Population dynamics of mutualism and intraspecific density dependence: how θ-logistic density dependence affects mutualistic positive feedback

@article{Moore2017PopulationDO,
  title={Population dynamics of mutualism and intraspecific density dependence: how $\theta$-logistic density dependence affects mutualistic positive feedback},
  author={Christopher M. Moore and Samantha A Catella and Karen C. Abbott},
  journal={bioRxiv},
  year={2017}
}
Mutualism describes the biological phenomenon where two or more species are reciprocally beneficial, regardless of their ecological intimacy or evolutionary history. Classic theory shows that mutualistic benefit must be relatively weak, or else it overpowers the stabilizing influence of intraspecific competition and leads to unrealistic, unbounded population growth. Interestingly, the conclusion that strong positive interactions lead to runaway population growth is strongly grounded in the… 
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References

SHOWING 1-10 OF 109 REFERENCES
A consumer-resource approach to the density-dependent population dynamics of mutualism.
TLDR
The results suggest that the C-R interaction can provide a broad mechanism for understanding density-dependent population dynamics of mutualism, and unifying predation, competition, and mutualism under the common ecological framework of consumer-resource theory.
The struggle for existence. How the notion of carrying capacity, K, obscures the links between demography, Darwinian evolution and speciation
TLDR
Widespread use of r-K (‘carrying capacity’) models of population growth appears to have catalysed fundamental discords in ecology, and between ecology and evolution.
Network structural properties mediate the stability of mutualistic communities.
TLDR
It is shown that structural properties can alter the stability of mutualistic communities characterized by nonlinear functional responses among the interacting species, and that interplay between the structure and function of ecological networks in general and consideration of mutualists interactions in particular may be key to understanding complexity-stability relationships of biological communities as a whole.
The architecture of mutualistic networks minimizes competition and increases biodiversity
TLDR
It is shown that nestedness reduces effective interspecific competition and enhances the number of coexisting species, and that a nested network will naturally emerge if new species are more likely to enter the community where they have minimal competitive load.
Population growth regulated by intraspecific competition for energy or time: some simple representations.
  • T. Schoener
  • Environmental Science
    Theoretical population biology
  • 1973
Richards-like two species population dynamics model
TLDR
A generalized Lotka–Volterra model with intraspecific competition with a forbidden region in the mutualism regime, and a survival/extinction transition with dependence on initial conditions for the competition regime is presented.
On the structural stability of mutualistic systems
TLDR
The concept of structural stability is extended to community ecology in order to account for the set of conditions leading to the stable coexistence of all species within a community, and a mathematical framework based on the concept ofStructural stability is introduced to explain such a disparity of results.
Numerical responses in resource-based mutualisms: A time scale approach.
  • T. Revilla
  • Environmental Science
    Journal of theoretical biology
  • 2015
Model selection analysis of temporal variation in benefit for an ant-tended treehopper.
TLDR
Results presented here show that temporal changes in the relative magnitude of direct and indirect benefit components of ant tending, especially the effectiveness of predator protection by ants, qualitatively change the overall pattern of density-dependent benefit between years with maximum benefit shifting from treehoppers in small to large aggregations.
Pattern of variation in avian population growth rates.
  • B. SaetherS. Engen
  • Environmental Science
    Philosophical transactions of the Royal Society of London. Series B, Biological sciences
  • 2002
TLDR
The concept of population prediction interval can be useful in evaluating the consequences of large uncertainties in parameter estimates, as well as strong stochastic effects on the population dynamics, which will often make even short-term population projections unreliable.
...
...