Evol Ecol Res 11: 153-175 (2009)     Full PDF if your library subscribes.

Superinfections and adaptive dynamics of pathogen virulence revisited: a critical function analysis

Barbara Boldin, Stefan A.H. Geritz and Éva Kisdi

Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

Correspondence: É. Kisdi, Department of Mathematics and Statistics, University of Helsinki, PO Box 68, FIN-00014 Helsinki, Finland.
e-mail: eva.kisdi@helsinki.fi


Background: Superinfections are known to facilitate the co-existence of several pathogen strains in a host population. Previous models have demonstrated that pathogen virulence may undergo evolutionary branching, whereby an ancestral strain splits into two strains of different virulence. Evolutionary branching depends on the superinfection function as well as the trade-off between virulence and transmission, but reliable empirical data for these functions are scarce.

Aim: To find necessary and sufficient conditions for evolutionary branching in an SI model (where S stands for susceptible and I for infected/infectious) with superinfections under any conceivable transmission–virulence trade-off.

Methods: Adaptive dynamics and critical function analysis.

Assumptions: The superinfection function is assumed to be differentiable, but otherwise arbitrary. We consider three different modes of host population dynamics: constant population size, constant population birth rate, and logistic population growth in the absence of pathogens.

Results: In the constant population birth rate model, evolutionary branching can always occur if the convexity of the trade-off falls in a certain range; this range can however be narrow, especially if the singularity is at high virulence and relatively low transmission. With constant population size and with logistic growth, mutual exclusion of strains occurs near some singularities, which excludes evolutionary branching in part of the parameter space.

Comparison of methods: We show how critical function analysis relates to a more traditional analysis of the model via pairwise invasibility plots and bifurcation plots of evolutionary singularities.

Keywords: adaptive dynamics, co-existence of pathogen strains, critical function analysis, evolutionary branching, superinfection model, trade-off, virulence evolution.

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