delesalle (1994) Muenchow & Delesalle (1994) Goulson et al. (1998b)

Source: Adapted from Ohashi & Yahara (1999).

nectar production per flower from bottom to top (Pyke 1978a; Best & Bierzychudek 1982; but see Corbet et al. 1981). Pollinators moving vertically up each inflorescence, therefore, may experience a gradual decrease in gain per flower. Even without a spatial gradient of nectar productivity, pollinators that preferentially probe fresh flowers with higher nectar productivity (Gori 1989; Kevan et al. 1990; Oberrath & Bohning-Gaese 1999) may also experience patch depression, because they are increasingly likely to encounter an old, less-rewarding flower as they stay longer on a plant.

Another possibility is revisitation of flowers that it has previously probed, receiving little or no nectar. If the risk of revisiting flowers increases with the number of flowers probed, patch depression will result, even in the absence of variation in nectar productivity among flowers. In the few published studies, flower revisitation rates, defined as the fraction of flower visits that are to a flower previously probed while the pollinator was on the same plant, are low (2.9% in Pyke 1979; 3.5% in Pyke 1982; 0.2% and 3.0% in Galen & Plowright 1985). However, if pollinators avoid revisitation by curtailing their visit duration on plants, low frequency of total revisitation does not necessarily mean that it cannot cause patch depression. To evaluate flower revisitation, we must investigate whether the revisitation rate increases with the number of flowers probed on a plant. To our knowledge, only three field studies quantified this relationship (Pyke 1978&, 1981a, 1982), where revisitation rate increased with the number of flowers probed (up to approximately 10%-50% before all available flowers were probed). In an experimental study, Redmond & Plowright (1996) have also reported that revisitation rate increased with the number of flowers probed within a patch (up to approximately 25%).

To what degree can a pollinator remember flowers that it has previously probed on a plant.? Pollinators often possess large long-term memory capacity for spatial information, such as the location of the home, the nest, and of flower patches, as well as their positions relative to surrounding landmarks (Heinrich 1976; Gould 1986; Menzel et al. 1996). However, the spatial scale on which they can use spatial long-term memory may be limited because a pollinator may probe hundreds of flowers during each foraging trip (Brown & Demas 1994). Even if a pollinator could use long-term memory, the need to browse its "library" at every flower may cause a time delay (Chittka et al. 1999). In fact, honeybees and vertebrates use short-term memory ("spatial working memory") for avoiding revisitation of food sources (Brown & Demas 1994; Brown et al.

1997). If short-term memory capacity is limited, the risk of flower revisitation would increase with the number of flowers probed. This scenario is rather speculative and clearly needs further exploration.

A pollinator's directionality in its foraging movement within a patch may help pollinators to avoid revisitation, irrespective of their spatial memory ability. For example, pollinators usually move in the same direction on plants with simple vertical inflorescences (Darwin 1876; Benham 1969), so that they seldom revisit flowers (Heinrich 1975; Pyke 1978a; Best & Bierzychudek 1982). In addition, the presence of landmarks may also promote movement directionality (Pyke & Cartar 1992; Redmond & Plowright 1996). Interestingly, Pyke & Cartar (1992) suggested that such a directional movement itself is partially constrained by pollinators' spatial memory ability for patch arrival direction. At present, we know very little about the perceptual and memory mechanisms underlying such effects.

Other potential mechanisms for avoiding flower revisitation are perceptual discrimination of nectar (Heinrich 1979a) or footprints (scent marks: Goulson et al. 1998a; electrostatic change: Erickson & Buchmann 1983). The availability of such mechanisms is likely to depend on pollinators' abilities to discriminate the cues and on pollinator visitation frequency (Dreisig 1995). Therefore, it will require careful investigation to determine how these mechanisms are effective for avoiding revisitation in the context of natural foraging.

The effect of flower number

Recently we have developed a theoretical model to predict the relationship between the optimal number of flowers probed per plant and floral display size (Ohashi & Yahara 1999). We considered the increasing risk of revisitation to be the major cause of depression for a pollinator foraging on a plant, as it seems to be a very probable mechanism. To incorporate this effect into the model, we assumed that a pollinator remembers probing a maximum of m flowers on the plant and avoids revisiting them. We referred to m as "memory size", although it incorporates effects of both the actual memory capacity and of other factors discussed above. If the memory size (m) is limited, as we have noted, the risk of revisitation would increase with the number of flowers probed. Furthermore, larger displays offer more flowers from which to choose, which would decrease the risk of revisitation (e.g., see Table 14 in Pyke 1982). We also incorporated the cost of interplant movement by defining the mean discounting rate for visiting another plant as k = [(flight time between flowers within a plant) + (handling time per flower)]/[(flight time between plants) + (handling time per flower)] (0 < k ^ 1). For simplicity, the rate of energy expenditure was assumed to be constant. Then, the following formula approximates the relationship between the optimal number of flowers per plant and the display size:

tc = (1 -k) F + mk (F > m), tc = F (F < m) (14.1)

where tc is the number of flowers probed per plant and F is the size of floral display.

The observed data (Table 14.1; Fig. 14.1B) agree well with the prediction ofour model (Fig. 14.2B). First, pollinators probe fewer flowers than available. Second, the number of flowers probed increases with, but less rapidly than, the size of floral display (but see Sih & Baltus 1987). Third, the number of flowers per plant increased more rapidly with floral display size in low-density plant populations than it did in high-density populations (Klinkhamer et al. 1989; Klinkhamer & de Jong 1990).

It is worth noting that the aim of our model is not to demonstrate a patch-leaving rule that visitors actually follow, but simply to find the ideal point ofplant departure for pollinators. In nature, it is well known that pollinators often leave the plant just after probing one to two flowers with little or no nectar (Fig. 14.3) (Pyke 1978&, 1982; Thomson etal. 1982; Hodges 1985). Pollinators usually do not have "complete information" on the nectar distribution on the current plant, so that such a simple probabilistic rule may provide a practical method for pollinators to approach the purely mathematical optimum (see also McNamara & Houston 1980; Iwasa etal. 1981). In a stochastic environment, probabilistic rules may work better than leaving plants deterministically following Eq. 14.1.

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