# Conservation of population size is required for self-organized criticality in evolution models

@article{Murase2018ConservationOP, title={Conservation of population size is required for self-organized criticality in evolution models}, author={Yohsuke Murase and Per Arne Rikvold}, journal={arXiv: Populations and Evolution}, year={2018} }

We study models of biological evolution and investigate a key factor to yield self-organized criticality (SOC). The Bak-Sneppen (BS) model is the most basic model that shows an SOC state, which is developed based on minimal and plausible assumptions of Darwinian competition. Another class of models, which have population dynamics and simple rules for species migrations, has also been studied. It turns out that they do not show an SOC state although the assumptions made in these models are…

## 4 Citations

Out of Africa by spontaneous migration waves

- Geography, Biology
- 2018

A spatially explicit, stochastic numerical model that includes ongoing mutations, demic diffusion, assortative mating and migration waves suggests that one or more out-of-Africa migrations would probably have been accompanied by numerous smaller migration waves across the world.

Out of Africa by spontaneous migration waves

- Medicine, GeographyPloS one
- 2019

A spatially explicit, stochastic numerical model that includes ongoing mutations, demic diffusion, assortative mating and migration waves suggests that one or more out-of-Africa migrations would probably have been accompanied by numerous smaller migration waves across the world.

Motif dynamics in signed directional complex networks

- Computer Science, Physics
- 2020

M motif dynamics is proposed, which is a study to investigate the change in the number of motifs and applied to an open evolving network model and empirical data, and it is confirmed that a non-cyclic motif has a greater correlation with the system size than a cyclic structural motif.

## References

SHOWING 1-10 OF 80 REFERENCES

Are critical phenomena relevant to large-scale evolution?

- Biology, MedicineProceedings of the Royal Society of London. Series B: Biological Sciences
- 1996

The current evidence from the fossil record is explored, showing that some properties that are suggestive of critical dynamics would also be the result of random phenomema.

The tangled nature model as an evolving quasi-species model

- Biology, Physics
- 2003

We show that the tangled nature model can be interpreted as a general formulation of the quasi-species model by Eigen et al in a frequency-dependent fitness landscape. We present a detailed…

Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

- Biology, PhysicsJournal of mathematical biology
- 2007

The long-time dynamical properties of two individual-based models of biological coevolution, which self-optimize through mutation and selection to approximately maximize a community potential function, are compared.

Emergence of a complex and stable network in a model ecosystem with extinction and mutation.

- Biology, MedicineTheoretical population biology
- 2003

Random walk in genome space: a key ingredient of intermittent dynamics of community assembly on evolutionary time scales.

- Biology, MedicineJournal of theoretical biology
- 2010

Evolution as a self-organized critical phenomenon.

- Biology, MedicineProceedings of the National Academy of Sciences of the United States of America
- 1995

A simple mathematical model of biological macroevolution describes an ecology of adapting, interacting species that evolves to a "self-organized critical" state where periods of stasis alternate with avalanches of causally connected evolutionary changes.

Punctuated equilibria and 1/f noise in a biological coevolution model with individual-based dynamics.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

A study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution that provides selection through a reproduction probability that contains quenched, random interspecies interactions and genetic variation through a low mutation rate.

Time-dependent extinction rate and species abundance in a tangled-nature model of biological evolution.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

We present a model of evolutionary ecology consisting of a web of interacting individuals, a tangle-nature model. The reproduction rate of individuals characterized by their genome depends on the…

Proof of breaking of self-organized criticality in a nonconservative abelian sandpile model

- Mathematics, MedicinePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

A rigorous proof is given that the BTW model loses SOC as soon as the annihilation rate becomes positive and a nonconservative Abelian sandpile model is defined on a square lattice.

A simple model for skewed species-lifetime distributions

- Physics
- 2010

A simple model of a biological community assembly is studied. Communities are assembled by successive migrations and extinctions of species. In the model, species are interacting with each other. The…