  .___________________________________________________________.
  |            ------------------------------------           |
  |             D I P L O G E N   -  User's Manual            |
  |            ------------------------------------           |
  |    Qualitative inheritance analysis of zymograms and      |
  |      DNA electropherograms in diploid individuals         |
  |                                                           |
  |  Developed for free distribution by: Elizabeth M. Gillet  |
  |      Inst. Forstgenetik, Universitaet Goettingen          |
  |      Buesgenweg 2, D-37077 Goettingen; egillet@gwdg.de    |
  |                                                           |
  |                     September 1998                        |
  |___________________________________________________________|

Given the banding patterns of the zymograms or DNA 
electropherograms of a genetically closed sample of diploid 
individuals, <DIPLOGEN> systematically generates all hypotheses 
for the mode of inheritance of these patterns that conform to 
certain qualitative rules for the genetic interpretation of 
single bands. Both dominance and codominance as modes of gene 
action can be detected. These rules follow from formulation of 
the concept of << TRANSMISSION HOMOLOGY >> within single 
individuals and sets of individuals (Gillet 1996).

This manual is published and <DIPLOGEN> is available on the 
internet under URL:
       http://www.uni-forst.gwdg.de/forst/fg/index.htm

__________________________________________________________________


CONTENTS:

 1. Inheritance analysis                  2

 2. Sampling strategies                   3

 3. Elementary zones                      7

 4. Zymograms                             8

 5. DNA electropherograms                10
  
 6. Generating hypotheses                11

 7. Input file for <DIPLOGEN>            13

 8. Running <DIPLOGEN>                   14

 9. References                           17

10. Technical considerations             17

                                                            Page 2
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1. INHERITANCE ANALYSIS
__________________________________________________________________

The purpose of inheritance analysis of a genetic trait is to 
determine the << MODE OF INHERITANCE >> of the trait expressions.
The two components of a mode of inheritance are the

(1) << MODE OF TRANSMISSION >> : number of loci, identification
     of the alleles at each locus;

(2) << MODE OF GENE ACTION >> : intra- and interlocus 
    interactions between alleles (dominance, codominance, 
    epistasis).

Where obtainable, progenies of controlled crosses or self-
fertilization are used to infer mode of inheritance. In forest 
tree species, for example, this is often infeasible, so that other
methods must be sought. <DIPLOGEN> systematically generates all
possible hypotheses for mode of inheritance of isoenzyme or
DNA-banding patterns that can explain the given set of banding
patterns, under the assumption of their "genetic closure" (see
below).

-- homomeric: the product of two genes of the same type at one 
   locus;
-- intralocus heteromeric: consists of subunits encoded by two 
   genes of different types at one locus (polymeric enzyme 
   systems only);
-- interlocus heteromeric: consists of subunits encoded by the 
   genes (of different types) at more than one locus (polymeric 
   enzyme systems only);
-- post-translational modification (PTM): 

Specification of the mode of inheritance involves identification
of the origin of each band as a molecule consisting of how many 
subunits coded by which alleles at which loci. In some cases, even
the absence of a band must be interpreted as the presence of a 
"null allele" (that produces a defective subunit) at some locus.

For DNA banding patterns, the number of bands per pattern can be
very much larger than for isoenzymes. Other than the fact that 
genetic closure may require larger samples, their inheritance
analysis is, however, no different than for a monomeric enzyme
system allowing for "null alleles" but without PTM. 

                                                            Page 3
__________________________________________________________________

2. SAMPLING STRATEGIES
__________________________________________________________________

GENETIC CLOSURE

<DIPLOGEN> ideally requires as input the banding patterns of a
genetically closed sample of individual banding patterns, which is
explained as follows. Assuming complete genetic control of the 
banding patterns, each pattern is the expression of an 
individual's diploid genotype at the controlling loci. A sample of
banding patterns is defined to be  << GENETICALLY CLOSED >>, if 
it contains all possible patterns that can result as combinations
of the genes in the sample. Thus all constructible homo- and 
heterozygote genotypes must be present at each locus as well as 
all possible interlocus combinations of these single-locus 
genotypes. The genetic closure of a sample can only be judged 
retrospectively, i.e., after inheritance analysis has been 
successful in identifying loci and alleles. Nevertheless, sampling
strategies can be devised to increase the chances of obtaining a 
genetically closed sample. 

SUFFICIENT SAMPLE SIZE

Given a desired probability for genetic closure of a sample, the
sufficient sample size is a function of the number of genotypes
and the frequency of the rarest genotype among the total 
collection of individuals from which a random sample is drawn. If
these can be estimated, the sufficient (or minimum) sample size
required to ensure with the given probability that all genotypes 
are detected can be calculated after Gregorius (1980). The 
frequency of the rarest genotype depends on the manner of 
association of alleles in the genotypes at each locus as well as 
on the association of the genotypes between loci, information 
which is of course not available at the outset of the study. The 
sufficient sample size increases for decreasing minimum genotype 
frequency.

                                                            Page 4
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SAMPLING PROGENY FROM SELF-FERTILIZATION OF A SINGLE INDIVIDUAL

Genetic closure is easiest to achieve by sampling progeny from
self-fertilization of a single individual, where possible. The 
number of genotypes and the expected frequency of the rarest 
genotype depend on several unknown quantities: the number of loci 
at which the individual is heterozygous, the mode of gene action 
(codominance vs. dominance/recessiveness) between the two alleles 
at a heterozygous locus, the segregation proportions at each of 
these loci, and the recombination frequencies between these loci. 

If the individual is heterozygous at m of the loci that produce
the banding pattern, then the frequency of the rarest genotype is
maximal, if segregation at each heterozgous locus is regular 
(1:1), the alleles of the different loci are randomly associated 
among the individual's gametes, and gametic fusion is also at 
random (implying random association of genotypes between loci 
among the progeny). In this case, the rarest genotype at each 
locus has the expected frequency 0.25, regardless of whether the 
mode of gene action is codominance or dominance. The rarest 
multilocus genotypes are then those that are homozygous at all
loci, each of which has the expected frequency (0.25)^m. However,
the minimum sample size is largest for codominance at all loci, 
since the number of constructible genotypes is greatest. In 
practice, the expected frequency must be estimated by assuming 
limits on segregation distortion and recombination fractions based
on information gained from other systems. In general, the wider 
these limits are allowed to be, the larger will be the sufficient 
sample size.

If the above ideal conditions can be assumed for the alleles at 
all loci controlling the banding patterns in the parents, and
the mode of gene action is codominance at all loci, then Table 1 
gives sufficient sample sizes to ensure a given probability of 
genetic closure of a sample of the individual's progeny from 
self-fertilization.

                                                            Page 5
__________________________________________________________________

TABLE 1: For sampling of progeny produced by a single individual
         by self-fertilization, minimum sample size is given that
         ensures a given probability of genetic closure of the 
         sample under the following assumptions:
         (1) the parent is heterozygous at m of the loci that
             control the banding pattern; 
         (2) segregation of the alleles at each of the m loci is 
             regular (1:1);
         (3) the genotypes at the different loci show random
             association among the progeny;
         (4) each locus shows codominance of gene action.
.__________________________________________________________.
| Parent |No.of  |Frequency   | Minimum sample size such   |
| hetero-|geno-  |of rarest   | that probability of genetic|
| zygous |types  |genotype in | closure is greater than    |
| at m   |in     |progeny     |                            |
| loci   |progeny| =(0.25)^m  |    80%      90%      95%   |
|________|_______|____________|____________________________|
|   1    |    3  |  0.500000  |      9      13       19    |
|   2    |    9  |  0.062500  |     57      79      104    |
|   3    |   27  |  0.015625  |    304     396      500    |
|   4    |   81  |  0.003906  |   1504    1879     2297    |
|________|_______|____________|____________________________|
__________________________________________________________________

SAMPLING INDIVIDUALS IN POPULATIONS

Collections of individuals from large natural populations may be 
genetically closed. The frequency of the rarest genotype depends 
on the frequency distribution of multilocus genotypes among the 
parents of this population, the gametic phases in linkage groups 
in each parent, the individual gamete production (fecundity), 
gametic selection, and of course viability selection.

If the sampled population can be assumed to be genetically closed,
and if it is possible to estimate the frequency of the rarest
genotype in the population, then Table 2 gives sufficient sample
sizes to ensure a given probability of genetic closure. The number
of genotypes is taken to be the maximal number 1/(frequency of
rarest genotype). 

SEQUENTIAL SAMPLING OF INDIVIDUALS

Since sufficient sample sizes are rarely exactly calculable, a
sequential sampling scheme among individuals with the potential
for genetic closure may be most appropriate: sampling continues
until <DIPLOGEN> succeeds in finding a hypothesis. 

                                                            Page 6
__________________________________________________________________

TABLE 2: For sampling individuals in a large population, minimum
         sample size to ensure a given probability of detecting 
         all genotypes that are present at relative frequencies
         not less than a given minimum frequency is given. The
         number of genotypes actually present in the population
         is assumed to equal 1/(minimum genotype frequency). 
         Word of warning: A sample of sufficient size to detect 
         all genotypes can, however, only be genetically closed
         if the sampled population itself is genetically closed. 
  .__________________________________________________.
  | To detect      | Minimum sample size such that   |
  | all genotypes  | probability of detection of all |
  | that have      | such genotypes is greater than  |
  | frequency      |                                 |
  | not less than  |     95%       99%      99.9%    |
  |________________|_________________________________|
  |     0.500      |      6         8         11     |
  |     0.400      |      7        10         14     |
  |     0.300      |     11        15         22     |
  |     0.200      |     21        28         39     |
  |     0.100      |     51        66         88     |
  |     0.090      |     57        74         99     |
  |     0.080      |     65        84        112     |
  |     0.070      |     77        99        131     |
  |     0.060      |     92       119        156     |
  |     0.050      |    117       149        194     |
  |     0.040      |    152       192        249     |
  |     0.030      |    212       265        341     |
  |     0.020      |    341       422        536     |
  |     0.010      |    754       916       1146     |
  |     0.009      |    850      1030       1285     |
  |     0.008      |    972      1174       1462     |
  |________________|_________________________________|
   After Gregorius (1980).
__________________________________________________________________

                                                            Page 7
__________________________________________________________________

3. ELEMENTARY ZONES
__________________________________________________________________

Given a sample of banding patterns, the path of migration of bands
is divided into  << ELEMENTARY ZONES >>, abbreviated  << EZONE >>
in <DIPLOGEN>, such that 
(1) each elementary zone contains a band of at least one banding
    pattern;
(2) any two bands of different patterns that appear in this 
    elementary zone are considered to represent the "same" band 
    (in general, identical isoenzymes or DNA fragments).
Qualitative inheritance analysis of the banding patterns consists
in interpretation of the patterns of band appearance in the
elementary zones. 

For this purpose, elementary zones are classified into the
following types:

An elementary zone is  << FIXED >>, if a band appears in this zone
   in all of the patterns. The lack of variation in a fixed zone
   prohibits its interpretation.

A non-fixed elementary zone is  << DEPENDENT >>  on a second
   non-fixed elementary zone, if whenever a band appears in the
   one zone of any pattern, a band is also present in the second
   zone. A zone can be dependent on more than one zone (besides
   itself).

A non-fixed elementary zone i is  << INDEPENDENT >>, if it is
   not dependent on any other elementary zone, i.e., if for each
   other non-fixed elementary zone j, there exists a banding
   pattern that exhibits a band in i but no band in j. 

Two non-fixed elementary zones are  << EQUIVALENT >>, if each
   zone is dependent on the other, i.e., if in every banding
   pattern bands appear either in both zones or in neither zone.
   The relation "equivalence", denoted "~", partitions the set of
   elementary zones into  << EQUIVALENCE CLASSES >>  of elementary
   zones, since it is reflexive (Z~Z), symmetric (Z~Y==>Y~Z), 
   and transitive (Z~Y and Y~X ==> Z~X).

                                                            Page 8
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4. ZYMOGRAMS
__________________________________________________________________

Isoenzymes are defined as "electrophoretically separable variants
of one enzyme ... system" (Bergmann et al. 1989). For isoenzyme
banding patterns (zymograms), the development of a computer 
program for the formulation of hypotheses on the mode of 
inheritance is a complex task, due to the different ways in which
isoenzymes expressed in haploid tissue correspond to genes at
loci. Whereas each enzyme molecule of a monomeric enzyme system is
the product of the gene at a single locus, polymeric enzymes are
formed from two or more enzyme subunits, each of which is the
product of the gene at a locus. Four types of enzyme molecule
occur in diploid tissue. 

TYPES OF ISOENZYMES

<< HOMOMERIC >>  isoenzymes consist of subunits that are encoded 
   by genes of the same type at the same locus. Monomeric
   isoenzymes, which consist of only a single subunit, are treated
   as homomerics.

<< INTRALOCUS HETEROMERIC >>  isoenzymes consist of subunits
   encoded by two genes of different types (alleles) at the same 
   locus. 

<< INTERLOCUS HETEROMERIC >>  isoenzymes consist of subunits
   encoded by genes at two (or more) different loci. 

<< POST-TRANSLATIONAL MODIFICATION (PTM) >> is an enzyme molecule,
   the electrostatic charge or molecular conformation of which was
   modified, probably by the product of a gene considered to 
   belong to the "genetic background" (i.e. not coding for 
   subunits of the enzyme system being studied). PTM affects the
   migration velocity through the gel. If not all molecules of a
   particular subunit structure in an individual are modified, PTM
   results in the appearance of one or more additional bands in
   the zymogram. Two types of PTM of molecules of a given subunit 
   structure can be distinguished within a collection of
   individuals in its environment: A PTM of a particular molecule
   will be termed  << FIXED >>, if the PTM occurs in all members
   possessing the molecule, and otherwise << FACULTATIVE >>.

                                                            Page 9
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INTERPRETATION OF BANDING PATTERNS

The strategy formulated by Gillet (1996) is to identify all
elementary zones that contain homomeric isoenzymes and then to
partition these zones into disjoint sets such that each set
represents a complete set of transmission homologous gene types,
i.e., the set of all alleles of a locus. Thus, the alleles present
at each locus in the sample of banding patterns are represented 
by a set of elementary zones, and the alleles present in any 
given banding pattern are revealed by the appearance of a band in
either only one (individual is homozygous) or two (individual is 
heterozygous) or even in none (individual is homozygous for "null 
allele") of these zones.

>> Non-fixed elementary zones of homomerics are independent: 
   If the sample of banding patterns is genetically closed, then 
   all non-fixed elementary zones representing homomerics are 
   independent. In the other direction, all elementary zones 
   representing homomerics are independent, with only one rare
   exception: The facultative PTM of a homomeric at a fixed locus
   will also be independent.

>> Zones of intra- and interlocus heteromerics are dependent: 
   The appearance of a band representing an interlocus heteromeric
   depends on the appearance of the two bands representing the 
   corresponding homomerics. An exception is the case in which one
   of the genes is a null allele that produces the heteromeric but
   not the homomeric.

>> Zones of PTM are dependent: 
   Appearance of a band in an elementary zone representing a PTM
   is dependent on the appearance of the unmodified isoenzyme (as
   long as not all molecules are modified and the zone of the
   unmodified isoenzyme is not fixed). This dependence
   distinguishes the elementary zones of heteromerics and PTM's
   from those of homomerics. 

                                                           Page 10
__________________________________________________________________

5. DNA ELECTROPHEROGRAMS
__________________________________________________________________

TYPES OF DNA FRAGMENT

In DNA electrophoresis, each elementary zone represents a DNA
fragment "encoded" by a single gene, since fragments analogous to
heteromeric isoenzymes and post-translational modification are 
thought not to occur. 

INTERPRETATION OF BANDING PATTERNS

>> Non-fixed elementary zones are independent and represent a
   single gene at some locus: 
   If the sample of banding patterns is genetically closed, then 
   all non-fixed elementary zones are independent and represent
   a single gene at some locus. 

Conversely, if an elementary zone in a given sample is found not 
to be independent, the sample cannot be genetically closed, and no
hypothesis can be formulated. 

If all elementary zones show independence for the given sample,
the qualitative interpretation of the banding patterns is the same
as for monomeric isoenzymes without post-translational 
modification. The "null alleles" that often occur in DNA analysis,
especially in RAPD, are also analogous to the "null alleles" of 
isoenzyme analysis. 

Thus the genetic interpretation of DNA electropherograms is
conceptionally much simpler than that of isoenzyme banding
patterns. The number of elementary zones can, however, be much
larger (e.g. DNA fingerprints), requiring a much larger sample
to ensure genetic closure.

                                                           Page 11
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6. GENERATING HYPOTHESES
__________________________________________________________________

<DIPLOGEN> systematically generates all possible modes of 
inheritance under the assumption that the independent elementary
zones exactly correspond to the genes. First, all possible modes 
of transmission are generated as all possible partitions of the 
set of independent elementary zones, such that at least two zones
are assigned to each subset. Since independent zones are 
non-fixed, the requirement of at least two zones per subset 
corresponds to the presence of at least two alleles at each 
non-fixed locus.

For each such partition, and thus each possible mode of 
transmission, all hypotheses on the mode of gene action are 
generated by running through all possible combinations of 
codominance resp. dominance in the presence of a (recessive) 
"null allele" at the different loci. 

Each hypothesis on the mode of inheritance is subsequently tested
by constructing the set of all banding patterns, considering only 
the independent elementary zones, that would be found in a 
genetically closed set of individuals and comparing them to the 
observed set of banding patterns, likewise considering only the 
independent zones. If the two sets of patterns exactly match (or,
in the case of Ezone splitting, if at least 3/4 of the expected
banding patterns were observed), <DIPLOGEN> prints out the mode of
inheritance as a hypothesis.

SPLITTING ELEMENTARY ZONES

It frequently happens that single isoenzymes or DNA fragments 
that are produced by genes at different loci nonetheless migrate 
to the same position in the gel. Since their respective bands are 
usually indistinguishable (except for the rare case that 
differences in band intensity are interpretable), they will be 
assigned to the same elementary zone. Since this elementary zone 
has two different genetic interpretations, <DIPLOGEN> is unable to
formulate a hypothesis for mode of inheritance. 

To alleviate this problem, <DIPLOGEN> provides the option of
splitting one elementary zone at a time into two zones,
alternately assigning the band appearing in the original zone in
a banding pattern to either one or to both of the new zones. All
combinations of assignment to the first new zone, the second new
zone, and to both new zones are produced among all of the banding
patterns that exhibit a band in the original zone. 

                                                           Page 12
__________________________________________________________________

If a banding pattern exhibits a band in the elementary zone to be
split, there are three ways of assigning this band to the two new
zones: 
 - band appears in new zone 1 but not 2   (splitting code 1)
 - band appears in new zone 2 but not 1   (splitting code 2)
 - band appears in both new zones 1 and 2 (splitting code 0).
If N banding patterns exhibit a band in the elementary zone to be
split, there are 3^N ways to assign the band to one or both of the
new zones among the N patterns. Subtracting the three trivial
cases where for each banding pattern the band is always assigned
to the same new zone or to both zones, there remain 3^N-3 ways to
split the bands appearing in the original elementary zone over the
two new zones. Considering that each of these 3^N-3 cases has a
symmetric counterpart that gives the same banding pattern (i.e.,
when all splitting codes 1 are replaced by 2 and all 2's by 1's),
a total of (3^N-3)/2 different ways to distribute the N bands over
two new elementary zones exist.

EXAMPLE 1: For the sample of isoenzyme banding patterns to the 
           left, no hypothesis can be formulated for which the 
           sample is genetically closed. By splitting elementary 
           zone 3 into the two zones 3x and 6x, as done in the 
           right diagram, a hypothesis can be formulated for 
           which the sample is genetically closed: Elementary 
           zones 1 and 6x are alleles of locus 1 with intralocus 
           heteromeric 2, and zones 3x and 5 are alleles of 
           locus 2 with intralocus heteromeric 4. 

      1 2 3 4 5 6 7 8 9                 1 2 3 4 5 6 7 8 9
    .___________________.             .___________________. 
E 1 | - - -       - - - |         E 1 | - - -       - - - |
z 2 |             - - - |  ===>   z 2 |             - - - |
o 3 | -   - - - - - - - |         o 3x| -   - -   - -   - |
n 4 |     -     -     - |         n 6x|       - - - - - - |
e 5 |   - -   - -   - - |         e 4 |     -     -     - |
    |___________________|           5 |   - -   - -   - - |
                                      |___________________|

                                                           Page 13
__________________________________________________________________

7. INPUT FILE FOR <DIPLOGEN>
__________________________________________________________________

The input to the program is a matrix of zeros and ones that 
represents the different banding patterns observed in a 
(hopefully) genetically closed sample of diploid individuals.
After the elementary zones of the patterns have been defined, 
each banding pattern can be described by a list of ones and zeros 
indicating presence or absence, respectively, of a band in the 
successive elementary zones.

To input m banding patterns, the user applies any text editor to
prepare a data file (unformatted, ASCII characters only)
consisting of m+3 lines (optionally m+2) as described in the
following:

FORMAT OF INPUT FILE

Line 1:    n       = integer specifying number of different
                     elementary zones

Line 2:    (nI1)   = usual FORTRAN format specification for
                     reading banding patterns as a list of
                     integers, each of width 1.
                     Other FORTRAN formats for reading list of
                     integers can be specified, e.g. to include
                     blanks of width w by wX (X-format) or define
                     each of k integers to be of width w by kIw.

Lines 3 to m+2, one line for each banding pattern conforming to
                     the format defined in Line 2: 
           A list of length n of 0's and 1's representing the 
           banding pattern, where the entry in the j-th position
           of the list specifies the presence or absence of a band
           in the j-th elementary zone: 
           -> "1" signifies presence
           -> "0" signifies absence

Line m+3:  A "9" in the first position (according to format
           specification in Line 2) ends reading of the input
           file.
           Alternatively, the file can be terminated at the end
           of the last line that defines a banding pattern. No
           carriage return may follow; otherwise, <DIPLOGEN> will
           read the following and any further empty lines as the
           banding pattern "000...0".

Banding patterns that are encountered more than once can be
included in the input file as often as they appear, since
<DIPLOGEN> recognizes redundant patterns and prints the number of
times each pattern is encountered.

                                                           Page 14
__________________________________________________________________

EXAMPLE 2

 Schematic representation       Corresponding
   of banding patterns          input data file,
                                two possible variants

      1 2 3 4 5 6 7 8 9         6             6
    .___________________.       (6I1)         (3I1,1X,3I1)
E 1 | - - -       - - - |       100100        100 100
z 2 |             - - - |       100001   OR   100 001
o 3 |       - - - - - - |       100111        100 111
n 4 | -   - -   - -   - |       001100        001 100
e 5 |     -     -     - |       001001        001 001
  6 |   - -   - -   - - |       001111        001 111
    |___________________|       111100        111 100
                                111001        111 001
                                111111        111 111
                                9             9
__________________________________________________________________

8. RUNNING <DIPLOGEN>
__________________________________________________________________

When started, <DIPLOGEN> asks for the name of an input file that
was prepared previously using a standard text editor (see Section
7 above). It then poses the following questions:

CHOOSE INPUT FILE

>> Name of input data file [default extension = .dat]: >>

   Include path if data file is not located in the same directory
   as the program. If the file's extension is ".dat", it can be
   omitted and is supplied by the program. For example, the file
   "d:\path\infile.dat" can be given as "d:\path\infile", but
   "e:\zymo.tst" must be fully given. 

>> ** File does not exist: XXX 

   If named file, here XXX, is not found, you are prompted to
   retry. Check path designation. 

                                                           Page 15
__________________________________________________________________

CHOOSE OUTPUT DEVICE

>> Output device? Screen only="s" or File+Screen="f" 
   [default="s"] : >>

   - An answer of "s" causes all output to appear on the screen
     only - no output is saved for later reference. 
   - An answer of "f" causes all output to be saved in the output
     file and abbreviated output to simultaneously appear on the
     screen.

SPECIFY OUTPUT FILE

>> Name of output file [default = XXX.out] ? : >>

   Press ENTER to give the output file the same path and filename
   (here represented by XXX) as the input file and the extension
   ".out". Otherwise, type complete path, filename and extension
   as desired.
   
>> ** File XXX.out already exists. Append="a", Overwrite="o"? : >>
   
   - An answer of "a" causes new output to be appended to the end
     of the existing file XXX.out without changing previous
     contents of the file.
   - An answer of "o" causes new output to be written at the
     beginning of XXX.out, and all previous contents of the file
     are lost.

SPECIFY TYPE OF BANDING PATTERNS

>> Type of pattern?: 
   Zymogram = "z", DNA electropherogram = "d" [default = "z"] >>

   - If the answer is "d", <DIPLOGEN> treats all bands as alleles
     at some locus. In terms of programming technique, all bands
     are handled as if they were monomeric (thus homomeric)
     isoenzymes in a system allowing "null alleles" but without
     PTM.

                                                           Page 16
__________________________________________________________________

GENERATING ADDITIONAL HYPOTHESES BY SPLITTING ONE EZONE INTO TWO
OVERLAPPING EZONES

>> Do you want to search for overlapping Ezones (epistasis)? : 
   Yes="y", No="n" [default="n"] : >>

   See Section 6 above.
  
>> Which Ezone should be split into two new Ezones? 
   Ezone N = "N", All Ezones = "0", End program = "-1" 
   [no default]: >>

   - If the answer is a positive integer "N", then only elementary
     zone N is split. 
   - If the answer is "0", all elementary zones are split, one at
     a time.
   - If the answer is "-1", the program is terminated.

>> If an Ezone exhibits a band in N patterns, there are (3^N-3)/2
   ways to distribute the N bands over two new Ezones, such that
   for each of the N patterns, a band appears in at least one of
   the new zones.
   Input maximal N not greater than nn for which Ezone splitting 
   is to be performed [no default] : >> 

   - An answer of "N" causes only those Ezones to be split in
     which min(N,nn) or fewer banding patterns exhibit a band,
     where nn is originally set in <DIPLOGEN> to equal 8. 

                                                           Page 17
__________________________________________________________________

9. REFERENCES
__________________________________________________________________

Bergmann F, Gillet EM. 1996. Phylogenetic relationships among pine
   species inferred from different numbers of 6PGDH loci. 
   Plant Systematics and Evolution 208, 25-34.

Bergmann F, Gregorius H-R, Scholz F. 1989. Isoenzymes, indicators
   of environmental impacts on plants or environmentally stable
   gene markers? In: Scholz F, Gregorius H-R, Rudin D (eds.): 
   Genetic Effects of Air Pollutants in Forest Tree Populations. 
   Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, pp 3-6.

Gregorius H-R. 1980. The probability of losing an allele when
   diploid genotypes are sampled. Biometrics 36, 632-652.




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10. TECHNICAL CONSIDERATIONS
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<DIPLOGEN> is written in Fortran~77. The version available on the
internet under URL:
       http://www.uni-forst.gwdg.de/forst/fg/index.htm
is compiled for DOS and runs with Windows, but compilation for 
other systems may be possible upon request.  

The program DIPLOGEN.EXE and this User's Manual DIPLUSER.TXT are
offered for free distribution. The copyright and all rights remain
with the author. No guarantee can be given that the program is
free of errors nor that all possible hypotheses are actually
found, despite considerable efforts to achieve this. As always,
responsibility for the correct interpretation of the results lies
with the user.

E-Mail of author: egillet@gwdg.de
