### Abstract

We analyze the so‐called ‘exponential decay’ model of pollen transfer for the case in which pollinators visit a fraction of the open flowers on a plant. The analysis is limited to the simplest case of a self‐incompatible species, in which self pollen does not interfere with seed set. Plants can manipulate the number of flowers visited per pollinator approach by adjusting attractiveness of flowers so as to maximize pollen export (male fitness). In the model the length of the visitation sequence that is optimal for the plant f̂ always decreases with pollen deposition rate k_{1}, pollen uptake rate k_{2}, and the number of pollinator approaches to the plant X, but increases with the total number of flowers F. We assume that the average number of pollinator approaches X increases with the total number of flowers F, but slower than proportionality. It then follows that the optimal fraction of flowers a pollinator visits after arriving on the plant (f̂/F) decreases with the total number of flowers F. Furthermore, the male fitness gain per flower generally decreases with number of flowers, except for the condition of ‘inefficient’ pollen transfer with very small values of k_{1}, k_{2}, and X, or when the plant has only a few flowers. The latter conditions should favour high nectar production and mass blooming. The known range of parameters suggests that male fitness increases with the total number of flowers slower than proportionality.

Original language | English |
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Pages (from-to) | 439-453 |

Number of pages | 15 |

Journal | Journal of Evolutionary Biology |

Volume | 8 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 1995 |

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### All Science Journal Classification (ASJC) codes

- Ecology, Evolution, Behavior and Systematics

### Cite this

*Journal of Evolutionary Biology*,

*8*(4), 439-453. https://doi.org/10.1046/j.1420-9101.1995.8040439.x

**Why pollinators visit only a fraction of the open flowers on a plant : The plant's point of view.** / Iwasa, Yoh; De Jong, T. J.; Klinkhamer, P. G L.

Research output: Contribution to journal › Article

*Journal of Evolutionary Biology*, vol. 8, no. 4, pp. 439-453. https://doi.org/10.1046/j.1420-9101.1995.8040439.x

}

TY - JOUR

T1 - Why pollinators visit only a fraction of the open flowers on a plant

T2 - The plant's point of view

AU - Iwasa, Yoh

AU - De Jong, T. J.

AU - Klinkhamer, P. G L

PY - 1995/1/1

Y1 - 1995/1/1

N2 - We analyze the so‐called ‘exponential decay’ model of pollen transfer for the case in which pollinators visit a fraction of the open flowers on a plant. The analysis is limited to the simplest case of a self‐incompatible species, in which self pollen does not interfere with seed set. Plants can manipulate the number of flowers visited per pollinator approach by adjusting attractiveness of flowers so as to maximize pollen export (male fitness). In the model the length of the visitation sequence that is optimal for the plant f̂ always decreases with pollen deposition rate k1, pollen uptake rate k2, and the number of pollinator approaches to the plant X, but increases with the total number of flowers F. We assume that the average number of pollinator approaches X increases with the total number of flowers F, but slower than proportionality. It then follows that the optimal fraction of flowers a pollinator visits after arriving on the plant (f̂/F) decreases with the total number of flowers F. Furthermore, the male fitness gain per flower generally decreases with number of flowers, except for the condition of ‘inefficient’ pollen transfer with very small values of k1, k2, and X, or when the plant has only a few flowers. The latter conditions should favour high nectar production and mass blooming. The known range of parameters suggests that male fitness increases with the total number of flowers slower than proportionality.

AB - We analyze the so‐called ‘exponential decay’ model of pollen transfer for the case in which pollinators visit a fraction of the open flowers on a plant. The analysis is limited to the simplest case of a self‐incompatible species, in which self pollen does not interfere with seed set. Plants can manipulate the number of flowers visited per pollinator approach by adjusting attractiveness of flowers so as to maximize pollen export (male fitness). In the model the length of the visitation sequence that is optimal for the plant f̂ always decreases with pollen deposition rate k1, pollen uptake rate k2, and the number of pollinator approaches to the plant X, but increases with the total number of flowers F. We assume that the average number of pollinator approaches X increases with the total number of flowers F, but slower than proportionality. It then follows that the optimal fraction of flowers a pollinator visits after arriving on the plant (f̂/F) decreases with the total number of flowers F. Furthermore, the male fitness gain per flower generally decreases with number of flowers, except for the condition of ‘inefficient’ pollen transfer with very small values of k1, k2, and X, or when the plant has only a few flowers. The latter conditions should favour high nectar production and mass blooming. The known range of parameters suggests that male fitness increases with the total number of flowers slower than proportionality.

UR - http://www.scopus.com/inward/record.url?scp=0028984073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028984073&partnerID=8YFLogxK

U2 - 10.1046/j.1420-9101.1995.8040439.x

DO - 10.1046/j.1420-9101.1995.8040439.x

M3 - Article

AN - SCOPUS:0028984073

VL - 8

SP - 439

EP - 453

JO - Journal of Evolutionary Biology

JF - Journal of Evolutionary Biology

SN - 1010-061X

IS - 4

ER -