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Ammonoid genus diversity through the Paleozoic. Arrows and expanded spindles show Frasnian/Famennian (367 Ma), Devonian/Mississippian (354 Ma), and Permian/Triassic (250 Ma) mass extinctions (13, 19). Intervals 1 to 14 correspond to chronostratigraphic divisions in Figs. 2 and 3; for abbreviations see (20). 

Ammonoid genus diversity through the Paleozoic. Arrows and expanded spindles show Frasnian/Famennian (367 Ma), Devonian/Mississippian (354 Ma), and Permian/Triassic (250 Ma) mass extinctions (13, 19). Intervals 1 to 14 correspond to chronostratigraphic divisions in Figs. 2 and 3; for abbreviations see (20). 

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The septal sutures of 588 genera of Paleozoic ammonoids showed a 1600 percent increase in mean complexity over 140 million years. Within 475 ancestor/ descendant pairs, descendants were more than twice as likely to be more complex than their ancestors. Twelve subclades (373 genera) averaged 34 percent increased complexity. These patterns are compat...

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... Given this, we use two different quantitative measures of morphological complexity, and stress that our results do not necessarily apply to complexity in general but to complexity as defined by these measures. There are other possible measures of complexity ( Saunders et al., 1999;McShea, 1996;Fleming and Mcshea, 2013) but they are not as easy to quantify in an objective way as we attempt here or are not easy to apply directly to 3D morphologies. Roughly, our two measures reflect the likelihood of randomly guessing the position of a cell in 3D space knowing the position of its neighbors at different distances but knowing nothing about the developmental mechanism that produced such morphology. ...
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Embryonic development involves gene networks, extracellular signaling, cell behaviors (cell division, apoptosis, adhesion, etc.) and mechanical interactions. How should gene networks, extracellular signaling and cell behaviors be coordinated to lead to complex and robust morphologies? To explore this question, we randomly wired genes and cell behaviors into a huge number of networks in EmbryoMaker. EmbryoMaker is a general mathematical model of animal development that simulates how embryos change, i.e. how the 3D spatial position of cells change, over time due such networks. Real gene networks are not random. Random networks, however, allow an unbiased view on the requirements for complex and robust development. We found that the mere autonomous activation of cell behaviors, especially cell division and contraction, was able to lead to the development of complex morphologies. We also found that complex morphologies tend to be less robust to noise than simple morphologies. However, we found that morphologies that developed through extracellular signaling and complex gene networks were, on average, more robust to noise. This stabilization occurs when gene networks and extracellular signaling partition the embryo into different regions where cell behaviors are regulated in slightly different ways. Our results are consistent with theories proposing that morphological complexity arose in early metazoan evolution as a consequence of the cell bio-mechanics already present in protozoa and that robustness evolved by the co-option of gene networks and extracellular cell signaling.
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... However, Wagner's later study of early Paleozoic snails did include phylogenetic data, and it did show nonrandom evolution within lineages after controlling for apparent sorting among lineages (Wagner 1996). Likewise, recent results on body mass in mammals (Alroy 1998) and suture complexity in ammonites (Saunders et al. 1999 ) also can only be interpreted as showing nonrandom evolution within lineages. Still, though, these three studies didn't try to quantify the relative importance of withinand among-lineage factors—they merely sought to establish the fact that within-lineage trends are real. ...
... Instead, most paleontological studies plot morphological distributions directly against time, or present a series of histograms or scatter plots depicting the same morphospace in different time slices (for example, all Cretaceous species in one plot and all Paleocene species in another). Many recent papers have employed this approach , including studies of palynomorphs (Lupia 1999), foraminiferans (Norris 1991; Arnold et al. 1995), trilobites (Foote 1991; Sundberg 1996; Smith and Lieberman 1999), crustaceans (Wills 1998), bivalves (Jablonski 1996), rostroconchs (Wagner 1997), gastropods (Roy 1994Roy , 1996 Wagner 1996 ), ammonites (Boyajian and Lutz 1992; Dommergues et al. 1996; Saunders and Work 1996; Saunders et al. 1999), brachiopods (Carlson 1992 ), blastozoans (Foote 1992), crinoids (Foote 1995 ), echinoids (Eble 1998), ungulates (Jernvall et al. 1996), and even theropod dinosaurs (Gatesy and Middleton 1997). The distributions (often derived from multivariate analysis of complex FIGURE 3. Sketched patterns of progressive morphospace occupation implied by distinct evolutionary dynamics . ...
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The study of evolutionary trends is one of the oldest and most intriguing topics in evolutionary biology and paleobiology (McNamara 1990). Workers since Cuvier, Lyell, and Owen have wanted to know if the fossil record demonstrates “progression” within temporal sequences of related organisms. Regardless of whether changes in the average values of morphological characters are progressive in any meaningful sense, these changes are still of great interest. In practice, questions about trends are most commonly framed by paleontologists in terms of “complexity” (however defined) or body size (McShea 1998a). Research on evolutionary trends has intensified over the last few years, bringing several fundamental conceptual issues to a head. Here I analyze these conceptual problems, concluding that paleontologists should largely abandon a key method used in most studies: comparing among-species morphological distributions in successive time slices, irrespective of phylogenetic patterns. These data supposedly may distinguish random evolution, constant directional trends, and diffusion away from morphological boundaries. However, many other simple evolutionary dynamics may result in the same nonrandom trends, making it difficult to distinguish qualitatively distinct mechanisms using time-slice data. Thus, I will try to show that comparisons between ancestral and descendant morphologies need to be made instead. The fundamental problem here is not so much mathematical or statistical as conceptual. Null hypotheses have not always been framed rigorously, and the logical connection between underlying hypotheses and methods for testing these hypotheses has sometimes been weak. Although paleontologists have long since embraced the use of null models, they still do not employ a single, straightforward definition of “randomness” (Eble 1999). As a result, different authors use different null hypotheses, and depending on their conceptual outlooks they may interpret the same kinds of patterns as either confirming or refuting the existence of trends. Considering the volume of literature and the century-long …