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This paper considers a tri-trophic food chain in which the top predator (intraguild predator) also feeds on the basal resource. We refer to the model as intraguild predation. We analyze its dynamics from an evolutionary perspective. The attack rate or foraging effort of the middle species (intraguild prey) for the basal resources is assumed to be evolvable and is also assumed to be traded off with the vulnerability to being attacked by the top predator. We focus on the analysis of the evolutionary dynamics of the attack rate using the adaptive dynamics approximation of mutation limited evolution. In particular, the critical function analysis is applied. This study reveals that the evolutionary dynamics of the intraguild predation system is completely characterized by the concavity of the trade-off function and admits trichotomous dynamic scenarios: (1) when the trade-off function is more concave than the critical function, an evolutionary singular strategy exists and is a repeller; (2) when the trade-off function is less concave than the critical function, the evolutionary singular strategy is convergence stable and turns into an evolutionary branching point, in which case the monomorphic intraguild prey will split into two different types; (3) when the trade-off function is convex, the evolutionary singular strategy turns into a continuous stable strategy and is uninvadable. Our theoretical analysis suggests that the adaptive foraging behavior may strongly influence the community stability. Consequently, it may promote the diversity of intraguild prey and the persistence of the system on the evolutionary timescale, which highlight a more comprehensive mechanistic understanding of the intricate interplay between ecological and evolutionary force. This modeling approach provides a venue for research on indirect effects from an evolutionary perspective. [ABSTRACT FROM AUTHOR]

Abstract: We use adaptive dynamics and pairwise invadability plots to examine the evolutionary dynamics of host resistance to microparasitic infection transmitted indirectly via free stages. We investigate trade-offs between pathogen transmission rate and intrinsic growth rate. Adaptive dynamics distinguishes various evolutionary outcomes associated with repellors, attractors or branching points. We find criteria corresponding to these and demonstrate that a major factor deciding the evolutionary outcome is whether trade-offs are acceleratingly or deceleratingly costly. We compare and contrast two models and show how the differences between them lead to different evolutionary outcomes. [Copyright &y& Elsevier]

Abstract: In evolutionary history, several events have occurred at which mixotrophs specialized into pure autotrophs and heterotrophs. We studied the conditions under which such events take place, using the Dynamic Energy Budget (DEB) theory for physiological rules of the organisms’ metabolism and Adaptive Dynamics (AD) theory for evolutionary behavior of parameter values. We modeled a population of mixotrophs that can take up dissolved inorganic nutrients by autotrophic assimilation and detritus by heterotrophic assimilation. The organisms have a certain affinity for both pathways; mutations that occur in the affinities enable the population to evolve. One of the possible evolutionary outcomes is a branching point which provides an opportunity for the mixotrophic population to split up and specialize into separate autotrophs and heterotrophs. Evolutionary branching is not a common feature of the studied system, but is found to occur only under specific conditions. These conditions depend on intrinsic properties such as the cost function, the level of the costs and the boundaries of the trait space: only at intermediate cost levels and when an explicit advantage exists to pure strategies over mixed ones may evolutionary branching occur. Usually, such an advantage (and hence evolutionary branching) can be induced by interference between the two affinities, but this result changes due to the constraints on the affinities. Now, only some of the more complicated cost functions give rise to a branching point. In contrast to the intrinsic properties, extrinsic properties such as the total nutrient content or light intensity were found to have no effect on the evolutionary outcomes at all. [Copyright &y& Elsevier]

Abstract: We determine the adaptive dynamics of a general Lotka–Volterra system containing an intraspecific parameter dependency – in the form of an explicit functional trade-off between evolving parameters – and interspecific parameter dependencies – arising from modelling species interactions. We develop expressions for the fitness of a mutant strategy in a multi-species resident environment, the position of the singular strategy in such systems and the non-mixed second-order partial derivatives of the mutant fitness. These expressions can be used to determine the evolutionary behaviour of the system. The type of behaviour expected depends on the curvature of the trade-off function and can be interpreted in a biologically intuitive manner using the rate of acceleration/deceleration of the costs implicit in the trade-off function. We show that for evolutionary branching to occur we require that one (or both) of the traded-off parameters includes an interspecific parameter dependency and that the trade-off function has weakly accelerating costs. This could have important implications for understanding the type of mechanisms that cause speciation. The general theory is motivated by using adaptive dynamics to examine evolution in a predator–prey system. The applicability of the general theory as a tool for examining specific systems is highlighted by calculating the evolutionary behaviour in a three species (prey–predator–predator) system. [Copyright &y& Elsevier]