Copyright ©1995 Lee M. Silver
Suppliers of Mice
A.1 Major suppliers of common inbred and outbred strainsa
A.2 Other commercial sources of micea
A.1 Major suppliers of common inbred and outbred strainsa
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251 Ballardvale St.
Wilmington, MA 01887 |
FAX: 508-658-7132 |
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Indianapolis, IN 46229 |
FAX: 317-894-4473 |
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600 Main St. Bar Harbor, ME 04609-0800 |
FAX: 207-288-3398 |
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33 Hover Avenue
Germantown, NY 12526 |
FAX: 518-537-7287 |
aListed in alphabetical order
A.2 Other commercial sources of micea
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Fremont, CA 94538 |
FAX: 510-683-8712 |
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Mountain View, CA 94043 |
FAX: 415-964-3537 |
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Scottsdale, PA 15683 |
FAX: 412-887-3582 |
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St. Petersburg, FL 33710 |
FAX: 813-347-2957 |
aListed in alphabetical order
Appendix B
Computational Tools and Electronic Databases
B.1 On-line electronic databases
B.1.1 Mouse genetics
B.1.2 Humans and other organisms
B.2 Mouse Genetics Community Bulletin Board
B.3 Computer Programs
B.3.1 Linkage analysis
B.3.2 Mouse colony management and genetic databases
B.1 On-line electronic databases
An ever-increasing amount of genetic information can be easily accessed and selectively retrieved over the Internet by using a software interface protocol known as Gopher, developed at the University of Minnesota. Any researcher with an Internet link can take advantage of this protocol by loading onto their computer a platform-specific version of a "Gopher client program" available without charge from the Gopher development group. Their E-mail address is [Gopher@boombox.micro.umn.edu]. Versions of the Gopher client program are available for all common operating systems that run on IBM-compatible PCs, Macintoshs, workstations, minicomputers, and mainframes. The Gopher program takes advantage of the custom features of each local machine type and allows a user to move seemingly seamlessly among different computer locations (called Gopher Holes) around the world where database searches can be conducted and selected data can be retrieved in a simple manner.
With the addition of the NCSA Telnet protocol, direct Internet links can also be made to login-based servers on the Gopher network. Another Gopher-like tool called Fetch (developed at Dartmouth College and also available free to non-profit organizations and individuals) provides Macintosh users with the ability to download files from FTP (File Transfer Protocol) sites in a transparent manner. For more information on this program, send an E-mail message to Fetch@Dartmouth.edu.
As this book is being written, the Gopher software and its associated formats are still less than three years old and expanding rapidly. It is a near-certainty that the data sources described below will be enriched and supplemented with new sources of information and modes for their retrieval. In addition, other more sophisticated electronic highways are under development. The most advanced of these, known as the "World Wide Web (WWW)", can be accessed with the use of NCSA Mosaic client software. You should contact your local computer advisor for up-to-the-date information on the most advanced system available at the time of this reading.
B.1.1 Mouse genetics
The central database server for mouse geneticists is located at the Jackson Laboratory. It can be reached in a number of different ways: (1) By using Gopher to trace a path from the "Home Gopher Hole" at the University of Minnesota through the U.S. to Maine to "The Jackson Laboratory." (2) By pointing Gopher directly at GOPHER.INFORMATICS.JAX.ORG, (3) By using NCSA Mosaic to connect to the Jackson Laboratory through the World Wide Web. This Gopher Hole contains a number of useful databases including the Mouse Locus Catalog ( or MLC), and the Genomic Database of the Mouse (or GBASE).
MLC originated as an electronic version of the chapter entitled "Catalog of mutant genes and polymorphic loci" (Green, 1989) in the Lyon and Searle compendium Genetic Variants and Strains of the Laboratory Mouse. It is updated regularly by staff members of the Jackson Laboratory led by Dr. M.T. Davisson and Dr. D. P. Doolittle. Each locus is represented by a separate record within the database that contains a detailed description of phenotype and other characteristics. The entire database can be searched to retrieve a list of loci (with associated descriptions and citations) that contain a particular search word or combination of words anywhere within the locus record.
GBASE is a comprehensive database at the Jackson Laboratory containing mouse mapping information. Investigators must login to GBASE (as a guest) to access the data contained within it. GBASE can be reached either through Gopher or via a direct internet linkage with the NCSA Telnet protocol. Once on-line, an investigator can retrieve the accumulated linkage data published on any set of loci, linkage maps, as well as allele distribution patterns for common inbred strains and all associated citations. For further assistance, send an E-mail message to mgi-help@Jax.Org.
The Jackson Laboratory database server also has catalog files that can be downloaded with information on available mouse strains and mutant stocks (both live and in the form of DNA samples). Many other sources of genetic information, both at the Jackson Laboratory and elsewhere are also accessible through this Gopher Hole. One can jump from this Gopher Hole directly to the "Computational Biology" gopher hole with human genetic data at Johns Hopkins University (described below), and one can also search through the Genbank sequence database directly from here. It is also possible to download updated data files for use by the Encyclopedia of the Mouse Genome which is described below.
The Genome Center at the Whitehead Institute, MIT provides a highly specialized but very useful source of information through either an automated E-mail query and answer protocol or anonymous FTP (File Transfer Protocol). This Genome Center has characterized and mapped over 3,000 polymorphic mouse microsatellite markers (as of Januray, 1994) that are each defined by a unique pair of oligonucleotide primers. By filling-out and transmitting a special E-mail query form, an investigator can receive an automatic response containing information about sets of microsatellite markers defined by various criteria, including chromosomal location and polymorphisms between particular strains. It is possible to retrieve primer sequences as well as a graphical representation of a chromosome map that shows the microsatellites (in Macintosh PICT format suitable for incorporation into all Mac drawing programs). To receive a blank E-mail query form and instructions for its use, send an E-mail message with the single word help to genome_database@genome.wi.mit.edu. Data can also be retrieved by anonymous ftp to genome.wi.mit.edu. For more information, contact Lincoln Stein at the Whitehead Institute [Email address: lstein@genome.wi.mit.edu].
B.1.2 Humans and other organisms
A central Gopher Hole for human genetic information is maintained at Johns Hopkins University. It can be reached by tracing a path through Maryland to Johns Hopkins University to "Computational Biology" or by means of the Jackson Laboratory Gopher hole described above. Once there, you should work your way down through the "Genome Project" to the "Genome Data Base (GDB) folder." Once you have reached this location, it becomes possible to search various databases of human genetic information including the Genome Database (GDB) itself, which is a compendium of human mapping data, other genetic information, and citations. At this Gopher Hole, it is also possible to search the electronic version of Victor McKusicks Mendelian Inheritance of Man (called OMIM) which contains comprehensive records on all defined human loci. For further information, the GDB staff can be reached at the E-mail address [Help@gdb.org] or the mailing address [GDB User Support, Genome Data Base, Johns Hopkins University, 2024 E. Monument Street, Baltimore, MD 21205-2100.]
Other Gopher Holes dedicated to the human genome project are maintained at the Genethon Center in France (point to [Gopher.genethon.fr 70]), and the UK Mapping Project (point to [Menu.crc.ac.uk 70]). A database of Drosophila mapping information is maintained at Indiana University (point to [fly.bio.indiana.edu]) and the yeast database is maintained at Stanford University (point to genome.stanford.edu]). Mapping information on C. elegans is maintained at the MRC in Cambidge, England; contact Richard Durbin for further information (E-mail address is [rd@mac-lib.cam.ac.uk]).
B.2 Mouse Genetics Community Bulletin Board
An electronic Bulletin Board (called MGI-LIST) has been set up at the Jackson Laboratory with E-mail addresses of mouse geneticists throughout the world. The Mouse Genome Informatics Group at the JAX will use this Bulletin Board to make announcements of new software and data sets for the Encyclopedia of the Mouse Genome described below. In addition, all subscribers will be able to broadcast to, and receive messages of interest from, all other linked-up members of the community. If you would like to subscribe to this Bulletin Board, send a message that reads "subscribe mgi-list <your name>" to listserver@informatics.jax.org. For further information or help, send an E-mail message to mgi-help@informatics.jax.org.
B.3 Computer Programs
B.3.1 Linkage analysis
Numerous computer programs are available for the determination of linkage relationships among loci typed in large numbers of individuals. Most of these were developed for the analysis of complex human pedigrees with algorithms that incorporate Maximum Likelihood Estimation statistics (Elston and Stewart, 1971) and provide LOD score (Morton, 1955) output. Although these pedigree-based programs can be used for the analysis of mouse linkage data, they are usually less than optimal for this task. First, it is often not possible to derive unequivocal haplotype information for all individuals studied in a human pedigree, and as such, pedigree-based programs are not oriented toward this type of analysis which is so common in mouse linkage studies (see figure 9.15). Second, for most studies, mouse geneticists will not need to avail themselves of the sophisticated Maximum likelihood/LOD score estimation tools required for human pedigree analysis. Two linkage programs developed specifically for mouse linkage studies Map Manager and GENE-LINK are described below. In addition, the most useful multi-locus pedigree-based program Mapmaker is also described. Other pedigree-based linkage analysis packages are listed and reviewed by Bryant (1991).
Map Manager is a Macintosh program that can be used for the analysis of linkage data obtained from a backcross, F1 X F1 intercross, or from a group of recombinant inbred strains (Manly, 1993). It was written by Dr. Kenneth F. Manly and is made available without charge from the author. Map Manager uses a standard Macintosh format and is both extremely versatile and extremely easy to use. It allows easy storage, display, and retrieval of information from mapping experiments. The strain distribution patterns (SDPs) obtained with newly typed loci can be evaluated rapidly to determine likely map positions relative to other loci in the database. The program is distributed with a large database of previously published RI strain distribution patterns which greatly facilitates the RI analysis of new loci. Map Manager has many other sophisticated features including a statistical evaluation package and various output options, as well as a means for importing and exporting data to and from spreadsheets or Mapmaker files (see below). It can be obtained from the author on disk or by anonymous ftp or gopher from several sites including {mcbio.med.buffalo.edu}, {hobbes.jax.org}, {ftp.bio.indiana.edu}, and {ftp.embl-heidelberg.de}. For further information, Dr. Manly can be contacted at the E-mail address [Kmanly@mcbio.med.buffalo.edu] or at Roswell Park Cancer Institute, Buffalo, New York 14263.
GENE-LINK is a DOS program that can be used for the analysis of linkage data from a backcross (Montagutelli, 1990). It was written by Dr. Xavier Montagutelli and has been made available to investigators without cost. It will provide best-fit map positions for entered strain distribution patterns. For further information, Dr. Montagutelli can be contacted at Institut Pasteur de Paris, 25 Rue du Docteur Roux, 75724 Paris, Cedex 15, France.
Mapmaker and Mapmaker/QTL are a pair of pedigree-based programs written by Dr. Eric Lander and his colleagues for constructing linkage maps from raw genotyping and phenotyping data recovered from large numbers of loci (Lander et al., 1987). These programs use a highly efficient algorithm for "likelihood of linkage" computations. They can be run on UNIX-based workstations or VAX minicomputers running under the VMS operating system. The programs and a manual are available from the author for licensing to academic researchers. Mapmaker is most useful to mouse geneticists for the analysis of linkage data obtained from an F1 x F1 intercross. Mapmaker/QTL can be used for the analysis of quantitative traits. For further information, contact Dr. Eric Lander, Whitehead Institute, 9 Cambridge Center, Cambridge, MA 02142.
B.3.2 Mouse colony management and genetic databases
MacMice and Mendel's Lab are Macintosh-based programs that can be used for keeping track of a breeding mouse colony with records for animals, litters, and samples derived from them. The programs are described more fully in chapter 3 (Silver, 1986; Silver, 1993b). They were written by the author of this book and can be licensed for use from Mendel's Software. Click on the following site: for further information and ordering details, or send a FAX to Mendel's Software at 609-924-4382.
Appendix C
Source Materials for Further Reading
C.1 Selected monographs and books
C.1.1 General
C.1.2 Genetic information
C.1.3 Experimental embryology
C.1.4 Others topics
C.2 Selected Journals and Serials of Particular Interest
C.2.1 Original articles
C.2.2 Reviews
C.1 Selected monographs and books
C.1.1 General
Green, M. C. & Witham, B. A. (1991). Handbook on Genetically Standardized JAX Mice, Fourth edition, The Jackson Laboratory, Bar Harbor. [Provided free upon request.]
Foster, H. L., Small, J. D. & Fox, J. G., eds. (1982). The Mouse in Biomedical Research, Diseases. Academic Press, New York. [A series of four volumes with comprehensive coverage of all aspects of mouse biology and breeding]
Altman, P. L. & Katz, D. (1979). Inbred and Genetically Defined Strains of Laboratory Animals: Part I, Mouse and Rat., Biological Handbooks , 3rd edition, Fed. Amer. Soc. Exp. Biol., Bethesda. [Tables of information for different strains of mice.]
Klein, J. (1975). Biology of the Mouse Histocompatibility-2 Complex, Springer-Verlag, New York. [The title is misleadingly narrow; a general discussion of mouse genetics.]
Crispens, C. G. (1975). Handbook on the Laboratory Mouse, C.C. Thomas, Springfield, Ill. [Information on strains not commonly used today.]
Green, E. L., ed. (1966). Biology of the Laboratory Mouse, 2nd edition, McGraw-Hill, New York. [Reprinted by Dover (New York) in 1968 and 1975; Comprehensive for its time.]
C.1.2 Genetic information
Mammalian Genome: Special Issue published annually by Springer-Verlag, New York, with reports from the mouse chromosome mapping committees.
Lyon, M. F. & Searle, A. G., eds. (1989). Genetic Variants and Strains of the Laboratory Mouse., 2nd edition, Oxford University Press, Oxford. [The "Bible" for mouse geneticists: description and references for all known mutant loci along with other genetic information. Look for newer edition.]
Silvers, W. K. (1979). The Coat Colors of the Mouse, Springer-Verlag, New York. [Excellent coverage of this particular subject. Sadly, now out-of-print.]
C.1.3 Experimental embryology
Hogan, B., Beddington, R., Costantini, F. & Lacy, E. (1994). Manipulating the Mouse Embryo: A laboratory Manual, Second Edition, Cold Spring Harbor Laboratory Press, Cold Spring Harbor. [The bible for embryological manipulations.]
Wassarman, P. M. & DePamphilis, M. L., eds. (1993). Guide to Techniques in Mouse Development, Methods in Enzymology , 225, Academic Press, San Diego. [Comprehensive coverage of techniques used for developmental analysis.]
Kaufman, M. H. (1992). An Atlas of Mouse Development, Academic Press, San Diego. [Photomicrographs of embyo sections.]
Rugh, R. (1968). The Mouse: Its Reproduction and Development, Oxford University Press, New York. [Source of information.]
C.1.4 Others topics
Berry, R. J. & Corti, M., eds. (1990). Biological Journal of the Linnean Society, volume 41, Academic Press, London. [Proceedings from a conference on the evolution, population biology, and systematics of the mouse.]
Potter, M., Nadeau, J. H. & Cancro, M. P., eds. (1986). The Wild Mouse in Immunology, Curr. Topics Micro. Immunol. , volume 127, Springer-Verlag, New York. [Proceedings from a conference on the evolution and systematics of the mouse.]
Klein, J. (1986). Natural History of the Major Histocompatibility Complex, John Wiley & Sons, New York. [Comprehensive discussion of various topics in mouse genetics, evolution, and population biology.]
Green, E. L. (1981). Genetics and Probability in Animal Breeding Experiments, Oxford University Press, New York. [General presentation of the statistical principles of genetic analysis.]
Morse, H. C., ed. (1978). Origins of Inbred Mice, , Academic Press, New York. [Interesting proceedings on historical aspects.]
Simmons, M. L. & Brick, J. O. (1970). The Laboratory Mouse: Selection and Management, Prentice-Hall, Englewood Cliffs, NJ.
Cook, M. J. (1965). The Anatomy of the Laboratory Mouse, Academic Press, New York. [An atlas of anatomical drawings].
C.2 Selected Journals and Serials of Particular Interest
C.2.1 Original articles
Cell
Cytogenetics and Cell Genetics
Genes and Development
Genetical Research
Genetics
Genomics
Immunogenetics
Journal of Heredity
Mammalian Genome
Mouse Genome (formerly Mouse Newsletter)
Nature
Nature Genetics
Proceedings of the National Academy of Science USA
Science
C.2.2 Reviews
Annual Review of Genetics
Current Opinion in Genetics and Development
Trends in Genetics
Appendix D
Statistics
D.1 Confidence limits and median estimates of linkage distance
D.1.1 The special case of complete concordance
D.1.2 The general case of one or more recombinants
D.1.3 A C program for the calculation of linkage distance estimates and confidence intervals
D.2 Quantitative differences in expression between two strains
D.1 Confidence Limits and Median Estimates of Linkage Distance
D.1.1 The special case of complete concordance
To illustrate the statistical approach used to estimate confidence limits on experimentally-determined values for linkage distances, it is useful to first consider the special case where two linked loci show complete concordance or no recombination (symbolized asR = 0) in their allelic segregations among a set of N samples derived either from recombinant inbred strains or from the offspring of a backcross. Let us define the true recombination fraction Q as the experimental fraction of samples expected to be discordant (or recombinant) when N approaches infinity. Then the probability of recombination in any one sample is simply Q, and the probability of non-recombination, or concordance, is simply (1 - Q). As long as multiple events are completely independent of each other, one can calculate the probability that all of them will occur by multiplying together the individual probabilities associated with each event. Thus, if the probability of concordance in one sample is (1 Q), then the probability of concordance in N samples is: .
In most experimental situations, the known and unknown variables are reversed in that one begins by determining the number of discordant (or recombinant) samples i that occur within a total set of N as a means to estimate the unknown true recombination fraction Q. When no discordant samples are observed, the probability term just derived can be used with the substitution of the random variable q in place of Q, to provide a continuous probability density function indicative of the relative likelihoods for different values of Q between 0.0 (complete linkage) and 0.5 (no linkage).
? ?(D.1)
This equation reads "the probability that the true recombination fraction Q is equal to a particular value q is the function of q given as the last term in the equation". For both RI data and backcross data, Q is related directly to linkage distance in centimorgans d. In the case of backcross data, and for values of Q less than 0.20 (see section 7.2.2.3), recombination fractions are converted into centimorgan estimates through simple multiplication:
?d = 100Q. ?(D.2)
In the case of RI data, this conversion is combined with the Haldane-Waddington equation (9.8) to yield:
? ?(D.3)
An example of the probability density function associated with the experimental observation of complete concordance among 50 backcross samples is shown in figure D.1. Each value of N will define a different function, but in all cases, the curve will look the same with only the steepness of the fall-off increasing as N increases. In all cases, the "maximum likelihood estimate" for the true recombination fraction defined as the value of Q associated with the highest probability will be zero. But, since this maximum likelihood value is located at one end of the probability curve, it does not provide a useful estimate for the likely linkage distance. A better estimate would be the value of Q which defines the midpoint below which and above which the true recombination fraction value is likely to lie with equal probability; this is the definition of the median recombination fraction estimate . In mathematical terms, the value of is defined at the line which equally divides the area of the complete probability density given by equation D.1 (see figure D.1).
Confidence limits are also defined by circumscribed portions of the entire probability density; the portion that lies outside a confidence interval is called a. For example, in the case of a 95% confidence inerval, a = (1 - 0.95) = 0.05. It is standard practice to assign equal portions of a to the two "tails" of the probability density located before and after the central confidence interval. Thus, the lower confidence limit is defined as the value of q bordering the initial a/2 fraction of the area under the entire probability curve. The upper confidence limit is defined as the value of q that borders the ultimate a/2 fraction of the area under the entire probability curve; this is equivalent to saying that a (1 a/2) fraction of area lies ahead of the upper confidence limit.
In mathematical terms, the area beneath the entire probability density curve is equal to the definite integral of equation D.1 over the range of legitimate values for q between 0.0 and 0.5. To determine the fraction of the probability density that lies in the region between Q = 0 and any arbitrary Q = x, it is necessary to integrate over the probability density function (equation D.1) between these two values, and divide the result by the total area covered by the probability density. This provides the probability that the true recombination fraction is less than or equal to x.
? ?(D.4)?
By standard methods of calculus, equation D.4 can be reduced analytically to the form:
? ?(D.5)
And this equation can be reformulated to yield x as a function of .
? ?(D.6)?
By solving equation D.6 for different values of , one can obtain critical values of x that define the median estimate of the recombination fraction from , lower confidence limits from , and upper confidence limits from . Once a solution for x has been obtained, it can be converted into a linkage distance value with either equation D.2 for backcross data or equation D.3 for RI strain data. Solutions to equation D.6 over a range of N RI strains and backcross animals are shown in figures 9.8, 9.16, and 9.17.
D.1.2 The general case of one or more recombinants
The statistical approach described above can be generalized to any case of i discordant (or recombinant) samples observed among a total of N RI strains or backcross animals that have been typed for two loci. As in the special case above, one can arrive at a probability for the occurrence of multiple events by multiplying together the individual probabilities for each event. In the general case, there will be i events of discordance, each with an individual probability equal to the true recombination fraction Q, and (N i) events of concordance, each with an individual probability of (1 Q). These terms are multiplied together along with a "binomial coefficient" that counts the the permutations in which the two types of events can appear to produce the "binomial formula":
? ?(D.7)
When the true recombination fraction is known, the binomial formula can be used to provide the probability that i events of discordance will be observed in any set of N samples. But once again, the situation encountered by geneticists is usually the reverse one in which i and N are discrete values determined by the experiment and the true recombination fraction Q is unknown. In this case, one can substitute the random variable q in place of Q in equation D.7 to generate a probability density function that provides relative likelihoods for different values of Q between 0.0 (complete linkage) and 0.5 (no linkage). In this use of the binomial formula, the factorial fraction (known as the binomial coefficient) remains constant for all values of q and can be eliminated since the purpose of the function is to provide relative probabilities only:
? ?(D.8)
An example of the probability density function associated with the experimental observation of one discordant RI strain among a total of 26 samples is shown in figure D.2. As one can easily see, the distribution is highly skewed toward higher recombination fractions. Each discrete pair of values i and N will define a different function. When both i and N are large, the density function will approximate a normal distribution. However, with the results typically obtained in contemporary mouse linkage studies, the density function is likely to be significantly skewed as shown in figure D.2 and as such, it is usually not possible to take advantage of the simplified statistical tools developed specially for use with the normal distribution.
A median estimate of linkage distance as well as lower and upper confidence limits can be obtained in the same manner described in the special case of no recombination described above. This can be accomplished by substituting equation D.8 in place of the two occurrences of equation D.1 within equation D.4:
? ?(D.9)
The general form of the integral in this equation cannot be solved analytically but a short computer program can be used to estimate solutions and provide critical values of x for defined probability values. The computer program has been written to generate minimum and maximum values in terms of centimorgan distances for discrete experimentally-determined values of i and N from either backcross or RI data. The program was used to generate the values shown in Tables D.1, D.2, D.3, D.4, D.5, and D.6 for 68% and 95% confidence intervals, but it is possible to generate confidence limits for any other integer percentile confidence interval. The program will also calculate maximum likelihood and median estimates of linkage distance. It is listed below as a self-contained unit that should be ready for compiling with any standard C compiler on any computer.
D.1.3 A C program for the calculation of linkage distance estimates and confidence intervals
/*** A C program for the calculation of linkage distance estimates and confidence intervals ***/
#include <stdio.h>
double ?Pin(double r,int i,int N); double pow(double x, double y); double convert(double r);
static?int crosstype;
main()
{?FILE ?*fopen(), *file;
?int ?i=1, istart=1, ifin=50, iinc=1, N=100, P;
?char?input;
?double?Pin(), dmin, dmax, r,rtop, dmean, smean, Nrmlize=0.0, Sum=0.0, convert(), min, max;
?while(1){
??printf("Enter the type of cross:1 for backcross,2 for RI analysis,or 3 to quit:");
??scanf("%d",&crosstype);
??if(crosstype != 2 && crosstype != 1) exit(0);
??printf("Enter the confidence level as an integer number(e.g. 95 for 95%%):");
??scanf("%d", &P);
??min = (1-((double)P/100.0))/2; max = 1- min;
??printf("Enter with comma delimiters->i-start,i-end,i-increment,and N,then return\n:>");
??scanf ("%d,%d,%d,%d", &istart,&ifin,&iinc,&N);
??printf(" i , dist / medn , min. / max. (values in cM assuming complete interference)\n");
??for ( i = istart; i <= ifin ; i += iinc){
???for ( r = .0001, Nrmlize = 0 ; r <.5 ; r += .0001)
????Nrmlize += Pin(r,i,N);
???for ( r = .0001, Sum =0; Sum < min && r< .5; r += .0001)
????Sum += Pin(r,i,N)/Nrmlize;
???dmin = convert(r);
???for (; Sum < .5 && r< .5; r += .0001)
????Sum += Pin(r,i,N)/Nrmlize;
???dmean = convert(r);
???for (; Sum < max && r< .5 ; r += .0001)
????Sum += Pin(r,i,N)/Nrmlize;
???dmax = convert(r);
???smean = convert((double)i/N);
???printf("%3d, %4.1f / %4.1f , %4.1f / %4.1f\n",i,smean,dmean,dmin,dmax);}
?}}
double convert(double r)
{?double rmean;?int x=0;
?if(crosstype == 1)?return(100*r);
?if(crosstype == 2)?return( r*100/(4 - 6*r) );}
double Pin(double r ,int i ,int N)
{?double?pow();
?return ((pow(r,i))*(pow(1-r,N-i)));}
/************************ END OF PROGRAM ***********************/
D.2 Quantitative differences in expression between two strains
How does one determine whether two populations of animals defined by different inbred strains are showing a significant difference in the expression of a trait? The answer is with a test statistic known as the "t-test" or "Students t-test". To apply this test, one needs to use a pair of only three values derived from an analysis of the expression of the trait in sets of animals from each inbred strain. First is the number of animals examined in each inbred set (N1 and N2). Second is the mean level of expression for each set (m1 and m2) calculated as:
? ?(D.10)
where xi refers to the expression value obtained for the ith sample in the set. Third is the variance of each set of animals ( and ) calculated as:
? ?(D.11)
With values for the variance of each sample set and the size of each set, one can calculate a combined parameter refered to as the "pooled variance":
? ?(D.12)
Finally, one can use the value obtained for the pooled variance together with the samples sizes and sample means to obtain a "t value":
? ?(D.13)
One final combined parameter is required to convert the t value into a level of significance the number of degrees of freedom df.
? ?(D.14)
With values for t and df, one can obtain a P value from a table of critical values for the t distribution found in Table D.7.
Appendix E
Glossary of Terms
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