@article{BengfortvanVelzenGaedke2017,
  author    = {Bengfort, Michael and van Velzen, Ellen and Gaedke, Ursula},
  title     = {Slight phenotypic variation in predators and prey causes complex predator-prey oscillations},
  series = {Ecological Complexity},
  volume    = {31},
  journal   = {Ecological Complexity},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1476-945X},
  doi       = {10.1016/j.ecocom.2017.06.003},
  pages     = {115 -- 124},
  year      = {2017},
  abstract  = {Predator-prey oscillations are expected to show a 1/4-phase lag between predator and prey. However, observed dynamics of natural or experimental predator-prey systems are often more complex. A striking but hardly studied example are sudden interruptions of classic 1/4-lag cycles with periods of antiphase oscillations, or periods without any regular predator-prey oscillations. These interruptions occur for a limited time before the system reverts to regular 1/4-lag oscillations, thus yielding intermittent cycles. Reasons for this behaviour are often difficult to reveal in experimental systems. Here we test the hypothesis that such complex dynamical behaviour may result from minor trait variation and trait adaptation in both the prey and predator, causing recurrent small changes in attack rates that may be hard to capture by empirical measurements. Using a model structure where the degree of trait variation in the predator can be explicitly controlled, we show that a very limited amount of adaptation resulting in 10-15\% temporal variation in attack rates is already sufficient to generate these intermittent dynamics. Such minor variation may be present in experimental predator-prey systems, and may explain disruptions in regular 1/4-lag oscillations.},
  language  = {en}
}
@article{KlauschiesCoutinhoGaedke2018,
  author    = {Klauschies, Toni and Coutinho, Renato Mendes and Gaedke, Ursula},
  title     = {A beta distribution-based moment closure enhances the reliability of trait-based aggregate models for natural populations and communities},
  series = {Ecological modelling : international journal on ecological modelling and engineering and systems ecolog},
  volume    = {381},
  journal   = {Ecological modelling : international journal on ecological modelling and engineering and systems ecolog},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3800},
  doi       = {10.1016/j.ecolmodel.2018.02.001},
  pages     = {46 -- 77},
  year      = {2018},
  abstract  = {Ecological communities are complex adaptive systems that exhibit remarkable feedbacks between their biomass and trait dynamics. Trait-based aggregate models cope with this complexity by focusing on the temporal development of the community's aggregate properties such as its total biomass, mean trait and trait variance. They are based on particular assumptions about the shape of the underlying trait distribution, which is commonly assumed to be normal. However, ecologically important traits are usually restricted to a finite range, and empirical trait distributions are often skewed or multimodal. As a result, normal distribution-based aggregate models may fail to adequately represent the biomass and trait dynamics of natural communities. We resolve this mismatch by developing a new moment closure approach assuming the trait values to be beta-distributed. We show that the beta distribution captures important shape properties of both observed and simulated trait distributions, which cannot be captured by a Gaussian. We further demonstrate that a beta distribution-based moment closure can strongly enhance the reliability of trait-based aggregate models. We compare the biomass, mean trait and variance dynamics of a full trait distribution (FD) model to the ones of beta (BA) and normal (NA) distribution-based aggregate models, under different selection regimes. This way, we demonstrate under which general conditions (stabilizing, fluctuating or disruptive selection) different aggregate models are reliable tools. All three models predicted very similar biomass and trait dynamics under stabilizing selection yielding unimodal trait distributions with small standing trait variation. We also obtained an almost perfect match between the results of the FD and BA models under fluctuating selection, promoting skewed trait distributions and ongoing oscillations in the biomass and trait dynamics. In contrast, the NA model showed unrealistic trait dynamics and exhibited different alternative stable states, and thus a high sensitivity to initial conditions under fluctuating selection. Under disruptive selection, both aggregate models failed to reproduce the results of the FD model with the mean trait values remaining within their ecologically feasible ranges in the BA model but not in the NA model. Overall, a beta distribution-based moment closure strongly improved the realism of trait-based aggregate models.},
  language  = {en}
}