Transfer functions for estimating paleoecological conditions (pH) from East African
diatoms
F. Gassel & F. Tekaia 2
l Ecole Normale Superieure, 92260, Fontenay-aux-Roses, France
2 Laboratoirede Statistique, 4 Place Jussieu, 75230, Paris Cedex 5, France
Keywords: paleolimnology, diatoms, East Africa, transfer functions, pH-indicators
Abstract
Our purpose is to establish the quantitative relationship between recent diatom floras and ecological
parameters, in order to extrapolate the results to the past. The parameter pH is here considered as an
example.
This work is based on the study of about 160 diatom samples from East Africa and of their corresponding
biotopes. We propose some statistical methods to interpret the data.
Correspondence analysis allows us to define the pH-indicator species. The regression calculations allow
pH values to be calculated using the percentage of the diatom species in a sample.
Introduction
Material studied and data collection
Our goal is to use fossil diatoms to quantify
paleoecological conditions in East African lakes.
This objective necessitates the following steps:
a) studying the relationships between recent diatom communities and their corresponding biotopes
of a statistically representative number of samples
taken from East Africa;
b) establishing an equation (transfer function)
which would allow the value of an ecological parameter to be calculated, from the relative percentages of diatom species in a sample;
c) extending the correlation to fossil samples
once transfer functions are established for recent
diatoms.
This paper is intended to demonstrate the methods of approach used rather than to present final
results. The parameter pH is exemplified since so
far it appears to be the environmental factor indicated best by diatom floras.
East African lakes are numerous and diversified.
During the Quaternary they underwent wide fluctuations in water-level and water chemistry which
have been recorded by changes in fossil diatom
assemblages (Richardson & Richardson 1972;
Holdship 1976; Harvey 1976; Richardson et al.
1978; Gasse 1975, 1977, 1980).
The modern samples were collected from 98 stations (lakes, swamps, peat-pogs, rivers and thermal
springs) situated between 12 N and 12 S latitude,
26 ° E and 43 E longitude, and ranging from 155 m
below sea-level to 4 000 m.a.s.l. Detailed description of the localities will appear elsewhere (Gasse
1983). In most cases, pH, conductivity and temper'ature were measured in the field when the diatoms
were collected. The pH ranges from about 5 to 10.9,
and the conductivity from about 10 to 50 000 S
cm 1. Chemical analyses of the corresponding waters were published by Talling & Tailing (1965),
Tailing (1976), Kilham (1971), and Gasse (1975).
The water temperature varies from a few degrees
above zero in the mountains to 35 C in the deserts.
Hydrobiologia 103, 85-90 (1983).
© Dr W. Junk Publishers, The Hague. Printed in the Netherlands.
86
It reaches 55 C in thermal springs.
Two principal chemical types of water can be
distinguished: the sodium-bicarbonate-carbonate
type, corresponding to the majority of the samples,
were the factors pH, alkalinity and conductivity are
strongly and positively correlated between themselves, and the sodium-chloride type which has a
pH near 7.
The following analyses are based on 156 contemporary diatom samples including phytoplankton,
periphyton and mud. For each sample, a systematic
inventory was established and the percentage of
each taxon was evaluated by counting 300 to
1000 valves distributed on four slides. 579 species
and varieties were identified. The check-list and
autecological data will appear elsewhere (Gasse
1983).
Statistical methods used
As considerable progress has been made in the
establishment of transfer functions between microorganism assemblages and ecological parameters
(Kipp 1976; Roux 1979; Bryson& Kutzbach 1974),
we attempt here to apply such methods to diatoms.
Correspondenceanalysis (CA)
The CA method (Benzecri 1973; Lebart et al.
1977; Benzecri 1980) aims at synthethizing the information contained in a data matrix and visualizing the relationships between the elements of two
sets i (e.g. taxa percentages) and j (e.g. samples).
The main properties and examples for defining diatom assemblages are given by Gasse & Tekaia
(1979, 1982).
Table I
Table 3
classes pH
pH,
species
I
i
pHZ pH3 pH4
- -
kc
s~~~I
Table 2
samples
1
pH I
PH
j
n
I
pH
22
~0
PH3
0
pH4
4
0
Table 4
Table 5
classes pH
pH
pH 2 pH 3 pH
4
,[
species
i
__
-
s~~~I
Tables 1 5. Tables submitted to correspondence analysis (CA).
k!
87
We present here the types of tables which have
undergone factor analysis and indicate for each table
whether it is considered as a principal table (defining a factorial axis), or as a supplementary element
of another table. The supplementary element does
not participate in the definition of the axes, but is
placed with regard to the axes defined by the principal table.
In Tables 1-5, n and s refer to the number of
samples and species, respectively. Table 1 is the
initial table where the intersection of the row i and
the column j is the percentage of species i in the
sample j. In Table 2, sample j is also defined by its
pH. One can consider breaking down this parameter into classes as follows: pH,, 5-6.9 (37 samples);
pH 2, 7-7.9 (36 samples); pH 3, 8-8.6 (38 samples);
pH 4 , 8.7-10.9 (37 samples).
If the pH of sample j is equal to 5.5 (class pH,),
the value is coded as 1000, meaning that this parameter is I in this class, where it is found, but 0 in
all others. Table 2 will be placed as supplementary
to Table 1.
Table 3 is constructed from Table 1. If kic is
designated as the value found at the intersection of
the species i and the pH class c, ki, is the sum of the
percentages pij of species i in the samples j situated
in the class c of pH. Table 3 will be analyzed as a
principal table. Table 1 is added to it as the supplementary table.
Table 4 is the table of presence-absence; it is
obtained from Table I by replacing the values that
are not 0 by . If the species i is present in the
sample j, pij = , if not pij = 0.
Table 5 is constructed from Table 4 in the same
manner as Table 3 from Table I. In this case, ki is
the number of times that the species i is present in
the samples found in the class c of pH. This table
will be analyzed as a principal table and Table 4 will
be added to it as a supplementary element.
In our case, the number of species is high (579).
Therefore, we cannot carry out regressions from
Table I because it would give illusory results. It is
known that the quality of a regression is based on
the coefficient of multiple correlation R; the more
this coefficient approaches 1, the better the regression. In cases where the independent variables are
numerous, a high coefficient is obtained even if
some are independent of the variable to be explained. It is therefore necessary to reduce the
number of independent variables so that a significant result can be obtained. To do this a CA of the
initial table (Table 1) is carried out (Cazes 1978;
Roux 1979) and the 579 species are reduced to a
number of factors. Each sample is defined by its
co-ordinates on the factors which are now considered as the independent variables. An advantage
of proceeding in this manner is that the new variables are not correlated between themselves, and the
problem of an unstable coefficient of multiple
correlation is avoided. On the other hand the inconvenience of this procedure is that it involves a
table of 7 dimensions (if 7 factors are kept), and
only a part of the initial formation is retained. It is
necessary to ensure that the most important part of
the information has been kept on the factorial space
obtained. It is for this reason that we have analyzed
Table 3 with Table I as a supplementary table. CA
of Table 3 defines only 3 factors, and allows all the
information to be maintained.
Establishing a transferfunction
Starting with the results obtained from CA and
the regression analysis, it is possible to establish a
transfer function which is represented by thd following formula:
S
y(j) =
aipij +
ej
Regression analysis
The goal of regression analysis (Cazes 1978; Benzecri 1978) is to establish a transfer function that
uses the distribution of the species in a sample to
determine the approximate value of an ecological
parameter. The species play the role of independent
variables, and the ecological parameter which is to
be estimated is the dependent variable.
where: s is the number of species
YO) is the estimated value of the parameter y
in sample j
Pij is the percentage of the species i in the
sample j
y is the mean of the parameter y for all the
samples
88
ej
ai
ai 1 -
Results
is the difference between the estimated
value and the measured value of the
parameter y in sample j
is the coefficient of species i
1
b!
b2
X/Xl GI (i) +
100
'kI
dAX2
pH-indicatorspecies
b3
G2 (i) + dAX3
G3 (i)
where A1, X2, X3 are the relative inertias, respectively, to the I st, 2nd and 3rd factorial axis constructed
by CA of Table 3.
Gl (i), G2 (i) and G3 (i) are the coordinates of the
species i on the I st, 2nd and 3rd factorial axis from
Table 3, respectively.
b l , b2 and b3 are the regression coefficients obtained from Table 3 with Table I as the supplementary table.
The selection of indicator species is carried out by
treating the data with CA. We considered the species percentages and analysed Table 2 followed by
Table as a supplementary table (CA-percentage).
We eliminated those species which were present in
less than 3 samples and those with a percentage of
less than 5% in any sample. The CA was then conducted with 245 taxa and 156 samples. Figure
shows the projection of the species points and pHclasses on the factorial plane 1-2. The species
characterizing each class of pH are situated close
to the corresponding pH point. In Table 6, we have
selected some of the species which have a strong
influence on the definition of the factorial axes.
AXIS 2
109 I
3708 4040
4
4
1.L
620
is907
2903
Lo10
12
391291
ty!Ly
2503 o
101 3520
5338 2935
2507
1630
~93
4501
5325 2630
2630
502
4030
15325
1
\
~~~~~~~~~1907
\104
5409 34
3910 34
3913742
391
203748
2908
2610
640 1655
3204
4203 3756
2904
3765
1401 0
3201
470
37
32606
5424
EZ.
3810
3938
~
,629
......
___1
1904
1917 19182611
52- \
;.
604208
70
370
370139
926 39065
325
3701
11~ ~~~~
4_____3925
1301
1912 5407
5003
~~~~~pHCLASSES:~
p5304
pH CLASSES
: pH1
5-6.9
pH2 : 7-7.9
pH3 8-8.6
pH4 :8.7-10.9501
8.7-109
pH4
360 : DIATOMSPECIES,NUMERICAL
CODE
360 :pH-INDICATOR
2
295
9
362
361
36
366
361
37
37'
37
371
393
394
~~~~~~~~~~~~~~~~~~~~~~4808
L931
4022 4044 3730
2401
241
1
351 5430 /
3932
4602
___
___
3922
3911
375
5005
4610
904
3654
4036 3507
B2
1403
607
~~~~~~~~-540142
2305 3728
32 2403
5401
/
1 6 365
/
--
AXIS
394
~~~~~~~~~~4
2
4614 3625 2613
32613
3923
361
\3712
3511
102 2915
3
4017
42
422
42
6-- 4003 393640353935 5417
3608
4240
3518
4224
25 I1
H
2916 3508
3914
1620N 3
3504 2912
3631
3717 3762
3T
1939
01
2930
2612 3501
3501
3647 -l
207 J
K360
37i 23~03
30 3731
36
3506 3509 1002
-764
1670\ 3616 901
16351690
0
3940 - 2404 3901 3740 /
5335\
3671
3916
3512 \
=
335
/
2l'5
302 \302/
3513
3744
302
3j
13 30
301
/
_.
25
_~~~~~~~~~~~0
Fig. 1. Correspondence analysis (CA) based on Table I (initial table, 245 taxa, 156 samples), and Table 2 (supplementary table,
156 samples, 4 pH classes). Projection of the species points and pH classes on factorial plane 1-2. The underlined species are those having
an important contribution in the definition of the factorial axes. Their taxonomy is given in Table 6. On the right, the points
corresponding to the species indicated in the vertical column were clustered round point pH ,.
89
Table 6. pH-indicator diatoms in East Africa.
pH
.
(4
<
U
pH
pH
:
<
U
pH
: 5 6.9
Pinnularia graciloides
Pinnulariaappendiculata
Pinnulariaobscura
Pinnulariamicrostauron
Pinnulariacardinalis
Eunotia praerupta
Eunotia af. pseudoveneris
Melosira distans v. africana
Cymbellafonticola
Navicula bryophila
Navicula subtilissima
Navicula tantula
Stauroneis nana
Surirella ovata
Gomphonema olivaceum
Diploneiselliptica
near 7
Pinnulariatropica
Pinnulariaacrosphaeria
Pinnulariaborealis
Eunotia lunaris
Eunotiaflexuosa
Cocconeis thumensis
Stauroneis anceps
Cocconeis diminuta
Nitzschia linearis
Nitzschia umbonata
Navicula perpusilla
Achnanthes minutissima
Navicula symmetrica
Amphora tenerrima
Mastogloia elliptica
Pinnulariainterrupta
Nitzschia kutzingiana
: 7-7.9
Synedra acus + v.
Cyclotella stelligera
Gomphonema parvulum
Navicula salinicola
Navicula iranensis
Navicula cryptocephala
Nitzschia elegantula
Nitzschia palea
Melosira distans
Melosira varians
Amphora coffaeaformis
Melosira agassizii
Fragilariapinnata
: 8 8.6
Melosira italica+ v.
Melosira granulata
Melosira nyassensis
Fragilariabrevistriata
Fragilarialeptostauron
Un
U
Amphora ovalis
Melosira granulatav. angustissima
Epithemia zebra
Cocconeisplacentula
Nitzschia amphibia
Campylodiscus clypeus
pH
near 8.6
Stephanodiscus astraea
Rhopalodiagibba
Synedra rumpens v. neogena
Nitzschia lancettula
Nitzschiafonticola
Fragilarialapponica
Fragilariaconstruens
Fragilariapinnatav. trigona
Stephanodiscusdamasii
Stephanodiscus hantzschii
Synedra berolinensis
Nitzschiafrustulum
Cyclotella meneghiniana
Chaetoceros muelleri
pH
: 8.6-10.9
Anomoeoneis sphaerophora+ v.
Rhopalodia gibberula
Cyclotella ocellata
Epithemia argus
Nitzschia subrostrata
Nitzschia vitraea
Nitzschia sigma
Nitzschia estohensis
Nitzschia latens
Nitzschia pusilla
Anomoeoneis costata
Navicula damasii
Navicula irregularis
Navicula elkab
Thalassiosirafaurii
Thalassiosirarudolfi
Cyclotella iris
e
cn
<
These species seem to display a clear preference
for a given pH or pH class. If they are abundant,
and if several taxa characteristic of the same pH
class are associated in a sample, they can be considered as good pH-indicators for the investigated
area.
A CA taking into account the presence-absence
of taxa was also carried out. Most of the species
situated around the pH l point in Fig. I also characterize this class by their presence. But the effects of
pH above 7 do not show up clearly. Many species
are able to tolerate a wide range of pH, but the
90
species preference, deduced from the CA percentage, is a more sensitive indicator than the species
tolerance.
Transferfunction
We have carried out regressions using the methods described above, and successively considered
presence-absence (CA with principal Table 5, supplementary Table 4) and species percentage (CA
with principal Table 3, supplementary Table 1) situations. The coefficients of multiple correlation,
calculated by the method of least squares, are
R = 0.745, and R' = 0.857, respectively. The best
result is obtained by taking into account species
percentage.
We applied the transfer function established
above to the 156 recent samples. The difference
between the estimated values and the measured
values is <±0.3 in 43% of the cases, <±0.5 in 65%
of the cases, <± 1.0 in 90% of the cases.
Large differences (<1.2) are observed in only two
cases which correspond to the highest measured
values (10.3, 10.9) that were underestimated by our
calculation.
Before using the transfer function on fossil samples the stability of the formula must be tested by
applying it to new modern samples. In addition
other improvements might be added; we are especially hoping to reduce the number of taxa necessary in its application.
Acknowledgements
We are grateful to Dr. J. Talling, Professor
R. B. Wood, Professor J. Kalff, Dr. P. Kilham, and
Dr. F. A. Perrott for having collected and sent numerous recent diatom samples. We would also like
to thank Professor J. P. Benzecri for his criticism
and comments. This work was supported by the
Centre National de la Recherche Scientifique and
the Ecole Normale Superieure de Fontenay-auxRoses.
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