Isocline

Abstract: Many pathogens and parasites attack multiple host species, so their ability to invade a host community can depend on host community composition. We present a graphical isocline framework for studying disease establishment in systems with two host species, based on treating host species as resources. The isocline approach provides a natural generalization to multi-host systems of two related concepts in disease ecology – the basic reproductive rate of a parasite, and threshold host density. Qualitative isocline shape characterizes the threshold community configurations that permit parasite establishment. In general, isocline shape reflects the relative forces of inter- and intraspecific transmission of shared parasites. We discuss the qualitative implications of parasite isocline shape for issues of mounting concern in conservation ecology.

Abstract: I explore the relation between optimal foraging and the geometrical character of the predator isocline. Two basic models are discussed. The first is a multispecies generalization of Holling's "disc" equation. If a predator can rapidly discriminate among prey types, it is argued that its isoclines should not have positive slopes. Isoclines with positive slopes may occur if the predator must invest time discriminating between prey of unequal value, and there is a high absolute abundance of the better quality prey species. For a food-limited predator, however, selection should moderate the degree of rightward slope. In the second model, encounter and capture rates vary directly with relative prey abundance because of switching behavior. A number of published switching models are shown to produce isoclines with partially positive slopes. If the attack rates on each of two prey species are functionally related, it is argued that an optimally foraging predator will either have rectangular isoclines or isoclines...

Abstract: Available evidence and a new argument support the graphical theory of predation In particular, the prey isocline can have positive slope over lower prey densities Hence, from what is already known about the predator-prey interaction, high predatory efficiency, meaning the predator's ability to reproduce successfully in the presence of few prey, can be a source of instability, perhaps even resulting in the predator's extinction

Abstract: Two simulation models are presented which predict the impact of local and episodic applications of pesticide on the dynamics of invertebrate metapopulations. Both models assume that invertebrates disperse at particular rates over a matrix of fields and that each field experiences a specific pesticide regime. Model 1 investigates the population dynamics of a polyphagous predator which experiences direct mortality from pesticide exposure but is unaffected by the availability of the targeted pest. Model 2 investigates a similar system but also considers the dynamics of the pest, which is influenced both by predation and by pesticide exposure. Using stability diagrams and isocline portraits we characterize the likely long-term effects of factors such as the frequency and extent of spraying, factors which have hitherto not been widely considered in general pesticide models