Nicholas A. Yager

Agent-Based Exploration of Plant-Pollinator Mutualism

08 Dec 2013

From as early as 1869, apiarists have reported a set of symptoms in which colonies lose many adult worker bees leaving behind large stores of food, brood, and even the queen. Colony Collapse Disorder, as described above, continued at a steady incidence rate of ~17-20% in the 1990s and early 2000s. The rate of CCD started to increase, however, in November of 2006 to between 30% and 90% (an admittedly large range).


Figure 1: A European honey bee Apis mellifera extracts nectar from an Aster flower using its proboscis. Tiny hairs covering the bee's body maintain a slight electrostatic charge, causing pollen from the flower's anthers to stick to the bee, allowing for pollination when the bee moves on to another flower. Image released into the public domain by John Severns.

Bees are an important component in the pollination of plants, particularly in modern agriculture where bees are known to pollinate over 120 different species of crop. Given that pollinators, such as bees, are known to develop mutualistic relationships with particular species of plants, Matthew Taylor, Andrew Patt, and I set out to create an agent-based model to explore how obligate pollination affects the dynamics of plant competition.

We started by creating a simulation in which two species of flowering plant compete for reproductive space in a torus shaped world, the specifics of which are depicted in the compartment model in Figure 2. The real magic happens in the interactions between pollinators and the plants. In orderi for plants to reproduce, the pollinators must land on the plants and transfer pollen with a compatible chromosome. On the pollinator side, pollinators travel around the world in a correlated random walk, landing on flowers based on predetermined preferences all the while transfering previous plants' genetic material.

compartment model

Figure 2: Compartment model of the simulation's interactions. Plant populations are determined by the number of seeds created and the mortality rate for the particular species. Seed output is determined by a pollinator's ability to gather and transmit pollen. Pollinators are recruited and derecruited based on their ability to gather pollen from a valid plant species.

Space being the primary limiting factor in growth, the creation of empty space required a mechanism for plant death. We used psudo-realistic mortality rates for plants wighting approximately 500 grams, following the mortality prediction work done by Michael W. McCoy and James F. Gillooly. All simulations started with a 90% populated world with a variable starting proportion of "red" and "blue" plants.

simulation example

Figure 3: Animated view of a 50% red plant simulation without obligate pollinators. The colors of cells represent the color of the plant. Black cells represent empty cells. As the animation progress, the stochastic placement of seeds and pollinators results in an evolving system ending in this case with red domination.

From this general guideline, a simulation was created in C. To compare outcomes , we defined "win" scenarios; situations in which one species had a larger population at the end of a simulation, or had driven the other species to extinction. We then set up simulations at various proportions of red plants and found the proportion of simulations in which red plants "won" at the observed seed proportion. The outcomes of these scenarios are plotted in Figure 4, which shows a sigmoidal curve centered around a population of 50% red plants having equal odds of wining a simulation.

red wins data

Figure 4: Proportion of wins for red plants by starting proportion of red plants. Each point represents the proportion of red wins out of 20 trials, sorted by the starting proportion of red plants. The color is the relative color makeup of the world at the start of the simulation. The curve is a classic sigmoidal curve, which would suggest cooperativity where large populations of a species results in further propagation of the species at a higher rate.

Due to the abstract nature of the simulation, the only way to verify the accuracy of our model was to have a redundant system running in a different language written in a clean room scenario following the same spec. To that end, we created another simulation in R to follow the same guidelines, with the only difference being the starting population size (approximately 10%). These two models were compared using the data described above, as shown in Figure 5, and are thought to behave very similarly despite the different interpretations.


Figure 5: Comparison of C and R simulations, verifying simulated results. The R simulation, as shown in orange, is differs from the C simulation in that that pollinators are represented as a probability of a plant getting pollinated, whereas the C simulation uses agents that transport pollen. The simulations also differ in initial population size, where the C simulation initially saturates the world and the R simulation starts with a population of 20 plants. These differences are reflected in the diminished cooperativity, as shown in the shallower slope in the R simulation. It should be noted that both simulations result in the sigmoidal plot with an inflection point about an initial frequency of 0.5 red plants.

With the accuracy of our simulations verified, we examined the effect of an obligate pollinator on the "win" frequency. Within our simulations, we assigned a species of pollinator a specific attraction to only red plants, effectively doubling the possible pollination events. The "win" frequency was plotted for this scenario in the same fashion as in Figure 5. As shown in Figure 6, there is a sigmoidal curve with an inflection point focused around an equal probability of winning. The position is shifted to the left, however, suggesting that the red plant is capable of winning a simulation with a much smaller starting population so long as it has the obligate pollinator.

obligate plot

Figures 6: Obligate pollination results in an extreme competitive advantage. Similar to Figure 5, the red-obligate pollination scenario presents a sigmodial curve of cooperativity between the pollinators and the plants. This curve, however, has been shifted to the left, suggesting that the red plants will have a 50% chance of winning with as low as a 0.17 or 0.18 starting frequency.

Assuming that our model reflects the natural process of pollination, our data suggest that an obligate pollinator would be very beneficial to its mutual partner. This could be used to the advantage of agriculture if a pollinator could be modified or trained to highly favor one source of pollen over another. The ramifications of such highly competitive plants could reduce our dependence on pesticides, improve declining bee populations, and potentially result in better crop yields.

Furthermore, our model suggests that plants are extremely dependent on the surrounding pollinator population. As such, if the rate of CCD were to increase, it could bode ill for many in the agricultural industry.

In the months ahead, Matt Taylor, Andrew Patt, and I will continue refining our model with:

We aim to better understand the dynamics of pollination, and to adjust our model to be descriptive about the world. Other interests we are considering are examining an evolutionary approach to forming mutualistic relationships, and examining competition on large scales between multiple species.

As a side note, Figure 3 was created in R using the Animate package. A rundown on how to use the Animate package will up in the coming week with instructions on how to make GIFs.

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