Modelling temperature-dependent dynamics of single and mixed infections in a plant virus

Multiple viral infection is an important issue in health and agriculture with strong impacts on society and the economy. Several investigations have dealt with the population dynamics of viruses with different dynamic properties, focusing on strain competition during multiple infections and the effects on viruses’ hosts. Recent interest has been on how multiple infections respond to abiotic factors such as temperature (T). This is especially important in the case of plant pathogens, whose dynamics could be affected significantly by global warming. However, few mathematical models incorporate the effect of T on parasite fitness, especially in mixed infections. Here, we investigate simple mathematical models incorporating thermal reaction norms (TRNs), which allow for quantitative analysis. A logistic model is considered for single infections, which is extended to a Lotka-Volterra competition model for mixed infections. The dynamics of these two models are investigated, focusing on the roles of T-dependent replication and competitive interactions in both transient and asymptotic dynamics. We determine the scenarios of co-existence and competitive exclusion, which are separated by a transcritical bifurcation. To illustrate the applicability of these models, we ran single- and mixed-infection experiments in plants growing at 20º C and 30º C using two strains of the plant RNA virus Pepino mosaic virus. Using a macroevolutionary algorithm, we fitted the models to the data by estimating the TRNs for both strains in single infections. Then, we used these TRNs to feed the mixed-infection model estimating the strength of competition. We found an asymmetrical pattern in which each strain dominated at different T values due to differences in their TRNs. We also identified that T can modify competition interference greatly for both isolates. The models proposed here can be useful for investigating the outcomes of multiple-infection dynamics under abiotic changes and have implica