ISOLATION BY DISTANCE WEB SERVICE WITH INCORPORATION OF DNA DATA SETS. A Thesis. Presented to the. Faculty of. San Diego State University

Transcription

1 ISOLATION BY DISTANCE WEB SERVICE WITH INCORPORATION OF DNA DATA SETS A Thesis Presented to the Faculty of San Diego State University In Partial Fulfillment of the Requirements for the Degree Master of Science in Computational Science with Concentration in Professional Applications by Eric C. Ngan Fall 006

2 ii Copyright 006 by Eric C. Ngan All Rights Reserved

3 iii ABSTRACT OF THE THESIS Isolation by Distance Web Service with Incorporation of DNA Data Sets by Eric C. Ngan Master of Science in Computational Science with Concentration in Professional Applications San Diego State University, 006 Isolation by Distance Web Service (IBDWS) is a web interface program used to determine whether genetic divergence of populations correlate with geographic distances, provided a raw data set with codominant markers (e.g., microsatellites). In addition, the relationship between genetic distance and geographic distance can be determined using several statistical tests. The current implementation, IBDWS.6, requires raw data sets of non-dna data, or predetermined genetic distances that can be tedious and time consuming for users to calculate. An expansion of IBDWS.6 is proposed to accommodate DNA data sets. These data sets consist of sequences from multiple individuals for the same gene, along with a population number for each individual. Genetic distances for all pairs of populations are then calculated and fed back into the original IBDWS code for data processing. Input files to this extension require a specific file format and will undergo extensive error checks prior to data processing. The aim of this extension is to provide a user friendly interface and detailed feedback when errors occur. The new version of IBDWS (3.0) will be hosted at All documentation is available under the About IBDWS link at the top of the homepage.

4 iv TABLE OF CONTENTS PAGE ABSTRACT...iii LIST OF TABLES... v LIST OF FIGURES... vi ACKNOWLEDGEMENTS...vii CHAPTER 1 INTRODUCTION... 1 IMPLEMENTATION INPUT CALCULATING GENETIC DISTANCES GENETIC VS. GEOGRAPHIC DISTANCE METHODS OUTPUT FUTURE DEVELOPMENTS CONCLUSION REFERENCES... 18

5 v LIST OF TABLES PAGE Table 4.1. Base Pair Classifications of Differences under Uncorrected/JC Model... 8 Table 4.. Base Pair Classifications of Differences under Kimura s P Model... 9

6 vi LIST OF FIGURES PAGE Figure 3.1. Screen shot of basic settings for input of raw DNA data. The first five options are new to IBDWS Figure 6.1. Screen shot of IBDWS 3.0 output

7 vii ACKNOWLEDGEMENTS Special thanks to Julia Turner for assisting in the creation and deployment of IBDWS 3.0. Additional thanks to Dr. James Otto for helping set up the server cluster and administration details to host IBDWS 3.0.

8 1 CHAPTER 1 INTRODUCTION Isolation by distance (IBD) is defined as a decrease in genetic similarity among populations as the geographic distance between them increases [1]. The theory behind IBD is that if dispersal is spatially limited, individuals from populations that are in close proximity to one another are more likely to interact and therefore have a higher chance to mate, than with individuals in more distant populations. As a result, allele frequencies in populations that are closer to one another will likely be more similar than in populations that are further apart. Isolation by Distance Web Service (IBDWS) is a web interface that determines genetic distances between all pairs of populations in a data set, and tests whether there exists a correlation between genetic distances and geographic distances. The Mantel Test and RMA regression, discussed in Chapter 5, are the statistical analysis methods used in determining this correlation. The purpose of this thesis is to illustrate the expansion of IBDWS.6, which incorporates the addition of DNA data sets for input. More information about the original IBDWS can be found at Currently, an obstacle for users of IBDWS is the need to calculate all pairwise genetic distances between populations for DNA data sets prior to using IBDWS. This task can be time consuming, and requires use of a second software program. The newly implemented expansion allows users to submit DNA data sets directly for analysis. IBDWS recognizes DNA data sets encoded in a modified Fasta format. Following a standard Fasta block [], the input file contains information that relates each individual to an allele sequence (one for haploid, two for diploid genes), and to a population. Genetic distances between all population pairs are automatically generated from the input data, and transferred to the original IBDWS code for analysis of correlation between genetic and geographic distances. Output is unchanged from IBDWS.6, with the exception that genetic distances between populations and allele sequences are included.

9 The program that is most similar in functionality to IBDWS 3.0 is Arlequin v.3, currently available at Arlequin is a comprehensive program which can compute genetic distances with DNA data sets, and test for IBD using Mantel tests. What makes IBDWS unique from Arlequin is that IBDWS 3.0 is able to do statistical analysis on genetic and geographic distance correlation. A graph of the populations data points and reduced major axis (RMA) regression line is also provided in the IBDWS output. By placing IBDWS 3.0 online, users may conduct analyses without the need to install the software locally on their system. This removes the limitations of implementing operating system-specific local software. With IBDWS 3.0, users can now take advantage of its functions with their DNA data sets and ease of use through any web browser. IBDWS is hosted at

10 3 CHAPTER IMPLEMENTATION IBDWS 3.0 can be access through any web browser at ibdws.sdsu.edu/. Input data may be entered directly through the supplied text area or uploaded as a plain text file. Upon submission, a cgi script retrieves and processes the form data. The cgi script is written in C++ and compiled with the Unix g++ compiler. Extensive error checking for properly formatted input from the user is done through calling an embedded Python (.4) code in the cgi. Python provides powerful regular expression patterns, allowing easy parsing of submitted DNA sequences for erroneous characters. In addition to erroneous character checking, checks are performed for input data format requirements. Example: validate population numbers, individual numbers, individual-population association, sequential population numbering, presence of required markers, and same DNA sequence length. Further detail regarding requirements and specific input formatting can be referenced in the Appendix. Upon successful error checking, the Python code returns the properly formatted input data along with memory allocation parameters. Dynamically allocated arrays for input data storage are initialized with the returned memory allocation parameters. This implementation minimizes the usage of memory while allowing for efficient data lookup through array indices. User choice ofφ or detailed in Chapter 4. ST F ST genetic distances are then calculated through the steps A graph illustrating the population data points of genetic vs. geographic distances and RMA regression line is available in JPEG and Vector-based Postscript format. This graph is generated using the C++ library, CGraph. The Mantel test provided in the output tests whether the association of the genetic vs. geographic distance relationship is significant. Chapter 5 will discuss the methods involved in the calculation of the RMA regression line and Mantel test.

11 4 CHAPTER 3 INPUT IBDWS 3.0 can parse a new input file format, in addition to those already available in IBDWS.6. DNA input files can be uploaded as an ASCII text file or copied into the text field provided on the web page. This requires DNA sequence encodings for alleles of a gene to be entered in Fasta format []. Next, each individual entered (assigned by individual number) needs to be associated with an allele sequence name and population number. Geographic information must be provided following the population information along with optional indicator information. All alleles submitted will automatically be labeled a unique allele number starting from 1 and incremented for each successive allele entered. For specific details regarding the input file format, refer to the Appendix. Various settings are new to the DNA analysis option in IBDWS 3.0 that were not present in the.6 version. Figure 3.1 displays the five new settings added to the webpage. Two types of genetic distances between populations are available: Traditional F ST and Φ ST [3]. A setting to choose the type of genetic distance between two sequences are also available. Genetic distance between pairs of sequences is required for calculating that when Φ ST, so Φ ST is selected, additional options for calculating the sequence distances become available. These options reflect assumptions about the underlying model of molecular evolution. The treatment of unknown base pairs and gaps in a sequence can be additionally customized through radio buttons. More details regarding calculations of genetic distance among sequences and among populations are provided in chapter 4. Finally, an option to treat multiple consecutive gaps as one is available. When selected, successive base pair positions of a current gap that are also gaps will be ignored. See the Appendix for examples of this option.

12 Figure 3.1. Screen shot of basic settings for input of raw DNA data. The first five options are new to IBDWS

13 6 CHAPTER 4 CALCULATING GENETIC DISTANCES Pairwise population genetic distances require the utilization of genetic distances between each pair of sequences (based on a model of molecular evolution). This expansion provides four forms of pairwise allelic genetic distance. The first form is the uncorrected genetic distance between two allele sequences. This form is the proportion of difference after a simple count of the number of different nucleotide base positions between two sequences. The second form (proposed by Jukes and Cantor) is known as the Jukes-Cantor Model of molecular evolution. Jukes and Cantor (JC) proposed that a simple count of nucleotide base pair differences may be a significant underestimation of the actual number of substitutions since the sequences last shared a common ancestor [4]. After an extended period of time, a particular site may undergo multiple changes, eventually reverting back to the original base pair. Thus, the relationship between observed divergence and actual divergence begins approximately linear but plateaus at a maximum observed divergence of To account for the true number of substitutions (genetic distance K) between two sequences, JC derived the following equation: K = 3 4 ln 1 ( p). 4 3 Here, p is the fraction of nucleotides that a simple count reveals to be different between two sequences. K may possess a value between 0 and +. The third form, (proposed by Kimura) called Kimura s Two-Parameter Model (Kimura s P), accounts for the different rates of transitions and transversions [4]. Nucleotides are split into two categories, purines and pyrimidines. Purines (guanine and adenine) have a two-ring nitrogenous base structure while pyrimidines (cytosine, thymine, and uracil) have a one-ring nitrogenous base structure. Transition is a mutation in which a nucleotide mutation exchanges a purine for another or a pyrimidine for another. Transversion is a mutation in which a purine is exchanged for a pyrimidine or vice versa. Transitions are more common than transversions since they do not involve the change of their nitrogen

14 bases. Transversion do require a change in nitrogen bases and therefore occur less frequently. The redundancy of the genetic code also favors transitions, since they are less likely to change the amino acid translation. Kimura s Two-Parameter Model equation is: K = 1 ln P Q 1 ln Q Here, P is the fraction of changes between two sequences that are transitions, and Q is the fraction that are transversions. The final form represents a basic measure of whether two sequences differ or not, which will be called the flag form. A 1 indicates that the two sequences are different in one or more base pair positions, while a 0 indicates that they are identical. This form is utilized for the traditional F ST genetic distance measure between two populations. Two additional characters outside of the four nucleotides are permitted in the DNA input data. These two characters are N (or? ) and - (or : ). An N represents an unknown nucleotide while a - represents a gap in the alignment of the sequences (resulting from the insertion or deletion of a nucleotide). Options are available to treat N as missing data or a match to any nucleotide. A - can have the option to be treated as a fifth state, transition or transversion for Kimura s P model, or missing data. Tables 4.1 and 4. illustrate the treatment of all possible base pair comparisons under the first three models of molecular evolution. A CUT indicates that the base pair position is ignored and the total sequence length is reduced by one. A 1 signifies that the contrast is treated as a base pair difference, and 0 signifies a base pair match. I and V stand for a transition and transversion respectively. A j, k Once calculated, the pairwise allelic genetic distance values are stored into matrix A. will contain the uncorrected, Jukes-Cantor, Kimura or flag values between allele number j and allele number k, depending on which molecular model the user has chosen. Each population contains a collection of user-defined allele (obtained from the Fasta entries which may not be unique) assignments to individuals in a population. For haploid data, one individual will bear one user-defined allele. For diploid data, each individual will have two user-defined alleles. Alleles within a population are not required to be unique as populations are allowed to contain more than one of the same user-defined allele. Refer to 7

15 8 Table 4.1. Base Pair Classifications of Differences under Uncorrected/JC Model the Appendix for more information on input data formatting. The genetic distance between all assigned user-defined alleles to individuals can now be simply indexed through matrix A. The genetic distance Φ ST between two populations is calculated through formulas provided by Weir [3] and Excoffier et al. [5]. A slight modification to the variable

16 9 Table 4.. Base Pair Classifications of Differences under Kimura s P Model names is made for clarification purposes. The equation in calculating the genetic distance between two populations is: MDA MDW Φ ST =. (1) MDA+ ( n 1) MDW Here MDA is the mean genetic distance deviations between two gene copies, where one is chosen from each of the two populations. MDW is the mean genetic distance between gene copies within each of the two populations being analyzed. As can be seen from the formula, Φ ST is a statistic which evaluates the distance between populations using the MDA and c

17 10 MDW statistics from a standard AMOVA framework. The populations are maximally differentiated when they share no alleles in common and the genetic variation within each population is zero. These mean deviations are components of variance of alleles among and within populations. MDA and MDW are defined by: MDA = SDA/(m-1), MDW = SDW/(n* - m), where m represents the total number of populations. n* is defined to be: m = = n* n, where ni is the number of gene copies in population i. Since the IBD analysis only requires genetic distances between pairs of populations, m will always be so MDA=SDA and MDW=SDW/(n* - ). SDA and SDW are the sum of the deviations among populations and within a population respectively. SDW is calculated through summing the pairwise genetic distances for all the gene copies within a population. SDW is given as follow for population i: i 1 i 1 ni 1 ni = 1 A j k= j+ 1 j, k ni SDW =. pop i SDA is given by the difference between the sum deviations total among all gene copies in both populations to the sum deviations within the two populations. So, where, SDA= SDT SDW pop SDW SDT poph, popi = N h pop i 1 N 1 N = 1 A j k= j+ 1 j, k where N is the total number of gene copies that encompasses population h and i. SDT can also be rewritten as, SDT pop, pop h i = n h + n nh 1 nh j= nh k= ni n 1 n ( Aj k + Aj k + Aj k) 1 i i i Equation a can now be restated as h j= 1 k= j+ 1, i j= 1 k= 1,, j= 1 k= j+ 1, j= nh k= ni ( nhsdwpop + Aj k nisdwpop ) SDT = 1 poph popi h j k n + n +, = 1 = 1, i. (a). (b)

18 With SDW for all populations calculated, processing time is reduced since only the middle term in the parenthesis of equation b requires computation. In calculating the genetic distance between all alleles, this exhibits a run time complexity of O( N allele L) where the number of user defined alleles and L is the length of the sequence. SDW exhibits a run time of ( ) O and SDA exhibits a run time of ( ) n i O n n. h i 11 Nallele is

19 1 CHAPTER 5 GENETIC VS. GEOGRAPHIC DISTANCE METHODS Original IBDWS provides several of analysis in population genetics. A major area of interest for population geneticists is testing for a correlation between genetic distance and geographic distance. By representing the genetic and geographic distances in matrices, a Mantel test can be performed to test the correlation between the two matrices. Given genetic distance matrix A (unrelated to above) and geographic distance matrix B, a Z test statistic and r correlation can be obtained. The Z test statistic is given as: Z N = i, j A ij B ij, with N being the dimension of the two square matrices. The value of Z corresponds to the correlation between A and B. Similarly, r ranges from -1 to 1 with 1 representing a perfect correlation. r is given as: i= 1 j= 1 ( A A)( B B) N N 1 ij ij r( AB) =, N N 1 s s where s A and s B are the standard deviations of A and B. IBDWS also allows for an indicator matrix to be entered for correlation analysis. If entered, a partial Mantel test will be performed. The partial Mantel test determines the correlation between the genetic distance and geographic distance, after controlling the effects of the indicator matrix. Conversely, one can calculate the correlation between the genetic distance and indicator matrix after controlling for geographic distance. The correlation variable r for the partial Mantel test is given as: r( AB) r( AC) r( BC) r( AB. C) =. 1 r ( AC) 1 r ( BC) A B

20 13 IBDWS allows the option to randomize the matrices and perform the Mantel test. After ordering the list of randomized Z values, the probability of the empirical data is calculated by determining where the empirical value falls in an ordered list from random data. Reduced major axis regression is a linear representation of the correlation between genetic and geographic distances. RMA calculations include the slope and intercept of the relationship. When an independent variable x is measured with error, an RMA regression is more suitable than a standard ordinary least squares regression [6]. Otherwise, error in the independent variable leads to biased estimates of slope [7]. Slope and intercept of the data are given as: Slope ( y) ( x) SS y Y = b n RMA =± =±, SS X x n Intercept = a = y b x. RMA RMA Correlation value, r, represents the strength of the scatter of the points in relation to the line. If all the points were to lie exactly on the line (meaning there is a definite correlation between genetic and geographic distance), r = r would equal to 1. SS SS x xy SS y, r is defined as: where SS xy ( ) ( x)( y ) xy =. n Additional options to log the genetic and/or geographic distance are also available.

21 14 CHAPTER 6 OUTPUT Genetic distances are calculated automatically once the DNA data set is uploaded. All population and allele sequence pairwise genetic distance values are accessible through the new genetic distances button provided on the output page. These genetic distances are used for the original IBDWS analysis. No additional changes are incorporated to the output in the expansion. The purpose of the expansion is to solely build upon the input data, allowing DNA data sets to be submitted. Arlequin, a free software, has similar analyses to IBDWS 3.0. Although the genetic distances between two populations are calculated using identical formulas, genetic distances between two alleles may differ, depending on presence of gaps and unknowns. When no gaps and unknowns are introduced, then the genetic distance between Arlequin and IBDWS 3.0 are identical. When gaps and unknowns are introduced in the sequences, then the genetic distances will differ from the default settings in Arlequin. Refer back to Table 4.1 and Table 4. for base pair classifications of differences in IBDWS 3.0. Output webpage of IBDWS are split in two vertical frames. The left frame outputs up to four analyses of Mantel tests depending on user options. The right frame displays the graph of population data points along with an overlay of the RMA regression line. A drop down bar underneath the graph allows for navigation to different graphs from different analyses. Figure 6.1 illustrates a sample output of IBDWS.

22 Figure 6.1. Screen shot of IBDWS 3.0 output. 15

23 16 CHAPTER 7 FUTURE DEVELOPMENTS IBDWS is a very computationally intensive program largely due to the matrix randomization and sorting. Current research is being done in utilizing parallelization for a more efficient process time. Future developments may include: multilocus analysis, genetic distances within individuals, geographic distances through longitude and latitude coordinates, and genetic distances through phylogenetic trees. Every major update to IBDWS will be referenced by an increment of the leading number in the version number. Every minor update for bug fixes will have an increment to the number following the period in the version number. In this particular case, since a major functionality was integrated to IBDWS, the version number is changed from.6 to 3.0.

24 17 CHAPTER 8 CONCLUSION IBDWS.6 was limited to input data that required specific raw data format or preprocessed genetic distance values. With the addition of DNA data sets to IBDWS.6, users gain the ability to take full advantage of the statistical tests without the need of secondary software to calculate genetic distance values between population sets. This will allow a wider range of population geneticists to utilize IBDWS that previously were not able to do so without spending significant time setting up the input data. The resulting output has remained unchanged except for an addition of display of the genetic distances calculated.

25 18 REFERENCES [1] S. Wright, Isolation by Distance, Genetics, vol. 8, pp , [] Computational Molecular Biology and Bioinformatics, University of Southern California, FASTA Format, 1996, (last accessed November 9, 006). [3] B. Weir, Genetic Data Analysis II. Sunderland: Sinauer Associates, Inc., [4] R.D. Page and E.C. Holmes, Molecular Evolution: A Phylogenetic Approach. Malden: Blackwell Publishing, Inc., November [5] L. Excoffier, P. Smouse, and J.M. Quattro, Analysis of Molecular Variance Inferred From Metric Distances Among DNA Haplotypes: Application to Human Mitochondrial DNA Restriction Data, Genetics, vol. 131, pp , February 199. [6] R.R. Sokal and F.J. Rohlf, Biometry. New York: Freeman, [7] A.J. Bohonak, IBD (Isolation By Distance): A Program for Analysis of Isolation by Distance, Journal of Heredity, vol. 93, pp , 00. [8] J.L. Jensen, A.J. Bohonak, and S.T. Kelley, Isolation by distance, Web Service, BMC Genetics, vol. 6.13, March 005.