During a primary immune response generally two classes of antibody are produced, immunoglobulin M (IgM) and immunoglobulin G (IgG). It is currently thought that some lymphocytes which initially produce IgM switch to the production of IgG with the same specificity for antigen. During a secondary immune response IgG is the predominant antibody made throughout the response. In this paper we address the question of why such apparently complicated modes of response should have been adapted by evolution. We construct mathematical models of the immune response to growing antigens which incorporate complement dependent cell lysis. By comparing the times required to eliminate antigen we show that under certain conditions it is advantageous for an animal to switch some of its lymphocytes from IgM to IgG production during a primary response, but yet to secrete only IgG during a secondary response. The sensitivity of such a conclusion to parameter variations is studied and the biological basis and implications of our models are fully discussed.
We present two models for phenotypic-dependent interspecific competition. In both cases the survivorship of individuals of one population depends on the entire phenotypic distribution of the other species. The first model considers a continuously varying metric trait, with assortative or random mating; the second model examines a character controlled by two alleles at a single locus. Pursuing the notion that each population maximizes its mean fitness we define a vector-optimum strategy using the concepts of cooperative and competitive optima. It is found that the dynamical constraints placed on the equations of motion by Mendelian genetics often prevent a population from evolving to a strategic optimum. However, for the single locus case with complete dominance, the competitive optimum always coincides with some dynamical equilibrium on the Hardy-Weinberg manifold.
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