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Passive partner choice through exploitation barriers

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Abstract

Floral features that affect the efficiency with which pollinators can harvest their resources, or the profitability they obtain from them, affect the foraging decisions of pollinators. Foraging choices of pollinators, in turn, affect pollen flow: increases in flower constancy lead to more efficient pollen transport. It follows that exploitation barriers—flower traits that differentially affect net intake rates of potential visitors—will promote resource partitioning and enhance pollen export. In this paper we first generalise foraging models to show that exploitation barriers can lead to partial resource partitioning even when flowers are randomly distributed in space. Then we develop a model to study how the foraging rules of pollinators, pollen removal and pollen deposition, affect pollen flow. The model shows that resource partitioning, even incomplete, can substantially increase the efficiency of pollen flow. Finally, we use computer simulations to demonstrate that exploitation barriers promoting partial resource partitioning can evolve. Many of the flower traits associated with pollination syndromes have small but consistent effects on the efficiency with which different taxonomic groups exploit flowers, and can be considered exploitation barriers. Even if these barriers are not strong enough to promote strict specialisation, and may have little effect on the female component of fitness when pollinators are not a limiting resource, they are likely to be selected because they enhance the male component of fitness.

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Acknowledgments

This work was supported by the Ministerio de Ciencia e Innovación/FEDER (Project CGL2010-16795 to MARG and LS). S.S acknowledges support by the National Natural Science Foundation of China grant No. 31100277 and the Fundamental Research Funds for the Central Universities (lzujbky-2013-99).

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Correspondence to Luis Santamaría.

Appendix

Appendix

Generalities

We used a genetic algorithm to calculate the optimal foraging strategy of pollinators. Each generation 200 pollinators (100 of each species) foraged on a 100 × 100 square lattice (with periodic boundary conditions) containing one flower per cell. Cells were randomly assigned to plant species each generation (equal probability of belonging to each species; no spatial correlations). Pollinators, endowed with a genetically determined foraging strategy, foraged throughout the season (for most generations, 20,000 time units). At the end of the season a new generation of pollinators was produced: pollinators that obtained more nectar produced more offspring, and mutations were introduced to probe new foraging strategies. The process was iterated for 10,000 generations.

Nectar production

The volume of nectar per flower, V, increased according to

$$V = 1 - e^{ - \theta t}$$
(10)

where θ is a parameter that determines the rate of nectar production and t represents the time since the flower was last visited.

Movement rules

At the beginning of each generation, pollinators were located at random positions of the grid. Thereafter, pollinators moved from the flower they occupied to one of its nearest neighbours, consumed the nectar encountered and moved on to a new flower. The program kept track of the amount of nectar ingested by each pollinator through the season. The foraging strategy of a pollinator simply determined to which flower it moved. It was coded in two genes (pollinators were haploid, and had a single copy of each gene) determining the attractiveness of flowers of each species, αA and αB. A pollinator on a flower had 8 nearest neighbours, indexed by l = 1, 2, … 8. Each neighbour was assigned a weight,

$$w_{l} = \frac{{\alpha_{l} }}{{d_{l} }}$$
(11)

where dl represents the distance the pollinator must travel to reach the flower (dl = 1.414 for flowers along the diagonal, and dl = 1 otherwise), and the probability that the pollinator visited flower l was 0 if it was being exploited by another pollinator or had been visited by the focal pollinator in the ten previous rounds, and otherwise

$$p_{l} = C \cdot e^{{w_{l} }}$$
(12)

where C is a normalisation constant.

Time budgets

The duration of a foraging cycle (time from the departure from one flower to the departure from the following flower) was equal to the sum of three terms: travel time, handling time and ingestion time.

We assumed that all pollinators flew at the same speed, equal to 1 grid cell per time unit. Travel time was therefore equal to 1 or 1.414 time units—depending on whether the pollinator travelled along one axis or along the diagonal.

Handling time, τij, had a species-specific component—determined by the phenotype of flowers and pollinators—and an individual component—determined by experience. The minimum and maximum handling times, Tmin,ij and Tmax,ij, were determined by the flower and pollinator species. Unexperienced individuals required a greater time, Tmax,ij, to get access to the nectar provided by the flower. Every time an i pollinator visited a j flower, the corresponding handling time decreased according to

$$\tau_{ij}^{{\prime }} = \varsigma \cdot \tau_{ij} + \left( {1 - \varsigma } \right) \cdot T_{min,ij}$$
(13)

Due to cognitive constraints, however, the handling time increased when the individual visited a flower of the opposite species (Laverty 1980; Lewis 1986). Specifically, we assumed that every time pollinators visited a flower of the opposite species, handling times at j flowers increased according to

$$\tau_{ij}^{{\prime }} = \varsigma \cdot \tau_{ij} + \left( {1 - \varsigma } \right) \cdot T_{max,ij}$$
(14)

As a result of 13 and 14, if a pollinator specialised on a particular flower type it achieved the minimum handling time at that flower type—at the cost of experiencing the maximum handling time if it once visited the other flower species. For pollinators visiting both flower types, handling times oscillated between their maximum and minimum values.

It takes longer to exploit flowers with more resources—a process encoded in the ingestion time. For simplicity, we assumed that ingestion time was proportional to the amount of nectar consumed.

Selection

At the end of the season we normalised the amount of intake consumed by the kth pollinator, Ik:

$$\bar{I}_{k} = \frac{{I_{k} - I_{min} }}{{I_{max} - I_{min} }}$$
(15)

where Imax and Imin represent the maximum and minimum intakes by pollinators of the focal species. From this normalised intake we obtained the individual payoff, ωk:

$$\omega_{k} = e^{{2\cdot\bar{I}_{k} }}$$
(16)

Payoffs were used to select the “parents” of the pollinators that constituted the following generation. We selected parents at random, with probabilities proportional to ωk, with the constraint that one individual could not produce more than five offspring. Of every ten parents chosen, nine produced identical offspring. For the tenth parent, preference genes, αA and αB, had a 0.2 probability of mutating. Mutations steps were normally distributed, with mean zero and standard deviation 0.03. Preference genes were constrained to lie in the interval (10−4, 10).

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Rodríguez-Gironés, M.A., Sun, S. & Santamaría, L. Passive partner choice through exploitation barriers. Evol Ecol 29, 323–340 (2015). https://doi.org/10.1007/s10682-014-9738-3

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