Exploring Phylogenetic Relationships in Drosophila with Ciliate - - PowerPoint PPT Presentation

Exploring Phylogenetic Relationships in Drosophila with Ciliate Operations

Anna Nelson

Department of Mathematics, Boise State University AAAS Pacific Division, 93rd Annual Meeting

25 June 2012

• A. Nelson

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Background

Acknowledgements

The research resulted from the 2011 Boise State University REU in Mathematics with Jacob Herlin from University of Northern Colorado under the mentorship of Dr. Marion Scheepers from Boise State

• University. We gratefully acknowledge Boise State University for hosting

and the National Science Foundation for funding the project under grant number DMS 1062857

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Background

What is a phylogenetic relationship?

Phylogenetics is the study of evolutionary relationships between groups of organisms.

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Background

What is a phylogenetic relationship?

Phylogenetics is the study of evolutionary relationships between groups of organisms. Described by using phylogenetic trees

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Background

What is a phylogenetic relationship?

Phylogenetics is the study of evolutionary relationships between groups of organisms. Described by using phylogenetic trees

Image courtesy of DroSpeGe: Drosophila Species Genomes. http://insects.eugenes.org/DroSpeGe

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Background

Genetic Operations

Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome

• 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila

Pseudoobscura and their use in the study of the history of the species. Proceedings of the National Academy of Science 22(1936), 448 - 350.

• A. Nelson

() Phylogenetic Relationships 25 June 2012 4 / 19

Background

Genetic Operations

Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome Reversals have been the main genetic operation used to decrypt 1

• 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila

Pseudoobscura and their use in the study of the history of the species. Proceedings of the National Academy of Science 22(1936), 448 - 350.

• A. Nelson

() Phylogenetic Relationships 25 June 2012 4 / 19

Background

Genetic Operations

Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome Reversals have been the main genetic operation used to decrypt 1 Using a canonical reference species, use number of reversals as a measure of evolutionary distance from other species.

• 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila

Pseudoobscura and their use in the study of the history of the species. Proceedings of the National Academy of Science 22(1936), 448 - 350.

• A. Nelson

() Phylogenetic Relationships 25 June 2012 4 / 19

Background

Genetic Operations

Genetic operations that cause DNA to be scrambled result from breaking and rejoining the chromosome Reversals have been the main genetic operation used to decrypt 1 Using a canonical reference species, use number of reversals as a measure of evolutionary distance from other species.

• 1A. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila

Pseudoobscura and their use in the study of the history of the species. Proceedings of the National Academy of Science 22(1936), 448 - 350.

• A. Nelson

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Background

Micronucleus and macronucleus of ciliates

Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments.

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Background

Micronucleus and macronucleus of ciliates

Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. Micronucleus: Long strands of DNA, encrypted version of

• macronucleus. Contain nonsense DNA that will be eliminated.
• A. Nelson

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Background

Micronucleus and macronucleus of ciliates

Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. Micronucleus: Long strands of DNA, encrypted version of

• macronucleus. Contain nonsense DNA that will be eliminated.

Macronucleus: Larger than the micronucleus and contains many short strands of DNA. Contain expressed DNA.

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Background

Micronucleus and macronucleus of ciliates

Ciliates are multinuclear (micronucleus and macronucleus) protozoans found in aqueous environments. Micronucleus: Long strands of DNA, encrypted version of

• macronucleus. Contain nonsense DNA that will be eliminated.

Macronucleus: Larger than the micronucleus and contains many short strands of DNA. Contain expressed DNA. Micronuclear DNA is decrypted to form macronuclear DNA using three ciliate operations: reversal, block interchange, excisionoperations: reversal, block interchange, excision

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Background

Macronuclear vs. Micronuclear DNA

Micronuclear DNA has three elements:

• 1. Macronuclear destined sequences (MDSs)
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Background

Macronuclear vs. Micronuclear DNA

Micronuclear DNA has three elements:

• 1. Macronuclear destined sequences (MDSs)
• 2. Internal eliminated sequences (IESs)
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Background

Macronuclear vs. Micronuclear DNA

Micronuclear DNA has three elements:

• 1. Macronuclear destined sequences (MDSs)
• 2. Internal eliminated sequences (IESs)
• 3. Pointers occur on the flanks of the MDSs
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Methodology

Pointer Lists

An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations.

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Methodology

Pointer Lists

An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers:

• A. Nelson

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Methodology

Pointer Lists

An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: [1, 4, −3, −2, 6, −5]

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Methodology

Pointer Lists

An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: [1, 4, −3, −2, 6, −5] [(1, 2), (4, 5), (4, 3), (3, 2), (6, 7), (6, 5)] Each pair (a, b) represents a section of genome spanning from a pointer a to a pointer b.

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Methodology

Pointer Lists

An algorithm was created to find a path from a signed permutation back to the canonical in terms of ciliate operations. Map a signed permutation where each elements represents a section of genome onto a list of pairs of pointers: [1, 4, −3, −2, 6, −5] [(1, 2), (4, 5), (4, 3), (3, 2), (6, 7), (6, 5)] Each pair (a, b) represents a section of genome spanning from a pointer a to a pointer b. [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5] We call this representation a pointer list.

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions: Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions:

1 n is even.

Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions:

1 n is even. 2 There is a unique i with µ = |xi| = min{|xj| : i ≤ j ≤ n}. (There is a

minimum element) Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

• A. Nelson

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions:

1 n is even. 2 There is a unique i with µ = |xi| = min{|xj| : i ≤ j ≤ n}. (There is a

minimum element)

3 There is a unique j with λ = |xi| = max{|xj| : i ≤ j ≤ n}. (There is a

maximum element) Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

• A. Nelson

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions:

1 n is even. 2 There is a unique i with µ = |xi| = min{|xj| : i ≤ j ≤ n}. (There is a

minimum element)

3 There is a unique j with λ = |xi| = max{|xj| : i ≤ j ≤ n}. (There is a

maximum element)

4 For each i ∈ {1, ..., n} with µ < |xi| < λ, there is a unique

j ∈ {1, ..., n}\{i} with |xi| = |xj|. (Each number has a pair) Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

• A. Nelson

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions:

1 n is even. 2 There is a unique i with µ = |xi| = min{|xj| : i ≤ j ≤ n}. (There is a

minimum element)

3 There is a unique j with λ = |xi| = max{|xj| : i ≤ j ≤ n}. (There is a

maximum element)

4 For each i ∈ {1, ..., n} with µ < |xi| < λ, there is a unique

j ∈ {1, ..., n}\{i} with |xi| = |xj|. (Each number has a pair)

5 For each odd i ∈ {1, ..., n}, xi ≤ xi+1 and xi · xi+1 > 0.

Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

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Methodology

Pointer Lists

We define a pointer list formally as a list L = [x1, x2, . . . xn] that satisfies the following six conditions:

1 n is even. 2 There is a unique i with µ = |xi| = min{|xj| : i ≤ j ≤ n}. (There is a

minimum element)

3 There is a unique j with λ = |xi| = max{|xj| : i ≤ j ≤ n}. (There is a

maximum element)

4 For each i ∈ {1, ..., n} with µ < |xi| < λ, there is a unique

j ∈ {1, ..., n}\{i} with |xi| = |xj|. (Each number has a pair)

5 For each odd i ∈ {1, ..., n}, xi ≤ xi+1 and xi · xi+1 > 0. 6 For each odd i, ∄ an odd j such that xi < xj < xi+1 < xj+1.

Example: [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, −5]

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Methodology

Excision

Excision: Remove given IESs

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Methodology

Excision

Excision: Remove given IESs

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Methodology

Excision

Excision: Remove given IESs

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Methodology

Excision

Excision: Remove given IESs Removal of pairs of the same pointer that are adjacent. [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, 5]

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Methodology

Excision

Excision: Remove given IESs Removal of pairs of the same pointer that are adjacent. [1, 2, 4, 5, −4, −3, −3, −2, 6, 7, −6, 5] [1, 2, 4, 5, −4, −2, 6, 7, −6, −5]

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers Moving together two pointers of opposite orientation with a reversal, setting up for an excision.

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers Moving together two pointers of opposite orientation with a reversal, setting up for an excision. [1, 2, 4, 5, −4, −2, 6, 7, −6, −5]

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Methodology

Reversal

Reversal: Reverse section of DNA between two oppositely oriented pointers Moving together two pointers of opposite orientation with a reversal, setting up for an excision. [1, 2, 4, 5, −4, −2, 6, 7, −6, −5] [1, 2, 4, 4, −5, −2, 6, 7, −6, −5]

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Methodology

Block interchange

Block interchange: Exchange DNA sections between two staggered pointers.

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Methodology

Block interchange

Block interchange: Exchange DNA sections between two staggered pointers.

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Methodology

Block interchange

Block interchange: Exchange DNA sections between two staggered pointers.

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Methodology

Block interchange

Block interchange: Exchange DNA sections between two staggered pointers. Represented by finding a 4-tuple of pointers (xi, xj, xk, xl) where xi = xk, and xj = xl and i < k < j < l. Take the section xk, . . . , xl (including the pointers) and the section xi+1, . . . , xj−1 (excluding the pointers), and swap them.

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Methodology

Block interchange

Block interchange: Exchange DNA sections between two staggered pointers. Represented by finding a 4-tuple of pointers (xi, xj, xk, xl) where xi = xk, and xj = xl and i < k < j < l. Take the section xk, . . . , xl (including the pointers) and the section xi+1, . . . , xj−1 (excluding the pointers), and swap them. [2, 8, 10, 11, 9, −2, −1, 10, 8, 9, −12, −11]

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Methodology

Block interchange

Block interchange: Exchange DNA sections between two staggered pointers. Represented by finding a 4-tuple of pointers (xi, xj, xk, xl) where xi = xk, and xj = xl and i < k < j < l. Take the section xk, . . . , xl (including the pointers) and the section xi+1, . . . , xj−1 (excluding the pointers), and swap them. [2, 8, 10, 11, 9, −2, −1, 10, 8, 9, −12, −11] [2, 8, 10, 10, 8, 9, 9, −2, −1, 11, −12, −11]

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Methodology

Boundary Excision

Boundary excision maps lists of length 4 onto lists of length 2. It only

• perates on lists of the following form:

[x, m, m′, x] where m, m′ are the maximum and minimum elements and x is some pointer.

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Methodology

Boundary Excision

Boundary excision maps lists of length 4 onto lists of length 2. It only

• perates on lists of the following form:

[x, m, m′, x] where m, m′ are the maximum and minimum elements and x is some pointer. [x, m, m′, x] ⇒ [m′, m]

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Methodology

Boundary Excision

Boundary excision maps lists of length 4 onto lists of length 2. It only

• perates on lists of the following form:

[x, m, m′, x] where m, m′ are the maximum and minimum elements and x is some pointer. [x, m, m′, x] ⇒ [m′, m] For example, [−2, −1, −3, −2] ⇒ [−3, −1] A list is considered sorted if it is in the form [µ, λ] or [−λ, −µ], where λ is the maximum element and µ is the minimum element. Thus, if a boundary excision is made, it will always be the final move in the sorting.

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Methodology

The Algorithm

(1) Map the signed permutation onto a list of signed pointers.

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Methodology

The Algorithm

(1) Map the signed permutation onto a list of signed pointers. (2) Do the any possible excisions or boundary excisions.

• A. Nelson

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Methodology

The Algorithm

(1) Map the signed permutation onto a list of signed pointers. (2) Do the any possible excisions or boundary excisions. (3) Search through the list, and keep memory of pairs of

• ppositely-oriented pointers and of pairs of equally-oriented pointers.
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Methodology

The Algorithm

(1) Map the signed permutation onto a list of signed pointers. (2) Do the any possible excisions or boundary excisions. (3) Search through the list, and keep memory of pairs of

• ppositely-oriented pointers and of pairs of equally-oriented pointers.

(4) Search through the list of equally-oriented pointers for a possible block interchange move. If one is found, do it and then go back to (2).

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Methodology

The Algorithm

(1) Map the signed permutation onto a list of signed pointers. (2) Do the any possible excisions or boundary excisions. (3) Search through the list, and keep memory of pairs of

• ppositely-oriented pointers and of pairs of equally-oriented pointers.

(4) Search through the list of equally-oriented pointers for a possible block interchange move. If one is found, do it and then go back to (2). (5) Do the reversal represented by the first element of the list of equally-oriented pairs, then go to (2).

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Methodology

Some Theorems

Theorem The algorithm runs in polynomial time. Specifically, the worst-case complexity is O(n3).

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Methodology

Some Theorems

Theorem The algorithm runs in polynomial time. Specifically, the worst-case complexity is O(n3). Theorem A correctly-formed pointer list of length n ≥ 4 is always in the domain of

• f a reversal, excision, block interchange or boundary excision.
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Methodology

Some Theorems

Theorem The algorithm runs in polynomial time. Specifically, the worst-case complexity is O(n3). Theorem A correctly-formed pointer list of length n ≥ 4 is always in the domain of

• f a reversal, excision, block interchange or boundary excision.

Theorem The algorithm will always find a path to either [µ, λ] or [−λ, −µ], and thus will always terminate.

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Results

Data Analysis

Data was collected from Flybase.org in a text file that had the genes from

• ur reference species and their orthologs on other species’ genome. Given

the relative location and orientation of the genes for the following species, permutations were created based on their genomes.

1 Simulans 2 Sechellia 3 Yakuba 4 Erecta 5 Virilis 6 Grimshawi 7 Mojavensis 8 Melanogaster

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Results

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Results

Data Analysis

The algorithm produced these total numbers for every Muller element added together: Species Reversal Interchange Boundary Total Divergence

• D. sechellia

15 1460 3 1478 5.4 mya

• D. simulans

24 508 532 5.4 mya

• D. erecta

30 658 688 12.6 mya

• D. yakuba

47 438 1 486 12.6 mya

• D. mojavensis

189 986 2 1177 62 mya

• D. virilis

194 1278 2 1474 62 mya

• D. grimshawi

197 1459 3 1659 62 mya

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Results

The Future

Here are some further areas we have to explore: 1. We conjecture that our algorithm minimizes the number of reversal moves in its reversal path. We have yet to prove this.

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Results

The Future

Here are some further areas we have to explore: 1. We conjecture that our algorithm minimizes the number of reversal moves in its reversal path. We have yet to prove this. 2. Develop an algorithm to find the shortest possible ciliate operation path.

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Results

The Future

Here are some further areas we have to explore: 1. We conjecture that our algorithm minimizes the number of reversal moves in its reversal path. We have yet to prove this. 2. Develop an algorithm to find the shortest possible ciliate operation path. 3. Look at more species in the Drosophila genus and see if the correlation between ciliate operation path length and divergence time holds.

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Results

Bibliography

Sridhar Hannenhalli, Pavel A. Pevzner Transforming Cabbage into Turnip: Polynomial Algorithm for Sorting Signed Permutations by Reversals. Journal of the ACM, Vol. 46, No. 1, 1999. Pavel Pevzner, Glenn Tesler Genome Rearrangements in Mammalian Evolution: Lessons from Human and House

• Henomes. Genome Research, Vol. 13, 2003.

Arjun Bhutkar, Stephen W. Schaeffer, Susan M. Russo, Mu Xu, Temple F. Smith, William M. Gelbart Chromosomal Rearrangement Inferred From Comparisons of 12 Drosophila Genomes. Genetics, Vol 197, 2008.

• J. Ranz, D. Maurin, Y. Chan, M. Von Grotthuss, L. W. Hillier, J. Roote, M. Ashburner, C. M. Bergman Principles of

Genome Evolution in the Drosophila melanogaster Species Group. PLoS Biology, Vol. 5, Issue 6, 2007.

• A. Ehrenfeucht, T.Harju, I. Petre, D. M. Prescott, G. Rozenberg Computation in Living Cells. Springer-Verlag Berlin

Heidelberg, 2004.

• S. Tweedie, M. Ashburner, K. Falls, P. Leyland, P. McQuilton, S. Marygold, G. Millburn, D. Osumi-Sutherland, A.

Schroeder, R. Seal, H. Zhang and The FlyBase Consortium FlyBase: enhancing Drosophila Gene Ontology annotations. Nucleic Acids Research, Vol. 37, 2009.

• A. H. Sturtevant and Th. Dobzhansky. Inversions in the third chromosome of wild races of Drosophila Psuedoobscura and

their use in the study of the history of the species. Proceedings of the National Academy of Science 22(1936), 448 - 350.

• A. Nelson

() Phylogenetic Relationships 25 June 2012 19 / 19