Paleontological Journal, Vol. 36, No. 2, 2002, pp. 121-130. Translated from Paleontologicheskii Zhurnal. No. 2, 2002, pp. 3-13.

Original Russian Text Copyright © 2002 by Markov.

English Translation Copyright © 2002 by MAIK "Nauka/Interperiodica" (Russia).

Mechanisms Responsible for the Increase in the Taxonomic Diversity in the Phanerozoic Marine Biota

A. V. Markov

Paleontological Institute, Russian Academy of Sciences, Profsoyuznaya ul. 123, Moscow, 117997 Russia Received October 2, 2000

Abstract—Taxonomic diversity dynamics is traditionally interpreted using exponential or logistic models of diversification, both of which are based on the assumption that the rate of origination (and sometimes also the rate of extinction) depends on the level of taxonomic diversity. Paleontological data, however, give inadequate support for this assumption. Therefore, an alternative model is suggested: the generic origination rate is sto­chastically constant and does not depend on the diversity level; genera differ in their vulnerability; the extinc­tion probability for each genus during each time interval depends on its vulnerability only. Apparently, the most important factor of the increase in diversity in marine biota during the Phanerozoic was a stepwise increase in the mean generic durations. There were four such steps: Cambrian, Ordovician-Permian, Mesozoic, and Cen-ozoic. This stepwise increase in generic durations was partly due to the successive replacement of dominating groups, but to a larger extent, it was due to the generic durations that increased within each group at each suc­cessive step.

INTRODUCTION

According to paleontological data, the generic diversity of marine biota increased during the Phanero­zoic. This increase is clearly traceable in the Ordovi-cian and Meso-Cenozoic, with a pause in the Silurian-Permian. Like any quantitative rule based on the fossil record, this increase could be partly artifactual. Of sev­eral objections raised by skeptics, one can mention the unequal completeness of different parts of the record and also the "pull of the Recent" effect (Raup, 1979). The latter means that the modem biota is studied better than those of the geological past. Due to this fact, the durations of existence in many genera surviving up to the Recent appear to be artificially overrated. For exam­ple, a modem abyssal genus known to be a fossil from the only Late Cretaceous find would be interpreted as having existed throughout the Cenozoic. However, if the modem biota is known with the same degree of completeness as the fossil, this genus should be consid­ered as being extinct in the Late Cretaceous.

Until more complete databases containing informa­tion about the time intervals where each genus is really recorded are created, we cannot judge to what degree the Meso-Cenozoic diversity increase depends on the pull of the Recent.

It is easy to prove formally that the incompleteness of the fossil record and such effects as the pull of the Recent are theoretically able to distort the real evolu­tionary patterns and diversity dynamics in almost any way, especially assuming that completeness of different parts of the fossil record and other distorting factors cannot be estimated quantitatively or are unknown. In this case, any effective numerical analysis of paleonto­logical data becomes impossible.

Over the last three decades, the reliability of numer­ical estimates of the diversity of fossil organisms was widely and actively discussed in the literature. No one point of view prevailed, but, nevertheless, most experts agree that the fossil record is representative enough to demonstrate the main trends ofbiotic evolution, includ­ing numerical ones (Raup, 1991; Benton, 1999; etc.).

As for the general increase in taxonomic diversity during the Phanerozoic, it is accepted as real by most authors, and even a "rule of increasing biospheric diversity" was formulated (Alekseev, 1998). At the same time, the actual magnitude of this increase remains unknown. Thus, Sepkoski (1994) analyzed dif­ferent models describing the correlation of the studied part of the fossil record and the biotic diversity that actually existed in the past and concluded that, at present, we are unable to decide if the diversity of spe­cies of marine biota in the Cenozoic increased by an order of magnitude relative to the Paleozoic or by 1.5-2 times only.

In this paper, we analyze the increase in generic diversity of the Phanerozoic marine biota as shown by the fossil record. We try to find its causes and mecha­nisms, not examining in detail the problem of a possible correlation of this observed increase with the actual one. We take into account that (1) most experts agree that the fossil record as a whole reflects adequately the real history of biota and (2) even if the apparent biotic diversity increase in the Phanerozoic is artifactual and there was no actual increase; nevertheless, it is useful to know what the components of this integral artifact are.

Before turning to the analysis of the models used to describe and explain general trends in the taxonomic diversity dynamics, it is necessary to point out some important features of this dynamics that are often not taken into consideration.

First, analyzing the taxonomic diversity dynamics from the graphs of the number oftaxa, it is necessary to know that the shape of such graphs is almost com­pletely determined by long-lived taxa. For example, in Phanerozoic marine biota, more than one-third of the genera have a point stratigraphical distribution, i.e., did not cross any boundary between substages. The number of such ephemeral genera did not increase or decrease during the Phanerozoic, fluctuating chaotically around the constant average level of 100-150 genera per sub-stage. After excluding these genera from consideration, an overall shape of the generic diversity graph remains virtually unchanged (Sepkoski, 1996; Markov, 2001). These genera are not taken into account herein.

Second, the Meso-Cenozoic increase in generic diversity occurred entirely owing to the genera surviv­ing up to the Recent. If they are excluded from the con­sideration, the number of genera in the Mesozoic does not surpass the Paleozoic level, and there is not much left from the Cenozoic biota at all. This fact indicates that the Meso-Cenozoic diversity increase could have depended quite markedly on the pull of the Recent effect.

MATERIAL AND METHODS

A database created by J.J. Sepkoski was used, which contains information on the stratigraphical distribution for the overwhelming majority of marine animal genera known in the fossil state. The first and last appearances for the genera are given according to the substage scale dividing the Phanerozoic into 166 intervals. Thereafter, the first date of appearance of the genus in the record is termed origination for short, and the last appearance date is termed extinction. It is clear that, in most cases, the appearance of the genus in the record corresponds, not to its actual origin, but to the time when it becomes rather abundant and widespread. In calculations, only those genera are taken into account that undoubtedly crossed at least one boundary between substages and have an origination and extinction dated at least up to stage. There are 17168 genera satisfying these conditions in the database. The genera with a pointed stratigraphi­cal distribution were excluded from consideration, because they produce more noise than reliable results (Sepkoski, 1996; Markov, 2001).

In addition to other parameters, we use generic durations (GD). It is difficult to calculate this parameter for the genera surviving up to the Recent. The real dura­tion of their existence is unknown, but their elimination from the analysis will cause flagrant errors (e.g., the most stable genera, in other words the best products of evolution, will be excluded). Therefore, it is necessary to calculate the expected duration of existence for these genera using the general rules of extinction (Markov, 2000).

In the database, modern genera are those that crossed at least one stratigraphical boundary (Pleis­tocene and Holocene). The genera appearing later were not included in the database. The latter fact is impor­tant, because a considerable part (more than one-third) of the fossil marine genera becomes extinct prior to crossing any boundary. After crossing the first bound­ary, the probability of extinction decreases abmptly and changes comparatively little after that. Therefore, the genera that survived from the Pleistocene into the Holocene will subsequently most probably become extinct with a nearly constant rate. Note that the mod­em anthropogenic crisis is no obstacle for such extrap­olation. Crises associated with the increase in extinc­tion rates took place repeatedly during the Phanerozoic, and their impact can be taken into account when calcu­lating the expected extinction rate of modem genera. If even the development of mankind will alter the rules of biospheric evolution, we can believe that not the actual future duration of generic existence is calculated but only that which should be expected without man's interference. In addition, this value can be used as an average index of generic vulnerability.

To calculate the expected extinction rate for the gen­era crossing the Pleistocene/Holocene boundary, the relative extinction rate was determined for the genera crossing other boundaries in the Cenozoic. It was found that the genera that crossed any boundary (from Danian to Oligocene; data are too scanty for later epochs) sub­sequently went extinct with a nearly constant relative rate about 0.7-0.6% of genera for 1 Myr, the rate being nearer to 0.7 for the earlier and to 0.6 for the later boundaries. The decrease in the number of genera after any boundary is well described by an exponential curve (/?² > 0.93), the mass extinction at the end of the Eocene not affecting this rule significantly.

Based on the above, the following algorithm of cal­culating durations for extant genera was constmcted. A generator of random numbers produces time after time the numbers between 0 and 1 until the next one in turn is less than 0.006. The number of random numbers generated prior to this event is added to the existence duration of this genus (Myr) from its origination to the Recent. In such a way, existence of the genus in the future is simulated, with the extinction probability for each suc­cessive Myr being 0.6%. Below (if not stated otherwise), this correction is used when calculating the GD.

To estimate the accuracy of such a correction, let us conduct an experiment. Set an imaginary observer at the beginning of the Valanginian. The data for the fol­lowing stages are unknown to him. Repeat our calcula­tions from the position of this observer. Imagine that our observer wishes to estimate the durations for the genera surviving up to his time (beginning of the Val­anginian). To have an opportunity to check the results, assume that our observer is interested in the very same genera whose durations are known to us exactly (i.e., those that became extinct from the Valanginian to Holocene). There are 589 such genera (crossing Berri-asian/Valanginian boundary, not surviving into Holocene, dated at least to stage). For our Valanginian observer, the mean duration of these genera without the correc­tion is 38.3 Myr; we (post-Pleistocene observers) know that their mean GD is in fact twice as long (82.4 Myr). Imagine that our observer wishes to calculate the cor­rection for extant genera as described above. Naturally, as a standard, he will select Jurassic boundaries (sepa­rated from his time by 10-20 substages) rather than Cenozoic boundaries. Assuming that the genera in question will go extinct after the Berriasian/Valangin-ian boundary at the same rate as after the Aalen-ian/Bajocian boundary, he obtains an estimate of 93.4 Myr; taking the Bathonian/Callovian boundary as a standard, the estimate is 75.6 Myr; finally, guessing to average the data for these two boundaries, he obtains a value very close to the correct one, 86.9 Myr.

It should be noted that, for this experiment (requir­ing quite extensive calculations), the author did not spe­cially select those boundaries that give the most accu­rate correction and took the first arbitrary ones. For other boundaries, no calculations were conducted.

The experiment shows convincingly that the above correction produces good results, and, in addition, it is better than calculating the durations of the extant gen­era without correction, i.e., considering the Recent as an extinction interval.

MECHANISMS OF DIVERSITY INCREASE:

EXPONENTIAL AND LOGISTIC MODELS OF DIVERSIFICATION

There are several models of diversification describ­ing the increase in biotic diversity in different ways. Usually, these models are based on the assumption that the origination rate (and sometimes also extinction rate) is determined by the taxonomic diversity level. The most popular are exponential and logistic models (Sep-koski and Kendrick, 1993; Benton, 1999).

Exponential (expansionistic) models are based on the hypothesis that the number of genera normally increases in a geometrical progression. The more gen­era exist, the more often new genera should appear. Taxa are likened to multiplying individuals. The ability of living organisms to colonize a new ecological space is interpreted as the main factor limiting the diversity increase (Cailleux, 1950; Benton, 1995).

Logistic (equilibrium) models are based on the idea that with the increase in diversity, the rate of origination of new taxa should decrease. Sometimes, this model is supplemented by an assumption on the extinction rate growing proportional to the number of existing taxa. In logistic models, the diversity tends to a stable equi­librium level, and, after reaching it, the origination of new forms just compensates for the extinction of the old ones. The main factor determining the diversifica­tion rate in such models is usually the number of vacated niches or the volume of available space (eco­logical, adaptive, space of resources, etc.) in ecosys­tems. In this case, taxa are again likened to individuals in the population, with their number being controlled by the quantity of necessary resources (Carr and Kitch-ell, 1980; Sepkoski, 1991b, 1992; Markov and Naim-ark,1998).

According to Benton (1999), the question of the choice between exponential and logistic model makes sense, touching the basis of our understanding of evo­lution: whether the species develop in narrow limits of interspecific interactions (equilibrium hypothesis) or the evolution is limited only by the ability of species to col­onize new ecological space (expansionistic hypothesis).

However, both points of view can be easily com­bined in a single model, assuming that when there are plenty of free ecological space (e.g., after the mass extinction), the diversification follows the exponential model and, with saturation of communities and reduc­tion of the number of available niches, the diversity increase gradually approaches the logistic model.

To reproduce in a model the diversity dynamics observed in reality (e.g., that of Phanerozoic marine biota), a simple method is usually applied. The Phaner­ozoic is divided into sections, and for each of them, suitable parameters of either the exponential or logistic model are selected. Between these sections, singular events are inserted, their causes being hypothesized as external to biota (mass extinctions, rarely great radia­tions). It is clear that with these sections numerous enough, one can obtain virtually any pattern of diver­sity dynamics, including the observed pattern.

A common basis of all these models is the hypothe­sis that the origination rate is directly linked to the tax­onomic diversity level. This assumption looks so natu­ral that, to date, little attention was paid to whether or not it is confirmed by paleontological data.

This question appears to be a basic one. Models are used to describe and explain the observed diversity dynamics. This dynamics is calculated from the data on the first and last appearances of each taxon in the record (Fig. la). The same data allow one to compute the rates of taxa origination and extinction in each time interval as easily as the number of taxa. If the observed diversity dynamics are indeed explainable by correlation of orig­ination rate with the number of taxa, then we can expect that in the fossil record, the observed origination rate should correlate with the observed number of taxa. You see that both the diversity dynamics and origination rate are calculated from the same data, so one cannot assume that one of these parameters is known to us bet­ter than another.

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Fig. 1. Generic diversity dynamics, origination and extinction rates in marine animals: (a) number of genera; (b) number of genera (/) passing into given substage from the previous one and (2) originating during given substage; (c) number of genera going extinct during each substage. Included are genera dated no less than up to stage and crossing at least one boundary between substages. Zero of horizontal scale is 10 Myr before the beginning of Cambrian.

 

DOES THE GENERIC ORIGINATION RATE CORRELATE WITH THE NUMBER OF EXISTING GENERA?

Paleontological data do not confirm the hypothesis that the origination rate of new genera directly depends on the number of already existing genera (Fig. Ib). The correlation coefficient between the number of genera originating in a given substage and the number of gen­era passing into this substage from the preceding one is only 0.57. A comparison of the graphs shows only a slight similarity of the dynamics in two parameters, with the similarity apparently reflecting not the rela­tionship between the origination rate and the number of genera but rather the opposite: the relationship between the cumulated number of genera and their origination rate in preceding epochs.

Another mode of graphic representation of the same data is shown in Fig. 2, with the number of genera passing into a given substage from the preceding one along the horizontal axis, and the number of genera originating in a given substage along the vertical one. It has appeared that dividing the Phanerozoic into small intervals, one can reveal something similar to the relationship laid in the basis of the exponential and logistic models of diversifica­tion; namely, when the diversity is low, its increase is par­alleled by the increase in origination rate; reaching a cer­tain diversity level, the correlation becomes inverted (a further increase in diversity is accompanied by a decrease in the origination rate). In the graphs, such a cor­relation is reflected by the dome-shaped curves (Fig. 2).

However, we obtain such curves, at least slightly resembling the dome, only for some intervals. The best "domes" were obtained for the Silurian (Fig. 2a). Early to mid-Cretaceous (Berriasian-Conjacian; Fig. 2b), and Triassic; much less distinct patterns are observed in the Cenozoic (Fig. 2c), Ordovician, and Jurassic; for the remaining intervals, we failed to reveal anything like the "dome-shaped" correlation. No correlation is found for the Phanerozoic as a whole. Therefore, the fossil record gives no sound evidence to claim that the origination rate is correlated in a definite way with the diversity level, although one cannot deny entirely such a possibility. It is worth mentioning that analogous attempts to reveal any relationships between the diver­sity level and such parameters as the absolute extinction rate or the difference between the absolute origination and extinction rates gave negative results (we failed to find even such a weak relationship as that between the diversity and origination rate).

As shown above, though the exponential and logis­tic models cannot be considered senseless, it is reason­able to look for other models, with a correlation between the origination rate and diversity being not strong or even absent altogether.

As such an alternative, a model with a stochastically constant origination level can be proposed. In this model, the number of genera appearing during any interval depends on nothing and is determined inciden­tally. The simplest version of this model was discussed earlier (Markov, 2001).

The model is based on the following assumptions. (1) The absolute origination rate of the genera is sto­chastically constant (in computer simulation, the origi­nation interval for each genus is set by the random choice of one of the time scale intervals). This assump­tion does not contradict the data on marine biota from the Cambrian to Cenozoic inclusive. (2) Genera differ in their vulnerability or in their ability to withstand eliminating factors. The genera with a low vulnerability appear more rarely than the highly vulnerable genera. (3) Once appeared, each genus exists and passes from interval to interval until it goes extinct. When passing into each following interval, a random number is taken and compared with the value of generic sustainability (inverse vulnerability). If the first number is greater, the genus goes extinct. Therefore, the probability of generic extinction during any time interval is deter­mined by the ratio of the generic sustainability to the intensity of external eliminating factors. The sustain­ability is considered constant for each genus (it is deter­mined by its adaptation ability, eurytopicity, and plas­ticity), and for eliminating factors, it is considered as stochastically fluctuating. As a result, the extinction probability for the genus remains stochastically con­stant during its existence.

In such a model with a stochastically constant orig­ination and the extinction probability stochastically constant for each genus, the total number of genera does not remain constant at all, as one might assume. An increase in diversity is observed, occurring due to the gradual accumulation of the less vulnerable genera

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Fig. 2. Correlation of origination rate and diversity level:

(a) Silurian; (b) Early and mid-Cretaceous (up to Conja-cian); (c) Cenozoic. Horizontal axis: number of genera pass­ing into given substage from the previous one; vertical axis: number of genera originating during given substage. Points correspond to substages and connected by line according to time sequence (time arrow from left to right). Included are genera dated no less than up to stage and crossing at least one boundary between substages.

in the biota. This increase slows gradually and reaches a plateau. Therefore, with such a model, one could explain the diversity dynamics of the marine biota in the Ordovician-Permian, but to reproduce the Meso-Cenozoic dynamics, this model needs additional assumptions. Generally, we can conclude that the dynamics of the generic origination rate taken by them­selves is not sufficient to adequately explain the observed diversity increase in the marine biota during the Phanerozoic. Below, the rules associated with the extinction of genera (extinction rate and vulnerability) are considered.

MECHANISMS OF