J05H037/

N Eng y LIBRARlES

lllllllllll“ll\l lllll‘llll‘ll

. 3 1293 00533 0364

LIERARY
Michigan State
University

l

 

 

 

 

 

This is to certify that the

thesis entitled
A COMPARATIVE STUDY OF INTRASPECIFIC
GENETIC HETEROGENEITY IN ACANTHAMOEBA

EQLXEEAEé (AMOEBIDA, ACANTHAMOEBIDAE),
BY ISOENZYME ANALYSIS

presented by

 

WAN GNAN HU

has been accepted towards fulfillment
of the requirements for

MASTER degree in W SCIENCE

Major professor 2\

MS U is an Affirmative Action/Equal Opportunity Institution

 

 

Date AUG. 8, 1988

 

0-7639

 

_— fi* W..%. ‘— »- * —-

 

{M811
LlBRARiES

*7

M..--

) . 1" a.
1‘; ‘1’ C t ,,.‘

’\

“'2

 

RETURNING MATERIALS:

book drop to
remove this checkout from
your record. FINES will
be charged if book is
returned after the date

stamped below.

Place in

 

 

 

A COMPARATIVE STUDY OF iNTRASPECIFiC GENETIC HETEROGENEITY
IN ACANTHAMOEBA POLYPHAQA
(AMOEBIDA. ACANTHAMOEBIDAE).

BY iSOENZYME ANALYSIS

By

Wang-nan Hu

A THESIS

Submitted to
Michigan State University
in partial Fulfillment of the requirements
for the degeree of

MASTER OF SCIENCE

Department of Biological Science

1988

ABSTRACT

A COMPARATIVE STUDY OF iNTRASPECIFIC GENETIC HETEROGENEITY
iN ACANTHAMOEBA POLYPHAQA
(AMOEBIDA. ACANTHAMOEBIDAE).
BY ISOENZYME ANALYSIS
By

Wang-nan Hu

The intraspecific genetic heterogeneity of
Acanthamoeba golxghaga. a free-living. asexual amoeba from
natural soil populations, was examined by isoenzyme
analysis. In this study. 15 isoenzymes were used to analyze
random. clonal isolates of amoebae from soil at three
different study sites. Isolates were obtained from a
northern hardwood forest in Michigan in 1986 and 1987. The
results showed that 1, there were no statistically
significant differences in mean genetic distances between
sites and between the two years: the mean genetic distances
ranged from 0.42 to 0.50; 2, analysis of zymograms suggest
that this species may be a diploid organism: 3. greater
genetic heterogeneity exists in natural populations of this
organism than those of sexual reproductive organisms. but
similar to those of asexual organisms. The reason for this
may be due to the absence of sexual reproduction or due to

rare genetic recombination.

Dedicated to my wonderful parents.

my lovely wife and my daughter

iii

ACKNOWLEDGEMENT

I wish to express my thanks to Dr. R. Neal Band. my
major professor. for his guidance and encourgement during
the course of this study.

1 also wish to thank Dr. Stephen C. Bromley. my
advisor. and Dr. Will J. Kopachik. my comittee member for
their helpful suggestions in preparing my thesis.

Special thanks are extended to Dr. H. T. Band. Dr.
Stephen M. Milligan and Ms. Laura J. Anderson for their kind
help.

Finally. 1 would like to thank all the people who have

assisted me in completion of my research.

1v

CONTENTS

Page

LIST OF TABLES ' vii
LIST OF FIGURES viii
INTRODUCTION 1
MATERIALS AND METHODS 3
Sampling location and collection procedure 3
Microorganism identification and clonal isolation 3
Strains 4

Culture methods and sample preparation for isoenzyme
electrophoresis

Gel preparation

Gel electrophoresis

lsoenzymes studied. staining recipes and staining time

Loci and allele assignment

Null alleles

The estimation of genetic distances

RESULTS

Genotypes

Control experiment

Repeated experiment

Genetic variation

wwwmmmmmmwmms

Statistics
DISCUSSION IO
LITERATURE CITED l6

TABLES l9

FIGURES

APPENDIX

v1

35

36

LIST OF TABLES

Table Page
I. lsoenzymes studied. staining time. recipes and
gel electrophoresis concentrations for each
isoenzymes 19
II. Genotypes (site A. 1986) 20
III. Site A (1986). Nei’s genetic distances 21
IV. Genotypes (site 8. I986) 22
V. Site B (1986). Nei’s genetic distances 23
VI. Genotypes (site C. 1986) 24
VII. Site C (1986). Nei’s genetic distances 25
VIII.Genotypes (site A. 1987) 26
IX. Site A (1987). Nei's genetic distances 27
X. Genotypes (site 8. I987) 28
XI. Site 8 (I987). Nei’s genetic distances 29
XII. Genotypes (site c.1987) 30
XIII. Site C (1987). Nei’s genetic distances 31
XIV. Statistics for genetic distance (1986) 32
XV. Statistics for genetic distance (1987) 33
XVI. Two—way ANOVA for genetic distance 34

V11

LIST OF FIGURES
Page
1. Diagram of characteristic isozyme patterns expected
in heterozygotes. 35

viii

INTRODUCTION

Isoenzyme banding pattern analysis with electrophoresis
has been widely used in the identification of species and to
survey intra- or interspecies genetic diversity. Among
amoebae. species and strains of Acanthamoeba and Naeglecia
have been studied.(7.ll.l7).

However. in most previous work the data were
obtained from a limited number of axenic laboratory strains.
Also considerable genetic selection may take place in
establishing axenic cultures of amoebae. At this point. the
genetic heterogeneity of the parent. natural population for
each laboratory strain is unknown (11).

The intraspecific heterogeneity of Acanthamoeba
eglyghaga was examined by Jacobson & Band (II). In the
present study. a comparative analysis of isoenzymes for two
consecutive years was performed to determine if the
intraspecific genetic heterogeneity of Acanthamoeba
polyehaga remained the same or changed. when using natural
populations. A. polypnggg is a free-living. asexual amoeba.
found widely in soil and freshwater. The isolates were
obtained from a northern hardwood forest at three different
sites in 1986 and 1987. The population size of soil amoebae
(number of amoebae per gram soil) for these two years at the
study sites was smaller than previous years. possibly due to

dry weather (13).

The results indicated that the genetic heterogeneity

within A. polyphaga was high. The mean genetic distance

 

calculated was 0.42 to 0.50. However. there were no
statistically significant differences in average

heterogeneity between the two years and between the sites.

MATERIAL AND METHODS

Sampling location and collection procedure; Random soil
samples were collected from three sites (A. B. C) in
Dickinson County. Michigan. Sites A and C were located in
Felch township at lat. 46°07’N. long. 87°54'w and lat.
46°03'N long. 87°55'N. respectively. while site B was
located in Norway township at lat. 45°56’N. long. 87°56’w.
Each site consisted of a 10 by 20 meter area in a northern
hardwood forest (11).

With the aid of a tube sampler (diameter : 2 cm.) both
organic and mineral layers were collected and subsequently
two inches from each horizon was brought back to the
laboratory. Amoebae were isolated from the soil samples
using a 96—multi—well plate. soil dilution technique and
Escherichigicoli (strain K-lZ) as the food organism (11).
The above procedures were followed between the months of
June to October for the two consecutive years of 1986
through 1987.

Microorganism identification:§nd clgggigisolation.
Microorganisms were identified as Acantnamoeba lexehaga on
the basis of cyst morphology (16). To each well identified
as containing A. golxehaga. one drop of LS saline (50 mM

NaCl. 4.6 mM MgSO 0.36 mM CaCl2)(2) was added; then the

49
amoebae were withdrawn with a pipet and placed in a Petri
dish containing LS saline and agar (1.51 w/v) (LS-agar). To

obtain single amoebae for clonal isolates. a piece of agar

4
which contained the smallest number of A. polyphagg was cut
out and placed on the lower edge of a slanted Petri dish
containing LS-agar. Then amoebae were cultured at 23°C with
E. coli (K—12) spread over the dish. The amoebae migrated
from the lower edge towards the top of the Petri dish and
distributed widely. A single amoeba was isolated from this
plate. Then. the cyst shape was checked again and the same
procedure was repeated one more time.

Strains. A total of 30 strains of A. polyphagg were
randomly isolated and cloned from 30 soil samples of the
three sites. 10 strains per site. for each year tested.

Culture method§_§nd samp;§:pre2§;§tion for isoenzyme
electrophoresis; E. coli (K-12) was cultured in 200 ml LB
medium (NaCl 10 g. Bacto Tryptone 10 g. Bacto Yeast Extract
5 g. Difco Laboratories. Detroit. Mi. U.S.A.. H20 to I
Liter. pH 7.5) for 18 - 20 hr at 37°C. The bacteria were
harvested by centrifugation (9000 g) and washed two times in
LS saline. then suspended in 30 ml of LS saline and
distributed in 10 ml volumes to three 250 ml plastic tissue
culture flasks (Corning Science Products). Subsequently.
clonal isolates of Awgpolypnggg were inoculated into these
tissue culture flasks and incubated at 23°C. Once the peak
of population growth was reached (about 36 - 72 hr). the
amoebae from three flasks. representing 18-24 x 106 amoebae.

were harvested by centrifugation. washed twice in LS saline

to remove bacteria and pelleted. The amoebae were then

5

suspended in 200 ul of lysis buffer and frozen over liquid

N until electrophoresis. Lysis buffer consisted of 10 mM

2
Tris. 1 mM EDTA. (pH 6.8) to which 0.05 mM NADP was added
before use.

Gel gregaration. A vertical discontinous polyacrylamide
gel slab was used (12). Spacer gel was 6% (w/v) (pH 6.7) and
resolving gel (pH 8.2) was used at different concentrations

(Table 1).

Gel electrophoresis. Samples were removed from liquid

 

N2. thawed at room temperature. suspended in 200 ul of
sample solution (10 ml glycerol. 90 ml electrode buffer
(12)). After centrifugation in a microcentrifuge (Fisher
model 2358) for 30 sec. 50 ul of sample supernatant was
injected into gel electrophoresis wells. Gel electrophoresis
was run with cold water in an ice bath: running time was
about 8 hr at 200 v with pH 8.2 electrode buffer. Control
experiments with E. cgli. (K-12) was also carried out on the
same gel in order to differentiate between the bands of A;
golyghaga and E. coli. A 50 ul sample of 250 mg
(dryweight)/ml bacterial supernatant was loaded into a gel
well. When a different bacteria species. Klebgiella
engummiae was used as the food source for A. polypgggg. the
zymograms were the same.

lsoenzymes studied, staining recipes and stainigg time.

Fifteen isoenzymes were examined (Table I). Staining was

6

done in darkness at 37°C: chemical reagents for staining
were from Sigma Chemical Company.

Loci and:g;lele assignment. Loci assigned were based
on clustering patterns and numbered from anode to the
cathode according to each isoenzyme banding pattern (17).
The alleles at each locus (based on banding patterns in
which one band represents a homozygote and multiple bands a
heterozygote (10)). were also coded from the most anodic
band to the most cathodic band. Homozygotes were designated
by one number and heterozygotes by two numbers.
Heterozygous monomers consisted of two electrophoretic
bands. dimers three bands. trimers four bands and so on.
with the homozygote represented by the two outer bands of
the respective heterozygote (10).

Null alleles. The absence of isoenzyme activity at each
corresponding locus was defined as a "null allele". and also
given a 0 number in order to be in agreement with the allele
assignment for each locus.

The ggtimation of gggetic distanceg; Calculations of
genetic distance were based on Nei's standard formula (14)
and done with the aid of a computer program (8. 9). Genetic
distance is the genetic difference between populations as
expressed by a function of gene frequences. Nei’s standard
genetic distance formula is a statistical method by which
the average number of codon differences per locus can be

estimated from gene frequency data. The frequencies of

7

alleles segregating at each locus is as follows : it will be
equal to I for a homozygote with a given allele. the
frequency of the other allele at the same locus then being
0. For a heterozygote. the two alternative alleles of a
given locus both have a frequency 0.5. Hence the alleles
frequencies have value 0. 0.5 and 1 (17) (see Appendix A for

further detail).

RESULTS

Genotypegg The zymograph of the 30 isolates for each
year showed monomorphic and polymorphic banding patterns. A
total of 30 loci were assigned. Three out of 30 loci were
monomorphic. AAP 2. PGM 2 and LTD 2 (for abbreviations see
Table I). Tables II. IV. VI. VIII. X and X11 showed the
genotypes for each clonal isolate of different sites and
different years based on allelic frequencies. These tables
indicated varying degrees of diversity in genotypes among
the polymorphic loci and there was not any two isolates
which had the same patterns over the 30 loci. For example.
between the isolates 4 and 5 (site A. 1987 at Table VIII).
27 (including three monomorphic loci) out of 30 loci showed
the same genotypes. two loci (ME 5 HK) had one common allele
at each locus and one locus (SOD 2) between the isolates had
unlike alleles. Between the isolates 2 and 8 (site 8. 1986
at Table IV). however. only eight out of 30 loci had the
same genotypes. eight loci had a common allele in each locus
and the other 14 loci had unlike alleles. The differences
between any other paired-isolates in genotypes varied
between these two extremes.

Control exoeriment. No isoenzyme activity of E. goli
was detected on these gels. confirming that all the bands

belonged to amoebae.

9

Regeated experiment. In later. repeated experiments for
isolates with fresh cell extract were done and identical
banding patterns were observed. The results indicated that
the banding patterns for isolates were stable over a period
of time.

fignetic varlgtion. Genetic distances between clonal
isolates from each site were calculated and given in Tables
III. V. VII. IX. XI and XIII.. The values of genetic
distance ranged from 0.067 to 0.839 over the three sites and
the two years. The two extreme values were the allelic
comparisons made between isolates 4 and 5 (site A. 1987) and
isolates 2 and 8 (site 8. 1986).

Statistics; Mean genetic distances for each site
(Tables XIV s XV). one-way analysis of variance for three
soil sites each year (Tables XIV s XV) and two-way analysis
of variance for different sites and different years (Table
XVI) were done respectively. The values of mean genetic
distance ranged from 0.42 (site A. 1986) to 0.50 (site B.
1986). Yet. there were no statistically significant
differences in the average genetic distances calculated
between the sites and between the years (in one—way and
two-way analysis of variance). Therefore. it was concluded
that there was no change in genetic distances between the
two consecutive years and there were no differences due to

site effects.

DISCUSSION

The level of ploidy of A. polyphagg is unknown (4).
However. the zymograms showed complex banding patterns at
most of the loci. One possible explanation. in terms of the
multiple banding patterns. is that the double-band pattern
was not due to heterozygotes. but due to the mixing of two
clonal isolates. this was unlikely. For example. isolate 2
(table VIII. 1987) showed double bands at the GDH 2 locus
(genotype 1/2). One may think that this was the result of
mixing of isolates 3 and 4 (genotypes 2 a I). but this
assumption could not be explained by the banding pattern in
ICU and LDH for isolate 2 (genotypes 1/3 a 0). The
genotypes of isolate 3 and 4 at these two loci were 1 a 1
and 0 a 1/2. There may exist two other explanations for the
complex banding patterns such as gene duplication in a
haploid organism or alternative splicing of a transcript.
However. this is not my case because 25 out of 30 loci
showed multiple bands. Therefore. the above two
possibilities cannot explain the high frequencies of
multiple banding paterns even if they are not rare events.
The banding patterns for several enzymes suggested that A;
golyghaga may be a diploid organism because the zymograms of
several enzymes showed that the banding patterns were
similar to those patterns commonly observed in diploid

organisms. For instance. at LDH. PGM 1 and ME loci zymograms

10

ll

exhibited three band—patterns. of which the middle band was
stained more darkly than the two outside bands (the
activities of the isozymes formed in heterozygotes are 1:2:1
for dimer. see Fig.1) and the three bands exhibited
equidistance between bands. This is the typical dimeric
heterozygous pattern. found in diploid organism (5.10 8 18).
When the number of chromosomes in a species is difficult to
count. zymograms of isoenzymes are used to estimate the
ploidy level (4). Although this is a good method to be used
for estimating ploidyism. it may not be as accurate. and
therefore. it is not the most reliable method. My data
didn't rule out the possibility of polyploidy in this
species. In Amoeba proteus. it was reported that there may
exist polyploid cells in its natural population. and they
may play a role in genetic variability of those asexually
growing organisms (1). Because there is no closer diploid
species of this genus as a control to compare the zymograms
and sometimes the banding patterns between diploid and
polyploid organism for some enzymes may be the same (19).
therefore. it is difficult to Judge whether A. gglxghaga is
a polyploid species. More other lines of evidence are needed
to prove it further. In zymograms. the complex banding
patterns and high loci numbers for some enzymes may be due
to the addition of genome. or by the gene duplication and

then during the course of evolution they diverged.

12

Nei’s genetic distance measure has been widely used to
evaluate the genetic variation within species or between
species. This method applies to any kind of organism without
regard of ploidy or mating scheme. This is because the
definition of 1 and D (see Appendix A) depends solely on
gene frequencies rather than on others (14). The mean
genetic distances 1 calculated of A. polyphagg ranged from
0.42 to 0.50. It was much greater than those of
multicellular. sexual organisms within species (15). For
example. within the Qrogophilg willistoni group. the genetic
distance is 0.008 - 0.049. However. the value of genetic
distance between the sibling species of Q. willistoni group
is 0.54 i 0.05. non—sibling species of D.willi§toni group is
1.1 t 0.06 (15). For the unicelluar. free—living amoebae of
the genus Naegleria. including three species. N;
lovaniensis. N. fowleri and N. australiensis. the genetic
distances within each species were obviously low (17) and
similar to those of sexual organisms (15). The mean genetic
distance for N. lovaniensig was 0.081. for N. fowleri 0.022
and for N. australiensis 0.023; six to twenty times lower
than that of A.;polypbggg. In contrast. the value of
interspecific genetic distance was 1.222 between N;
lovgniengig and N. fowleri. 3.733 between N. lovgniensis and
N. australiensis and 3.273 between N. fowleri and N;
gustraliensis. On the basis of the statistical analyses of

their data and other evidence. Cariou 8 Pernin speculated

13

that genetic recombination existed in Naegleria (5). Based
upon the above examples. the heterogeneity within 5;
gglyghaga is similar to that which is derived from
comparisons made between sibling species of the Q;
willistoni group. and much greater than that within each
species of Ngegleria. If A. polyphagg were a sexually
reproducing organism. the value of genetic distance within
this species could not possibly be so high. Here is another
example. There was little genetic diversity when analysing
isozyme banding patterns (14 out of 16 loci is the same)
among sexual isolates in Dictxgstelium discoideum. which
are simple soil amoebae. In contrast. asexual isolates
differed from sexual isolates at 13 of 16 loci. High
heterogeneity existed between sexual isolates and asexual
isolates (3). i think the high genetic heterogeneity of A;
gglyghaga may be due to the accumulation of mutations and
the absence of sexual reproduction or very rare genetic
recombination. thus inhibiting the gene flow. Interestingly.
a chi-square test showed that. of the genotype frequencies.
14 out of 25 polymorphic loci in this species didn’t fit the
Hardy-Weinberg Equilibrium. Thus. if mating between
isolates occurred. it was rare and not random. Similar high
genetic heterogeneity within Trxpgnosoma cruzi. which is a
unicelluar. diploid parasite. has been reported. The mean
genetic distance of this species was 0.757 (18). Their

statistical study indicated that large linkage

14

disequilibrium between alleles existed at paired loci. which
reached maximum possible values for almost all of the locus
pairs (20). The authors stated that this result was most
consistent with the hypothesis that genetic recombination is
absent or very rare in T. cruzi natural populations. There
is no definitive evidence for sexual reproduction of A;
golyghaga (4). These data don't eliminate the possibility of
mating in this species. but more direct evidence is needed.
An idea. which if achieved would yield such proof. would be
to genetically mark isolates differently. For example. one
could use two different genetic markers to mark two or more
different strains: the different strains would then be
mixed. cultured. and processed through electrophoresis. If
it was found that in one cell the genetic markers of the two
different strains existed. one could infer that mating
occurred.

The genetic distances calculated by Jacobson (11) for
the A. polyphagg ranged between 0.286 and 2.106 over three
sites and mean genetic distance were 1.06 to 1.15. which
were higher than my results. Two possible explanations for
that is this. One is that fewer strain numbers were used and
fewer loci were used as well. The data were based on 15
strains and 10 loci. but my data came from 30 strains and 30
loci. The result I calculated showed that the value of the
mean genetic distance decreased by increasing the numbers of

strains and loci used. According to this. the value of the

15

mean genetic distance within species may be related to the
number of strains and loci that were used. To obtain more
reliable results. a greater number of isolates were compared
using many different isoenzymes. This idea was also
supported by statistics. the larger number of strains you
use. the shorter confidence interval of the mean. i.e. the
more accurate mean internal.

The other explanation may be due to climate. which may
be an important factor that affects the genetic
heterogeneity within this species. The population sizes
(number of amoebae per gram soil) of A. polyphggg in 1986
(8-16x103 amoebae/per gram soil) and 1987 (20-50x103
amoebae/per gram soil) were much smaller due to a drought
(13) in the sampling areas than that in 1985 (1.1-1.6x106
amoebae/per gram soil)(the isolates Jacobson (11) used were
from 1985). During the wet season. there were more kinds of
food for amoebae and less presure of genetic selection.
therefore decreasing competition within and between the
species. large pooulation sizes and greater genetic
diversity. On the other hand. a dry season provides less
kinds of food. increasing competition and greater presure of

genetic selection. small population sizes and less genetic

diversity within species.

LITERATURE CITED

1. Afon’kin. 8. Yu. 1986. Polyploid cells in AmoebaNprotggg
culture. Acta Protozool.. 25 : 41 - 54.

2. Band. R. N. s Morlock. S. 1969. The respiratory
metabolism of Acanthamoeba rhgoggg during encystation.
J. Gen. Microbiol.. 59 : 351 - 358.

3. Briscoe. D. A.. Gooley. A. A.. Bernstein. R. L.. Mckay.
G. M. 5 Williams. K. L. 1987. Genetic diversity in
cellular slime molds : Allozyme electrophoresis and a
monoclonal antibody reveal cryptic species among
Dictyggteligm discoideum strains. Genetics 117 : 213 -
220.

4. Byers. T. J. 1986. Molecular biology of DNA in
Acanthamoeba. Amoeba. Entamoeba. and Naegleria.

Interngtiong) review of cytology. Vol. 99. p. 311.

 

5. Cariou. M. L. a Pernin. P. 1987. First evidence for
diploidy and genetic recombination in free-living
amoebae of the genus Naegleria on the basis of
electrophoretic variation. Genetics 115 : 265 - 270.

6. Daggett. P.-M. 8 Nerad. T. A. 1983. Procedures for
isoenzyme electrophoretic analysis. American Tyge
Culture Coligction. Rockville. Maryland. USA.

7. De Jonckheere. J. F. 1983. Isoenzyme and total protein
analysis by agarose isoelectric focusing. and taxonomy
of the genus Acanthamoeba. J. Protozool.. 30 : 701 -

706.

16

17

8. Green. D. M. 1979. A BASIC computer program for

calculating indices of genetic distance and similarity.

J. Hered.. 70 429 - 430.

9. ----------- . 1984. Calculation of indices of genetic
distance and similarity : unbiased estimation corrected
for sample size in BASIC computer program. J. Hered..
75 : 415.

10. Harris. H. 1976. Handbook of enzyme electrophoresis in
human genetics. North-Holland Publishing Co..
Amsterdam.

11. Jacobson. L. M. 8 Band. R. N. 1986. Genetic
heterogeneity in a natural population of Acanthamoeba
golyghaga from soil. and isoenzyme analysis. g;
Protozool.. 34 : 83 - 86.

12. Maizel. J. V. 1971. Polyacrylamide gel electrophoresis
of viral proteins. in methods in virology. academic
Press. New York. pp. 179 - 24.

13. National Oceanic and Atmospheric Administration. 1987.
Climatological data. Michigan. Dec. 1987. Vol.102
No. 12.

14. Mei. M. 1972. Genetic distance between populations. Am;
Ngt.. 106 : 283 - 292.

15. ------ . 1987. Molecular evolutionary genetics. Columbia
University press. New York.

16. Page. F. C. 1967. Re-definition of the genus

Acanthamoeba with descriptions of three species. g;

Protozool.. l4 . 703 — 724.

17.

18.

I9.

20.

18

Pernin. P.. Cariou. M.-L 8 Jacquier. A. 1985.
Biochemical identification and phylogenetic
relationships in free-living amoebae of the genus
Naegleria. J. Protozool.. 32 : 592 -603.

Tibayrenc. M. 8 Ayala. F. J. 1988. Isozyme variability
in Trypanosomg cruzi. the agent of Chagas’ disease :
genetical. taxonomical. and epidemiological
significance. Evolution. 42 : 277 - 292.

Wright. C. A. 8 Rollinson. D. 1981. Analysis of enzymes
in the Bulinug;tropicus/trunggtgg comples (Mollusca:
Planorbidae). J.;Ngt. Higt. 15 : B73 — 885.

Zhang. 0.. Tibayrenc. M. 8 Ayala. F. J. 1988. Linkage
disequilibrium in natural populations of Trxganosoma

cruzi (flagellate). the agent of Chagas' Disease. g;

 

Protozool.. 35 : 81 — 85.

19

TABLE I. lsoenzymes studied. staining time. recipes and gel
electrophoresis concentrations for each isoenzyme. -

 

Resolving Staining Staini g

 

Isoenzyme Geli!) time(hr)a recipe
Acetyl esterase (AE) 10.75 3 A
Arginine amino peptidase (AAP) 10 overnight A
Butyryl esterase-2 (BE-2) 10.75 2.5 A
Glutamate dehydrogenase (GDH) 10.75 2.5 B
Hexokinase (HK) 10.75 2 B
B—hydroxybutyrate dehydrogenase 10.75 2 8

(B-HBDH)
Isocitrate dehydrogenase (1CD) 10 2 B
Lactate dehydrogenase (LDH) 10.75 2.5 A
Leucine amino peptidase (LAP) 10 overnight A
Malic enzyme (ME) 10 1.5 B
Phosphoglucomutase (ROM) 10 1 B
6—phosphogluconate dehydrogenase 11.25 2.5 B
(6-PGD)
Propionyl esterase (PE) 10.75 3 B
Superoxide dismutase (500) 11.25 overnight B
L-threonine dehydrogenase (LTD) 10.75 1.5 B

 

gStaining in the dark at 37°C.
A. from Daggett (6): B. from Pernin (l7).

TABLE II. Genotypes (site A. 1986)8

20

 

Clonal isolates

 

 

Loci l 2 3 4 5 6 7 8 9 10
AE 1 O 0 3 1/4 3 1/4 1/4 3 1/4 1/4
AE 2 1/2 2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 I/Z
AE 3 1/3 1/2 1/3 l/Z 1/3 1/3 1/3 1/3 1/3 1/2
AE 4 2/3 2 2 1/5 2 1/5 1/5 2 1/5 1/5
AAP l 1 1/2 1/3 l/3 1/3 1/2 1/3 1/3 1/2 1/2
AAP 2 1 l l l i I I i i i
BE-Z 1 0 0 0 0 O 1/2 1/2 1/2 1/2 1/2
BE-Z 2 1/2 1 1/2 1 1/2 1 l l l 1
BE-Z 3 1/2 2 1/2 2 1/2 2 2 2 2 2
BE-Z 4 2 l l l 1 1/2 1/2 i/2 1/2 1/2
BE-Z 5 1 i I I 1 1/2 1/2 1/2 I/2 I/Z
BE-Z 6 i I/2 1/2 1/2 1/2 1 1 1 I I
GDH 1 0 I I I l i 1 0 I
GDH 2 1/2 1 1/2 2 2 1 1/2 1/2 2 I
HK 2 l I I i I I l 1 1
B-HBDH 2 0 2 1/2 2 0 2 2 0 0
1CD 1/3 2 2/3 1/3 1 2 2 2 Z 3
LDH 1/2 I 1/2 0 1/2 I/Z 1/2 0 1/2 1/2
LAP 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2 2 2
ME 1/2 I l I i I i/2 1/2 1/2 1/2
PGM 1 1/2 0 1/2 0 1/2 1/2 1/2 1/2 1/2 1/2
PGM 2 l l l I I I 1 i i i
6-PGD 1/2 0 I 0 l/2 0 1/2 1/2 0 0
PE 1 2 2 2 2 1/4 1/4 1/4 2 1/4 1/4
PE 2 1/5 2/5 1/5 2/5 2/4 2/4 2/4 2/5 2/4 2/4
PE 3 O 0 0 0 1/3 1/3 1/3 0 1/3 1/3
500 l 3 1 2/3 2/3 2/3 1/3 1/3 2/3 1/3 1/3
500 2 1/2 1 1/2 1 i 2 1/2 1 1/2 1/2
LTD 1 2 1/2 1/2 1/2 2 1/2 1/2 1/2 1/2 1/2
LTD 2 i I l i I l I l i l

 

, 5 Abbreviations represent the loci coding for the various enzymes. the
mumbers representing multiple forms of the enzyme. Alleles are numbered

from the most anode to the most cathod. Homozygotes are designated by

one and heterozygotes by two numbers; 0 reprsents a null allele.

TABLE III. Site A (1986). Nei's genetic distances.8

21

 

Clonal isolates

 

 

l 2 3 4 5 6 7 8 9 10

1 - 0.572 0.323 0.548 0.452 0.710 0.533 0.366 0.613 0.681
2 - 0.345 0.293 0.518 0.388 0.517 0.467 0.500 0.415
3 - 0.314 0.189 0.525 0.385 0.261 0.646 0.580
4 - 0.372 0.519 0.456 0.389 0.513 0.457
5 - 0.536 0.326 0.400 0.530 0.550
6 - 0.141 0.516 0.150 0.109
7 - 0.310 0.194 0.210
8 - 0.399 0.571
9 - 0.173
10 -

 

aNull alleles included.

22

 

 

 

TABLE 1v. Genotypes (site e. 1986)8
Clonal isolates

Loci 1 2 3 4 5 6 7 8 9 10

AE 1 3 0 3 3 1/4 1/4 1/4 1/4 3 1/4
AE 2 1/2 1/2 1/2 1/2 0 0 0 0 1/2 0

AE 3 2/3 1/3 1/3 1/3 0 0 0 0 1/3 0

AE 4 2 2 2/3 2 1/5 1/5 3/5 1/5 2 1/5
AAP I 1 1/3 1/3 1/3 1/2 1/3 1/2 1/2 1/2 1/3
AAP 2 l 1 l 1 1 i 1 1 1 I

BE-2 1 0 1/2 2 0 1/2 0 1/2 1/2 1/2 1/2
BE-Z 2 1/2 1/2 1 1/2 1 1/2 1 1 I I

BE-2 3 1/2 1/2 1/2 2 2 1/2 2 2 2 2

BE-2 4 1 1 1 1/2 1/2 1/2 1/2 1/2 1/2 1/2
BE-2 5 1 I 1 1/2 1/2 1 1/2 1/2 1/2 2

BE-Z 6 1 I 1 1/2 2 2 l 1 I 1

GDH 1 1 0 0 1 1 1 1 1 1 1

GDH 2 1 2 2 1 1 1/2 1 l 1 2

HK ' 2 2 2 1 1 2 1 1 1 1

B-HBDH 1 2 2 0 0 0 0 0 0 1

1CD 2 0 3 1 2 2 2 2 1 2/3
LDH 0 1/2 0 0 1/2 0 1/2 1/2 1/2 1/2
LAP 1/2 1/2 1/2 2 1/2 1/2 1/2 2 2 2

ME 1 1/2 1 1 1/2 1/2 1 2 1 1/2
PGM 1 0 1/2 1/2 0 1/2 1 1/2 1/2 1/2 1/2
PGM 2 I 1 I 1 1 1 I 1 1 1

6-PGD 1 1 2 0 1 1/2 I 0 l 0

PE 1 2 2 2 1/4 1/4 1/4 1/4 1/4 2 1/4
PE 2 1/5 1/5 1/5 4 2/4 2 2/4 2/4 1/5 4

PE 3 0 0 O 1/3 1/3' 1/3 1/3 1/3 0 1/3
500 1 1/3 2/3 3 3 1/3 2/3 1/3 1/3 1/3 1/3
500 2 2 I 2 1 2 1 2 2 2 1

LTD 1 2 1/2 2 2 2 1/2 1/2 1/2 1/2 1/2
LTD 2 1 1 1 I I I 1 i I 1

 

a Abbreviations represent the loci coding for the various enzymes. the
numbers representing multiple forms of the enzyme. Alleles are numbered
from the most anode to the most cathod. Homozygotes are designated by

one and heterozygotes by two numbers; 0 represents a null allele.

TABLE V. Site 8 (1986). Nei's genetic distances.

23

 

Clonal isolates

 

 

l 2 3 4 5 6 7 8 9 10
l - 0.502 0.381 0.527 0.596 0.539 0.521 0.690 0.350 0.756
2 ~ 0.304 0.758 0.828 0.637 0.728 0.839 0.496 0.608
3 - 0.644 0.804 0.689 0.689 0.816 0.463 0.768
4 - 0.538 0.447 0.538 0.512 0.453 0.384
5 - 0.336 0.087 0.139 0.328 0.322
6 - 0.423 0.454 0.749 0.533
7 - 0.125 0.239 0.276
8 - 0.340 0.243
9 - 0.479
10 -

 

aNull alleles included.

TABLE VI. Genotypes (site c. 1986)8

24

 

Clonal isolates

 

 

Loci 1 2 3 4 5 6 7 8 9 10
AE 1 2 3 3 0 3 1/4 1/4 1/4 1/4 1/4
AE 2 0 1/2 1/2 1/2 1/2 1/2 2 1/2 1/2 1/2
AE 3 1/3 1/3 1/3 1/3 1/3 1/2 1/2 1/2 1/2 1/2
AE 4 2/4 2 2 2 2 1/5 1/5 1/5 1/5 1/5
AAP 1 1/3 1 1/3 1/3 1/2 1/2 1/3 1/3 1/2 1/3
AAP 2 1 1 I 1 I i 1 l 1 i
BE-2 1 0 0 2 1/2 2 1/2 1/2 1/2 1/2 1/2
BE-2 2 1 1/2 1/2 l [/2 i I 1 1 I
BE-Z 3 1/2 2 1/2 1/2 1/2 2 2 2 2 2
BE-2 4 2 1 l 1 1 1/2 1/2 1/2 1/2 1/2
8E-2 5 0 1 1 l 1 1/2 1/2 1/2 1/2 1/2
BE-2 6 1/2 1 1/2 1/2 1/2 1 I 1 1 1
GDH l 0 1 1 1 0 1 0 1 1 0
GDH 2 1/2 I 1 1/2 2 1/2 1 l 1 1/2
MK 2 2 I 1 2 1 1 2 1 1
B-HBDH 2 2 2 2 1/2 2 2 0 0 0
ICD 3 1/3 1/2 1/2 2/3 2 2 2 2 2
LOH 1/2 0 1/2 1/2 1/2 1/2 1/2 1/2 1/2 1/2
LAP 1/2 1 1/2 1/2 1 1/2 1/2 1/2 1/2 2
ME 1/2 1 1 1 1 1/2 1 1/2 1 1/2
PGM 1 1/2 1/2 1/2 1/2 1/2 1/2 1/2 0 1/2 1/2
6-PGD 1/2 2 1 l 1 1/2 1/2 0 0 0
PE 1 2/3 2 2 2 2 1/4 1/4 1/4 1/4 1/4
PE 2 3/5 2/5 1/5 1/5 1/5 4 2/4 4 4 4
PE 3 2/3 0 0 O 0 1/3 1/3 1/3 1/3 1/3
500 1 1/3 1/3 3 2/3 2/3 2/3 1/3 1/3 1/3 1/3
500 2 1/2 1/2 1 1 1 1 1/2 1/2 2 1
LTD 1 2 2 1/2 2 2 2 2 2 2 2
LTD 2 1 I 1 1 1 l l l 1 1

 

5 Abbreviations represent the loci coding for the various enzymes. the
numbers representing multiple forms of the enzyme. Alleles are numbered
from the most anode to the most cathod. Homozygotes are designated by
one and heterozygotes by two numbers: 0 represents a null allele.

TABLE VII. Site C (1986). Nei's genetic distances.8

25

 

Clonal isolates

 

 

2 3 4 5 6 7 8 9 10
1 0.511 0.670 0.594 0.520 0.635 0.519 0.705 0.791 0.658
2 - 0.287 0.348 0.339 0.555 0.529 0.598 0.609 0.816
3 - 0.104 0.226 0.404 0.433 0.638 0.548 0.596
4 - 0.243 0.326 0.406 0.606 0.518 0.526
5 - 0.547 0.559 0.721 0.781 0.654
6 - 0.142 0.241 0.179 0.182
7 - 0.284 0.191 0.166
8 - 0.122 0.178
9 - 0.148
10 -

 

aNull alleles included.

26

TABLE VIII. Genotypes (site A. 1987)8

 

Clonal isolates

 

 

Loci 1 2 3 4 5 6 7 8 9 10
AE 1 2/3 1 2/3 2/3 2/3 2/3 2/3 3 2/3 2
AE 2 1/2 1/2 [/2 2 2 2 2 1/2 1/2 1/2
AE 3 l 1 1 0 0 2 2 2 1 1/2
AE 4 1 1 1 1/2 1/2 1/2 1/2 1/2 1 I
AAP 1 1/3 1 1/3 1/2 1/2 1/2 1/3 1/2 1/3 1
AAP 2 l 1 1 1 1 i I I 1 l
BE-2 1 0 0 2 1/2 1/2 1/2 0 0 1/2 1/2
8E-2 2 1/2 2 2 1/2 1/2 2 2 1/2 2 2
BE-2 3 1/2 1/2 1/2 2 2 1 2 1/2 1/2 2
BE-Z 4 2 0 2 1/2 1/2 1/2 1 1/2 2 2
BE-2 5 1 1 1 1/2 1/2 1/2 0 1/2 1 1
BE-2 6 1 I l l 1 1/2 1 2 l 1
GDH 1 0 0 l 1 l 1 1 1 1 0
GDH 2 1 1/2 2 1 1 1 1/2 1 1/2 1/2
HK 2 2 2 1 1/2 1 2 2 2 2
B-HBDH I 2 2 0 0 0 0 0 2 1/2
ICD 1 1/3 1 1 1 3 1/3 1 l l
LDH 0 0 0 1/2 1/2 1/2 1/2 1 0 0
LAP 1/2 2 1/2 2 2 2 1/2 1/2 1/2 1/2
ME I 1 1 1 1/2 1 1/2 1 l 1
PGM I 0 1 0 1/2 1/2 1/2 1 1/2 0 0
PGM 2 1 1 1 1 1 l 1 1 l l
6-PGD 0 1/2 1/2 I 1 1 0 1 0 1
PE 1 1/2 1 1/2 3 3 1/2 1/2 1/2 1/2 2
PE 2 1/3 1/3 1/3 2 2 2 2 2/3 1/3 1/3
PE 3 1/2 1/2 1/2 2/3 2/3 2/3 2/3 2/3 1/2 1/2
500 1 2 2 2/3 1/3 1/3 1/3 1/3 1/3 2 2/3
500 2 2 2 1/2 0 2 1/3 1/3 1/3 2 1/2
LTD 1 1/2 1/2 1/2 2 2 1/2 1/2 1/2 1/2 1/2
LTD 2 1 I l 1 1 l 1 1 l 1

 

. a Abbreviations represent the loci coding for the various enzymes. the
numbers representing multiple forms of the enzymes. Alleles are numbered
from the most anode to the most cathod. Homozygotes are designated by
one and heterozygotes by two numbers; 0 represents a null allele.

TABLE IX.

Site A (1987). Nei's genetic distances.8

27

 

Clonal isolates

 

 

2 3 4 5 6 7 8 9 10
1 0.281 0.266 0.770 0.661 0.832 0.640 0.578 0.147 0.197
2 - 0.315 0.813 0.702 0.735 0.661 0.659 0.298 0.326
3 - 0.641 0.579 0.628 0.619 0.556 0.078 0.151
4 - 0.067 0.262 0.444 0.372 0.672 0.592
5 - 0.299 0.389 0.350 0.570 0.533
6 - 0.345 0.246 0.682 0.618
7 - 0.303 0.590 0.630
8 - 0.607 0.548
9 - 0.187
10 -

 

aNull alleles included.

28

TABLE x. Genotypes (site B. 1987)8

 

Clonal isolates

 

 

Loci I 2 3 4 5 6 7 8 9 10
AE 1 1/2 2/3 2/3 3 1/3 2/3 2/3 2/3 1/2 [/2
AE 2 1/2 2 2 2 1/2 2 1/2 1/2 1/2 1/2
AE 3 1 2 1 0 2 2 1/2 1 1 1
AE 4 1 1/2 1/2 1/2 1 1/2 0 1/2 1 1
AAP 1 1 1/2 1/2 1 1/3 1/2 1 1/3 1 1/3
AAP 2 1 I 1 1 l 1 i 1 1 1
BE-Z l 2 2 1/2 1/2 2 1/2 2 1 1/2 1/2
BE-Z 2 2 2 1/2 1/2 1/2 1/2 1/2 1/2 2 2
BE-Z 3 1/2 2 1 1 1/2 1 1/2 2 1/2 1/2
BE-Z 4 0 1/2 1/2 1/2 0 1/2 1 1 1 1
BE-Z 5 1 1/2 0 1/2 1 1/2 1 0 1 1
8E-2 6 1 1 1 i l 1 1 1 l I
GDH l 0 0 l I 1 I 1 1 0 1
GDH 2 2 1 1 1 1/2 1 1/2 1/2 1/2 1/2
MK 2 1/2 2 1/2 2 1/2 2 1/2 2 2
B-HBDH 2 1/2 0 0 2 2 2 0 2 2
ICD 2 1 1 1 1/3 I l 0 1 0
LDH 0 1 1/2 1/2 0 1/2 I 1 0 0
LAP 1/2 0 2 1/2 1/2 1/2 1/2 0 1/2 1/2
ME 1 1/2 1 l 1 i 1 1/2 1 1
PGM 1 0 1/2 1/2 0 0 1/2 0 1/2 0 1
PGM 2 1 1 1 l I 1 l I 1 1
6-PGD 1 0 0 1/2 2 1 0 2 0 0
PE 1 1/2 1/2 1/2 2 1/2 2 1/2 1/2 1/2 1/2
PE 2 1/3 2 2 2 1/3 2 1/3 3 1/3 1/3
PE 3 1/3 1/2 1/2 2/3 1/3 2/3 1/2 2/3 1/2 1/2
500 1 2/3 1/3 1/3 1/3 2/3 1/3 2 1/3 2/3 2/3
500 2 2 1/3 1/3 1/3 2 3 2 1/3 2 2
LTD 1 1/2 2 2 1/2 1/2 1/2 1/2 1/2 0 1/2
LTD 2 1 l 1 1 1 i 1 1 1 1

 

a Abbreviations represent the loci coding for the various enzymes. the
numbers representing multiple forms of the enzyme. Alleles are numbered
from the most anode to the most cathod. Homozygotes are designated by
one and heterozygotes by two numbers: 0 represents a null allele.

29

TABLE XI. Site 8 (I987). Nei's genetic distances.8

 

Clonal isolates

 

 

1 2 3 5 6 7 8 9 10
l - 0.692 0.747 0.671 0.225 0.639 0.374 0.818 0.205 0.291
2 - 0.352 0.457 0.629 0.314 0.461 0.537 0.507 0.579
3 - 0.248 0.640 0.265 0.438 0.405 0.518 0.444
4 - 0.474 0.185 0.444 0.500 0.581 0.640
5 - 0.463 0.273 0.682 0.313 0.291
6 - 0.433 0.586 0.589 0.511
7 - 0.618 0.236 0.270
8 - 0.714 0.457
9 - 0.186
10 -

 

a Null alleles included.

TABLE x11. Genotypes (site c. 1987)8

30

 

Clonal isolates

 

 

Loci 1 2 3 4 5 6 7 8 9 10
AE 1 3 2/3 2/3 2/3 1/3 2/3 2/3 2/3 1/2 2/3
AE 2 1/2 2 2 2 1/2 1/2 2 2 1/2 2
AE 3 1 l 1 0 1 1 1 1/2 1 2
AE 4 I 1 1/2 1/2 1 1 1/2 1 1 1
AAP I 1 1 1/2 1/2 1/3 1/3 1/3 1/3 1/1 I
AAP 2 1 I 1 l 1 1 1 1 1 1
8E-2 1 2 0 1/2 1/2 0 0 i 0 2 1/2
8E-2 2 2 2 1/2 1/2 2 2 1/2 1/2 0 1/2
BE-Z 3 1/2 2 1 2 1/2 1/2 1/2 2 1/2 2
BE-2 4 2 1 1/2 1/2 1 0 i 2 0 2
BE-Z 5 1 1 0 1/2 1 1 0 1 I 1
BE-2 6 1 l 1 1 l 1 l 1 l 1
GDH 1 1 0 0 1 l 1 1 1 1 1
GDH 2 1/2 1 l 1 1 1/2 1/2 1/2 1/2 1/2
HK 2 2 1 1/2 2 2 1/2 2 2 2
B-HBDH 2 0 0 0 2 0 2 1 2 I/2
ICD l 0 1 1/3 1 2 3 1 2 I
LDH 0 0 1/2 1/2 0 0 0 i 0 0
LAP 1/2 1/2 2 2 1/2 1/2 1/2 1/2 1/2 1/2
ME 1 I 1 1/2 1 1 1/2 1 i l
PGM 1 1 0 1/2 1/2 1 1 1/2 0 i 0
PGM 2 1 I 1 l 1 1 l 1 1 1
6-PGD l 0 0 l 0 0 2 0 0 0
PE 1 1/2 1/2 1/2 3 1/2 2 2 1 1/2 1/2
PE 2 1/3 1/3 2 2 1/3 1/3 1/3 3 1/3 3
PE 3 1/3 1/3 2/3 2/3 1/3 1/3 2/3 2/3 1/3 2/3
500 1 2 2/3 1/3 1/3 2/3 2/3 1/3 2/3 2/3 2/3
500 2 2 1/2 1/3 0 2 1/2 1/3 1/2 2 1/2
LTD 1 1/2 1/2 1/2 2 1/2 1/2 1/2 1/2 1/2 0
LTD 2 I l 1 i 1 1 1 1 l 1

 

3 Abbreviations represent the loci coding for the various enzymes. the
numbers representing multiple forms of the enzyme. Alleles are numbered
from the most anode to the most cathod. Homozygotes are designated by

one and heterozygotes by two numbers; 0 represents a null allele.

TABLE x111. Site c (1987). Nei’s genetic distances.8

31

 

Clonal isolates

 

 

1 2 3 4 5 6 7 8 9 10
l - 0.416 0.621 0.571 0.178 0.298 0.487 0.380 0.243 0.294
2 - 0.475 0.629 0.241 0.243 0.522 0.322 0.431 0.351
3 - 0.394 0.543 0.570 0.434 0.562 0.693 0.620
4 - 0.650 0.660 0.534 0.570 0.773 0.589
5 - 0.184 0.398 0.316 0.210 0.345
6 - 0.456 0.379 0.174 0.411
7 - 0.638 0.491 0.520
8 - 0.459 0.158
9 - 0.395
10 -

 

a Null alleles included.

32

TABLE x1v. Statistics for genetic distance (1986) a

 

 

Site Mean genetic distance 1_SD
A 0.4213 1 0.151
8 0.5084 1 0.199
C 0.4522 1 0.208

 

One-way ANOVA : (for site A. B and C)

d.F. M.$.
Among 2 0.0729
Within 132 0.0340

F = 2.144 (NS)

 

aAbbreviations : 50. standard deviation; ANOVA. analysis of variance:
d.f.. degree of freedom: M.S.. mean square: F. F-test: NS. not
significant at the 0.05 level.

33

TABLE XV. Statistics for genentic distance (1987) a

 

 

Site Mean genetic distance 1 SD
A 0.4764 1 0.209
8 0.4644 1 0.168
C 0.4406 1 0.157

 

One-way ANOVA : (for site A. B and C)

dOfO ".8.
Among 2 0.0151
Within 132 0.0323

F a 0.4675 (NS)

 

aAbbreviations : 50. standard deviation: ANOVA. analysis of variance:
d.f.. degrees of freedom; M.S.. mean square: F. F-test; NS. not
significant at the 0.05 level.

34

TABLE xvi. Two-way ANOVA a

 

 

Source of variation df M.S. F
Site 2 MSI=0.0452 MSI/MS4=1.3373 NS
Year 1 M52=1.9818E-06 MSZ/MS4=I E-04 NS
Site x Year 2 MS3=0.0573 MSB/MS4=I.6953 NS
Experiment error 264 MS4=0.0338

 

a Abbreviations: ANOVA. analysis of variance: df. degree of freedom;
M.S.. mean square; F. F-test; NS. not significant at the 0.05 level.

3S

IIonozygote Heterozygote Ibnozygote

 

 

 

- III-II IIIIII
Monomer
IIIIIII iii-III
— -
Dimer III-III
— ——
—— -
Trimer """'
_
_ —
—-— _
—
Tetramer 'l'l'l'
_
- ——

 

 

Fig.1. Diagram of characteristic isozyme patterns expected in
heterozygotes in the case of enzymes which are nononérs.
diners. tricners or tetraners. The activities of the
isozymes formed in heterozygotes are 1:1 for monomers.
1:2:1 for diners. 1:3:3zl for triners. 1:4:6:4:1 for
tetramers and so on.

(from re£.10)

36

APPENDIX
The Nei’s standard genetic distance between two
populations X and Y is : D = -Logel. where I is the
noramlized identity of genes between X and Y with repect to
all loci. 1 = ny / Jny. Let x‘ and y‘ be the frequencies

of the ith alleles in X and Y. respectively. The probability

2 in

of identity of two randomly chosen genes is Jx={;x'
population X. while it is Jy=£y'2 in pOpulation Y. The

probability of identity of two genes. chosen at random. one
from each of the populations. is nye‘z_x'y'; then designate

Jx. Jy and ny the arithmetric means if Jx' J and ny over

Y
all loci. including monomorphic ones. respectively. if we
have the gene frequencies from both populations. the genetic
distance between these two populations can be calculated. If
populations X and Y have the same genefrequencies. then i =

1. D = 0: if X and Y don't have the same gene frequencies.

then I = 0. D =00.

"lllllilllllliililllli