Browsing by Subject "Critical function analysis"

Sort by: Order: Results:

Now showing items 1-5 of 5
  • Lehtinen, Sami O.; Geritz, Stefan A.H. (2019)
    We investigate the coevolution of cannibalistic predators and timid prey, which seek refuge upon detecting a predator. To understand how the species affect each other’s evolution, we derived the ecological model from individual-level processes using ordinary differential equations. The ecological dynamics exhibit bistability between equilibrium and periodic attractors, which may disappear through catastrophic bifurcations. Using the critical function analysis of adaptive dynamics, we classify general trade-offs between cannibalism and prey capture that produce different evolutionary outcomes. The evolutionary analysis reveals several ways in which cannibalism emerges as a response to timidity of the prey. The long-term coevolution either attains a singularity, or becomes cyclic through two mechanisms: genetical cycles through Hopf bifurcation of the singularity, or ecogenetical cycles involving abrupt switching between ecological attractors. Further diversification of cannibalism occurs through evolutionary branching, which is predicted to be delayed when simultaneous prey evolution is necessary for the singularity’s attainability. We conclude that predator-prey coevolution produces a variety of outcomes, in which evolutionary cycles are commonplace.
  • Kisdi, Eva (2015)
    Evolutionary singularities are central to the adaptive dynamics of evolving traits. The evolutionary singularities are strongly affected by the shape of any trade-off functions a model assumes, yet the trade-off functions are often chosen in an ad hoc manner, which may unjustifiably constrain the evolutionary dynamics exhibited by the model. To avoid this problem, critical function analysis has been used to find a trade-off function that yields a certain evolutionary singularity such as an evolutionary branching point. Here I extend this method to multiple trade-offs parameterized with a scalar strategy. I show that the trade-off functions can be chosen such that an arbitrary point in the viability domain of the trait space is a singularity of an arbitrary type, provided (next to certain non-degeneracy conditions) that the model has at least two environmental feedback variables and at least as many trade-offs as feedback variables. The proof is constructive, i.e., it provides an algorithm to find trade-off functions that yield the desired singularity. I illustrate the construction of trade-offs with an example where the virulence of a pathogen evolves in a small ecosystem of a host, its pathogen, a predator that attacks the host and an alternative prey of the predator.
  • Weigang, Helene C.; Kisdi, Eva (2015)
    Resources invested in dispersal structures as well as time and energy spent during transfer may often decrease fecundity. Here we analyse an extended version of the Hamilton-May model of dispersal evolution, where we include a fecundity-dispersal trade-off and also mortality between competition and reproduction. With adaptive dynamics and critical function analysis we investigate the evolution of dispersal strategies and ask whether adaptive diversification is possible. We exclude evolutionary branching for concave trade-offs and show that for convex trade-offs diversification is promoted in a narrow parameter range. We provide theoretical evidence that dispersal strategies can monotonically decrease with increasing survival during dispersal. Moreover, we illustrate the existence of two alternative attracting dispersal strategies. The model exhibits fold bifurcation points where slight changes in survival can lead to evolutionary catastrophes. (C) 2015 Elsevier Ltd. All rights reserved.
  • Fan, Ruili; Geritz, Stefan A. H. (2021)
    We study the evolution of virulence of an endemic pathogen in response to healthcare interventions which affect host recovery and pathogen transmission. By anticipating the evolutionary response of the pathogen we may develop effective long-term management strategies for controlling the impact of the endemic on the society. To that end, we use standard Adaptive Dynamics techniques in an SIS model. The recovery rate and the transmission rate, both of which can be affected by healthcare interventions, are used as evolutionary control variables. The effect of interventions may be density-independent (self-help based on healthcare instructions) or density-dependent (when assistance of a healthcare worker is required). We consider the evolutionary response of the pathogen both to abrupt changes and to gradual changes in the level of healthcare intervention. Healthcare intervention is optimised for three alternative objectives: minimisation of virulence, minimisation of the probability that an infected individual dies of the disease, and total eradication of the endemic. We find that the optimal strategy may depend on the objective. High levels of healthcare intervention may eradicate the pathogen, but this option may not be available for budgetary reasons or otherwise. Counterintuitively, to minimise virulence, one should keep healthcare interventions at a minimum, while to minimise the probability for an infected individual to die of the disease, both low and high levels of healthcare intervention suffice. Changes in the level of healthcare intervention should be implemented fast (not gradually) in order to avoid sudden changes in pathogen evolution and the possible emergence of multiple simultaneously coexisting pathogen strains. (C) 2021 The Author(s). Published by Elsevier Ltd.