@article{EhrlichKathGaedke2020,
  author    = {Ehrlich, Elias and Kath, Nadja Jeanette and Gaedke, Ursula},
  title     = {The shape of a defense-growth trade-off governs seasonal trait dynamics in natural phytoplankton},
  series = {The ISME journal},
  volume    = {14},
  journal   = {The ISME journal},
  number    = {6},
  publisher = {Nature Publishing Group},
  address   = {London},
  issn      = {1751-7362},
  doi       = {10.1038/s41396-020-0619-1},
  pages     = {1451 -- 1462},
  year      = {2020},
  abstract  = {Theory predicts that trade-offs, quantifying costs of functional trait adjustments, crucially affect community trait adaptation to altered environmental conditions, but empirical verification is scarce. We evaluated trait dynamics (antipredator defense, maximum growth rate, and phosphate affinity) of a lake phytoplankton community in a seasonally changing environment, using literature trait data and 21 years of species-resolved high-frequency biomass measurements. The trait data indicated a concave defense-growth trade-off, promoting fast-growing species with intermediate defense. With seasonally increasing grazing pressure, the community shifted toward higher defense levels at the cost of lower growth rates along the trade-off curve, while phosphate affinity explained some deviations from it. We discuss how low fitness differences of species, inferred from model simulations, in concert with stabilizing mechanisms, e.g., arising from further trait dimensions, may lead to the observed phytoplankton diversity. In conclusion, quantifying trade-offs is key for predictions of community trait adaptation and biodiversity under environmental change.},
  language  = {en}
}
@article{EhrlichBecksGaedke2017,
  author    = {Ehrlich, Elias and Becks, Lutz and Gaedke, Ursula},
  title     = {Trait-fitness relationships determine how trade-off shapes affect species coexistence},
  series = {Ecology : a publication of the Ecological Society of America},
  volume    = {98},
  journal   = {Ecology : a publication of the Ecological Society of America},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0012-9658},
  doi       = {10.1002/ecy.2047},
  pages     = {3188 -- 3198},
  year      = {2017},
  abstract  = {Trade-offs between functional traits are ubiquitous in nature and can promote species coexistence depending on their shape. Classic theory predicts that convex trade-offs facilitate coexistence of specialized species with extreme trait values (extreme species) while concave trade-offs promote species with intermediate trait values (intermediate species). We show here that this prediction becomes insufficient when the traits translate non-linearly into fitness which frequently occurs in nature, e.g., an increasing length of spines reduces grazing losses only up to a certain threshold resulting in a saturating or sigmoid trait-fitness function. We present a novel, general approach to evaluate the effect of different trade-off shapes on species coexistence. We compare the trade-off curve to the invasion boundary of an intermediate species invading the two extreme species. At this boundary, the invasion fitness is zero. Thus, it separates trait combinations where invasion is or is not possible. The invasion boundary is calculated based on measurable trait-fitness relationships. If at least one of these relationships is not linear, the invasion boundary becomes non-linear, implying that convex and concave trade-offs not necessarily lead to different coexistence patterns. Therefore, we suggest a new ecological classification of trade-offs into extreme-favoring and intermediate-favoring which differs from a purely mathematical description of their shape. We apply our approach to a well-established model of an empirical predator-prey system with competing prey types facing a trade-off between edibility and half-saturation constant for nutrient uptake. We show that the survival of the intermediate prey depends on the convexity of the trade-off. Overall, our approach provides a general tool to make a priori predictions on the outcome of competition among species facing a common trade-off in dependence of the shape of the trade-off and the shape of the trait-fitness relationships.},
  language  = {en}
}