FRAGMENTA MINERALOGICA ET PALAEONTOLOGICA

10. 1981 p. 19-26

The possibilities of quantitative evaluation in palaeontology presented on some Upper Oligocène floras

By

L . H A B L Y

(Received December 4, 1980)

A b s t r a c t : Researches of recent btocoenoses result In an ever increas ing number of

equations wich make possible to express the character is t ics of floras or faunas by m e ­

ans of figures. These can be divided into two groups: 1. semi-quantitative figures,

re ferr ing only to species and 2. quantitative figures re ferr ing also to specimens as

wt.i l . F r o m the f irs t group the Jaccard-coefficient, the SiJrensen-index and the K o c h -

index, from the second group Shannon's diversity-index, uniformity, divergence-

difference, as well as the comparison by means of H o r n ' s "overlap"-Index of three

U;iper Ol igocène f loras wil l be presented.

M A T E R LA L AND M E T H O D

The Many Formation around Tatabánya contains a relatively r i ch Eger ian macroflora. The

greatest number of remains came from B a r o m á l l á s hi l l between V é r t e s s z o l o s and Tatabánya near

to the E 5 highway. (F ig . 1) . It consists mainly of l e a f - i m p r e s B i o n s amounting to 2300 pieces of

about a hundred different species . The remains are embedded in clay-bearing sandstone, relatively

we l l -preserved , oxidized, of brownish-reddish colour.

T h e r e is a great number of wel l -preserved members of the Lauraceae family, a remarkable

number of the representatives of the Taxodiaceae family, mainly Taxodium dublum (Sternberg)

Heer . T h e r e is a significant number of Arctotert iary elements mainly Carpinus grandis Ung. as

well as Betula and Salix species . The flora Is a character is t ica l ly Upper O l i g o c è n e mixed f lora,

compris ing both Paleotroplcal and Arctotert iary elements. T h e i r present-day relat ives can be

found mainly in South-East A s i a , but a great number of them can be traced also in North A m e r i c a .

A s far as the climate is concerned it can be supposed to have been relatively warm subtro­

pica l , wich Is proved a lso by the relationship with the South-EaBt Asiat ic flora as well as by

some morphological features.

The other Eger ian flora has been found in Tatabánya near the T u r u l - c l n e m a . The assemblage

consisting mainly of leaves is embedded in a coarse-grained sandstone, giving a relatively poor

preservation: in many cases even the secondary veins cannot be c learly seen. T h e i r number is

about 230, with taxa-number 42. It shows s i m i l a r character is t ics to the previous flora but with

complete absence of needle-casts . A s to f lora relations and cl imate, s i m i l a r statements can be

made with not too significant differences. F o r example, the f lora of B a r o m á l l á s shows s imi lar i ty

mainly with that of South Japan and China, l ess s imi lari ty with the flora of Malaysia and Indo­

nes ia . The flora of Tatabánya resembles mainly that of the latter a r e a .

The third flora was found In Tarján from a Mghway-cut along the road to Tatabánya, and on

the excavation site near i t . T h i s Is a poorly preserved flora containing a s m a l l number of leaf

remains , dating also from Eger ian . L i k e the one in Tatabánya, it has not yielded any needle-casts

remains , either. A s far as flora relationship and climate are concerned, on the whole, it r e s e m ­

bles the previous ones ( H A B L Y 1977).

F i g . 1. Map of the localities

In the following possibil it ies of semiquantitative and quantitative evaluation wil l be presented with the afore-mentioned three f loras used as examples . The method wi l l be presented not as a unique one but as a possible one, applicable also in palaeontology.

Two biocoenoses can be compared by means of the J A C C A R D (1908) and S 0 R E N S E N (1948) Indices:

C K = N 1 + N 2 - C

K: Jaccard coefficient G: the number of the common s p é c i i in the two floras or faunas N^: the species number of the f irst flora/fauna Ng: the species number of the second flora/fauna

The Sirfrensen-index: 2n C =

C B : the S í í r e n s e n - i n d e x njij: the number of the common s p é c i i nj: the species number of the f irst flora nk: the species number o f the second flora

A s It Is B e e n , both equations operate only with total Bpecles number and the number o f the mutual s p é c i i . K and C 8 can range between O and 1. If the floras compared contain n o common s p é c i i , i t i s O, i f they agree completely, i t i s 1.

The following equation can be regarded as a variety of the Sjrfrensen-index:

C « i o o = ^ b " 100

c: the number of the common s p é c i i a: the species number of the f irst flora/fauna b: the species number of the second flora

Bes ides the comparison of two assemblages it i s also possible to give one common index for severa l f loras . This has significance if floras/faunas of different formations belonging to the same stage are compared, and the individual formations contain severa l foss i l -assemblages . In this case the Koch-index can be applied (in Z H I L I N 1974):

= 100 (T-S) k (n-1) S

I ^ : the Koch-index n: the number of the f loras/faunas compared S: the global species number in the floras/faunas being compared T: B 1 + S 2 + S 3 + + s n = the species numbers of the fl or as / faun a s .

The other group of indices character iz ing floras and faunas differs bas ica l ly from the above-mentioned ones. While it i s sufficient to consider the species number in connection with the J a c c a r d - , S<$rensen-, Koch- indices , with the following ones the specimen-number and the quan­tity are important.

A very important character of a biocoenose is the diversity , the quantitative analysis of which can be made with the best resu l t by means of the Shannon diversity-index (SHANNON & W E A V E R 1949). T h i s i s very sensitive but It i s independent from external (testing, sampling) c ircumstantes .

s nj nj

H " " - f = 1 T T • l o g 2 " n -

H ' ' : the Shannon diversity- index nj: the specimen number of the i - th species in the flora N: the global specimen number of the flora s: the species-number In the f lora ni

— : the relative frequency of the 1-th species

O S H " € log 2 s

The diversity i s closely related to equitability. T h i s demonstrates the relationship between spe­cimen-numbers and spec ies -numbers .

T i l »

J " = -r o ^ j " $ 1 l o g 2 S

J * ' : equitability H* ' : Shannon's diversity index loggS: the highest number of the diversity-Index (binary log of specie s-number)

If we substitue species numbers in the equation, the resu l t wi l l be species divers i ty . It i s possible to calculate diversity with higher taxonomic categories; even in case of relat ively rough c a l c u l a ­tions (genus and famil ia level) good resul ts can be obtained.

F o r comparison - besides the comparison of H' ' -values obtained independently of each other - the equation of diversity difference (Hdjff) can be applied. The higher its value is the farther the two floras are from each other with regards to divers i ty .

H d i f f * H t "

H - + H»'

H d i f f d l v e r s i t v difference

H j ' : the diversity index of the f irs t flora

Hg' : the diversity index of the second flora

P i + P i , P l

H t = - r - ^ - . iog 2 s

p } = : the relative frequency of the 1-th species in the f irst f lora

n i p' = T S " : the relative frequency of the i-th species in the second f lora

I N

The measure of the value of the fraction in the equation is bit/ individuum. I f we multiply by N we obtain the diversity of the flora: H p = H " . N; the measure unite is bit . Applying further the above equation we can compute the divers i ty difference of the three floras at the same t ime.

H " + H ' * + H ' ' H , . „ = - H. diff t 3

H t = 3 l°h 3

The Horn (HORN 1966) "overlap" equation was obtained through severa l formulae with the help of information theory.

o X + Y . loggXfY - X l o g 2 X - Y l o g 2 Y

R o : the Horn overlap value xi : the frequency of the 1-th species in the f irst f lora yj : the frequency of the i - th species in the second f lora X : the total of frequencies in the f irst f lora Y : the total of frequencies in the second f lora

The above methods grant possibility for a more objective evaluation, and for a s impler , quicker and more exact comparison of foss i l f loras and faunas.

BAROM ALL AS

TATABANYA

TATABANYA

TARJÁN

BAROM ALLAS

TARJÁN

7j V/,

F i g . 2 . Comparison of the three floras by means of semi-quantitative method. The tendency of s i ­mi lar i t ies is the same on the bas i s of J a c c a r d and Sjrfrensen-index. The greatest s imi lar i ty could be seen between the V é r t e B s z ő l ő s ( B a r o m á l l á s ) and Tatabánya, the least s imi lar i ty i s between the

V é r t e s s z o l o s ( B a r o m á l l á s ) and Tarján floras

R E S U L T S

Table 1 presents the Indices obtained by the semiquantitative calculation of three Upper O l i g o c è n e floras from Tatabánya basin. A l l the indices seem to indicate s i m i l a r i t i e s . In a l l cases the greatest s imi lar i ty could be seen between the V é r t e s s z o l o s ( B a r o m á l l á a ) and the Tatabánya floras whereas the least s imi lar i ty could be discovered between the V é r t e s s z ő l ő s ( B a r o m á l l á s ) and the Tarján f loras. This Is demonstrated by Figure 2.

Table 1

V é r t e s s z ő l ő s ( B a r o m á l l á s ) -- T a t a b á n y a

Tatabánya

Tar ján

V é r t e s s z ő l ő s ( B a r o m á l l á s ) -- T a r j á n

K C s C s l 0 0 \

0.22 0.3496 34,96

0.15 0.2352 23.52 13.8655

0.08 0.1272 12.72

Table 2 presents the values yielded by the quantitative evaluation of the three floras tested. It is to be seen that from the point of view of diversity the V é r t e s s z o l o s ( B a r o m á l l á s ) and the Tatabánya floras stand nearest to each other, while the least s imi lar i ty can be discovered bet­ween V é r t e s s z ő l ő s and Tarján f loras . Values in Table 2 are shown in F i g . 3 by the use of geo­metr ica l constructions. It i s interesting to note that although the value of H ' ' is the highest in the V é r t e s s z ő l ő s flora, the Tar ján flora reaches the highest point of its own. The dotted line indicates the averages, so it can be seen what i s above and below the average value.

Table 2

N s logs H " J " Hdiff Hp

V é r t e s s z ő l ő s 996 ( B a r o m á l l á s )

Tatabánya 104

Tarján 14

Average values 371.3

101 6.6578 4.8849

42 5.3920 4.5481

9 3.1691 2.9396

50,66 5.0726 4.1242

0.7336 —I cv 4865.36 iL g

0.8434 £ ° 473,00 in ©

0.9273 d J 41.15

0.8347

The overlap value calculated by means of the Horn equation re fers not to species but to genera.

V é r t e s s z ő l ő s ( B a r o m á l l á s ) Tatabánya : R q = 0.7099

Tatabánya T a r j á n : R q = 0.6657

V é r t e s s z ő l ő s (Baromál lás ) Tar ján : R q = 0.6602

It can be seen that the highest overlap value was attained at the comparison of the V é r t e s s z ő l ő s and the Tatabánya f loras . This agrees with the finding that the H^iff of these is the smal lest; so both methods proved that these two floras are the most s i m i l a r . If we compare these with the K and C 8 values obtained by means of the semi-quantitative method we find no contradiction. The character i s t ic values, indices, coefficients of the floras have a member of systematic regulari ty . Whether this relation is r e a l or imaginary can be decided by calculating the correlat ion. Of the examined character i s t ics the closest positive correlat ion is shown by H ' ' and l o g 2 s . There i s a

negative correlation between J " and log2S. A weaker positive correlat ion exists between H " and s, and there i s a poor negative correlat ion between H ' 1 and J ' ' . With such a poor sampling the negative correlat ion observed between H ^ f f and R 0 can also be registered as poor.

°9 s BARQMÁLLÁ; > 1 "ATABÁNYA TARJÁN

logs •TT"

°9 s

1 logs •TT"

J' J'

BAROMÁLLÁ

TATABÁNYA

TATABÁNYA

TARJÁN

3AROMÁLLA

TARJÁN

s

F i g . 3 Comparison of the O l i g o c è n e floras by means of quantitative method. The first line of the figure demonstrates the diversity of floras and shows the rate between diversity and number of spec ies . The dotted line indicates the average values of the three f loras. The second line of the figure shows the equitability of the floras and the difference of the average equitability. The third

line demonstrates the diversi ty difference of the compared floras

DISCUSSION

The quantitative evaluation i s relat ively r a r e l y used In palaeontology. Many scientists do not attach great importance to specimen numbers and reason that it i s purely accidental how many

pieces are preserved from something. However, it is also accidental what remains at a l l . It i s n a ­

tural in palaeontology to operate w i t h e r r o r l imits; at any rate , t h i s does -not justify committing

further e r r o r s . On the bas is of the principle "much from many and little from few" there remained

more of thoBe species that were more numerous than from those existed in smal l er numbers.

During the history of the E a r t h may of course have occurred such processes , as the dissolution of

calcite skeleton, w h i c h fundamentally change the original conditions. In such cases the method

should be applied reasonably; its mechanical application apparently leads to ser ious mistakes .

The character i s t i c s and the surroundings of biocoenoses a r e represented most distinctly by

the prevail ing s p é c i i . In a given environment obviously those s p é c i i spread over a large terr i tory

for which the given conditions are optimal. Those represented by just a few specimens are probably

confined to micro-c l imates ; they are r e l i c s found shelter in favourable ecological niches or r e p ­

resent elements springing up later, when c ircumstances change. In case of floras the application

of the quantitative method has been attacked with the' argument that when a great number of l e a v e B

of the same tree are found, these are regarded as individual units when analysing the foss i l - f lora .

T h i s , however, i s excluded in the case of continental plants in clayey-sandy l ittoral sediments: the

leaves having necessar i ly been subject to transportation; chance of finding a great number of the

leaves of the same tree deposited in the sediment i s reduced to minimum. It must however, be

reckoned with in case of s tr ic t ly autochthon f loras .

Divers i ty Is a character i s t ic feature of biocoenoses. T h i s notion has long been recognised

also in palaeontology, but when comparing severa l biocoenoses it needs computations to determine

exactly which of them Is more d iverse . The determination of diversity makes it possible to gather

a great deal of valuable information about biocoenoses. The more diverse an assemblage the more

stable It i s . T h i s I s natural: if, for example, there are only two species one of which perishes in

the course of some negative effect the change w i l l be 50% whereas in case of an assemblage with

one hundred species the change wi l l be only 1%.

The application of t h i s method yields great help in paleoblogeographical studies. Conclusions

drawn from the comparison of f loras/faunas of larger t err i tor i e s may be subjective and therefore

different. Therefore it i s useful i f the author, in addition to his or her own opinion, gives a

number of objective f igures. The comparison of these is much quicker, more exact and s i m p l e r .

A s very few authors give specimen-numbers when analysing foss i l floras and faunas the Indices

cannot be calculated afterwards except by means of the semi-quantitative method on the basis of

species l i s t s . It would be beneficial to perform the qualitative evaluation when working on

new f loras/faunas, as wel l as when rev is ing old ones.

S U M M A R Y

The Upper O l i g o c è n e (Egerian) Many Formation of the Tatabánya basin yielded macrof lora in

three p laces . The floras show s imi lar i t i e s of composition. The largest of them ( V é r t e s s z o l o s )

contains also Taxodiaceae and Pinaceae, the other two only Clnnamomum and deciduous r e m a i n s .

A l l the three floras Bhow the mixing of Paleotropical and Arctotert iary elements. They show only

m i n o r differences as to f lora families since they belong to f loras of the same age and of adjacent

t err i tor i e s . They are related mainly to South-East A s i a n , in l e B s e r measure to North-American

f loras . The composition of the f lora suggests subtropical c l imate s i m i l a r to that of South-East

A s i a today. To character ize each flora, as well as to compare the three, indices have been p r o ­

posed using se ml-quantitative and quantitative methods. The equation of J a c c a r d , Koch, Sjirensen,

Shannon and Horn have been used. The resul ts are visually demonstrated by the charts Indicating

that the floras of V é r t e s s z o l o s ( B a r o m á l l á s ) and those of Tatabánya are the nearest re la t ives . L e s s

s imi lar i ty has been found between the floras of Tatabánya and T a r j á n , whereas the floras of V é r ­

tesszolos and Tar ján show the least s i m i l a r i t y .

The method of quantitative analysis has been widely used in recent l i terature, but it i s not

favoured in palaeontology. One of the reasons for this i s that such evaluation demands full inves t i ­

gation (each specimen has to be taken Into consideration). The other Is that the accidental nature

of fossllization r a i s e s doubts about the usefulness of the method. Selective fossllization i s such a

factor indeed, that cannot be reconstructed, but this alone does not provide good reason to

disregard real i t ies in favour of (further) subjective opinions. The method of course is only one of

the possibi l i t ies , yet i ts wider application in palaeontology might be profitable. It would probably

promote the advancement of palaeontology, it could facilitate the quicker and more exact c o m p a r i ­

son of floras/faunas both in time and space .

R E F E R E N C E S

H A B L Y , L . (1977): A Tatabányai medence f e l s o - o l i g o c é n korú flórája. - Doktori é r t e k e z é s , E L T E , Budapest, (manuscript)

HORN, H . S . (1966): Measurements of "overlap" in comparative Ecological Studies. - The A m e r i ­can Natura l i s t . , 100: 419-424.

J A C C A R D , P . (1908): Nouvelles recherces sur l a distribution florale. - B u l l . S o c . V a u d . S e i . N a t . , 44: 223-270.

SHANNON, C . E . & W E A V E R , W. (1949): The mathematical theory of communication. - U n i v . o f Rl inois P r e s s , Urbana .

S 0 R E N S E N , T . (1948): A method of establishing groups of equal amplitude in plant sociology based on s imi lar i ty of species content, and its application to the analyses of the vegetation on Danisch commons. - Kongel.Dansko Vidensk .Se l skat B io l .Shr i f t er , _5(4): 1-34.

Z H I L I N , S . G . (1974): The T e r t i a r y F l o r a s of the Plateau Ustjurt (Transcasp ia) . - L e n i n g r a d . . 1-122.

Author's address: D r . L i l l a H A B L Y

Botanical Department Hungarian Natural History Museum H-1097-Budapest Könyves Kálmán körút 40. Hungary