@article{vanVelzenGaedke2018,
  author    = {van Velzen, Ellen and Gaedke, Ursula},
  title     = {Reversed predator-prey cycles are driven by the amplitude of prey oscillations},
  series = {Ecology and evolution},
  volume    = {8},
  journal   = {Ecology and evolution},
  number    = {12},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {2045-7758},
  doi       = {10.1002/ece3.4184},
  pages     = {6317 -- 6329},
  year      = {2018},
  abstract  = {Ecoevolutionary feedbacks in predator-prey systems have been shown to qualitatively alter predator-prey dynamics. As a striking example, defense-offense coevolution can reverse predator-prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic 1/4-phase lag. From this key insight, it follows that in reversed cycles (i.e., -lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator-prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small-amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.},
  language  = {en}
}
@article{vanVelzenThieserBerendonketal.2018,
  author    = {van Velzen, Ellen and Thieser, Tamara and Berendonk, Thomas U. and Weitere, Markus and Gaedke, Ursula},
  title     = {Inducible defense destabilizes predator-prey dynamics},
  series = {Oikos},
  volume    = {127},
  journal   = {Oikos},
  number    = {11},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0030-1299},
  doi       = {10.1111/oik.04868},
  pages     = {1551 -- 1562},
  year      = {2018},
  abstract  = {Phenotypic plasticity in prey can have a dramatic impact on predator-prey dynamics, e.g. by inducible defense against temporally varying levels of predation. Previous work has overwhelmingly shown that this effect is stabilizing: inducible defenses dampen the amplitudes of population oscillations or eliminate them altogether. However, such studies have neglected scenarios where being protected against one predator increases vulnerability to another (incompatible defense). Here we develop a model for such a scenario, using two distinct prey phenotypes and two predator species. Each prey phenotype is defended against one of the predators, and vulnerable to the other. In strong contrast with previous studies on the dynamic effects of plasticity involving a single predator, we find that increasing the level of plasticity consistently destabilizes the system, as measured by the amplitude of oscillations and the coefficients of variation of both total prey and total predator biomasses. We explain this unexpected and seemingly counterintuitive result by showing that plasticity causes synchronization between the two prey phenotypes (and, through this, between the predators), thus increasing the temporal variability in biomass dynamics. These results challenge the common view that plasticity should always have a stabilizing effect on biomass dynamics: adding a single predator-prey interaction to an established model structure gives rise to a system where different mechanisms may be at play, leading to dramatically different outcomes.},
  language  = {en}
}
@misc{YamamichiKlauschiesMineretal.2019,
  author    = {Yamamichi, Masato and Klauschies, Toni and Miner, Brooks E. and van Velzen, Ellen},
  title     = {Modelling inducible defences in predator-prey interactions},
  series = {Ecology letters},
  volume    = {22},
  journal   = {Ecology letters},
  number    = {2},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {1461-023X},
  doi       = {10.1111/ele.13183},
  pages     = {390 -- 404},
  year      = {2019},
  abstract  = {Inducible defences against predation are widespread in the natural world, allowing prey to economise on the costs of defence when predation risk varies over time or is spatially structured. Through interspecific interactions, inducible defences have major impacts on ecological dynamics, particularly predator-prey stability and phase lag. Researchers have developed multiple distinct approaches, each reflecting assumptions appropriate for particular ecological communities. Yet, the impact of inducible defences on ecological dynamics can be highly sensitive to the modelling approach used, making the choice of model a critical decision that affects interpretation of the dynamical consequences of inducible defences. Here, we review three existing approaches to modelling inducible defences: Switching Function, Fitness Gradient and Optimal Trait. We assess when and how the dynamical outcomes of these approaches differ from each other, from classic predator-prey dynamics and from commonly observed eco-evolutionary dynamics with evolving, but non-inducible, prey defences. We point out that the Switching Function models tend to stabilise population dynamics, and the Fitness Gradient models should be carefully used, as the difference with evolutionary dynamics is important. We discuss advantages of each approach for applications to ecological systems with particular features, with the goal of providing guidelines for future researchers to build on.},
  language  = {en}
}
@article{vanVelzenGaedke2018,
  author    = {van Velzen, Ellen and Gaedke, Ursula},
  title     = {Reversed predator},
  series = {Ecology and Evolution},
  journal   = {Ecology and Evolution},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {2045-7758},
  doi       = {10.1002/ece3.4184},
  pages     = {1 -- 13},
  year      = {2018},
  abstract  = {Ecoevolutionary feedbacks in predator-prey systems have been shown to qualitatively alter predator-prey dynamics. As a striking example, defense-offense coevolution can reverse predator-prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼-phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾-lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator-prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small-amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.},
  language  = {en}
}
@misc{vanVelzenGaedke2018,
  author    = {van Velzen, Ellen and Gaedke, Ursula},
  title     = {Reversed predator},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-411652},
  pages     = {13},
  year      = {2018},
  abstract  = {Ecoevolutionary feedbacks in predator-prey systems have been shown to qualitatively alter predator-prey dynamics. As a striking example, defense-offense coevolution can reverse predator-prey cycles, so predator peaks precede prey peaks rather than vice versa. However, this has only rarely been shown in either model studies or empirical systems. Here, we investigate whether this rarity is a fundamental feature of reversed cycles by exploring under which conditions they should be found. For this, we first identify potential conditions and parameter ranges most likely to result in reversed cycles by developing a new measure, the effective prey biomass, which combines prey biomass with prey and predator traits, and represents the prey biomass as perceived by the predator. We show that predator dynamics always follow the dynamics of the effective prey biomass with a classic ¼-phase lag. From this key insight, it follows that in reversed cycles (i.e., ¾-lag), the dynamics of the actual and the effective prey biomass must be in antiphase with each other, that is, the effective prey biomass must be highest when actual prey biomass is lowest, and vice versa. Based on this, we predict that reversed cycles should be found mainly when oscillations in actual prey biomass are small and thus have limited impact on the dynamics of the effective prey biomass, which are mainly driven by trait changes. We then confirm this prediction using numerical simulations of a coevolutionary predator-prey system, varying the amplitude of the oscillations in prey biomass: Reversed cycles are consistently associated with regions of parameter space leading to small-amplitude prey oscillations, offering a specific and highly testable prediction for conditions under which reversed cycles should occur in natural systems.},
  language  = {en}
}