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Related Concept Videos

Competition02:34

Competition

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When organisms require the same limited resources within an environment, they may have to compete for them. Competition is a net-negative interaction. Even if two competing individuals or populations do not interact directly, the overall fitness of both competitors is lowered as a result of not having full access to the limited resource.
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Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly adapted organisms. Several factors constrain natural selection.
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Natural selection—probably the most well-known evolutionary mechanism—increases the prevalence of traits that enhance survival and reproduction. However, evolution does not merely propagate favorable traits, nor does it always benefit populations.
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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

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Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
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Types of Selection01:46

Types of Selection

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Natural selection influences the frequencies of particular alleles and phenotypes within populations in several different ways. Primarily, natural selection can be directional, stabilizing, or disruptive. Directional selection favors one extreme trait and shifts the population towards that phenotype while selecting against individuals displaying alternate traits. Stabilizing selection favors an intermediate trait with a narrow range of variation. Deviation from the optimal phenotype towards an...
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Updated: Dec 31, 2025

Deferred Growth Inhibition Assay to Quantify the Effect of Bacteria-derived Antimicrobials on Competition
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The competitive exclusion principle in stochastic environments.

Alexandru Hening1,2, Dang H Nguyen3

  • 1Sydney Mathematical Research Institute, University of Sydney, L4.42, Quadrangle A14, Sydney, NSW, Australia. alexandru.hening@tufts.edu.

Journal of Mathematical Biology
|January 11, 2020
PubMed
Summary

Environmental fluctuations, or stochasticity, can enable competing species to coexist, even with limited resources. Non-linear interactions or environmental state switching are key factors for this ecological phenomenon.

Keywords:
Competitive exclusionErgodicityLotka–VolterraLyapunov exponentReversalStochastic environment

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Area of Science:

  • Ecology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • The competitive exclusion principle posits that species competing for limited resources cannot coexist.
  • Hutchinson's 'paradox of the plankton' highlights empirical observations of numerous phytoplankton species coexisting despite limited resources.
  • Temporal environmental fluctuations are theorized to facilitate species coexistence by favoring different species at different times.

Purpose of the Study:

  • To investigate how variable (stochastic) environments enable competing species to coexist on fewer resources than species.
  • To explore the conditions under which the competitive exclusion principle breaks down.
  • To examine the role of environmental fluctuations, including white noise and environmental state switching, in promoting coexistence.

Main Methods:

  • Mathematical modeling of competing species with density-dependent factors.
  • Analysis of models with linear and non-linear dependencies between per-capita growth rates and resources.
  • Inclusion of white noise and discrete environmental state switching as sources of stochasticity.
  • Theoretical proofs and examples to demonstrate coexistence conditions.

Main Results:

  • Competitive exclusion occurs when environmental fluctuations are linear white noise and growth rates depend linearly on resources.
  • Coexistence is possible when growth rate dependence on resources is non-linear or the white noise term is non-linear.
  • Species coexistence is achievable even with linear growth rate dependencies when the environment switches randomly between states.
  • Demonstrated coexistence even when the same species is favored in different environmental states, challenging previous hypotheses.

Conclusions:

  • Stochastic environments can significantly alter the outcome of interspecific competition, enabling coexistence.
  • The nature of environmental fluctuations (e.g., linearity, state switching) and species' responses are critical determinants of coexistence.
  • This study provides theoretical support for empirical observations like the paradox of the plankton, offering new insights into ecological dynamics.