"A novel recursive growth feedback model of a plant and mycorrhizal fungus exchanging resources results in mutualism, parasitism and competition as emergent behaviours."Grasso, SallyThe evolution of mutualism and cooperation has been a research focus for the last half decade, yet many questions about these interactions remain unanswered. Plants and their symbionts, such as mycorrhizal fungi, provide an excellent system to study the evolution of mutualism and cooperation due to historic and contemporary examples of mutualism stability and breakdown. Popular approaches to modelling the evolution of cooperation between plants and mycorrhizal fungi, such as biological market theory, and evolutionary game theory, have resulted in increased understanding. However, they contain inbuilt restrictions which are sometimes counter to real life observations, creating limitations or over-simplifications within these models. For example, models that use common currencies or exchange rates risk treating chemical elements exchanged in resource trades as interchangeable, which violates Liebig’s law of the minimum. Another limitation is that the interaction type, mutualistic, parasitic etc., is often fixed throughout the model. To address some of these limitations, we developed a novel model of an individual plant growing in interaction and exchanging resources with an individual fungus. This novel model incorporates the fundamental principles of recursive growth feedback between individuals and Liebig’s law of the minimum. In this growth model the plant and fungus interact, acquire resources, exchange resources, and grow over ten time-steps. The organisms have a ‘specialized’ resource, carbon (C) in plants and phosphorus (P) in fungi, with nutrient uptake efficiency of that resource set at 100%. The nutrient uptake efficiency of the organisms’ ‘non-specialized’ resource was set between 0 and 100%. In each time-step both organisms gather both C and P, with the amount of each determined by each organism’s size and nutrient uptake efficiency. The organisms then give a proportion of their ‘specialised’ resource to the other and grow by an amount proportional to whichever resource is most limiting (Liebig’s law of the minimum). The growth model results were used to calculate the organisms’ fitness across resource sharing percentages (-100% to 100%) and determine the interaction type between the organisms at various sharing combinations, thus allowing interaction types to emerge from the model. Evolution of the organisms’ resources sharing strategy was simulated on the coupled fitness landscape using two different algorithms: a hill climb optimization and individual based evolution. Our evolution simulations resulted in either stable mutualism or extinction (equivalent to zero growth) of one or both organisms. Simulations starting in regions of mutualism, competition, or parasitism could move through these zones and end at a stable point in the mutualism zone. Other simulations starting in competition or parasitism zones resulted in extinctions. We also found that when the plant and fungus were both highly dependent on each other for nutrients the sharing strategy that resulted in maximum fitness for each organism was the same, and when one or both organisms became more efficient at acquiring their ‘non-specialized resource’ their optimum sharing strategy became less similar. Unlike other approaches, our growth model gives rise to competition, parasitism, and mutualism without explicitly assuming these interactions, allowing organisms to move between them. The assumption of Liebig’s law of the minimum together with resource sharing and coupled fitness feedback, can produce stable mutualism. These fundamental principles have been mostly lacking from previous models. Our model may be a more suitable base for models that explore the effect of mechanisms like partner choice on the stability of mutualism than existing models. |
« back