The Role of Game Theory in Evaluating the Evolutionary Stability of Plant-Pollinator Networks
In class we often discuss networks pertaining to friendships, social media platforms, and the web. However, some of the first and most important networks developed were food webs and those that modeled ecological processes. An example of this are the mutualistic interactions between species such as pollination and plant-fungus interactions that are ubiquitous in nature and are essential for ecosystem functioning. Often a multitude of species with different degrees of specialization form complex networks of interdependence. In a paper that was published this past spring by Soeren Metelmann et al. they presented a new game theory approach to model complex mutualistic interactions and applied it to pollination networks. The majority of plant species are pollinated by a large range of animals and theses pollinators often visit a wide range of plant species in return. An important aspect of such a network is that its structure strongly affects the fitness of individual plants. Pollinators that are specialized to a specific plant have a high rate of pollen transport, whereas the efficiency of pollination is low for generalist pollinators that pollinate multiple plant species.
Since the fitness of a plant not only depends on the strategy of the species but also the strategies of other plant species nearby, the situation can be regarded as a game between plant species. The researchers developed a game theoretical model in which the players are the different plant species. The plant fitness, measured by the efficiency of pollen transport, was the payoff. A mathematical model was developed to represent this game and was then implemented using Python. Each run started with a community in which plant and animal species were linked randomly. In each time step, one plant species was randomly chosen and a link was randomly attached or removed from it. The change was accepted if the pollination efficiency of the chosen plant species increased and rejected if it decreased. If the pollination efficiency stayed the same the change was accepted with a chance of 50%. This analysis revealed that there are multiple stable network structures and they form a gradient from generalism to specialism with increasing pollination service. Specifically, they found efficient communities only developed under pollination oversupply and pollination shortages led to selection of inefficient network structures. This suggests that the availability of pollination services is a key factor structuring pollination networks.
When we were first learning about game theory in class one of the games we were presented with was the prisoners dilemma. Interestingly, the payoff matrix for sever pollinator shortage shares basic features with the prisoner’s dilemma. The fitness for both plant species would be highest if both specialize, but such a network structure is not evolutionarily stable. Thus, when pollinators are scarce, plants suffer from both pollinator shortage and inefficient use of pollinators due to a “pollination dilemma”. This is similar to how prisoner A and prisoner B will be best rewarded if they both remain silent, but any rational prisoner will betray the other prisoner. Thus, they end up betraying each other and not maximizing their payoffs.
Biologists and ecologists have accumulated a huge amount of data about species interactions, and by utilizing game theory and network theory when analyzing this information we unlock the possibility of gleaming profound insights into our worlds ecological interactions.
https://www.biorxiv.org/content/biorxiv/early/2018/03/22/286294.full.pdf