• Corpus ID: 16071750

Interpretation and approximation tools for big, dense Markov chain transition matrices in ecology and evolution

@article{Reichel2014InterpretationAA,
  title={Interpretation and approximation tools for big, dense Markov chain transition matrices in ecology and evolution},
  author={Katja Reichel and Valentin Bahier and C{\'e}dric Midoux and Jean-Pierre Masson and Solenn Stoeckel},
  journal={arXiv: Quantitative Methods},
  year={2014}
}
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose considerable challenges as their size and their density increase. Big, dense transition matrices may easily defy both the computer's memory and the scientists' ability to interpret them, due to the very high amount of information they contain; yet… 

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References

SHOWING 1-10 OF 39 REFERENCES
Efficient methods for studying stochastic disease and population dynamics.
Bounded state space truncation and Censored Markov chains
TLDR
The proposed DPY algorithm, that computes a stochastic bound for a CMC, is proved to be optimal for the information they take into account, and it is shown how some additional knowledge on the chain can improve stochastically bounds for CMC.
A mathematical description of the inclusive fitness theory.
Stochastic formulation of ecological models and their applications.
Exploring Network Structure, Dynamics, and Function using NetworkX
TLDR
Some of the recent work studying synchronization of coupled oscillators is discussed to demonstrate how NetworkX enables research in the field of computational networks.
An introduction to stochastic processes with applications to biology
Review of Probability Theory and an Introduction to Stochastic Processes Introduction Brief Review of Probability Theory Generating Functions Central Limit Theorem Introduction to Stochastic
The Exact Distributions of F IS under Partial Asexuality in Small Finite Populations with Mutation
TLDR
A population genetics model based on genotypic states in a finite population with mutation is proposed, which distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift.
Tackling the population genetics of clonal and partially clonal organisms.
Influence of mutation rate on estimators of genetic differentiation - lessons from Arabidopsis thaliana
TLDR
Alternative measures of differentiation like F'STand D are not suitable for estimating effective migration rate and should not be used in studies of local adaptation and genetic differentiation should instead be measured using an estimator that takes mutation rate into account, such as ΦST.
A sexually neutral discrete Markov model for given sum males + females.
...
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