Studies of bacteriophage as therapeutic agents have had mixed and unpredictable outcomes. We argue that interpretation of these apparently paradoxical results requires appreciation of various density-dependent threshold e!ects. We use a mathematical model to delineate di!erent categories of outcome, including therapy by simple inundation, by active biocontrol, and by delayed active biocontrol. Counter-intuitively, there are situations in which earlier inoculation can be less e$cacious, and simultaneous inoculation with antibiotics can be detrimental. Predictions of therapeutic responses are made using formulae dependent on biologically meaningful parameters; experimental measurement of the parameters will be a prerequisite of application of the model to particular study systems. Such modelling can point to which aspects of phage biology might most fruitfully be engineered so as to enhance the viability of bacteriophage therapy.

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The specter of antibiotic-resistant bacteria has provoked renewed interest in the possible use of bacteriophages to control bacterial infections. We argue that clinical application of phage therapy has been held back by a failure to appreciate the extent to which the pharmacokinetics of self-replicating agents differ from those of normal drugs. For self-replicating pharmaceutical agents, treatment outcome depends critically on various density-dependent thresholds, often with apparently paradoxical consequences. An ability to predict these thresholds and associated critical time points is a necessity if phage therapy is to become clinically practicable.

Phage therapy is the use of bacteriophages as antimicrobial agents for the control of pathogenic and other problem bacteria. It has previously been argued that successful application of phage therapy requires a good understanding of the non-linear kinetics of phage–bacteria interactions. Here we combine experimental and modelling approaches to make a detailed examination of such kinetics for the important food-borne pathogen Campylobacter jejuni and a suitable virulent phage in an in vitro system. Phage-insensitive populations of C. jejuni arise readily, and as far as we are aware this is the first phage therapy study to test, against in vitro data, models for phage–bacteria interactions incorporating phage-insensitive or resistant bacteria. We find that even an apparently simplistic model fits the data surprisingly well, and we confirm that the so-called inundation and proliferation thresholds are likely to be of considerable practical importance to phage therapy. We fit the model to time series data in order to estimate thresholds and rate constants directly. A comparison of the fit for each culture reveals density-dependent features of phage infectivity that are worthy of further investigation. Our results illustrate how insight from empirical studies can be greatly enhanced by the use of kinetic models: such combined studies of in vitro systems are likely to be an essential precursor to building a meaningful picture of the kinetic properties of in vivo phage therapy.

Use of bacteriophage to control bacterial infections, including antibiotic-resistant infections, shows increasing therapeutic promise. Effective bacteriophage therapy requires awareness of various novel kinetic phenomena not known in conventional drug treatments. Kinetic theory predicts that timing of treatment could be critical, with the strange possibility that inoculations given too early could be less effective or fail completely. Another paradoxical result is that adjuvant use of an antibiotic can sometimes diminish the efficacy of phage therapy. For a simple kinetic model, mathematical formulae predict the values of critical density thresholds and critical time points, given as functions of independently measurable biological parameters. Understanding such formulae is important for interpreting data and guiding experimental design. Tailoring pharmacokinetic models for specific systems needs to become standard practice in future studies.

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A Fisherian model of sexual selection is combined with a diffusion model of mate dispersal to investigate the evolution of assortative mating in a sympatric population. Females mate with one of two types of polygynous males according to a male's display of one of two sex‐limited, autosomal traits; these male traits may be associated with differential phenotypic mortalities. Through a Fisherian runaway process, female preferences and male traits can become associated in linkage disequilibrium, leading to patterns of assortative mating. Dispersing males, whose rate of movement is dependent on mating success, carry female preference genes with them, and displaced males thereby produce daughters with preference genes for their respective traits in locally higher than average frequencies. The reduced diffusion of the more preferred males permits the success of other male types in adjacent areas. Thus, mating‐success dependent diffusion, when coupled with the rapid divergence in phenotypes possible under the Fisher process, can lead to the coexistence of two female preferences and two male traits in sympatry. We argue that many existing approaches to sympatric speciation fail to explain observed male polymorphisms because they exclude explicit spatial structure from their speciation models.