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Modeling neutral evolution of Alu elements using a branching process.

Kimmel M, Mathaes M - BMC Genomics (2010)

Bottom Line: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes.A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics, Rice University, Houston, TX 77005, USA. kimmel@rice.edu

ABSTRACT

Background: Alu elements occupy about eleven percent of the human genome and are still growing in copy numbers. Since Alu elements substantially impact the shape of our genome, there is a need for modeling the amplification, mutation and selection forces of these elements.

Methods: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes. From this model, we derive a limit frequency spectrum of the Alu element distribution, which serves as the theoretical, neutral frequency to which real Alu insertion data can be compared through statistical goodness of fit tests. Departures from the neutral frequency spectrum may indicate selection.

Results: A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.

Conclusions: This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

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Related in: MedlinePlus

Griffiths-Pakes branching process with infinite-allele mutations. A non-mutant clone of particles is evolving in time according to a single-type branching process (in our case, time dicrete). With probability μ per time step, a particle mutates and initates a clone of new previously nonexistent type, which evolves according to the same rules as the original non-mutant clone. As a result, a set of clones of different types emerges, spawning further clones, some of which may die out. Upper panel: low μ; lower panel: high μ.
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Figure 5: Griffiths-Pakes branching process with infinite-allele mutations. A non-mutant clone of particles is evolving in time according to a single-type branching process (in our case, time dicrete). With probability μ per time step, a particle mutates and initates a clone of new previously nonexistent type, which evolves according to the same rules as the original non-mutant clone. As a result, a set of clones of different types emerges, spawning further clones, some of which may die out. Upper panel: low μ; lower panel: high μ.

Mentions: Griffiths and Pakes [17] process is a modification of the standard Bienayme-Galton-Watson branching process to allow individuals infinitely many possible identifiable types. In our application, the types are alleles (variants) of the Alu sequence identified by specific point mutations. From time t = 0, a non-mutant clone of particles is evolving in time according to a single-type branching process (Figure 5). With probability μ per time step, a particle mutates and initates a clone of new previously nonexistent type, which evolves according to the same rules as the original non-mutant clone. As a result, a set of clones of different types emerges, spawning further clones, some of which may die out. We are interested in deriving, using Griffiths-Pakes [17] theory, expected frequencies of allele classes such that allele is in class k if it exists in k copies, for a specific biologically justifiable version of the process.


Modeling neutral evolution of Alu elements using a branching process.

Kimmel M, Mathaes M - BMC Genomics (2010)

Griffiths-Pakes branching process with infinite-allele mutations. A non-mutant clone of particles is evolving in time according to a single-type branching process (in our case, time dicrete). With probability μ per time step, a particle mutates and initates a clone of new previously nonexistent type, which evolves according to the same rules as the original non-mutant clone. As a result, a set of clones of different types emerges, spawning further clones, some of which may die out. Upper panel: low μ; lower panel: high μ.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2822525&req=5

Figure 5: Griffiths-Pakes branching process with infinite-allele mutations. A non-mutant clone of particles is evolving in time according to a single-type branching process (in our case, time dicrete). With probability μ per time step, a particle mutates and initates a clone of new previously nonexistent type, which evolves according to the same rules as the original non-mutant clone. As a result, a set of clones of different types emerges, spawning further clones, some of which may die out. Upper panel: low μ; lower panel: high μ.
Mentions: Griffiths and Pakes [17] process is a modification of the standard Bienayme-Galton-Watson branching process to allow individuals infinitely many possible identifiable types. In our application, the types are alleles (variants) of the Alu sequence identified by specific point mutations. From time t = 0, a non-mutant clone of particles is evolving in time according to a single-type branching process (Figure 5). With probability μ per time step, a particle mutates and initates a clone of new previously nonexistent type, which evolves according to the same rules as the original non-mutant clone. As a result, a set of clones of different types emerges, spawning further clones, some of which may die out. We are interested in deriving, using Griffiths-Pakes [17] theory, expected frequencies of allele classes such that allele is in class k if it exists in k copies, for a specific biologically justifiable version of the process.

Bottom Line: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes.A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Statistics, Rice University, Houston, TX 77005, USA. kimmel@rice.edu

ABSTRACT

Background: Alu elements occupy about eleven percent of the human genome and are still growing in copy numbers. Since Alu elements substantially impact the shape of our genome, there is a need for modeling the amplification, mutation and selection forces of these elements.

Methods: Our proposed theoretical neutral model follows a discrete-time branching process described by Griffiths and Pakes. From this model, we derive a limit frequency spectrum of the Alu element distribution, which serves as the theoretical, neutral frequency to which real Alu insertion data can be compared through statistical goodness of fit tests. Departures from the neutral frequency spectrum may indicate selection.

Results: A comparison of the Alu sequence data, obtained by courtesy of Dr. Jerzy Jurka, with our model shows that the distributions of Alu sequences in the AluY family systematically deviate from the expected distribution derived from the branching process.

Conclusions: This observation suggests that Alu sequences do not evolve neutrally and might be under selection.

Show MeSH
Related in: MedlinePlus