Paleontological Journal, Vol. 36, No. 2, 2002, pp. 121-130. Translated from Paleontologicheskii Zhurnal. No. 2, 2002, pp. 3-13.
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).
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.
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.
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
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 DIVERSITY INCREASE:
DECREASE OF EXTINCTION RATES OR APPEARANCE OF THE LESS AND LESS VULNERABLE TAXA
The assumption is often made that an important mechanism of the increase in marine biota diversity is the decrease of extinction rates. Usually, the relative extinction rate is analyzed (number of genera going extinct in each interval in percent of the total number of genera existing in that time). Indeed, the relative extinction rate gradually decreased during the Phanerozoic (Sepkoski, 1996). This argumentation is circular: diver-
Fig. 3. Dynamics of mean generic durations (GD): (a) mean GD for genera appearing in different time (horizontal axis: origination time; vertical axis: mean GD); (b) mean GD (sum of durations for all genera known from given substage divided by number of these genera); (c) sum of GD for all genera known from given substage. Zero of horizontal scale in (b) and (c) is 10 Myr before the beginning of Cambrian. Included are genera dated no less than up to stage and crossing at least one boundary between substages.
sity increases due to the decreasing relative extinction rate, but, possibly, the relative extinction rate itself decreases because of the increasing total diversity (the diversity level is included in the formula for calculating the relative extinction rate and is placed in the denominator of the fraction).
In addition, the generic origination rate cannot be linked directly to the current diversity level, as shown above. Therefore, it is reasonable to also doubt that the (absolute) extinction rate should be necessarily correlated to this level. Thus, doubts are inevitably raised how reasonable it is to analyze a parameter such as the relative extinction rate.
As for the absolute extinction rate (number of genera going extinct in each interval), this parameter during the Phanerozoic oscillated chaotically around nearly the same mean level (Fig. Ic).
One will obtain a more regular picture by calculating the mean durations for the genera, which are divided into groups according to their time of origination (Fig. 3a). In the chart, this parameter generally tends to increase stepwise. It means that the genera with different vulnerabilities originated in different periods (remember that we do not consider the genera with a pointed stratigraphical distribution, and that durations for the extant genera are calculated by the algorithm described above, see Material and Methods). The genera that originated in the Cambrian were the most vulnerable (mean GD = 18.6 Myr). In the Paleozoic, the less vulnerable genera appeared (mean GD fluctuating from 22.2 to 41.8 Myr depending on the period; on average, 30.8 for Ordovician-Devonian and 35.4 Myr for Carboniferous-Permian); in the Mesozoic even less vulnerable ones (from 56.6 in Jurassic to 71.6 Myr in Early Cretaceous); and, finally, in the Cenozoic, the
most stable genera originated (136.1 in Paleogene and 151.5 Myr in Neogene).
The graph of the mean GD (Fig. 3b) is also remarkable. It differs from the previous one in the genera arranged according not to the origination time but to the time of existence. Each point of the curve shows the mean duration for the genera existing in a given sub-stage. The graph demonstrates a linear increase continuing through the Phanerozoic with relatively minor perturbations. According to the dynamics of this parameter, all the Phanerozoic represents a single period of directed development, which is not divisible into any parts or stages.
A good method to represent the increase in diversity is also the total GD (Fig. 3c). This graph was analyzed in detail earlier (Markov, 2000). According to the dynamics of the total GD, the Phanerozoic is distinctly subdivided into four stages (Cambrian, Ordovician-Permian, Mesozoic, Cenozoic), and each of them is characterized by its own rate of linear increase in the total GD, with the rate growing abruptly from stage to stage. In this sense, the graph of the total GD (Fig. 3c) correlates well with that of the mean duration of new genera (Fig. 3a), demonstrating the same four stages or steps.
From the above, it is evident that the most important factor of the accelerated diversity increase observed in the Phanerozoic was neither the increasing origination rate nor the general decrease of the extinction rate due to any external causes but that the newly appearing genera were more and more stable and long lived (their stability increasing step by step). There were four such steps: Cambrian, Ordovician-Permian, Mesozoic, and Cenozoic.
POSSIBLE MECHANISMS OF DECREASING VULNERABILITY IN CHANGING ASSEMBLAGES OF GENERA
It is reasonable to raise the following question: why the durations for the newly appearing genera increased from step to step? Apparently, the ultimate biological causes of this phenomenon rest in the ecosystem evolution, in the rules of ecosystem regulation of biota. Detailed consideration of these problems is beyond the scope of this paper. However, before seeking the ultimate causes of the observed increase in the durations of new genera, it is necessary to analyze less complicate things, namely, what the real components of the values and graphs obtained by us are, so we should start the discussion not at the level of biological rules, but at the level of figures and calculation methods.
The most probable explanations of the observed stepwise increase in the durations of new genera seem to be the following: (1) artifact, (2) change of dominating groups (groups with long-lived genera replace the groups with short-lived ones after each crisis), and (3) synchronous increase in the durations of new genera in most groups (in the case, an assumption arises that ecosystems become restructured radically after the crisis and the new, more stable ecosystem stmcture promotes the decrease in extinction rates).
Let us to analyze these hypotheses in the following order. The increase observed could be an artifact due to the pull of the Recent. The stepped pattern in this case is explainable by the fact that after the crises at the Per-mian/Triassic and Cretaceous/Paleogene boundaries, which were due to abmpt changes in the taxonomic composition of biota, the proportion of extant genera increases sharply, stepwise, and durations for such genera could be somewhat overestimated. As mentioned above, without voluminous supplementary data, we cannot even roughly estimate the pull of the Recent effect on the results obtained. However, this hypothesis is not capable of explaining the unusually sharp, stepwise increase in the durations of new genera at the Cambrian/Ordovician boundary (i.e., that of the first and second steps). The "pull of the Recent" cannot affect the data on the Cambrian and Ordovician. In addition, if the pull of the Recent is so strong that it entirely determines the apparent increase in the durations of new genera during the Mesozoic and Cenozoic, then the entire observed Meso-Cenozoic diversity increase of marine biota inevitably turns out to be caused by this effect. In the case, one should accept that the generic diversity of marine biota remained nearly constant with minor fluctuations since the Ordovician up to the present.
Assuming that the observed increase in the mean duration of new genera is real, one should discuss two possible mechanisms (remember that we are speaking of proximate and not ultimate causes and mechanisms).
First, this increase can be explained by stepwise change in the dominating marine faunal groups. The most profound changes in dominants occurred after (or during) the greatest crises. This fact was reflected in the concept of the "evolutionary faunas" (Sepkoski, 1991a, 1992). Sepkoski singled out three evolutionary faunas:
Cambrian, Paleozoic, and Meso-Cenozoic. These faunas correspond well to our four steps, except for the fact that in the GD dynamics the Meso-Cenozoic stage is subdivided into two (Mesozoic and Cenozoic).
Possibly after the most important critical barriers in the marine biotic development (Ordovician radiation, end-Permian and end-Cretaceous mass extinctions), the dominating groups with high rates of taxonomic turnover (generic origination and extinction) were replaced by new dominants: the groups with low turnover rates. As a result, from one crisis to another, the degree of dominance of the groups with low turnover rates (i.e., with more stable genera) could have increased stepwise. Another possibility cannot be excluded: after these crises, all the biota could have changed in such a way that the more stable genera began to originate synchronously in most groups.
Table 1. Mean duration of trilobite genera having originated in different time (excluding the genera known from a single interval or dated less than up to the stage)
Therefore, it is necessary to know what the main factor determining durations of new genera is: group or epoch. If the first assumption is correct, then in the same group, the generic turnover rates should be nearly the same before and after the critical boundary and the dominance should pass from the groups with a high turnover to those with a low turnover. If the second assumption is true, then, within the same group after crossing the critical boundary, the genera that are more stable than before should originate.
The data available preclude us to choose one of these two hypotheses unequivocally. Some facts argue for the first one, and others argue for the second. The most interesting facts are considered below.
WHAT DO GENERIC DURATIONS DEPEND ON: HIGHER TAXA OR EPOCH?
First, consider a classical example of parallel development in two large competing groups: brachiopods and bivalves. In this case, the GD was calculated in two ways: with a correction (as described in Material and Methods) and without it. The reason is that the correction does not take into account the individual features of the taxa, resulting in that the difference between the taxa with a high and low generic turnover can be leveled. Nonetheless, GD without correction will most probably distort the real picture even more.
Calculating the GD without correction yields the following results. In the Cambrian, brachiopods dominated completely in this pair of taxa; the mean GD for brachiopods in this interval is 25.4 Myr. In the Ordovi-cian-Permian, along with dominating brachiopods, a quite diverse bivalve fauna already existed. In genera having originated in this time, the mean GD is 21.0 for brachiopods (about the value for the Cambrian) and 54.5 for bivalves (twice as high). In the Mesozoic, bivalves already dominated, brachiopods still being numerous but occupying a subordinate position. The mean GD for both groups is nearly the same as in the Paleozoic (20.1 and 50.3, respectively). In the Ceno-zoic, bivalves dominate even more markedly over brachiopods. In genera originating in the Cenozoic, the GD (without correction for the extant ones) is a very obscure value, so far as nearly all such genera (both in bivalves and brachiopods) are extant. Nevertheless, the GD without correction is again lower in brachiopods than in bivalves (21.1 versus 25.2).
Calculating the GD with a standard correction for the extant genera, we obtain different values, but the overall dynamics is similar. The mean GD in new genera was always higher in bivalves than in brachiopods; i.e., bivalves as a whole always show a lower generic turnover rate relative to brachiopods, and this relationship was retained both in the period ofbrachiopod dominance and in that of bivalve dominance.
Something similar is observed in another classical pair: cephalopods and fishes (plus fish allies). In the former, the mean GD (without correction) is 17.1 for the genera having originated in the Paleozoic and 10.5 for those in the Mesozoic; in the latter, 22.8 and 36.5, respectively. In fishes, the taxonomic turnover rate was always lower than in cephalopods. In this pair, the dominance of cephalopods decreased from stage to stage and that of the fishes increased.
These two examples seem to demonstrate that the rate of taxonomic turnover depends on the group rather than the epoch. However, there are much more examples arguing the contrary: that the epoch rather than the group is a determining factor.
A vivid example is provided by trilobites (Table 1). The table shows that the trilobite genera originating in the Cambrian had a lower GD than those originating later. The same relationship is retained if trilobites are divided into three groups (chiefly Cambrian orders, mixed ones, and chiefly post-Cambrian orders). In each of these groups, the genera originating in the Cambrian had a lower GD than those originating later. In trilobites, the GD was apparently more correlated with the epoch of origin of the genus than with the ordinal position.
In some phyla and classes, even not the change of dominants but the complete (or nearly so) change of the taxonomic composition at all levels up to the orders
Table 2. Mean generic duration in the major groups of marine animals depending on the origination time of the genus
occurred at the critical boundaries (it is especially characteristic of the Permian/Triassic boundary). In the case, there is no sense in discussing whether the mean GD changed due to advent of a new epoch or due to the change of dominating taxa. For example, in the class Crinoidea, the ordinal composition was almost totally renewed at the Permian/Triassic boundary. For the crinoid genera originating in the Paleozoic, the mean GD is 19.9, and for those originating in the Mesozoic, 37.1. In this case, it is unclear whether this increase was associated with the origin of new orders with a low generic turnover rate or with the conditions of crinoid environments having changed so that the generic extinction rate decreased.
The next table shows dynamics of the mean duration of new genera from step to step in 15 major groups of the Phanerozoic marine biota (Table 2). All values are calculated using the standard correction for extant genera (this is why Cenozoic values are so similar in different groups); only those genera are included that are dated at least up to stage and crossed at least one boundary between substages. As seen from the table, durations of new genera increased considerably from step to step in 11 of 15 groups; all these groups, except for tri-lobites, are flourishing to date.
In four groups (brachiopods, conodonts, graptolites, and cephalopods), the durations of new genera decreased or showed no distinct increase (in pre-Ceno-zoic time). All these groups either have become extinct or lost their dominance (as for cephalopods, of course, we mean forms with the outer shell and belemnites easily preserving as fossils).
One can assume that the increase in the mean duration of new genera within a higher taxon from step to step is not only a general rule of the evolution but also a guarantee (or indicator) of the evolutionary success of this taxon. To conclude, the observed stepwise increase in the durations of new genera is only partly explainable by the change of dominating groups (evolutionary faunas) and to a greater extent, reflects the changes proceeding in parallel in most higher taxa of marine animals.
(1) Taxonomic diversity dynamics are traditionally interpreted using the exponential or logistic models of diversification. These models are commonly based on the assumption that the origination rate of new taxa depends on the taxonomic diversity level. Paleontolog-ical data, however, give no sound support for such an assumption. If this correlation does exist, it is very weak and indirect.
(2) The observed dynamics of taxonomic diversity (including diversity increase) can sometimes be explained by a model in which the generic origination rate is stochastically constant and does not depend on the diversity level. The genera differ in their vulnerability; the extinction probability for each genus during each time interval depends on its vulnerability only. The resulting diversity increase reaching a plateau (as in the Paleozoic) occurs due to the gradual accumulation of long-lived, stable genera in the biota. A stepwise acceleration of the diversity increase (as at the beginning of the Ordovician, at the beginning of the Mesozoic, and at the beginning of the Cenozoic) is caused by the stepwise decrease in the vulnerability of newly originating genera.
(3) The most important mechanism of the diversity increase in the marine biota during the Phanerozoic was an increase in the mean duration of existence (stability) of the genera. The stability of newly appearing genera increased in steps; there were four such steps: Cambrian, Ordovician-Permian, Mesozoic, and Cenozoic.
(4) The stepwise increase in the generic durations took place partly due to successive replacement of dominating groups, usually resulting in the success of the groups with a lower generic turnover rate. However, to a larger extent, this increase occurred because the generic durations increased within each group at each successive step. Notably, those few groups where generic durations did not increase either went extinct or lost their dominance, whereas among the groups with a pronounced stepwise increase in the generic durations, this is tme only of trilobites, all the others having survived to date and still nourishing. The ultimate biological causes of the observed increase in the generic durations probably rest in the ecosystem evolution.
The author is deeply indebted to the late Prof. J.J. Sepkoski for the data and valuable advice. The study is supported by the Russian Foundation for Basic Research, project no. 01-05-99453.
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