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Quantitative Untersuchungen an Rhaetina Gregaria (Suess) (Brachiopoda) 3-35 © Biodiversity Heritage Library

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Quantitative Untersuchungen an Rhaetina Gregaria (Suess) (Brachiopoda) 3-35 © Biodiversity Heritage Library ZOBODAT - www.zobodat.at Zoologisch-Botanische Datenbank/Zoological-Botanical Database Digitale Literatur/Digital Literature Zeitschrift/Journal: Zitteliana - Abhandlungen der Bayerischen Staatssammlung für Paläontologie und Histor. Geologie Jahr/Year: 1974 Band/Volume: 3 Autor(en)/Author(s): Klören Christoph Artikel/Article: Quantitative Untersuchungen an Rhaetina gregaria (Suess) (Brachiopoda) 3-35 © Biodiversity Heritage Library, http://www.biodiversitylibrary.org/; www.zobodat.at 3 ZITTELIANA 3 3—35 München, 1. 10. 1974 Quantitative Untersuchungen an Rhaetina gregaria (Suess ) (Brachiopoda) Von CHRISTOPH KLÖREN1) Mit 31 Abbildungen und Tafeln 1—5 Zusammenfassung Am Beispiel einer rätisdien Terebratuliden-Fauna 5. Die Bildung von Quotienten y/x oder x/y (wenn (Bradiiopoda) werden quantitative Untersuchungs­ y = ax), bzw. nach Translation von Originaldaten techniken diskutiert und durchgeführt. die Bildung von Tangens oder Cotangens, ist dann gleichermaßen sinnvoll, wenn eine Schichtung der Methodische Ergebnisse Population nach dem relativen Alter nicht vorge­ 1 . Die für eine optimale Stichprobe geltenden Homo­ nommen wurde. Erfolgte eine Schichtung, so sind genitätskriterien können im Rahmen paläontologi- die Daten, die das relative Alter repräsentieren, im scher Stichproben nur näherungsweise erfüllt wer­ Nenner des Quotientenbruches zu führen. den, da die Inhomogenität bewirkenden Faktoren 6. Die Schätzung von Korrelationskoeffizienten für in Ausmaß und Richtung ihrer Wirksamkeit nur die ontogenetisch veränderten Merkmalspaare einer noch theoretisch, nicht aber konkret und damit eli­ Population liefert keine sinnvoll interpretierbaren minierbar zu erfassen sind. Ergebnisse. 2. Werden zum Zwecke der formalen Ausschaltung der ontogenetischen Variabilität aus den Indivi- Faunistische Ergebnisse duen-Daten (x u. y) einer paarigen Meßreihe Quo­ 1 . Die analysierten Individuen gehören den Arten tienten y/x gebildet, so sind diese vom ontogene­ Rhaetina gregaria (Suess ) und Rhaetina pyriformis tischen Zustand der Daten liefernden Individuen (Suess ) an. unabhängig, wenn das mittlere relative Wachstum der Population einer Geradegleichung der allge­ 2. Beide Populationen sind als „life assemblages“ im meinen Form y = ax folgt. Sinne Boucot ’s aufzufassen. Quotienten, die aus den Individuendaten einer Po­ 3. Die qualitative Differenzierung der beiden Popula­ pulation gebildet werden, deren relatives Wachstum tionen gelingt bei Individuen ab etwa 14 mm Län­ durch die allgemeine Gleichung y = ax + b oder ge. Eine Unterscheidung kleinerer Formen ist nur y = ax — b beschrieben werden kann, sind vom formal auf quantitativem Wege durchführbar. ontogenetischen Zustand der Daten liefernden Indi­ 4. Der Brachialapparat der Individuen von Rhaetina viduen abhängig. Solche Quotienten liefern daher gregaria (Suess ) erfährt eine Metamorphose. keine sinnvoll interpretierbaren Verteilungen. 3. Populationen, die durch Geraden der allgemeinen 5. Im Anschluß an die Metamorphose des Brachial­ Form y = ax + b bzw. y = ax — b beschrieben apparates von Rhaetina gregaria (Suess ) spaltet werden können, müssen durch Translation der Ori­ sich die Population in zwei quantitativ ermittelte ginaldaten in die allgemeine Form y = ax gebracht Teilkollektive auf, die sich zahlenmäßig etwa wie werden. Die aus den translatierten Originaldaten 1:1 verhalten. Es wird Sexual-Dimorphismus ver­ zu bildenden Quotienten sind als Tangens-Werte mutet. aufzufassen. 6. Alle gemessenen Daten, bzw. die aus ihnen errech- 4. An Populationen, deren mittleres relatives Wachs­ neten Kennwerte, haben primär nur Gültigkeit für tum einer gekrümmten Linie folgt, ist Schichtung die fossile Fauna, von der sie genommen wur­ dermaßen nach dem relativen Individualalter (z. den. Sie können, müssen aber nicht den quantitati­ B. x) vorzunehmen, daß die Schichten Teilabschnit­ ven „Zustand“ der Fauna vor ihrer Einbettung und te annähernd linearen Wachstums darstellen. Fossilisierung wiedergeben. ') Dr. Ch . Klören , 810 Blvd. Campbell, Chibougamau, P. Q., Canada. © Biodiversity Heritage Library, http://www.biodiversitylibrary.org/; www.zobodat.at 4 Summary Using a Rhaetian Terebratulid fauna (Brachiopoda) as an 5. The construction of the quotients y /x or x/y (if y = ax), example, quantitative investigation techniques are discussed or respectively the construction of tangents or cotangents and applied. after transposing original data, is equally correct if the grouping of the population according to relative age is Theoretical Results not undertaken. If the data, representing relative age 1. The criteria of homogenity in obtaining an optimal are grouped, they are placed in the denominator of the random sample can only be approximately fulfilled in fraction. the framework of paleontological random sampling, be­ 6. The evaluation of correlation coefficients for the onto- cause the factors which produce inhomogenity, as far as genitically changed characteristic pairs of a population their effectivity (dimension and direction) is concerned, do not deliver rationally interpretable results. can only be realized theoretically, but cannot be concre­ tely eliminated. Faunistical Results 2. The quotient y lx, constructed from the individual data 1. The analysed individuals belong to the species Rhaetina (x and y) is independent of the ontogenetic state of those gregaria (Suess ) and Rhaetina pyriformis (Suess ). individuals as long as the average relative growth of the 2. Both of these populations are to be considered „life population adheres to a linear equation having the gene­ assemblages" after Boucot . ral form y = ax. When the relative growth of a popu­ lation can be described by the general equation y = ax 3. Qualitative différenciation of individuals larger than + b or y = ax —b, the quotients, constructed from data about 14 mm is possible in both populations. Smaller derived from the individuals, are dependent upon the forms can only be distinguished by formal quantitative ontogenetic state of development of the individuals de­ means. livering the data. Therefore, such quotients do not re­ 4. The brachial apparatus of Rhaetina gregaria (Suess ) un­ flect rationally interpretable distributions. dergoes metamorphosis. 3. The original data of populations, which can be described 5. Following the metamorphosis of the brachial apparatus by the general equation y = ax + b or y = ax —b, of Rhaetina gregaria (Suess ), this population splits up must be transposed into the form y = ax. The quotients into two, quantitatively distinct, collectives in a 1 : 1 which are formed from the transposed original data are proportion. Sexual dimorphism is supposed. to be considered as tangent values. 6. All measured data, and respectively the index values 4. When the average relative growth describes a curve, the calculated there from, have validity only for the fossile population is to be grouped according to the relative age fauna from which they were derived. These data may, of the individuals (e. g. x), so that the single groups but must not necessarilly, reflect upon the quantitative approximately represent linear growth. state of the fauna before its burial and fossilisation. Inhalt Vorwort ........................................................................................................................................ 5 1. E inleitung................................................................................................................................... 5 2. M e th o d ik ................................................................................................................................... 6 2.1 Homogenität .................................................................................................................... 6 2.2 Das relative W achstum ..................................................................................................... 9 2.3 Q u o tie n te n ......................................................................................................................... 10 2.4 T a n g e n s .............................................................................................................................. 11 2.5 Nichtlineares relatives Wachstum im Rahmen des tg -K o n zep tes .............................. 12 2.6 Test auf Normalverteilung ........................................................................................... 14 2.7 Zerlegung von Misch Verteilungen ................................................................................. 15 2.8 K o rrelatio n ......................................................................................................................... 15 3. Das qualitative Erscheinungsbild der Terebratuliden-Fauna ............................................. 16 3.1 Rhaetina gregaria (Suess ), 1854 ...................................................................................... 16 3.2 Rhaetina pyriformis (Suess ), 1854 ................................................................................. 17 4. Ergebnisse der quantitativen Analyse ................................................................................. 18 4.1 Rhaetina gregaria (Suess ), 1854 ...................................................................................... 18 4.1.1 Die Häufigkeiten der Stadien des relativen A lte r s ............................................. 18 4.1.2 Das relative Wachstum von Dicke und Breite der G eh ä u se ............................... 18 4.1.3 Das relative Wachstum von Höhe und Breite
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