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Related Concept Videos

Competition02:34

Competition

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.
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Cooperative Allosteric Transitions01:58

Cooperative Allosteric Transitions

Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
Cooperative Allosteric Transitions01:58

Cooperative Allosteric Transitions

Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...
Cooperative Allosteric Transitions01:58

Cooperative Allosteric Transitions

Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...

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Updated: May 29, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

Competition and cooperation in one-dimensional stepping-stone models.

K S Korolev1, David R Nelson

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. papers.korolev@gmail.com

Physical Review Letters
|September 21, 2011
PubMed
Summary

Mutualism, essential for ecosystems, persists only in dense populations with frequent migration. Reduced density or migration leads to its loss through a directed percolation process.

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Area of Science:

  • Ecology
  • Evolutionary Biology
  • Microbial Ecology

Background:

  • Mutualism is a key evolutionary and ecological process.
  • Spatial dynamics and population fluctuations influence ecological interactions.
  • The persistence of mutualism, especially in microbial range expansions, requires further investigation.

Purpose of the Study:

  • To investigate the conditions under which mutualism persists in spatially structured populations.
  • To understand the role of population density and migration rates in maintaining mutualistic interactions.
  • To explore the phase transitions associated with the loss of mutualism.

Main Methods:

  • Mathematical modeling of mutualistic interactions.
  • Analysis of population dynamics with spatial degrees of freedom and number fluctuations.
  • Investigation of phase transitions using concepts from directed percolation (DP).

Main Results:

  • Mutualism is sustained only under conditions of high population density and frequent migration.
  • A decrease in density or migration leads to the loss of mutualism.
  • The loss of mutualism follows a directed percolation (DP) transition, with a phase diagram influenced by a symmetric DP (DP2) transition.

Conclusions:

  • Population density and migration are critical factors for the stability of mutualism.
  • The loss of mutualism can be modeled as a phase transition, similar to directed percolation.
  • These findings have implications for understanding microbial community dynamics and range expansions.